LMFDB - Embedded newform 52.2.l.b.19.4

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			19.4
Root			$-0.713659 - 1.22094i$ of defining polynomial
Character	$\chi$	$=$	52.19
Dual form			52.2.l.b.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41419 + 0.00757716i) q^{2} +(-1.40004 - 0.808315i) q^{3} +(1.99989 + 0.0214311i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(-1.97381 - 1.15372i) q^{6} +(-1.97429 - 0.529008i) q^{7} +(2.82806 + 0.0454612i) q^{8} +(-0.193255 - 0.334727i) q^{9} +O(q^{10})$	\(q+(1.41419 + 0.00757716i) q^{2} +(-1.40004 - 0.808315i) q^{3} +(1.99989 + 0.0214311i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(-1.97381 - 1.15372i) q^{6} +(-1.97429 - 0.529008i) q^{7} +(2.82806 + 0.0454612i) q^{8} +(-0.193255 - 0.334727i) q^{9} +(-2.17244 + 2.14928i) q^{10} +(1.12074 + 4.18264i) q^{11} +(-2.78260 - 1.64654i) q^{12} +(-2.92531 - 2.10774i) q^{13} +(-2.78801 - 0.763079i) q^{14} +(3.37433 - 0.904148i) q^{15} +(3.99908 + 0.0857196i) q^{16} +(4.14654 - 2.39401i) q^{17} +(-0.270763 - 0.474833i) q^{18} +(0.603848 - 2.25359i) q^{19} +(-3.08853 + 3.02304i) q^{20} +(2.33648 + 2.33648i) q^{21} +(1.55324 + 5.92356i) q^{22} +(2.45806 - 4.25748i) q^{23} +(-3.92266 - 2.34961i) q^{24} +0.330547i q^{25} +(-4.12098 - 3.00292i) q^{26} +5.47473i q^{27} +(-3.93701 - 1.10027i) q^{28} +(-2.94247 + 5.09651i) q^{29} +(4.77880 - 1.25307i) q^{30} +(0.420375 + 0.420375i) q^{31} +(5.65482 + 0.151526i) q^{32} +(1.81181 - 6.76178i) q^{33} +(5.88215 - 3.35417i) q^{34} +(3.82499 - 2.20836i) q^{35} +(-0.379313 - 0.673557i) q^{36} +(-1.86603 + 0.500000i) q^{37} +(0.871034 - 3.18244i) q^{38} +(2.39183 + 5.31550i) q^{39} +(-4.39069 + 4.25176i) q^{40} +(0.401924 + 1.50000i) q^{41} +(3.28653 + 3.32194i) q^{42} +(-5.59481 - 9.69049i) q^{43} +(2.15170 + 8.38882i) q^{44} +(0.806745 + 0.216167i) q^{45} +(3.50843 - 6.00228i) q^{46} +(-8.07035 + 8.07035i) q^{47} +(-5.52959 - 3.35253i) q^{48} +(-2.44422 - 1.41117i) q^{49} +(-0.00250460 + 0.467457i) q^{50} -7.74044 q^{51} +(-5.80510 - 4.27794i) q^{52} -1.33055 q^{53} +(-0.0414829 + 7.74233i) q^{54} +(-8.10346 - 4.67854i) q^{55} +(-5.55935 - 1.58582i) q^{56} +(-2.66702 + 2.66702i) q^{57} +(-4.19984 + 7.18515i) q^{58} +(6.48147 + 1.73670i) q^{59} +(6.76765 - 1.73588i) q^{60} +(0.358528 + 0.620988i) q^{61} +(0.591307 + 0.597677i) q^{62} +(0.204467 + 0.763079i) q^{63} +(7.99587 + 0.257134i) q^{64} +(7.69041 - 1.24922i) q^{65} +(2.61349 - 9.54874i) q^{66} +(6.84166 - 1.83322i) q^{67} +(8.34391 - 4.69887i) q^{68} +(-6.88277 + 3.97377i) q^{69} +(5.42600 - 3.09406i) q^{70} +(-0.454168 + 1.69498i) q^{71} +(-0.531319 - 0.955413i) q^{72} +(5.35696 + 5.35696i) q^{73} +(-2.64271 + 0.692957i) q^{74} +(0.267186 - 0.462779i) q^{75} +(1.25592 - 4.49398i) q^{76} -8.85061i q^{77} +(3.34223 + 7.53527i) q^{78} -1.11723i q^{79} +(-6.24150 + 5.97954i) q^{80} +(3.84554 - 6.66067i) q^{81} +(0.557032 + 2.12434i) q^{82} +(-2.45738 - 2.45738i) q^{83} +(4.62261 + 4.72276i) q^{84} +(-2.67784 + 9.99383i) q^{85} +(-7.83871 - 13.7466i) q^{86} +(8.23917 - 4.75689i) q^{87} +(2.97936 + 11.8797i) q^{88} +(1.88163 - 0.504180i) q^{89} +(1.13926 + 0.311814i) q^{90} +(4.66037 + 5.70880i) q^{91} +(5.00708 - 8.46180i) q^{92} +(-0.248748 - 0.928339i) q^{93} +(-11.4742 + 11.3519i) q^{94} +(2.52078 + 4.36612i) q^{95} +(-7.79451 - 4.78302i) q^{96} +(-1.32723 - 0.355630i) q^{97} +(-3.44591 - 2.01419i) q^{98} +(1.18345 - 1.18345i) 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 $

$2$	1.41419	+	0.00757716i	0.999986	+	0.00535786i
$2$	1.41419	+	0.00757716i	0.999986	+	0.00535786i
$3$	−1.40004	−	0.808315i	−0.808315	−	0.466681i	0.0380556	−	0.999276i	$-0.487884\pi$
$3$	−1.40004	−	0.808315i	−0.808315	−	0.466681i	−0.846370	+	0.532595i	$0.821217\pi$
$4$	1.99989	+	0.0214311i	0.999943	+	0.0107156i
$5$	−1.52798	+	1.52798i	−0.683334	+	0.683334i	−0.960750	−	0.277416i	$-0.910522\pi$
$5$	−1.52798	+	1.52798i	−0.683334	+	0.683334i	0.277416	+	0.960750i	$0.410522\pi$
$6$	−1.97381	−	1.15372i	−0.805803	−	0.471005i
$7$	−1.97429	−	0.529008i	−0.746210	−	0.199946i	−0.134374	−	0.990931i	$-0.542902\pi$
$7$	−1.97429	−	0.529008i	−0.746210	−	0.199946i	−0.611836	+	0.790984i	$0.709569\pi$
$8$	2.82806	+	0.0454612i	0.999871	+	0.0160730i
$9$	−0.193255	−	0.334727i	−0.0644182	−	0.111576i
$10$	−2.17244	+	2.14928i	−0.686985	+	0.679663i
$11$	1.12074	+	4.18264i	0.337915	+	1.26111i	0.900675	+	0.434494i	$0.143073\pi$
$11$	1.12074	+	4.18264i	0.337915	+	1.26111i	−0.562760	+	0.826620i	$0.690261\pi$
$12$	−2.78260	−	1.64654i	−0.803268	−	0.475315i
$13$	−2.92531	−	2.10774i	−0.811334	−	0.584583i
$13$	−2.92531	−	2.10774i	−0.811334	−	0.584583i
$14$	−2.78801	−	0.763079i	−0.745128	−	0.203942i
$15$	3.37433	−	0.904148i	0.871248	−	0.233450i
$16$	3.99908	+	0.0857196i	0.999770	+	0.0214299i
$17$	4.14654	−	2.39401i	1.00568	−	0.580632i	0.0957589	−	0.995405i	$-0.469472\pi$
$17$	4.14654	−	2.39401i	1.00568	−	0.580632i	0.909925	+	0.414773i	$0.136139\pi$
$18$	−0.270763	−	0.474833i	−0.0638195	−	0.111919i
$19$	0.603848	−	2.25359i	0.138532	−	0.517010i	−0.861426	−	0.507883i	$-0.830428\pi$
$19$	0.603848	−	2.25359i	0.138532	−	0.517010i	0.999958	−	0.00912654i	$-0.00290511\pi$
$20$	−3.08853	+	3.02304i	−0.690617	+	0.675972i
$21$	2.33648	+	2.33648i	0.509861	+	0.509861i
$22$	1.55324	+	5.92356i	0.331153	+	1.26291i
$23$	2.45806	−	4.25748i	0.512541	−	0.887747i	−0.487354	−	0.873205i	$-0.662038\pi$
$23$	2.45806	−	4.25748i	0.512541	−	0.887747i	0.999894	−	0.0145418i	$-0.00462896\pi$
$24$	−3.92266	−	2.34961i	−0.800709	−	0.479612i
$25$			0.330547i			0.0661093i
$26$	−4.12098	−	3.00292i	−0.808190	−	0.588922i
$27$			5.47473i			1.05361i
$28$	−3.93701	−	1.10027i	−0.744025	−	0.207931i
$29$	−2.94247	+	5.09651i	−0.546403	+	0.946398i	0.452114	+	0.891960i	$0.350670\pi$
$29$	−2.94247	+	5.09651i	−0.546403	+	0.946398i	−0.998517	+	0.0544380i	$0.982663\pi$
$30$	4.77880	−	1.25307i	0.872486	−	0.228779i
$31$	0.420375	+	0.420375i	0.0755017	+	0.0755017i	0.743849	−	0.668348i	$-0.232998\pi$
$31$	0.420375	+	0.420375i	0.0755017	+	0.0755017i	−0.668348	+	0.743849i	$0.732998\pi$
$32$	5.65482	+	0.151526i	0.999641	+	0.0267862i
$33$	1.81181	−	6.76178i	0.315396	−	1.17708i
$34$	5.88215	−	3.35417i	1.00878	−	0.575235i
$35$	3.82499	−	2.20836i	0.646541	−	0.373280i
$36$	−0.379313	−	0.673557i	−0.0632189	−	0.112259i
$37$	−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	$0.467428\pi$
$38$	0.871034	−	3.18244i	0.141300	−	0.516260i
$39$	2.39183	+	5.31550i	0.382999	+	0.851161i
$40$	−4.39069	+	4.25176i	−0.694229	+	0.672263i
$41$	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	$0.877972\pi$
$42$	3.28653	+	3.32194i	0.507122	+	0.512586i
$43$	−5.59481	−	9.69049i	−0.853200	−	1.47779i	−0.878305	−	0.478101i	$-0.841325\pi$
$43$	−5.59481	−	9.69049i	−0.853200	−	1.47779i	0.0251051	−	0.999685i	$-0.492008\pi$
$44$	2.15170	+	8.38882i	0.324382	+	1.26466i
$45$	0.806745	+	0.216167i	0.120263	+	0.0322242i
$46$	3.50843	−	6.00228i	0.517290	−	0.884988i
$47$	−8.07035	+	8.07035i	−1.17718	+	1.17718i	−0.196722	+	0.980459i	$0.563030\pi$
$47$	−8.07035	+	8.07035i	−1.17718	+	1.17718i	−0.980459	+	0.196722i	$0.936970\pi$
$48$	−5.52959	−	3.35253i	−0.798128	−	0.483896i
$49$	−2.44422	−	1.41117i	−0.349175	−	0.201596i
$50$	−0.00250460	+	0.467457i	−0.000354204	+	0.0661084i
$51$	−7.74044			−1.08388
$52$	−5.80510	−	4.27794i	−0.805023	−	0.593244i
$53$	−1.33055			−0.182765			−0.0913823	−	0.995816i	$-0.529129\pi$
$53$	−1.33055			−0.182765			−0.0913823	+	0.995816i	$0.529129\pi$
$54$	−0.0414829	+	7.74233i	−0.00564511	+	1.05360i
$55$	−8.10346	−	4.67854i	−1.09267	−	0.630854i
$56$	−5.55935	−	1.58582i	−0.742900	−	0.211914i
$57$	−2.66702	+	2.66702i	−0.353256	+	0.353256i
$58$	−4.19984	+	7.18515i	−0.551466	+	0.943457i
$59$	6.48147	+	1.73670i	0.843816	+	0.226100i	0.654732	−	0.755861i	$-0.272782\pi$
$59$	6.48147	+	1.73670i	0.843816	+	0.226100i	0.189084	+	0.981961i	$0.439448\pi$
$60$	6.76765	−	1.73588i	0.873699	−	0.224101i
$61$	0.358528	+	0.620988i	0.0459048	+	0.0795094i	0.888065	−	0.459718i	$-0.152050\pi$
$61$	0.358528	+	0.620988i	0.0459048	+	0.0795094i	−0.842160	+	0.539228i	$0.818716\pi$
$62$	0.591307	+	0.597677i	0.0750961	+	0.0759051i
$63$	0.204467	+	0.763079i	0.0257604	+	0.0961390i
$64$	7.99587	+	0.257134i	0.999483	+	0.0321418i
$65$	7.69041	−	1.24922i	0.953878	−	0.154946i
$66$	2.61349	−	9.54874i	0.321698	−	1.17537i
$67$	6.84166	−	1.83322i	0.835842	−	0.223963i	0.184581	−	0.982817i	$-0.440907\pi$
$67$	6.84166	−	1.83322i	0.835842	−	0.223963i	0.651261	+	0.758854i	$0.274241\pi$
$68$	8.34391	−	4.69887i	1.01185	−	0.569822i
$69$	−6.88277	+	3.97377i	−0.828588	+	0.478386i
$70$	5.42600	−	3.09406i	0.648531	−	0.369811i
$71$	−0.454168	+	1.69498i	−0.0538999	+	0.201157i	−0.987625	−	0.156834i	$-0.949871\pi$
$71$	−0.454168	+	1.69498i	−0.0538999	+	0.201157i	0.933725	+	0.357991i	$0.116538\pi$
$72$	−0.531319	−	0.955413i	−0.0626165	−	0.112597i
$73$	5.35696	+	5.35696i	0.626985	+	0.626985i	0.947308	−	0.320323i	$-0.103792\pi$
$73$	5.35696	+	5.35696i	0.626985	+	0.626985i	−0.320323	+	0.947308i	$0.603792\pi$
$74$	−2.64271	+	0.692957i	−0.307209	+	0.0805547i
$75$	0.267186	−	0.462779i	0.0308519	−	0.0534371i
$76$	1.25592	−	4.49398i	0.144064	−	0.515495i
$77$		−	8.85061i		−	1.00862i
$78$	3.34223	+	7.53527i	0.378433	+	0.853201i
$79$		−	1.11723i		−	0.125698i	−0.998023	−	0.0628489i	$-0.979981\pi$
$79$		−	1.11723i		−	0.125698i	0.998023	−	0.0628489i	$-0.0200186\pi$
$80$	−6.24150	+	5.97954i	−0.697821	+	0.668533i
$81$	3.84554	−	6.66067i	0.427282	−	0.740075i
$82$	0.557032	+	2.12434i	0.0615139	+	0.234594i
$83$	−2.45738	−	2.45738i	−0.269733	−	0.269733i	0.559260	−	0.828992i	$-0.311085\pi$
$83$	−2.45738	−	2.45738i	−0.269733	−	0.269733i	−0.828992	+	0.559260i	$0.811085\pi$
$84$	4.62261	+	4.72276i	0.504369	+	0.515296i
$85$	−2.67784	+	9.99383i	−0.290453	+	1.08398i
$86$	−7.83871	−	13.7466i	−0.845270	−	1.48234i
$87$	8.23917	−	4.75689i	0.883332	−	0.509992i
$88$	2.97936	+	11.8797i	0.317601	+	1.26638i
$89$	1.88163	−	0.504180i	0.199452	−	0.0534430i	−0.157710	−	0.987485i	$-0.550411\pi$
$89$	1.88163	−	0.504180i	0.199452	−	0.0534430i	0.357162	+	0.934042i	$0.383744\pi$
$90$	1.13926	+	0.311814i	0.120088	+	0.0328681i
$91$	4.66037	+	5.70880i	0.488540	+	0.598445i
$92$	5.00708	−	8.46180i	0.522024	−	0.882203i
$93$	−0.248748	−	0.928339i	−0.0257939	−	0.0962643i
$94$	−11.4742	+	11.3519i	−1.18347	+	1.17086i
$95$	2.52078	+	4.36612i	0.258626	+	0.447954i
$96$	−7.79451	−	4.78302i	−0.795524	−	0.488165i
$97$	−1.32723	−	0.355630i	−0.134760	−	0.0361088i	0.190809	−	0.981627i	$-0.438889\pi$
$97$	−1.32723	−	0.355630i	−0.134760	−	0.0361088i	−0.325568	+	0.945518i	$0.605556\pi$
$98$	−3.44591	−	2.01419i	−0.348090	−	0.203464i
$99$	1.18345	−	1.18345i	0.118942	−	0.118942i
$100$	−0.00708399	+	0.661055i	−0.000708399	+	0.0661055i
$101$	0.753397	+	0.434974i	0.0749658	+	0.0432815i	0.537014	−	0.843573i	$-0.319552\pi$
$101$	0.753397	+	0.434974i	0.0749658	+	0.0432815i	−0.462049	+	0.886855i	$0.652885\pi$
$102$	−10.9465	−	0.0586506i	−1.08386	−	0.00580727i
$103$	11.5743			1.14045			0.570225	−	0.821489i	$-0.306856\pi$
$103$	11.5743			1.14045			0.570225	+	0.821489i	$0.306856\pi$
$104$	−8.17712	−	6.09382i	−0.801833	−	0.597548i
$105$	−7.14019			−0.696811
$106$	−1.88165	−	0.0100818i	−0.182762	−	0.000979227i
$107$	−6.97804	−	4.02877i	−0.674593	−	0.389476i	0.123222	−	0.992379i	$-0.460677\pi$
$107$	−6.97804	−	4.02877i	−0.674593	−	0.389476i	−0.797815	+	0.602903i	$0.794011\pi$
$108$	−0.117330	+	10.9488i	−0.0112901	+	1.05355i
$109$	12.0811	−	12.0811i	1.15716	−	1.15716i	0.172075	−	0.985084i	$-0.444953\pi$
$109$	12.0811	−	12.0811i	1.15716	−	1.15716i	0.985084	−	0.172075i	$-0.0550472\pi$
$110$	−11.4244	−	6.67776i	−1.08928	−	0.636699i
$111$	3.01667	+	0.808315i	0.286330	+	0.0767218i
$112$	−7.84998	−	2.28478i	−0.741754	−	0.215892i
$113$	−4.47045	−	7.74305i	−0.420545	−	0.728405i	0.575448	−	0.817838i	$-0.304828\pi$
$113$	−4.47045	−	7.74305i	−0.420545	−	0.728405i	−0.995993	+	0.0894334i	$0.971494\pi$
$114$	−3.79190	+	3.75148i	−0.355144	+	0.351358i
$115$	2.74949	+	10.2612i	0.256391	+	0.956864i
$116$	−5.99383	+	10.1294i	−0.556513	+	0.940489i
$117$	−0.140190	+	1.38651i	−0.0129606	+	0.128183i
$118$	9.15289	+	2.50515i	0.842592	+	0.230617i
$119$	−9.45291	+	2.53290i	−0.866547	+	0.232190i
$120$	9.58391	−	2.40359i	0.874887	−	0.219416i
$121$	−6.71217	+	3.87527i	−0.610197	+	0.352298i
$122$	0.502322	+	0.880914i	0.0454781	+	0.0797542i
$123$	0.649762	−	2.42494i	0.0585871	−	0.218650i
$124$	0.831694	+	0.849712i	0.0746883	+	0.0763064i
$125$	−8.14498	−	8.14498i	−0.728509	−	0.728509i
$126$	0.283373	+	1.08069i	0.0252449	+	0.0962756i
$127$	0.775200	−	1.34269i	0.0687879	−	0.119144i	−0.829580	−	0.558388i	$-0.811420\pi$
$127$	0.775200	−	1.34269i	0.0687879	−	0.119144i	0.898368	+	0.439244i	$0.144753\pi$
$128$	11.3058	+	0.424223i	0.999297	+	0.0374964i
$129$			18.0895i			1.59269i
$130$	10.8852	−	1.70836i	0.954694	−	0.149833i
$131$			4.10898i			0.359003i	0.983758	+	0.179502i	$0.0574485\pi$
$131$			4.10898i			0.359003i	−0.983758	+	0.179502i	$0.942552\pi$
$132$	3.76833	−	13.4840i	0.327991	−	1.17363i
$133$	−2.38434	+	4.12979i	−0.206748	+	0.358099i
$134$	9.68932	−	2.54068i	0.837030	−	0.219482i
$135$	−8.36529	−	8.36529i	−0.719969	−	0.719969i
$136$	11.8355	−	6.58189i	1.01489	−	0.564393i
$137$	−3.06346	+	11.4330i	−0.261729	+	0.976786i	0.702493	+	0.711691i	$0.252070\pi$
$137$	−3.06346	+	11.4330i	−0.261729	+	0.976786i	−0.964222	+	0.265096i	$0.914596\pi$
$138$	−9.76368	+	5.56753i	−0.831140	+	0.473939i
$139$	−7.30191	+	4.21576i	−0.619340	+	0.357576i	−0.776612	−	0.629979i	$-0.783063\pi$
$139$	−7.30191	+	4.21576i	−0.619340	+	0.357576i	0.157272	+	0.987555i	$0.449730\pi$
$140$	7.69686	−	4.33449i	0.650504	−	0.366331i
$141$	17.8222	−	4.77545i	1.50090	−	0.402165i
$142$	−0.655125	+	2.39359i	−0.0549769	+	0.200865i
$143$	5.53745	−	14.5977i	0.463065	−	1.22072i
$144$	−0.744148	−	1.35517i	−0.0620123	−	0.112930i
$145$	−3.29133	−	12.2834i	−0.273330	−	1.02008i
$146$	7.53519	+	7.61637i	0.623617	+	0.630335i
$147$	2.28134	+	3.95140i	0.188162	+	0.325906i
$148$	−3.74255	+	0.959952i	−0.307636	+	0.0789075i
$149$	−1.36446	−	0.365606i	−0.111781	−	0.0299516i	0.202495	−	0.979283i	$-0.435095\pi$
$149$	−1.36446	−	0.365606i	−0.111781	−	0.0299516i	−0.314276	+	0.949332i	$0.601762\pi$
$150$	0.381359	−	0.652435i	0.0311378	−	0.0532711i
$151$	−6.88689	+	6.88689i	−0.560447	+	0.560447i	−0.929435	−	0.368987i	$-0.879705\pi$
$151$	−6.88689	+	6.88689i	−0.560447	+	0.560447i	0.368987	+	0.929435i	$0.379705\pi$
$152$	1.81017	−	6.34585i	0.146824	−	0.514716i
$153$	−1.60268	−	0.925305i	−0.129569	−	0.0748065i
$154$	0.0670625	−	12.5165i	0.00540405	−	1.00861i
$155$	−1.28465			−0.103186
$156$	4.66947	+	10.6816i	0.373857	+	0.855216i
$157$	14.0877			1.12432			0.562162	−	0.827027i	$-0.309970\pi$
$157$	14.0877			1.12432			0.562162	+	0.827027i	$0.309970\pi$
$158$	0.00846540	−	1.57997i	0.000673471	−	0.125696i
$159$	1.86282	+	1.07550i	0.147731	+	0.0852927i
$160$	−8.87199	+	8.40894i	−0.701393	+	0.664785i
$161$	−7.10515	+	7.10515i	−0.559965	+	0.559965i
$162$	5.48881	−	9.39034i	0.431241	−	0.737775i
$163$	−19.7316	−	5.28707i	−1.54550	−	0.414115i	−0.617461	−	0.786601i	$-0.711839\pi$
$163$	−19.7316	−	5.28707i	−1.54550	−	0.414115i	−0.928038	+	0.372486i	$0.878505\pi$
$164$	0.771655	+	3.00844i	0.0602561	+	0.234920i
$165$	7.56346	+	13.1003i	0.588815	+	1.01986i
$166$	−3.45659	−	3.49383i	−0.268283	−	0.271174i
$167$	−3.17054	−	11.8326i	−0.245344	−	0.915635i	−0.973210	−	0.229917i	$-0.926155\pi$
$167$	−3.17054	−	11.8326i	−0.245344	−	0.915635i	0.727867	−	0.685719i	$-0.240512\pi$
$168$	6.50149	+	6.71392i	0.501601	+	0.517990i
$169$	4.11482	+	12.3316i	0.316525	+	0.948584i
$170$	−3.86271	+	14.1129i	−0.296256	+	1.08241i
$171$	−0.871034	+	0.233393i	−0.0666096	+	0.0178480i
$172$	−10.9813	−	19.4998i	−0.837316	−	1.48684i
$173$	5.85764	−	3.38191i	0.445348	−	0.257122i	−0.260515	−	0.965470i	$-0.583893\pi$
$173$	5.85764	−	3.38191i	0.445348	−	0.257122i	0.705864	+	0.708348i	$0.250559\pi$
$174$	11.6878	−	6.66473i	0.886051	−	0.505252i
$175$	0.174862	−	0.652593i	0.0132183	−	0.0493314i
$176$	4.12338	+	16.8228i	0.310811	+	1.26807i
$177$	−7.67053	−	7.67053i	−0.576552	−	0.576552i
$178$	2.66480	−	0.698751i	0.199735	−	0.0523736i
$179$	3.83994	−	6.65097i	0.287011	−	0.497117i	−0.686084	−	0.727522i	$-0.740672\pi$
$179$	3.83994	−	6.65097i	0.287011	−	0.497117i	0.973095	+	0.230405i	$0.0740052\pi$
$180$	1.60877	+	0.449598i	0.119910	+	0.0335111i
$181$		−	10.6994i		−	0.795283i	−0.917541	−	0.397642i	$-0.869829\pi$
$181$		−	10.6994i		−	0.795283i	0.917541	−	0.397642i	$-0.130171\pi$
$182$	6.54741	+	8.10866i	0.485327	+	0.601054i
$183$		−	1.15921i		−	0.0856915i
$184$	7.14509	−	11.9287i	0.526743	−	0.879394i
$185$	2.08726	−	3.61524i	0.153458	−	0.265798i
$186$	−0.344743	−	1.31474i	−0.0252778	−	0.0964011i
$187$	14.6605	+	14.6605i	1.07208	+	1.07208i
$188$	−16.3127	+	15.9668i	−1.18973	+	1.16450i
$189$	2.89618	−	10.8087i	0.210666	−	0.786216i
$190$	3.53178	+	6.19363i	0.256223	+	0.449333i
$191$	−12.5176	+	7.22707i	−0.905745	+	0.522932i	−0.879060	−	0.476712i	$-0.841829\pi$
$191$	−12.5176	+	7.22707i	−0.905745	+	0.522932i	−0.0266854	+	0.999644i	$0.508495\pi$
$192$	−10.9867	−	6.82318i	−0.792897	−	0.492420i
$193$	−18.9062	+	5.06589i	−1.36089	+	0.364651i	−0.864145	−	0.503243i	$-0.832140\pi$
$193$	−18.9062	+	5.06589i	−1.36089	+	0.364651i	−0.496750	+	0.867894i	$0.665473\pi$
$194$	−1.87426	−	0.512986i	−0.134564	−	0.0368303i
$195$	−11.7767	−	4.46731i	−0.843344	−	0.319911i
$196$	−4.85792	−	2.87457i	−0.346994	−	0.205326i
$197$	0.687766	+	2.56678i	0.0490013	+	0.182875i	0.986089	−	0.166219i	$-0.0531559\pi$
$197$	0.687766	+	2.56678i	0.0490013	+	0.182875i	−0.937088	+	0.349094i	$0.886489\pi$
$198$	1.68260	−	1.66467i	0.119577	−	0.118303i
$199$	8.28694	+	14.3534i	0.587445	+	1.01749i	0.994566	+	0.104111i	$0.0331996\pi$
$199$	8.28694	+	14.3534i	0.587445	+	1.01749i	−0.407120	+	0.913374i	$0.633467\pi$
$200$	−0.0150270	+	0.934806i	−0.00106257	+	0.0661008i
$201$	−11.0604	−	2.96363i	−0.780142	−	0.209039i
$202$	1.06215	+	0.620846i	0.0747328	+	0.0436826i
$203$	8.50538	−	8.50538i	0.596960	−	0.596960i
$204$	−15.4800	−	0.165886i	−1.08382	−	0.0116144i
$205$	−2.90610	−	1.67784i	−0.202971	−	0.117185i
$206$	16.3683	+	0.0877003i	1.14043	+	0.00611037i
$207$	−1.90012			−0.132068
$208$	−11.5179	−	8.67980i	−0.798620	−	0.601836i
$209$	10.1027			0.698820
$210$	−10.0976	−	0.0541023i	−0.696801	−	0.00373342i
$211$	23.9352	+	13.8190i	1.64777	+	0.951341i	0.977956	+	0.208812i	$0.0669598\pi$
$211$	23.9352	+	13.8190i	1.64777	+	0.951341i	0.669815	+	0.742528i	$0.266373\pi$
$212$	−2.66094	−	0.0285151i	−0.182754	−	0.00195843i
$213$	2.00593	−	2.00593i	0.137444	−	0.137444i
$214$	−9.83777	−	5.75034i	−0.672496	−	0.393085i
$215$	23.3556	+	6.25813i	1.59284	+	0.426801i
$216$	−0.248888	+	15.4829i	−0.0169347	+	1.05348i
$217$	−0.607559	−	1.05232i	−0.0412438	−	0.0714364i
$218$	17.1765	−	16.9935i	1.16334	−	1.15094i
$219$	−3.16986	−	11.8301i	−0.214199	−	0.799403i
$220$	−16.1057	−	9.53020i	−1.08585	−	0.642526i
$221$	−17.1759	−	1.73665i	−1.15537	−	0.116820i
$222$	4.26003	+	1.16597i	0.285915	+	0.0782549i
$223$	2.93579	−	0.786643i	0.196595	−	0.0526775i	−0.159178	−	0.987250i	$-0.550884\pi$
$223$	2.93579	−	0.786643i	0.196595	−	0.0526775i	0.355773	+	0.934572i	$0.384218\pi$
$224$	−11.0841	−	3.29060i	−0.740586	−	0.219863i
$225$	0.110643	−	0.0638796i	0.00737618	−	0.00425864i
$226$	−6.26341	−	10.9840i	−0.416636	−	0.730648i
$227$	−2.44919	+	9.14049i	−0.162558	+	0.606675i	0.835781	+	0.549063i	$0.185015\pi$
$227$	−2.44919	+	9.14049i	−0.162558	+	0.606675i	−0.998339	+	0.0576122i	$0.981651\pi$
$228$	−5.39090	+	5.27659i	−0.357021	+	0.349450i
$229$	−3.49493	−	3.49493i	−0.230952	−	0.230952i	0.582138	−	0.813090i	$-0.302216\pi$
$229$	−3.49493	−	3.49493i	−0.230952	−	0.230952i	−0.813090	+	0.582138i	$0.802216\pi$
$230$	3.81055	+	14.5322i	0.251260	+	0.958224i
$231$	−7.15408	+	12.3912i	−0.470704	+	0.815283i
$232$	−8.55318	+	14.2795i	−0.561544	+	0.937494i
$233$			21.3205i			1.39675i	0.715731	+	0.698376i	$0.246094\pi$
$233$			21.3205i			1.39675i	−0.715731	+	0.698376i	$0.753906\pi$
$234$	−0.208761	+	1.95973i	−0.0136472	+	0.128112i
$235$		−	24.6627i		−	1.60882i
$236$	12.9250	+	3.61212i	0.841344	+	0.235129i
$237$	−0.903070	+	1.56416i	−0.0586607	+	0.101603i
$238$	−13.3874	+	3.51038i	−0.867778	+	0.227544i
$239$	−5.96711	−	5.96711i	−0.385981	−	0.385981i	0.487271	−	0.873251i	$-0.337993\pi$
$239$	−5.96711	−	5.96711i	−0.385981	−	0.385981i	−0.873251	+	0.487271i	$0.837993\pi$
$240$	13.5717	−	3.32652i	0.876050	−	0.214726i
$241$	5.36803	−	20.0338i	0.345785	−	1.29049i	−0.545906	−	0.837846i	$-0.683815\pi$
$241$	5.36803	−	20.0338i	0.345785	−	1.29049i	0.891692	−	0.452643i	$-0.149519\pi$
$242$	−9.52167	+	5.42953i	−0.612076	+	0.349023i
$243$	3.45593	−	1.99528i	0.221698	−	0.127997i
$244$	0.703706	+	1.24959i	0.0450502	+	0.0799968i
$245$	5.89097	−	1.57848i	0.376360	−	0.100845i
$246$	0.937263	−	3.42442i	0.0597577	−	0.218333i
$247$	−6.51644	+	5.31969i	−0.414631	+	0.338484i
$248$	1.16974	+	1.20796i	0.0742784	+	0.0767054i
$249$	1.45410	+	5.42677i	0.0921498	+	0.343908i
$250$	−11.4569	−	11.5803i	−0.724595	−	0.732402i
$251$	−2.95746	−	5.12248i	−0.186673	−	0.323328i	0.757466	−	0.652875i	$-0.226437\pi$
$251$	−2.95746	−	5.12248i	−0.186673	−	0.323328i	−0.944139	+	0.329547i	$0.893104\pi$
$252$	0.392556	+	1.53045i	0.0247287	+	0.0964095i
$253$	20.5624	+	5.50967i	1.29274	+	0.346390i
$254$	1.10646	−	1.89294i	0.0694253	−	0.118774i
$255$	11.8273	−	11.8273i	0.740651	−	0.740651i
$256$	15.9853	+	0.685599i	0.999082	+	0.0428500i
$257$	24.4854	+	14.1366i	1.52736	+	0.881819i	0.999472	+	0.0325029i	$0.0103478\pi$
$257$	24.4854	+	14.1366i	1.52736	+	0.881819i	0.527884	+	0.849316i	$0.322986\pi$
$258$	−0.137067	+	25.5820i	−0.00853340	+	1.59266i
$259$	3.94857			0.245352
$260$	15.4067	−	2.33348i	0.955483	−	0.144716i
$261$	2.27458			0.140793
$262$	−0.0311344	+	5.81089i	−0.00192349	+	0.358998i
$263$	11.6002	+	6.69738i	0.715299	+	0.412978i	0.813020	−	0.582236i	$-0.197822\pi$
$263$	11.6002	+	6.69738i	0.715299	+	0.412978i	−0.0977210	+	0.995214i	$0.531155\pi$
$264$	5.43132	−	19.0404i	0.334275	−	1.17185i
$265$	2.03305	−	2.03305i	0.124889	−	0.124889i
$266$	−3.40321	+	5.82226i	−0.208664	+	0.356986i
$267$	−3.04189	−	0.815072i	−0.186161	−	0.0498816i
$268$	13.7218	−	3.51960i	0.838193	−	0.214994i
$269$	−11.4654	−	19.8587i	−0.699060	−	1.21081i	−0.968793	−	0.247872i	$-0.920269\pi$
$269$	−11.4654	−	19.8587i	−0.699060	−	1.21081i	0.269733	−	0.962935i	$-0.413065\pi$
$270$	−11.7667	−	11.8935i	−0.716101	−	0.723816i
$271$	−2.48442	−	9.27197i	−0.150918	−	0.563232i	−0.999420	−	0.0340411i	$-0.989162\pi$
$271$	−2.48442	−	9.27197i	−0.150918	−	0.563232i	0.848503	−	0.529191i	$-0.177504\pi$
$272$	16.7876	−	9.21839i	1.01790	−	0.558947i
$273$	−1.91021	−	11.7596i	−0.115611	−	0.711724i
$274$	−4.41895	+	16.1452i	−0.266959	+	0.975370i
$275$	−1.38256	+	0.370455i	−0.0833714	+	0.0223393i
$276$	−13.8499	+	7.79958i	−0.833667	+	0.469479i
$277$	−0.952681	+	0.550031i	−0.0572411	+	0.0330482i	−0.528347	−	0.849028i	$-0.677188\pi$
$277$	−0.952681	+	0.550031i	−0.0572411	+	0.0330482i	0.471106	+	0.882076i	$0.343855\pi$
$278$	−10.3582	+	5.90657i	−0.621247	+	0.354252i
$279$	0.0594714	−	0.221950i	0.00356046	−	0.0132878i
$280$	10.9177	−	6.07148i	0.652457	−	0.362840i
$281$	6.74660	+	6.74660i	0.402469	+	0.402469i	0.879102	−	0.476634i	$-0.158143\pi$
$281$	6.74660	+	6.74660i	0.402469	+	0.402469i	−0.476634	+	0.879102i	$0.658143\pi$
$282$	25.2402	−	6.61836i	1.50303	−	0.394118i
$283$	−10.5772	+	18.3202i	−0.628746	+	1.08902i	0.359057	+	0.933316i	$0.383098\pi$
$283$	−10.5772	+	18.3202i	−0.628746	+	1.08902i	−0.987804	+	0.155705i	$0.950235\pi$
$284$	−0.944610	+	3.38003i	−0.0560523	+	0.200568i
$285$		−	8.15033i		−	0.482784i
$286$	7.94163	−	20.6021i	0.469599	−	1.21823i
$287$		−	3.17405i		−	0.187358i
$288$	−1.04210	−	1.92210i	−0.0614064	−	0.113261i
$289$	2.96254	−	5.13126i	0.174267	−	0.301839i
$290$	−4.56150	−	17.3961i	−0.267861	−	1.02153i
$291$	1.57072	+	1.57072i	0.0920770	+	0.0920770i
$292$	10.5985	+	10.8281i	0.620230	+	0.633667i
$293$	−4.68793	+	17.4956i	−0.273872	+	1.02210i	0.682722	+	0.730678i	$0.260796\pi$
$293$	−4.68793	+	17.4956i	−0.273872	+	1.02210i	−0.956594	+	0.291425i	$0.905871\pi$
$294$	3.19632	+	5.60533i	0.186413	+	0.326910i
$295$	−12.5572	+	7.24991i	−0.731109	+	0.422106i
$296$	−5.29997	+	1.32920i	−0.308054	+	0.0772581i
$297$	−22.8988	+	6.13573i	−1.32873	+	0.356031i
$298$	−1.92684	−	0.527376i	−0.111619	−	0.0305501i
$299$	−16.1643	+	7.27348i	−0.934803	+	0.420636i
$300$	0.544259	−	0.919779i	0.0314228	−	0.0531035i
$301$	5.91940	+	22.0915i	0.341188	+	1.27333i
$302$	−9.79158	+	9.68722i	−0.563442	+	0.557437i
$303$	−0.703192	−	1.21796i	−0.0403973	−	0.0699702i
$304$	2.60802	−	8.96054i	0.149580	−	0.513922i
$305$	−1.49668	−	0.401035i	−0.0856998	−	0.0229632i
$306$	−2.25948	−	1.32070i	−0.129166	−	0.0754996i
$307$	7.26086	−	7.26086i	0.414399	−	0.414399i	−0.468869	−	0.883268i	$-0.655338\pi$
$307$	7.26086	−	7.26086i	0.414399	−	0.414399i	0.883268	+	0.468869i	$0.155338\pi$
$308$	0.189679	−	17.7002i	0.0108079	−	1.00856i
$309$	−16.2045	−	9.35568i	−0.921843	−	0.532226i
$310$	−1.81675	−	0.00973401i	−0.103184	−	0.000552855i
$311$	−9.77167			−0.554101			−0.277050	−	0.960855i	$-0.589357\pi$
$311$	−9.77167			−0.554101			−0.277050	+	0.960855i	$0.589357\pi$
$312$	6.52259	+	15.1413i	0.369269	+	0.857207i
$313$	−31.6333			−1.78802			−0.894010	−	0.448047i	$-0.852120\pi$
$313$	−31.6333			−1.78802			−0.894010	+	0.448047i	$0.852120\pi$
$314$	19.9228	+	0.106745i	1.12431	+	0.00602397i
$315$	−1.47839	−	0.853550i	−0.0832980	−	0.0480921i
$316$	0.0239434	−	2.23432i	0.00134692	−	0.125691i
$317$	−14.7813	+	14.7813i	−0.830201	+	0.830201i	−0.987544	−	0.157343i	$-0.949707\pi$
$317$	−14.7813	+	14.7813i	−0.830201	+	0.830201i	0.157343	+	0.987544i	$0.449707\pi$
$318$	2.62624	+	1.53508i	0.147272	+	0.0860830i
$319$	−24.6146	−	6.59547i	−1.37815	−	0.369275i
$320$	−12.6104	+	11.8246i	−0.704944	+	0.661017i
$321$	6.51304	+	11.2809i	0.363522	+	0.629639i
$322$	−10.1019	+	9.99422i	−0.562957	+	0.556956i
$323$	−2.89123	−	10.7902i	−0.160873	−	0.600384i
$324$	7.83339	−	13.2382i	0.435188	−	0.735454i
$325$	0.696708	−	0.966950i	0.0386464	−	0.0536367i
$326$	−27.8643	−	7.62645i	−1.54326	−	0.422390i
$327$	−26.6794	+	7.14872i	−1.47537	+	0.395325i
$328$	1.06847	+	4.26036i	0.0589966	+	0.235239i
$329$	20.2025	−	11.6639i	1.11380	−	0.643051i
$330$	10.5969	+	18.5837i	0.583342	+	1.02300i
$331$	3.14630	−	11.7421i	0.172936	−	0.645407i	−0.823958	−	0.566651i	$-0.808239\pi$
$331$	3.14630	−	11.7421i	0.172936	−	0.645407i	0.996894	−	0.0787555i	$-0.0250946\pi$
$332$	−4.86181	−	4.96714i	−0.266827	−	0.272607i
$333$	0.527981	+	0.527981i	0.0289332	+	0.0289332i
$334$	−4.39410	−	16.7576i	−0.240434	−	0.916937i
$335$	−7.65280	+	13.2550i	−0.418117	+	0.724201i
$336$	9.14348	+	9.54405i	0.498818	+	0.520671i
$337$		−	18.7726i		−	1.02261i	−0.859401	−	0.511303i	$-0.829163\pi$
$337$		−	18.7726i		−	1.02261i	0.859401	−	0.511303i	$-0.170837\pi$
$338$	5.72572	+	17.4704i	0.311438	+	0.950267i
$339$			14.4541i			0.785041i
$340$	−5.56955	+	19.9291i	−0.302051	+	1.08081i
$341$	−1.28715	+	2.22941i	−0.0697031	+	0.120729i
$342$	−1.23358	+	0.323463i	−0.0667043	+	0.0174909i
$343$	14.1960	+	14.1960i	0.766513	+	0.766513i
$344$	−15.3819	−	27.6596i	−0.829337	−	1.49131i
$345$	4.44490	−	16.5886i	0.239305	−	0.893100i
$346$	8.30946	−	4.73829i	0.446719	−	0.254732i
$347$	6.91748	−	3.99381i	0.371350	−	0.214399i	−0.302698	−	0.953086i	$-0.597887\pi$
$347$	6.91748	−	3.99381i	0.371350	−	0.214399i	0.674048	+	0.738688i	$0.264554\pi$
$348$	16.5793	−	9.33665i	0.888746	−	0.500497i
$349$	9.90639	−	2.65441i	0.530277	−	0.142087i	0.0162607	−	0.999868i	$-0.494824\pi$
$349$	9.90639	−	2.65441i	0.530277	−	0.142087i	0.514016	+	0.857781i	$0.328157\pi$
$350$	0.252233	−	0.921568i	0.0134824	−	0.0492599i
$351$	11.5393	−	16.0153i	0.615924	−	0.854831i
$352$	5.70379	+	23.8219i	0.304013	+	1.26971i
$353$	−1.22350	−	4.56617i	−0.0651204	−	0.243033i	0.925692	−	0.378279i	$-0.123484\pi$
$353$	−1.22350	−	4.56617i	−0.0651204	−	0.243033i	−0.990812	+	0.135246i	$0.956817\pi$
$354$	−10.7895	−	10.9057i	−0.573455	−	0.579633i
$355$	−1.89594	−	3.28386i	−0.100626	−	0.174289i
$356$	3.77384	−	0.967977i	0.200013	−	0.0513027i
$357$	15.2818	+	4.09476i	0.808801	+	0.216718i
$358$	5.48081	−	9.37666i	0.289670	−	0.495572i
$359$	25.8704	−	25.8704i	1.36539	−	1.36539i	0.498492	−	0.866894i	$-0.333887\pi$
$359$	25.8704	−	25.8704i	1.36539	−	1.36539i	0.866894	−	0.498492i	$-0.166113\pi$
$360$	2.27170	+	0.648009i	0.119729	+	0.0341531i
$361$	11.7404	+	6.77834i	0.617918	+	0.356755i
$362$	0.0810714	−	15.1311i	0.00426102	−	0.795272i
$363$	12.5298			0.657642
$364$	9.19787	+	11.5168i	0.482099	+	0.603646i
$365$	−16.3707			−0.856880
$366$	0.00878354	−	1.63935i	0.000459123	−	0.0856903i
$367$	17.6675	+	10.2004i	0.922238	+	0.532454i	0.884348	−	0.466828i	$-0.154603\pi$
$367$	17.6675	+	10.2004i	0.922238	+	0.532454i	0.0378895	+	0.999282i	$0.487937\pi$
$368$	10.1949	−	16.8153i	0.531447	−	0.876559i
$369$	0.424416	−	0.424416i	0.0220942	−	0.0220942i
$370$	2.97918	−	5.09684i	0.154880	−	0.264972i
$371$	2.62688	+	0.703870i	0.136381	+	0.0365431i
$372$	−0.477572	−	1.86190i	−0.0247609	−	0.0965352i
$373$	10.3223	+	17.8788i	0.534471	+	0.925731i	0.999189	+	0.0402718i	$0.0128224\pi$
$373$	10.3223	+	17.8788i	0.534471	+	0.925731i	−0.464718	+	0.885459i	$0.653844\pi$
$374$	20.6216	+	20.8438i	1.06632	+	1.07781i
$375$	4.81961	+	17.9870i	0.248883	+	0.928845i
$376$	−23.1903	+	22.4566i	−1.19595	+	1.15811i
$377$	19.3498	−	8.70687i	0.996564	−	0.448427i
$378$	4.17765	−	15.2636i	0.214875	−	0.785076i
$379$	−13.7043	+	3.67206i	−0.703943	+	0.188621i	−0.592996	−	0.805205i	$-0.702055\pi$
$379$	−13.7043	+	3.67206i	−0.703943	+	0.188621i	−0.110947	+	0.993826i	$0.535388\pi$
$380$	4.94770	+	8.78575i	0.253811	+	0.450700i
$381$	−2.17063	+	1.25321i	−0.111205	+	0.0642040i
$382$	−17.7571	+	10.1256i	−0.908534	+	0.518072i
$383$	−4.01265	+	14.9754i	−0.205037	+	0.765207i	0.784402	+	0.620253i	$0.212970\pi$
$383$	−4.01265	+	14.9754i	−0.205037	+	0.765207i	−0.989438	+	0.144954i	$0.953697\pi$
$384$	−15.4856	−	9.73254i	−0.790247	−	0.496661i
$385$	13.5236	+	13.5236i	0.689225	+	0.689225i
$386$	−26.7753	+	7.02089i	−1.36283	+	0.357354i
$387$	−2.16244	+	3.74546i	−0.109923	+	0.190393i
$388$	−2.64668	−	0.739663i	−0.134365	−	0.0375507i
$389$		−	33.5493i		−	1.70102i	−0.525963	−	0.850508i	$-0.676295\pi$
$389$		−	33.5493i		−	1.70102i	0.525963	−	0.850508i	$-0.323705\pi$
$390$	−16.6206	−	6.40688i	−0.841618	−	0.324425i
$391$		−	23.5384i		−	1.19039i
$392$	−6.84826	−	4.10200i	−0.345889	−	0.207182i
$393$	3.32135	−	5.75274i	0.167540	−	0.290187i
$394$	0.953185	+	3.63513i	0.0480208	+	0.183135i
$395$	1.70710	+	1.70710i	0.0858935	+	0.0858935i
$396$	2.39214	−	2.34141i	0.120209	−	0.117660i
$397$	−3.22366	+	12.0309i	−0.161791	+	0.603813i	0.836637	+	0.547758i	$0.184519\pi$
$397$	−3.22366	+	12.0309i	−0.161791	+	0.603813i	−0.998428	+	0.0560542i	$0.982148\pi$
$398$	11.6106	+	20.3613i	0.581985	+	1.02062i
$399$	6.67635	−	3.85459i	0.334235	−	0.192971i
$400$	−0.0283343	+	1.32188i	−0.00141672	+	0.0660941i
$401$	−14.0736	+	3.77101i	−0.702802	+	0.188315i	−0.592485	−	0.805581i	$-0.701853\pi$
$401$	−14.0736	+	3.77101i	−0.702802	+	0.188315i	−0.110317	+	0.993896i	$0.535187\pi$
$402$	−15.6191	−	4.27496i	−0.779011	−	0.213215i
$403$	−0.343682	−	2.11577i	−0.0171200	−	0.105394i
$404$	1.49739	+	0.886044i	0.0744977	+	0.0440824i
$405$	4.30147	+	16.0533i	0.213742	+	0.797695i
$406$	12.0927	−	11.9638i	0.600150	−	0.593753i
$407$	−4.18264	−	7.24455i	−0.207326	−	0.359099i
$408$	−21.8905	−	0.351890i	−1.08374	−	0.0174211i
$409$	−18.7351	−	5.02006i	−0.926393	−	0.248226i	−0.236077	−	0.971734i	$-0.575862\pi$
$409$	−18.7351	−	5.02006i	−0.926393	−	0.248226i	−0.690316	+	0.723508i	$0.742528\pi$
$410$	−4.09708	−	2.39481i	−0.202340	−	0.118271i
$411$	13.5304	−	13.5304i	0.667407	−	0.667407i
$412$	23.1473	+	0.248050i	1.14038	+	0.0122206i
$413$	−11.8775	−	6.85750i	−0.584456	−	0.337436i
$414$	−2.68714	−	0.0143975i	−0.132066	−	0.000707600i
$415$	7.50966			0.368635
$416$	−16.2227	−	12.3622i	−0.795384	−	0.606106i
$417$	13.6306			0.667495
$418$	14.2872	+	0.0765499i	0.698810	+	0.00374418i
$419$	2.54287	+	1.46812i	0.124227	+	0.0717226i	0.560826	−	0.827934i	$-0.310484\pi$
$419$	2.54287	+	1.46812i	0.124227	+	0.0717226i	−0.436599	+	0.899656i	$0.643817\pi$
$420$	−14.2796	−	0.153022i	−0.696771	−	0.00746673i
$421$	−4.53947	+	4.53947i	−0.221240	+	0.221240i	−0.809021	−	0.587780i	$-0.800002\pi$
$421$	−4.53947	+	4.53947i	−0.221240	+	0.221240i	0.587780	+	0.809021i	$0.300002\pi$
$422$	33.7444	+	19.7241i	1.64265	+	0.960156i
$423$	4.26099	+	1.14173i	0.207177	+	0.0555128i
$424$	−3.76287	−	0.0604883i	−0.182741	−	0.00293757i
$425$	0.791331	+	1.37063i	0.0383852	+	0.0664851i
$426$	2.85197	−	2.82158i	0.138179	−	0.136706i
$427$	−0.379328	−	1.41567i	−0.0183570	−	0.0685092i
$428$	−13.8689	−	8.20663i	−0.670381	−	0.396683i
$429$	−19.5522	+	15.9614i	−0.943990	+	0.770626i
$430$	32.9820	+	9.02717i	1.59053	+	0.435329i
$431$	18.3194	−	4.90868i	0.882417	−	0.236443i	0.210967	−	0.977493i	$-0.432339\pi$
$431$	18.3194	−	4.90868i	0.882417	−	0.236443i	0.671450	+	0.741050i	$0.265672\pi$
$432$	−0.469292	+	21.8939i	−0.0225788	+	1.05337i
$433$	4.30614	−	2.48615i	0.206940	−	0.119477i	−0.392949	−	0.919560i	$-0.628545\pi$
$433$	4.30614	−	2.48615i	0.206940	−	0.119477i	0.599888	+	0.800084i	$0.295212\pi$
$434$	−0.851233	−	1.49279i	−0.0408605	−	0.0716563i
$435$	−5.32086	+	19.8577i	−0.255116	+	0.952105i
$436$	24.4197	−	23.9019i	1.16949	−	1.14469i
$437$	−8.11034	−	8.11034i	−0.387970	−	0.387970i
$438$	−4.39316	−	16.7540i	−0.209913	−	0.800539i
$439$	19.5845	−	33.9214i	0.934717	−	1.61898i	0.159580	−	0.987185i	$-0.448986\pi$
$439$	19.5845	−	33.9214i	0.934717	−	1.61898i	0.775137	−	0.631793i	$-0.217681\pi$
$440$	−22.7044	−	13.5996i	−1.08239	−	0.648335i
$441$			1.09086i			0.0519458i
$442$	−24.2768	−	2.58610i	−1.15473	−	0.123008i
$443$			38.1735i			1.81368i	0.421477	+	0.906839i	$0.361512\pi$
$443$			38.1735i			1.81368i	−0.421477	+	0.906839i	$0.638488\pi$
$444$	6.01567	+	1.68119i	0.285491	+	0.0797856i
$445$	−2.10471	+	3.64547i	−0.0997729	+	0.172812i
$446$	4.15774	−	1.09022i	0.196874	−	0.0516234i
$447$	1.61478	+	1.61478i	0.0763763	+	0.0763763i
$448$	−15.6501	−	4.73754i	−0.739398	−	0.223828i
$449$	−0.812961	+	3.03401i	−0.0383660	+	0.143184i	−0.982452	−	0.186515i	$-0.940281\pi$
$449$	−0.812961	+	3.03401i	−0.0383660	+	0.143184i	0.944086	+	0.329699i	$0.106947\pi$
$450$	0.156954	−	0.0894998i	0.00739890	−	0.00421906i
$451$	−5.82351	+	3.36221i	−0.274219	+	0.158320i
$452$	−8.77445	−	15.5810i	−0.412715	−	0.732870i
$453$	15.2087	−	4.07516i	0.714568	−	0.191468i
$454$	−3.53288	+	12.9079i	−0.165806	+	0.605796i
$455$	−15.8439	−	1.60198i	−0.742774	−	0.0751019i
$456$	−7.66376	+	7.42126i	−0.358888	+	0.347533i
$457$	−8.79773	−	32.8336i	−0.411541	−	1.53589i	−0.791665	−	0.610955i	$-0.790786\pi$
$457$	−8.79773	−	32.8336i	−0.411541	−	1.53589i	0.380125	−	0.924935i	$-0.375881\pi$
$458$	−4.91603	−	4.96899i	−0.229711	−	0.232186i
$459$	13.1065	+	22.7012i	0.611761	+	1.05960i
$460$	5.27875	+	20.5802i	0.246123	+	0.959556i
$461$	−22.9313	−	6.14442i	−1.06802	−	0.286174i	−0.318339	−	0.947977i	$-0.603125\pi$
$461$	−22.9313	−	6.14442i	−1.06802	−	0.286174i	−0.749678	+	0.661803i	$0.769792\pi$
$462$	−10.2111	+	17.4694i	−0.475065	+	0.812749i
$463$	−24.4048	+	24.4048i	−1.13419	+	1.13419i	−0.144713	+	0.989474i	$0.546226\pi$
$463$	−24.4048	+	24.4048i	−1.13419	+	1.13419i	−0.989474	+	0.144713i	$0.953774\pi$
$464$	−12.2041	+	20.1291i	−0.566559	+	0.934472i
$465$	1.79857	+	1.03840i	0.0834065	+	0.0481548i
$466$	−0.161549	+	30.1513i	−0.00748361	+	1.39673i
$467$	−17.7779			−0.822661			−0.411331	−	0.911486i	$-0.634936\pi$
$467$	−17.7779			−0.822661			−0.411331	+	0.911486i	$0.634936\pi$
$468$	−0.310078	+	2.76985i	−0.0143334	+	0.128037i
$469$	−14.4772			−0.668494
$470$	0.186873	−	34.8778i	0.00861981	−	1.60879i
$471$	−19.7234	−	11.3873i	−0.908807	−	0.524700i
$472$	18.2510	+	5.20616i	0.840072	+	0.239633i
$473$	34.2615	−	34.2615i	1.57535	−	1.57535i
$474$	−1.28897	+	2.20519i	−0.0592042	+	0.101288i
$475$	0.744917	+	0.199600i	0.0341791	+	0.00915828i
$476$	−18.9590	+	4.86292i	−0.868985	+	0.222892i
$477$	0.257134	+	0.445369i	0.0117734	+	0.0203921i
$478$	−8.39344	−	8.48387i	−0.383907	−	0.388043i
$479$	2.05936	+	7.68562i	0.0940943	+	0.351165i	0.996881	−	0.0789246i	$-0.0251487\pi$
$479$	2.05936	+	7.68562i	0.0940943	+	0.351165i	−0.902786	+	0.430090i	$0.858482\pi$
$480$	19.2182	−	4.60150i	0.877188	−	0.210029i
$481$	6.51257	+	2.47045i	0.296947	+	0.112643i
$482$	7.74324	−	28.2910i	0.352695	−	1.28862i
$483$	15.6907	−	4.20431i	0.713952	−	0.191303i
$484$	−13.5066	+	7.60625i	−0.613938	+	0.345739i
$485$	2.57138	−	1.48459i	0.116760	−	0.0674115i
$486$	4.90247	−	2.79552i	0.222380	−	0.126808i
$487$	5.88223	−	21.9528i	0.266549	−	0.994775i	−0.694746	−	0.719255i	$-0.744483\pi$
$487$	5.88223	−	21.9528i	0.266549	−	0.994775i	0.961295	−	0.275520i	$-0.0888500\pi$
$488$	0.985708	+	1.77249i	0.0446209	+	0.0802370i
$489$	23.3515	+	23.3515i	1.05599	+	1.05599i
$490$	8.34293	−	2.18764i	0.376895	−	0.0988275i
$491$	−0.0296046	+	0.0512767i	−0.00133604	+	0.00231409i	−0.866693	−	0.498843i	$-0.833759\pi$
$491$	−0.0296046	+	0.0512767i	−0.00133604	+	0.00231409i	0.865357	+	0.501157i	$0.167092\pi$
$492$	1.35142	−	4.83568i	0.0609266	−	0.218010i
$493$			28.1772i			1.26904i
$494$	−9.25581	+	7.47369i	−0.416439	+	0.336257i
$495$			3.61659i			0.162554i
$496$	1.64508	+	1.71715i	0.0738663	+	0.0771023i
$497$	1.79332	−	3.10611i	0.0804412	−	0.139328i
$498$	2.01526	+	7.68552i	0.0903059	+	0.344397i
$499$	−25.7335	−	25.7335i	−1.15199	−	1.15199i	−0.986153	−	0.165836i	$-0.946968\pi$
$499$	−25.7335	−	25.7335i	−1.15199	−	1.15199i	−0.165836	−	0.986153i	$-0.553032\pi$
$500$	−16.1145	−	16.4636i	−0.720661	−	0.736273i
$501$	−5.12559	+	19.1290i	−0.228994	+	0.854619i
$502$	−4.14361	−	7.26658i	−0.184938	−	0.324323i
$503$	−14.6397	+	8.45225i	−0.652753	+	0.376867i	−0.789510	−	0.613738i	$-0.789665\pi$
$503$	−14.6397	+	8.45225i	−0.652753	+	0.376867i	0.136757	+	0.990605i	$0.456332\pi$
$504$	0.543553	+	2.16733i	0.0242118	+	0.0965406i
$505$	−1.81581	+	0.486545i	−0.0808024	+	0.0216509i
$506$	29.0374	+	7.94754i	1.29087	+	0.353311i
$507$	4.20688	−	20.5908i	0.186834	−	0.914471i
$508$	1.57909	−	2.66860i	0.0700606	−	0.118400i
$509$	5.21379	+	19.4581i	0.231097	+	0.862466i	0.979870	+	0.199639i	$0.0639769\pi$
$509$	5.21379	+	19.4581i	0.231097	+	0.862466i	−0.748772	+	0.662827i	$0.769356\pi$
$510$	16.8156	−	16.6364i	0.744609	−	0.736672i
$511$	−7.74230	−	13.4101i	−0.342499	−	0.593226i
$512$	22.6011	+	1.09069i	0.998838	+	0.0482023i
$513$	12.3378	+	3.30591i	0.544728	+	0.145959i
$514$	34.5199	+	20.1775i	1.52261	+	0.889990i
$515$	−17.6853	+	17.6853i	−0.779308	+	0.779308i
$516$	−0.387677	+	36.1768i	−0.0170665	+	1.59260i
$517$	−42.8001	−	24.7107i	−1.88235	−	1.08677i
$518$	5.58404	+	0.0299189i	0.245349	+	0.00131456i
$519$	−10.9346			−0.479975
$520$	21.8057	−	3.18325i	0.956245	−	0.139595i
$521$	4.77166			0.209050			0.104525	−	0.994522i	$-0.466668\pi$
$521$	4.77166			0.209050			0.104525	+	0.994522i	$0.466668\pi$
$522$	3.21670	+	0.0172349i	0.140791	+	0.000754350i
$523$	−14.6805	−	8.47577i	−0.641932	−	0.370620i	0.143426	−	0.989661i	$-0.454188\pi$
$523$	−14.6805	−	8.47577i	−0.641932	−	0.370620i	−0.785358	+	0.619041i	$0.787521\pi$
$524$	−0.0880600	+	8.21748i	−0.00384692	+	0.358982i
$525$	−0.772315	+	0.772315i	−0.0337066	+	0.0337066i
$526$	16.3542	+	9.55929i	0.713076	+	0.416805i
$527$	2.74949	+	0.736723i	0.119769	+	0.0320921i
$528$	7.82521	−	26.8856i	0.340549	−	1.17005i
$529$	−0.584106	−	1.01170i	−0.0253959	−	0.0439870i
$530$	2.89053	−	2.85972i	0.125557	−	0.124218i
$531$	−0.671252	−	2.50515i	−0.0291299	−	0.108714i
$532$	−4.85691	+	8.20802i	−0.210574	+	0.355863i
$533$	1.98587	−	5.23511i	0.0860175	−	0.226758i
$534$	−4.29565	−	1.17572i	−0.185891	−	0.0508783i
$535$	16.8182	−	4.50643i	0.727115	−	0.194830i
$536$	19.4320	−	4.87342i	0.839333	−	0.210500i
$537$	−10.7522	+	6.20776i	−0.463990	+	0.267885i
$538$	−16.0639	−	28.1709i	−0.692562	−	1.21454i
$539$	3.16310	−	11.8049i	0.136245	−	0.508471i
$540$	−16.5503	−	16.9089i	−0.712213	−	0.727643i
$541$	−5.07631	−	5.07631i	−0.218248	−	0.218248i	0.589512	−	0.807760i	$-0.299320\pi$
$541$	−5.07631	−	5.07631i	−0.218248	−	0.218248i	−0.807760	+	0.589512i	$0.799320\pi$
$542$	−3.44319	−	13.1312i	−0.147898	−	0.564032i
$543$	−8.64852	+	14.9797i	−0.371143	+	0.642839i
$544$	23.8107	−	12.9094i	1.02088	−	0.553485i
$545$			36.9194i			1.58145i
$546$	−2.61230	−	16.6448i	−0.111796	−	0.712333i
$547$		−	32.0440i		−	1.37010i	−0.728494	−	0.685052i	$-0.759779\pi$
$547$		−	32.0440i		−	1.37010i	0.728494	−	0.685052i	$-0.240221\pi$
$548$	−6.37159	+	22.7990i	−0.272181	+	0.973925i
$549$	0.138574	−	0.240018i	0.00591421	−	0.0102437i
$550$	−1.95801	+	0.513420i	−0.0834899	+	0.0218923i
$551$	9.70865	+	9.70865i	0.413602	+	0.413602i
$552$	−19.6456	+	10.9252i	−0.836170	+	0.465006i
$553$	−0.591022	+	2.20572i	−0.0251328	+	0.0937969i
$554$	−1.35144	+	0.770631i	−0.0574173	+	0.0327410i
$555$	−5.84451	+	3.37433i	−0.248086	+	0.143232i
$556$	−14.6933	+	8.27454i	−0.623136	+	0.350919i
$557$	15.4125	−	4.12977i	0.653049	−	0.174984i	0.0829418	−	0.996554i	$-0.473568\pi$
$557$	15.4125	−	4.12977i	0.653049	−	0.174984i	0.570107	+	0.821570i	$0.306902\pi$
$558$	0.0857858	−	0.313430i	0.00363160	−	0.0132686i
$559$	−4.05856	+	40.1401i	−0.171659	+	1.69774i
$560$	15.4857	−	8.50352i	0.654392	−	0.359339i
$561$	−8.67499	−	32.3755i	−0.366258	−	1.36690i
$562$	9.48988	+	9.59212i	0.400306	+	0.404619i
$563$	−2.79472	−	4.84060i	−0.117783	−	0.204007i	0.801106	−	0.598523i	$-0.204246\pi$
$563$	−2.79472	−	4.84060i	−0.117783	−	0.204007i	−0.918889	+	0.394516i	$0.870912\pi$
$564$	35.7447	−	9.16840i	1.50512	−	0.386059i
$565$	18.6620	+	5.00047i	0.785116	+	0.210371i
$566$	−15.0970	+	25.8281i	−0.634572	+	1.08564i
$567$	−11.1157	+	11.1157i	−0.466818	+	0.466818i
$568$	−1.36147	+	4.77286i	−0.0571261	+	0.200265i
$569$	26.9010	+	15.5313i	1.12775	+	0.651106i	0.943368	−	0.331749i	$-0.107639\pi$
$569$	26.9010	+	15.5313i	1.12775	+	0.651106i	0.184381	+	0.982855i	$0.440972\pi$
$570$	0.0617563	−	11.5261i	0.00258669	−	0.482777i
$571$	9.21948			0.385823			0.192912	−	0.981216i	$-0.438207\pi$
$571$	9.21948			0.385823			0.192912	+	0.981216i	$0.438207\pi$
$572$	11.3871	−	29.0751i	0.476119	−	1.21569i
$573$	23.3670			0.976169
$574$	0.0240503	−	4.48872i	0.00100384	−	0.187356i
$575$	1.40730	+	0.812503i	0.0586883	+	0.0338837i
$576$	−1.45917	−	2.72612i	−0.0607987	−	0.113588i
$577$	−28.6991	+	28.6991i	−1.19476	+	1.19476i	−0.219044	+	0.975715i	$0.570294\pi$
$577$	−28.6991	+	28.6991i	−1.19476	+	1.19476i	−0.975715	+	0.219044i	$0.929706\pi$
$578$	4.22848	−	7.23415i	0.175882	−	0.300901i
$579$	30.5642	+	8.18966i	1.27021	+	0.340351i
$580$	−6.31904	−	24.6360i	−0.262384	−	1.02295i
$581$	3.55160	+	6.15155i	0.147345	+	0.255209i
$582$	2.20939	+	2.23320i	0.0915823	+	0.0925690i
$583$	−1.49119	−	5.56520i	−0.0617588	−	0.230487i
$584$	14.9063	+	15.3934i	0.616826	+	0.636981i
$585$	−1.90435	−	2.33277i	−0.0787353	−	0.0964481i
$586$	−6.76220	+	24.7066i	−0.279344	+	1.02062i
$587$	6.07956	−	1.62901i	0.250930	−	0.0672365i	−0.131161	−	0.991361i	$-0.541871\pi$
$587$	6.07956	−	1.62901i	0.250930	−	0.0672365i	0.382091	+	0.924125i	$0.375204\pi$
$588$	4.47774	+	7.95124i	0.184659	+	0.327904i
$589$	1.20120	−	0.693512i	0.0494945	−	0.0285757i
$590$	−17.8133	+	10.1576i	−0.733361	+	0.418183i
$591$	1.11186	−	4.14953i	0.0457359	−	0.170689i
$592$	−7.50525	+	1.83959i	−0.308464	+	0.0756065i
$593$	−23.4963	−	23.4963i	−0.964878	−	0.964878i	0.0345259	−	0.999404i	$-0.489008\pi$
$593$	−23.4963	−	23.4963i	−0.964878	−	0.964878i	−0.999404	+	0.0345259i	$0.989008\pi$
$594$	−32.4299	+	8.50359i	−1.33061	+	0.348907i
$595$	10.5736	−	18.3141i	0.433477	−	0.750804i
$596$	−2.72093	−	0.760412i	−0.111454	−	0.0311477i
$597$		−	26.7938i		−	1.09660i
$598$	−22.9145	+	10.1636i	−0.937044	+	0.415621i
$599$			23.9175i			0.977241i	0.872496	+	0.488621i	$0.162500\pi$
$599$			23.9175i			0.977241i	−0.872496	+	0.488621i	$0.837500\pi$
$600$	0.776656	−	1.29662i	0.0317069	−	0.0529344i
$601$	14.2083	−	24.6095i	0.579569	−	1.00384i	−0.415960	−	0.909383i	$-0.636554\pi$
$601$	14.2083	−	24.6095i	0.579569	−	1.00384i	0.995529	−	0.0944594i	$-0.0301123\pi$
$602$	8.20378	+	31.2865i	0.334361	+	1.27514i
$603$	−1.93581	−	1.93581i	−0.0788322	−	0.0788322i
$604$	−13.9206	+	13.6254i	−0.566421	+	0.554410i
$605$	4.33473	−	16.1774i	0.176232	−	0.657706i
$606$	−0.985221	−	1.72776i	−0.0400218	−	0.0701856i
$607$	30.3561	−	17.5261i	1.23211	−	0.711362i	0.264645	−	0.964346i	$-0.414745\pi$
$607$	30.3561	−	17.5261i	1.23211	−	0.711362i	0.967470	+	0.252984i	$0.0814120\pi$
$608$	3.75613	−	12.6522i	0.152331	−	0.513113i
$609$	−18.7829	+	5.03286i	−0.761122	+	0.203942i
$610$	−2.11356	−	0.578481i	−0.0855755	−	0.0234220i
$611$	40.6185	−	6.59800i	1.64325	−	0.266926i
$612$	−3.18534	−	1.88485i	−0.128760	−	0.0761906i
$613$	−2.36044	−	8.80929i	−0.0953373	−	0.355804i	0.901733	−	0.432293i	$-0.142295\pi$
$613$	−2.36044	−	8.80929i	−0.0953373	−	0.355804i	−0.997070	+	0.0764895i	$0.975629\pi$
$614$	10.3233	−	10.2132i	0.416613	−	0.412173i
$615$	2.71245	+	4.69809i	0.109376	+	0.189445i
$616$	0.402359	−	25.0301i	0.0162115	−	1.00849i
$617$	−7.34468	−	1.96800i	−0.295686	−	0.0792287i	0.107927	−	0.994159i	$-0.465579\pi$
$617$	−7.34468	−	1.96800i	−0.295686	−	0.0792287i	−0.403612	+	0.914930i	$0.632246\pi$
$618$	−22.8454	−	13.3535i	−0.918978	−	0.537157i
$619$	−25.6801	+	25.6801i	−1.03217	+	1.03217i	−0.0327040	+	0.999465i	$0.510412\pi$
$619$	−25.6801	+	25.6801i	−1.03217	+	1.03217i	−0.999465	+	0.0327040i	$0.989588\pi$
$620$	−2.56916	−	0.0275315i	−0.103180	−	0.00110569i
$621$	23.3086	+	13.4572i	0.935341	+	0.540019i
$622$	−13.8190	−	0.0740415i	−0.554093	−	0.00296879i
$623$	−3.98158			−0.159519
$624$	9.10948	+	21.4621i	0.364671	+	0.859173i
$625$	23.2380			0.929520
$626$	−44.7356	−	0.239690i	−1.78799	−	0.00957996i
$627$	−14.1442	−	8.16618i	−0.564867	−	0.326126i
$628$	28.1738	+	0.301916i	1.12426	+	0.0120478i
$629$	−6.54055	+	6.54055i	−0.260789	+	0.260789i
$630$	−2.08426	−	1.21829i	−0.0830391	−	0.0485377i
$631$	−20.8323	−	5.58201i	−0.829322	−	0.222216i	−0.180904	−	0.983501i	$-0.557902\pi$
$631$	−20.8323	−	5.58201i	−0.829322	−	0.222216i	−0.648418	+	0.761285i	$0.724569\pi$
$632$	0.0507904	−	3.15958i	0.00202033	−	0.125681i
$633$	−22.3402	−	38.6944i	−0.887945	−	1.53797i
$634$	−21.0156	+	20.7916i	−0.834637	+	0.825741i
$635$	0.867108	+	3.23609i	0.0344101	+	0.128420i
$636$	3.70238	+	2.19080i	0.146809	+	0.0868709i
$637$	4.17571	+	9.27991i	0.165448	+	0.367683i
$638$	−34.7598	−	9.51377i	−1.37616	−	0.376654i
$639$	0.655125	−	0.175540i	0.0259163	−	0.00694426i
$640$	−17.9232	+	16.6268i	−0.708476	+	0.657231i
$641$	−41.8746	+	24.1763i	−1.65395	+	0.954907i	−0.678522	+	0.734580i	$0.737379\pi$
$641$	−41.8746	+	24.1763i	−1.65395	+	0.954907i	−0.975426	+	0.220327i	$0.929287\pi$
$642$	9.12521	+	16.0027i	0.360143	+	0.631578i
$643$	0.0193750	−	0.0723085i	0.000764075	−	0.00285157i	−0.965543	−	0.260245i	$-0.916197\pi$
$643$	0.0193750	−	0.0723085i	0.000764075	−	0.00285157i	0.966307	+	0.257393i	$0.0828635\pi$
$644$	−14.3618	+	14.0572i	−0.565933	+	0.553932i
$645$	−27.6403	−	27.6403i	−1.08834	−	1.08834i
$646$	−4.00700	−	15.2814i	−0.157653	−	0.601238i
$647$	−1.86890	+	3.23703i	−0.0734741	+	0.127261i	−0.900422	−	0.435018i	$-0.856742\pi$
$647$	−1.86890	+	3.23703i	−0.0734741	+	0.127261i	0.826948	+	0.562279i	$0.190075\pi$
$648$	11.1782	−	18.6620i	0.439122	−	0.733112i
$649$			29.0561i			1.14055i
$650$	0.992606	−	1.36217i	0.0389332	−	0.0534289i
$651$			1.96440i			0.0769908i
$652$	−39.3477	−	10.9964i	−1.54097	−	0.430652i
$653$	−20.2252	+	35.0310i	−0.791473	+	1.37087i	0.133583	+	0.991038i	$0.457352\pi$
$653$	−20.2252	+	35.0310i	−0.791473	+	1.37087i	−0.925055	+	0.379833i	$0.875981\pi$
$654$	−37.7840	+	9.90751i	−1.47747	+	0.387414i
$655$	−6.27844	−	6.27844i	−0.245319	−	0.245319i
$656$	1.47875	+	6.03307i	0.0577354	+	0.235552i
$657$	0.757861	−	2.82838i	0.0295670	−	0.110345i
$658$	28.6586	−	16.3419i	1.11723	−	0.637074i
$659$	33.6653	−	19.4367i	1.31141	−	0.757145i	0.329084	−	0.944301i	$-0.393260\pi$
$659$	33.6653	−	19.4367i	1.31141	−	0.757145i	0.982330	+	0.187155i	$0.0599268\pi$
$660$	14.8453	+	26.3612i	0.577852	+	1.02611i
$661$	39.1027	−	10.4775i	1.52092	−	0.407529i	0.600874	−	0.799344i	$-0.294819\pi$
$661$	39.1027	−	10.4775i	1.52092	−	0.407529i	0.920044	+	0.391815i	$0.128153\pi$
$662$	4.53845	−	16.5818i	0.176392	−	0.644471i
$663$	22.6432	+	16.3149i	0.879387	+	0.633617i
$664$	−6.83791	−	7.06134i	−0.265362	−	0.274033i
$665$	−2.66702	−	9.95347i	−0.103423	−	0.385979i
$666$	0.742667	+	0.750668i	0.0287778	+	0.0290878i
$667$	14.4655	+	25.0550i	0.560108	+	0.970135i
$668$	−6.08713	−	23.7318i	−0.235518	−	0.918212i
$669$	−4.74609	−	1.27171i	−0.183494	−	0.0491671i
$670$	−10.9230	+	18.6872i	−0.421992	+	0.721950i
$671$	−2.19556	+	2.19556i	−0.0847586	+	0.0847586i
$672$	12.8583	+	13.5664i	0.496021	+	0.523336i
$673$	11.7053	+	6.75805i	0.451205	+	0.260504i	0.708339	−	0.705872i	$-0.249445\pi$
$673$	11.7053	+	6.75805i	0.451205	+	0.260504i	−0.257134	+	0.966376i	$0.582778\pi$
$674$	0.142243	−	26.5480i	0.00547898	−	1.02259i
$675$	−1.80965			−0.0696536
$676$	7.96489	+	24.7500i	0.306342	+	0.951922i
$677$	40.3341			1.55017			0.775083	−	0.631860i	$-0.217708\pi$
$677$	40.3341			1.55017			0.775083	+	0.631860i	$0.217708\pi$
$678$	−0.109521	+	20.4409i	−0.00420614	+	0.785029i
$679$	2.43220	+	1.40423i	0.0933392	+	0.0538894i
$680$	−8.02743	+	28.1414i	−0.307838	+	1.07918i
$681$	10.8174	−	10.8174i	0.414522	−	0.414522i
$682$	−1.83717	+	3.14306i	−0.0703490	+	0.120354i
$683$	7.08109	+	1.89737i	0.270950	+	0.0726010i	0.391736	−	0.920078i	$-0.371875\pi$
$683$	7.08109	+	1.89737i	0.270950	+	0.0726010i	−0.120786	+	0.992679i	$0.538541\pi$
$684$	−1.74697	+	0.448092i	−0.0667971	+	0.0171332i
$685$	−12.7885	−	22.1503i	−0.488623	−	0.846320i
$686$	19.9683	+	20.1835i	0.762395	+	0.770609i
$687$	2.06805	+	7.71806i	0.0789009	+	0.294462i
$688$	−21.5434	−	39.2326i	−0.821335	−	1.49573i
$689$	3.89226	+	2.80445i	0.148283	+	0.106841i
$690$	6.41164	−	23.4258i	0.244087	−	0.891805i
$691$	−22.4140	+	6.00581i	−0.852669	+	0.228472i	−0.658579	−	0.752512i	$-0.728842\pi$
$691$	−22.4140	+	6.00581i	−0.852669	+	0.228472i	−0.194090	+	0.980984i	$0.562175\pi$
$692$	11.7871	−	6.63789i	0.448078	−	0.252335i
$693$	−2.96254	+	1.71042i	−0.112537	+	0.0649735i
$694$	9.81291	−	5.59560i	0.372493	−	0.212406i
$695$	4.71558	−	17.5988i	0.178872	−	0.667560i
$696$	23.5171	−	13.0782i	0.891415	−	0.495728i
$697$	5.25760	+	5.25760i	0.199146	+	0.199146i
$698$	14.0297	−	3.67878i	0.531030	−	0.139244i
$699$	17.2337	−	29.8496i	0.651838	−	1.12902i
$700$	0.363690	−	1.30136i	0.0137462	−	0.0491870i
$701$		−	1.83613i		−	0.0693497i	−0.999399	−	0.0346748i	$-0.988960\pi$
$701$		−	1.83613i		−	0.0693497i	0.999399	−	0.0346748i	$-0.0110396\pi$
$702$	16.4402	−	22.5612i	0.620495	−	0.851519i
$703$			4.50718i			0.169992i
$704$	7.88575	+	33.7320i	0.297206	+	1.27132i
$705$	−19.9352	+	34.5288i	−0.750803	+	1.30043i
$706$	−1.69567	−	6.46672i	−0.0638174	−	0.243378i
$707$	−1.25732	−	1.25732i	−0.0472863	−	0.0472863i
$708$	−15.1758	−	15.5046i	−0.570341	−	0.582697i
$709$	1.37371	−	5.12676i	0.0515908	−	0.192540i	−0.935321	−	0.353800i	$-0.884889\pi$
$709$	1.37371	−	5.12676i	0.0515908	−	0.192540i	0.986912	+	0.161261i	$0.0515560\pi$
$710$	−2.65634	−	4.65837i	−0.0996906	−	0.174826i
$711$	−0.373965	+	0.215909i	−0.0140248	+	0.00809722i
$712$	5.34427	−	1.34031i	0.200285	−	0.0502303i
$713$	2.82305	−	0.756434i	0.105724	−	0.0283287i
$714$	21.5805	+	5.90657i	0.807628	+	0.221048i
$715$	13.8439	+	30.7662i	0.517734	+	1.15059i
$716$	7.82197	−	13.2189i	0.292321	−	0.494013i
$717$	3.53091	+	13.1775i	0.131864	+	0.492123i
$718$	36.7817	−	36.3897i	1.37268	−	1.35805i
$719$	−16.7047	−	28.9333i	−0.622979	−	1.07903i	−0.988928	−	0.148397i	$-0.952589\pi$
$719$	−16.7047	−	28.9333i	−0.622979	−	1.07903i	0.365949	−	0.930635i	$-0.380745\pi$
$720$	3.20771	+	0.933622i	0.119544	+	0.0347941i
$721$	−22.8510	−	6.12290i	−0.851015	−	0.228029i
$722$	16.5519	+	9.67485i	0.615997	+	0.360061i
$723$	−23.7091	+	23.7091i	−0.881750	+	0.881750i
$724$	0.229301	−	21.3977i	0.00852191	−	0.795238i
$725$	−1.68463	−	0.972624i	−0.0625657	−	0.0361223i
$726$	17.7195	+	0.0949400i	0.657633	+	0.00352355i
$727$	23.0787			0.855941			0.427970	−	0.903793i	$-0.359229\pi$
$727$	23.0787			0.855941			0.427970	+	0.903793i	$0.359229\pi$
$728$	12.9203	+	16.3567i	0.478858	+	0.606220i
$729$	−29.5245			−1.09350
$730$	−23.1513	−	0.124043i	−0.856868	−	0.00459104i
$731$	−46.3982	−	26.7880i	−1.71610	−	0.990790i
$732$	0.0248433	−	2.31829i	0.000918233	−	0.0856866i
$733$	31.3372	−	31.3372i	1.15746	−	1.15746i	0.172445	−	0.985019i	$-0.444833\pi$
$733$	31.3372	−	31.3372i	1.15746	−	1.15746i	0.985019	−	0.172445i	$-0.0551668\pi$
$734$	24.9080	+	14.5591i	0.919372	+	0.537388i
$735$	−9.52352	−	2.55182i	−0.351280	−	0.0941253i
$736$	14.5450	−	23.7029i	0.536136	−	0.873699i
$737$	15.3354	+	26.5617i	0.564886	+	0.978411i
$738$	0.603423	−	0.596991i	0.0222123	−	0.0219755i
$739$	9.57785	+	35.7450i	0.352327	+	1.31490i	0.883815	+	0.467836i	$0.154966\pi$
$739$	9.57785	+	35.7450i	0.352327	+	1.31490i	−0.531488	+	0.847066i	$0.678367\pi$
$740$	4.25176	−	7.18534i	0.156298	−	0.264138i
$741$	13.4233	−	2.18045i	0.493116	−	0.0801010i
$742$	3.70958	+	1.01531i	0.136183	+	0.0372733i
$743$	12.2084	−	3.27124i	0.447884	−	0.120010i	−0.0278251	−	0.999613i	$-0.508858\pi$
$743$	12.2084	−	3.27124i	0.447884	−	0.120010i	0.475709	+	0.879603i	$0.342191\pi$
$744$	−0.661271	−	2.63671i	−0.0242434	−	0.0966664i
$745$	2.64351	−	1.52623i	0.0968506	−	0.0559167i
$746$	14.4623	+	25.3623i	0.529503	+	0.928581i
$747$	−0.347651	+	1.29745i	−0.0127199	+	0.0474712i
$748$	29.0050	+	29.6334i	1.06053	+	1.08350i
$749$	11.6454	+	11.6454i	0.425513	+	0.425513i
$750$	6.67956	+	25.4736i	0.243903	+	0.930165i
$751$	10.7931	−	18.6941i	0.393844	−	0.682159i	−0.599109	−	0.800668i	$-0.704478\pi$
$751$	10.7931	−	18.6941i	0.393844	−	0.682159i	0.992953	+	0.118509i	$0.0378115\pi$
$752$	−32.9658	+	31.5822i	−1.20214	+	1.15168i
$753$			9.56224i			0.348467i
$754$	27.4303	−	12.1666i	0.998952	−	0.443081i
$755$		−	21.0461i		−	0.765946i
$756$	6.02367	−	21.5541i	0.219079	−	0.783913i
$757$	3.72408	−	6.45030i	0.135354	−	0.234440i	−0.790379	−	0.612619i	$-0.790116\pi$
$757$	3.72408	−	6.45030i	0.135354	−	0.234440i	0.925733	+	0.378179i	$0.123449\pi$
$758$	−19.4084	+	5.08916i	−0.704944	+	0.184847i
$759$	−24.3346	−	24.3346i	−0.883291	−	0.883291i
$760$	6.93043	+	12.4622i	0.251393	+	0.452053i
$761$	7.70710	−	28.7633i	0.279382	−	1.04267i	−0.673465	−	0.739219i	$-0.735195\pi$
$761$	7.70710	−	28.7633i	0.279382	−	1.04267i	0.952847	−	0.303450i	$-0.0981385\pi$
$762$	−3.07918	+	1.75584i	−0.111547	+	0.0636072i
$763$	−30.2425	+	17.4605i	−1.09485	+	0.632114i
$764$	−25.1887	+	14.1850i	−0.911297	+	0.513197i
$765$	3.86271	−	1.03501i	0.139657	−	0.0374208i
$766$	−5.78813	+	21.1477i	−0.209134	+	0.764098i
$767$	−15.2997	−	18.7417i	−0.552442	−	0.676723i
$768$	−21.8259	−	13.8810i	−0.787575	−	0.500888i
$769$	12.2981	+	45.8972i	0.443482	+	1.65510i	0.719914	+	0.694063i	$0.244181\pi$
$769$	12.2981	+	45.8972i	0.443482	+	1.65510i	−0.276433	+	0.961033i	$0.589152\pi$
$770$	19.0225	+	19.2274i	0.685522	+	0.692908i
$771$	−22.8537	−	39.5838i	−0.823056	−	1.42558i
$772$	−37.9187	+	9.72602i	−1.36472	+	0.350047i
$773$	24.8153	+	6.64923i	0.892543	+	0.239156i	0.675811	−	0.737075i	$-0.263794\pi$
$773$	24.8153	+	6.64923i	0.892543	+	0.239156i	0.216732	+	0.976231i	$0.430460\pi$
$774$	−3.08649	+	5.28042i	−0.110942	+	0.189801i
$775$	−0.138954	+	0.138954i	−0.00499136	+	0.00499136i
$776$	−3.73732	−	1.06608i	−0.134162	−	0.0382701i
$777$	−5.52817	−	3.19169i	−0.198322	−	0.114501i
$778$	0.254208	−	47.4451i	0.00911380	−	1.70099i
$779$	3.62309			0.129811
$780$	−23.4562	−	9.18650i	−0.839867	−	0.328929i
$781$	−7.59850			−0.271896
$782$	0.178354	−	33.2879i	0.00637794	−	1.19037i
$783$	−27.9020	−	16.1092i	−0.997137	−	0.575697i
$784$	−9.65368	−	5.85291i	−0.344774	−	0.209033i
$785$	−21.5258	+	21.5258i	−0.768288	+	0.768288i
$786$	4.74062	−	8.11032i	0.169092	−	0.289286i
$787$	−11.5106	−	3.08426i	−0.410309	−	0.109942i	0.0477596	−	0.998859i	$-0.484792\pi$
$787$	−11.5106	−	3.08426i	−0.410309	−	0.109942i	−0.458068	+	0.888917i	$0.651459\pi$
$788$	1.32044	+	5.14800i	0.0470389	+	0.183390i
$789$	−10.8272	−	18.7532i	−0.385458	−	0.667633i
$790$	2.40123	+	2.42710i	0.0854321	+	0.0863525i
$791$	4.72981	+	17.6519i	0.168173	+	0.627629i
$792$	3.40068	−	3.29308i	0.120838	−	0.117015i
$793$	0.260082	−	2.57227i	0.00923578	−	0.0913438i
$794$	−4.65004	+	16.9896i	−0.165024	+	0.602937i
$795$	−4.48970	+	1.20301i	−0.159233	+	0.0426664i
$796$	16.2653	+	28.8827i	0.576509	+	1.02372i
$797$	−12.3178	+	7.11167i	−0.436318	+	0.251908i	−0.702034	−	0.712143i	$-0.747725\pi$
$797$	−12.3178	+	7.11167i	−0.436318	+	0.251908i	0.265717	+	0.964051i	$0.414391\pi$
$798$	9.47085	−	5.40055i	0.335265	−	0.191177i
$799$	−14.1436	+	52.7845i	−0.500363	+	1.86738i
$800$	−0.0500863	+	1.86918i	−0.00177082	+	0.0660856i
$801$	−0.532395	−	0.532395i	−0.0188113	−	0.0188113i
$802$	−19.9314	+	5.22630i	−0.703801	+	0.184547i
$803$	−16.4025	+	28.4100i	−0.578832	+	1.00257i
$804$	−22.0561	−	6.16396i	−0.777858	−	0.217386i
$805$		−	21.7131i		−	0.765286i
$806$	−0.470002	−	2.99471i	−0.0165551	−	0.105484i
$807$			37.0707i			1.30495i
$808$	2.11088	+	1.26438i	0.0742605	+	0.0444809i
$809$	3.11393	−	5.39349i	0.109480	−	0.189625i	−0.806080	−	0.591807i	$-0.798415\pi$
$809$	3.11393	−	5.39349i	0.109480	−	0.189625i	0.915560	+	0.402182i	$0.131748\pi$
$810$	5.96147	+	22.7351i	0.209465	+	0.798829i
$811$	8.66022	+	8.66022i	0.304102	+	0.304102i	0.842616	−	0.538515i	$-0.181014\pi$
$811$	8.66022	+	8.66022i	0.304102	+	0.304102i	−0.538515	+	0.842616i	$0.681014\pi$
$812$	17.1921	−	16.8275i	0.603323	−	0.590529i
$813$	−4.01638	+	14.9893i	−0.140861	+	0.525699i
$814$	−5.86017	−	10.2769i	−0.205399	−	0.360205i
$815$	38.2281	−	22.0710i	1.33907	−	0.773113i
$816$	−30.9547	−	0.663508i	−1.08363	−	0.0232274i
$817$	−25.2168	+	6.75683i	−0.882225	+	0.236391i
$818$	−26.4571	−	7.24130i	−0.925050	−	0.253186i
$819$	1.01025	−	2.66320i	0.0353010	−	0.0930599i
$820$	−5.77592	−	3.41777i	−0.201704	−	0.119354i
$821$	−4.46914	−	16.6791i	−0.155974	−	0.582104i	−0.999020	−	0.0442618i	$-0.985906\pi$
$821$	−4.46914	−	16.6791i	−0.155974	−	0.582104i	0.843046	−	0.537842i	$-0.180760\pi$
$822$	19.2372	−	19.0321i	0.670973	−	0.663821i
$823$	−8.61216	−	14.9167i	−0.300201	−	0.519963i	0.675980	−	0.736920i	$-0.263720\pi$
$823$	−8.61216	−	14.9167i	−0.300201	−	0.519963i	−0.976181	+	0.216956i	$0.930387\pi$
$824$	32.7328	+	0.526182i	1.14030	+	0.0183304i
$825$	2.23508	+	0.598889i	0.0778157	+	0.0208506i
$826$	−16.7452	−	9.78783i	−0.582639	−	0.340562i
$827$	−7.89012	+	7.89012i	−0.274366	+	0.274366i	−0.830855	−	0.556489i	$-0.812148\pi$
$827$	−7.89012	+	7.89012i	−0.274366	+	0.274366i	0.556489	+	0.830855i	$0.312148\pi$
$828$	−3.80003	−	0.0407218i	−0.132060	−	0.00141518i
$829$	−17.8732	−	10.3191i	−0.620761	−	0.358396i	0.156404	−	0.987693i	$-0.450010\pi$
$829$	−17.8732	−	10.3191i	−0.620761	−	0.358396i	−0.777165	+	0.629297i	$0.783343\pi$
$830$	10.6201	+	0.0569019i	0.368630	+	0.00197509i
$831$	1.77839			0.0616917
$832$	−22.8484	−	17.6054i	−0.792125	−	0.610359i
$833$	−13.5134			−0.468213
$834$	19.2764	+	0.103281i	0.667485	+	0.00357634i
$835$	22.9245	+	13.2355i	0.793336	+	0.458033i
$836$	20.2043	+	0.216513i	0.698780	+	0.00748825i
$837$	−2.30144	+	2.30144i	−0.0795495	+	0.0795495i
$838$	3.58498	+	2.09548i	0.123841	+	0.0723871i
$839$	15.3139	+	4.10335i	0.528695	+	0.141663i	0.513286	−	0.858218i	$-0.328428\pi$
$839$	15.3139	+	4.10335i	0.528695	+	0.141663i	0.0154095	+	0.999881i	$0.495095\pi$
$840$	−20.1929	−	0.324602i	−0.696721	−	0.0111998i
$841$	−2.81628	−	4.87794i	−0.0971130	−	0.168205i
$842$	−6.45409	+	6.38530i	−0.222423	+	0.220052i
$843$	−3.99215	−	14.8989i	−0.137497	−	0.513146i
$844$	47.5716	+	28.1494i	1.63748	+	0.968943i
$845$	−25.1298	−	12.5551i	−0.864492	−	0.431908i
$846$	6.01722	+	1.64691i	0.206876	+	0.0566220i
$847$	15.3018	−	4.10010i	0.525776	−	0.140881i
$848$	−5.32096	−	0.114054i	−0.182723	−	0.00391663i
$849$	29.6169	−	17.0993i	1.01645	−	0.586848i
$850$	1.10871	+	1.94432i	0.0380284	+	0.0666898i
$851$	−2.45806	+	9.17360i	−0.0842612	+	0.314467i
$852$	4.05462	−	3.96864i	0.138909	−	0.135963i
$853$	−1.25966	−	1.25966i	−0.0431300	−	0.0431300i	0.685213	−	0.728343i	$-0.259709\pi$
$853$	−1.25966	−	1.25966i	−0.0431300	−	0.0431300i	−0.728343	+	0.685213i	$0.759709\pi$
$854$	−0.525717	−	2.00491i	−0.0179897	−	0.0686066i
$855$	0.974304	−	1.68754i	0.0333205	−	0.0577128i
$856$	−19.5512	−	11.7109i	−0.668246	−	0.400269i
$857$			2.39366i			0.0817658i	0.999164	+	0.0408829i	$0.0130171\pi$
$857$			2.39366i			0.0817658i	−0.999164	+	0.0408829i	$0.986983\pi$
$858$	−27.7716	+	22.4244i	−0.948106	+	0.765557i
$859$		−	17.8687i		−	0.609673i	−0.952405	−	0.304837i	$-0.901398\pi$
$859$		−	17.8687i		−	0.609673i	0.952405	−	0.304837i	$-0.0986018\pi$
$860$	46.5745	+	13.0161i	1.58818	+	0.443844i
$861$	−2.56563	+	4.44380i	−0.0874365	+	0.151444i
$862$	25.9444	−	6.80302i	0.883671	−	0.231712i
$863$	16.3496	+	16.3496i	0.556546	+	0.556546i	0.928322	−	0.371776i	$-0.121251\pi$
$863$	16.3496	+	16.3496i	0.556546	+	0.556546i	−0.371776	+	0.928322i	$0.621251\pi$
$864$	−0.829563	+	30.9586i	−0.0282223	+	1.05323i
$865$	−3.78287	+	14.1179i	−0.128621	+	0.480022i
$866$	6.10855	−	3.48327i	0.207577	−	0.118366i
$867$	−8.29535	+	4.78932i	−0.281725	+	0.162654i
$868$	−1.19250	−	2.11755i	−0.0404760	−	0.0718742i
$869$	4.67296	−	1.25211i	0.158519	−	0.0424751i
$870$	−7.67519	+	28.0423i	−0.260213	+	0.950725i
$871$	−23.8779	−	9.05775i	−0.809072	−	0.306910i
$872$	34.7153	−	33.6169i	1.17561	−	1.13841i
$873$	0.137454	+	0.512986i	0.00465212	+	0.0173620i
$874$	−11.4081	−	11.5310i	−0.385886	−	0.390043i
$875$	11.7717	+	20.3893i	0.397958	+	0.689283i
$876$	−6.08583	−	23.7267i	−0.205621	−	0.801652i
$877$	5.73412	+	1.53645i	0.193628	+	0.0518824i	0.354330	−	0.935121i	$-0.384709\pi$
$877$	5.73412	+	1.53645i	0.193628	+	0.0518824i	−0.160702	+	0.987003i	$0.551376\pi$
$878$	27.9533	−	47.8230i	0.943378	−	1.61395i
$879$	20.7052	−	20.7052i	0.698370	−	0.698370i
$880$	−32.0054	−	19.4045i	−1.07890	−	0.654125i
$881$	−32.1364	−	18.5540i	−1.08270	−	0.625099i	−0.151079	−	0.988522i	$-0.548275\pi$
$881$	−32.1364	−	18.5540i	−1.08270	−	0.625099i	−0.931625	+	0.363422i	$0.881608\pi$
$882$	−0.00826564	+	1.54269i	−0.000278318	+	0.0519451i
$883$	31.7405			1.06815			0.534077	−	0.845436i	$-0.320659\pi$
$883$	31.7405			1.06815			0.534077	+	0.845436i	$0.320659\pi$
$884$	−34.3125	−	3.84120i	−1.15405	−	0.129194i
$885$	23.4408			0.787955
$886$	−0.289247	+	53.9847i	−0.00971743	+	1.81365i
$887$	−32.1042	−	18.5354i	−1.07795	−	0.622356i	−0.147609	−	0.989046i	$-0.547158\pi$
$887$	−32.1042	−	18.5354i	−1.07795	−	0.622356i	−0.930343	+	0.366689i	$0.880491\pi$
$888$	8.49459	+	2.42311i	0.285060	+	0.0813141i
$889$	−2.24076	+	2.24076i	−0.0751526	+	0.0751526i
$890$	−3.00409	+	5.13945i	−0.100697	+	0.172275i
$891$	32.1691	+	8.61967i	1.07770	+	0.288770i
$892$	5.88810	−	1.51028i	0.197148	−	0.0505678i
$893$	13.3140	+	23.0605i	0.445536	+	0.771692i
$894$	2.27137	+	2.29584i	0.0759660	+	0.0767844i
$895$	4.29520	+	16.0299i	0.143573	+	0.535821i
$896$	−22.0964	−	6.81837i	−0.738188	−	0.227786i
$897$	28.5099	+	2.88264i	0.951918	+	0.0962484i
$898$	−1.17267	+	4.28452i	−0.0391326	+	0.142976i
$899$	−3.37939	+	0.905505i	−0.112709	+	0.0302003i
$900$	0.222642	−	0.125381i	0.00742140	−	0.00417936i
$901$	−5.51717	+	3.18534i	−0.183803	+	0.106119i
$902$	−8.26105	+	4.71069i	−0.275063	+	0.156849i
$903$	9.56947	−	35.7138i	0.318452	−	1.18848i
$904$	−12.2907	−	22.1011i	−0.408783	−	0.735070i
$905$	16.3485	+	16.3485i	0.543444	+	0.543444i
$906$	21.5389	−	5.64783i	0.715584	−	0.187637i
$907$	16.4743	−	28.5344i	0.547021	−	0.947468i	−0.451456	−	0.892294i	$-0.649095\pi$
$907$	16.4743	−	28.5344i	0.547021	−	0.947468i	0.998477	−	0.0551749i	$-0.0175716\pi$
$908$	−5.09398	+	18.2274i	−0.169050	+	0.604899i
$909$		−	0.336243i		−	0.0111525i
$910$	−22.3942	−	2.38556i	−0.742361	−	0.0790805i
$911$			22.6697i			0.751082i	0.926806	+	0.375541i	$0.122543\pi$
$911$			22.6697i			0.751082i	−0.926806	+	0.375541i	$0.877457\pi$
$912$	−10.8943	+	10.4370i	−0.360745	+	0.345605i
$913$	7.52427	−	13.0324i	0.249017	−	0.431310i
$914$	−12.1929	−	46.4997i	−0.403306	−	1.53807i
$915$	1.77126	+	1.77126i	0.0585559	+	0.0585559i
$916$	−6.91456	−	7.06436i	−0.228464	−	0.233413i
$917$	2.17368	−	8.11230i	0.0717813	−	0.267892i
$918$	18.3632	+	32.2032i	0.606075	+	1.06286i
$919$	−7.50982	+	4.33579i	−0.247726	+	0.143025i	−0.618723	−	0.785610i	$-0.712349\pi$
$919$	−7.50982	+	4.33579i	−0.247726	+	0.143025i	0.370997	+	0.928634i	$0.379016\pi$
$920$	7.30923	+	29.1444i	0.240978	+	0.960861i
$921$	−16.0346	+	4.29645i	−0.528357	+	0.141573i
$922$	−32.3827	−	8.86315i	−1.06647	−	0.291892i
$923$	4.90117	−	4.00106i	0.161324	−	0.131697i
$924$	−14.5729	+	24.6277i	−0.479413	+	0.810192i
$925$	−0.165273	−	0.616808i	−0.00543415	−	0.0202805i
$926$	−34.6980	+	34.3282i	−1.14025	+	1.12809i
$927$	−2.23679	−	3.87423i	−0.0734657	−	0.127246i
$928$	−17.4114	+	28.3740i	−0.571558	+	0.931423i
$929$	13.6363	+	3.65383i	0.447392	+	0.119878i	0.475479	−	0.879727i	$-0.342275\pi$
$929$	13.6363	+	3.65383i	0.447392	+	0.119878i	−0.0280869	+	0.999605i	$0.508942\pi$
$930$	2.53565	+	1.48213i	0.0831473	+	0.0486010i
$931$	−4.65615	+	4.65615i	−0.152599	+	0.152599i
$932$	−0.456923	+	42.6386i	−0.0149670	+	1.39667i
$933$	13.6807	+	7.89858i	0.447888	+	0.258588i
$934$	−25.1413	−	0.134706i	−0.822650	−	0.00440770i
$935$	−44.8018			−1.46518
$936$	−0.459498	+	3.91476i	−0.0150192	+	0.127958i
$937$	−8.23591			−0.269055			−0.134528	−	0.990910i	$-0.542952\pi$
$937$	−8.23591			−0.269055			−0.134528	+	0.990910i	$0.542952\pi$
$938$	−20.4735	−	0.109696i	−0.668484	−	0.00358170i
$939$	44.2880	+	25.5697i	1.44528	+	0.834434i
$940$	0.528549	−	49.3225i	0.0172394	−	1.60872i
$941$	4.15205	−	4.15205i	0.135353	−	0.135353i	−0.636184	−	0.771537i	$-0.719488\pi$
$941$	4.15205	−	4.15205i	0.135353	−	0.135353i	0.771537	+	0.636184i	$0.219488\pi$
$942$	−27.8064	−	16.2533i	−0.905983	−	0.529562i
$943$	7.37418	+	1.97590i	0.240136	+	0.0643443i
$944$	25.7711	+	7.50081i	0.838776	+	0.244131i
$945$	12.0902	+	20.9408i	0.393293	+	0.681203i
$946$	48.7121	−	48.1928i	1.58377	−	1.56688i
$947$	0.740729	+	2.76444i	0.0240705	+	0.0898322i	0.976916	−	0.213623i	$-0.0685264\pi$
$947$	0.740729	+	2.76444i	0.0240705	+	0.0898322i	−0.952846	+	0.303455i	$0.901860\pi$
$948$	−1.83956	+	3.10879i	−0.0597461	+	0.100969i
$949$	−4.37964	−	26.9619i	−0.142169	−	0.875219i
$950$	1.05194	+	0.287917i	0.0341296	+	0.00934127i
$951$	32.6424	−	8.74651i	1.05850	−	0.283625i
$952$	−26.8486	+	6.73345i	−0.870167	+	0.218232i
$953$	7.64309	−	4.41274i	0.247584	−	0.142943i	−0.371074	−	0.928603i	$-0.621010\pi$
$953$	7.64309	−	4.41274i	0.247584	−	0.142943i	0.618657	+	0.785661i	$0.287677\pi$
$954$	0.360263	+	0.631787i	0.0116639	+	0.0204549i
$955$	8.08391	−	30.1695i	0.261589	−	0.976264i
$956$	−11.8057	−	12.0614i	−0.381822	−	0.390094i
$957$	29.1303	+	29.1303i	0.941648	+	0.941648i
$958$	2.85409	+	10.8846i	0.0922115	+	0.351664i
$959$	12.0963	−	20.9514i	0.390610	−	0.676556i
$960$	27.2132	−	6.36180i	0.878301	−	0.205326i
$961$		−	30.6466i		−	0.988599i
$962$	9.19131	+	3.54304i	0.296340	+	0.114232i
$963$			3.11432i			0.100357i
$964$	11.1648	−	39.9502i	0.359594	−	1.28671i
$965$	21.1477	−	36.6288i	0.680767	−	1.17912i
$966$	22.2216	−	5.82682i	0.714967	−	0.187475i
$967$	31.1406	+	31.1406i	1.00142	+	1.00142i	0.999999	+	0.00141655i	$0.000450902\pi$
$967$	31.1406	+	31.1406i	1.00142	+	1.00142i	0.00141655	+	0.999999i	$0.499549\pi$
$968$	−19.1586	+	10.6544i	−0.615781	+	0.342444i
$969$	−4.67405	+	17.4438i	−0.150152	+	0.560376i
$970$	3.64767	−	2.08001i	0.117120	−	0.0667850i
$971$	−13.4730	+	7.77866i	−0.432370	+	0.249629i	−0.700356	−	0.713794i	$-0.746975\pi$
$971$	−13.4730	+	7.77866i	−0.432370	+	0.249629i	0.267986	+	0.963423i	$0.413642\pi$
$972$	6.95422	−	3.91627i	0.223057	−	0.125614i
$973$	16.6462	−	4.46034i	0.533653	−	0.142992i
$974$	8.48494	−	31.0009i	0.271875	−	0.993332i
$975$	−1.75702	+	0.790611i	−0.0562697	+	0.0253198i
$976$	1.38055	+	2.51412i	0.0441904	+	0.0804749i
$977$	−11.5672	−	43.1696i	−0.370069	−	1.38112i	−0.860417	−	0.509590i	$-0.829797\pi$
$977$	−11.5672	−	43.1696i	−0.370069	−	1.38112i	0.490348	−	0.871526i	$-0.336870\pi$
$978$	32.8466	+	33.2004i	1.05032	+	1.06163i
$979$	4.21761	+	7.30512i	0.134795	+	0.233473i
$980$	11.8151	−	3.03053i	0.377419	−	0.0968068i
$981$	−6.37859	−	1.70914i	−0.203653	−	0.0545686i
$982$	−0.0422552	+	0.0722909i	−0.00134842	+	0.00230689i
$983$	21.2250	−	21.2250i	0.676971	−	0.676971i	−0.282343	−	0.959314i	$-0.591112\pi$
$983$	21.2250	−	21.2250i	0.676971	−	0.676971i	0.959314	+	0.282343i	$0.0911115\pi$
$984$	1.94781	−	6.82835i	0.0620938	−	0.217680i
$985$	−4.97288	−	2.87109i	−0.158449	−	0.0914807i
$986$	−0.213503	+	39.8480i	−0.00679932	+	1.26902i
$987$	−37.7124			−1.20040
$988$	−13.1461	+	10.4991i	−0.418234	+	0.334021i
$989$	−55.0094			−1.74920
$990$	−0.0274035	+	5.11456i	−0.000870940	+	0.162551i
$991$	16.0337	+	9.25705i	0.509327	+	0.294060i	0.732557	−	0.680706i	$-0.238327\pi$
$991$	16.0337	+	9.25705i	0.509327	+	0.294060i	−0.223230	+	0.974766i	$0.571660\pi$
$992$	2.31345	+	2.44085i	0.0734522	+	0.0774970i
$993$	−13.8963	+	13.8963i	−0.440986	+	0.440986i
$994$	2.55963	−	4.37906i	0.0811866	−	0.138895i
$995$	−34.5940	−	9.26943i	−1.09670	−	0.293861i
$996$	2.79173	+	10.8841i	0.0884594	+	0.344875i
$997$	27.2779	+	47.2467i	0.863900	+	1.49632i	0.868135	+	0.496327i	$0.165318\pi$
$997$	27.2779	+	47.2467i	0.863900	+	1.49632i	−0.00423556	+	0.999991i	$0.501348\pi$
$998$	−36.1972	−	36.5871i	−1.14580	−	1.15815i
$999$	−2.73737	−	10.2160i	−0.0866064	−	0.323219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.2.l.b.19.4	yes	16
3.2	odd	2		468.2.cb.f.19.1		16
4.3	odd	2	inner	52.2.l.b.19.1	yes	16
8.3	odd	2		832.2.bu.n.383.2		16
8.5	even	2		832.2.bu.n.383.3		16
12.11	even	2		468.2.cb.f.19.4		16
13.2	odd	12		676.2.l.k.427.4		16
13.3	even	3		676.2.l.m.587.1		16
13.4	even	6		676.2.f.i.239.6		16
13.5	odd	4		676.2.l.i.319.3		16
13.6	odd	12		676.2.f.i.99.2		16
13.7	odd	12		676.2.f.h.99.7		16
13.8	odd	4		676.2.l.m.319.2		16
13.9	even	3		676.2.f.h.239.3		16
13.10	even	6		676.2.l.i.587.4		16
13.11	odd	12	inner	52.2.l.b.11.1	✓	16
13.12	even	2		676.2.l.k.19.1		16
39.11	even	12		468.2.cb.f.271.4		16
52.3	odd	6		676.2.l.m.587.2		16
52.7	even	12		676.2.f.h.99.3		16
52.11	even	12	inner	52.2.l.b.11.4	yes	16
52.15	even	12		676.2.l.k.427.1		16
52.19	even	12		676.2.f.i.99.6		16
52.23	odd	6		676.2.l.i.587.3		16
52.31	even	4		676.2.l.i.319.4		16
52.35	odd	6		676.2.f.h.239.7		16
52.43	odd	6		676.2.f.i.239.2		16
52.47	even	4		676.2.l.m.319.1		16
52.51	odd	2		676.2.l.k.19.4		16
104.11	even	12		832.2.bu.n.63.3		16
104.37	odd	12		832.2.bu.n.63.2		16
156.11	odd	12		468.2.cb.f.271.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.11.1	✓	16	13.11	odd	12	inner
52.2.l.b.11.4	yes	16	52.11	even	12	inner
52.2.l.b.19.1	yes	16	4.3	odd	2	inner
52.2.l.b.19.4	yes	16	1.1	even	1	trivial
468.2.cb.f.19.1		16	3.2	odd	2
468.2.cb.f.19.4		16	12.11	even	2
468.2.cb.f.271.1		16	156.11	odd	12
468.2.cb.f.271.4		16	39.11	even	12
676.2.f.h.99.3		16	52.7	even	12
676.2.f.h.99.7		16	13.7	odd	12
676.2.f.h.239.3		16	13.9	even	3
676.2.f.h.239.7		16	52.35	odd	6
676.2.f.i.99.2		16	13.6	odd	12
676.2.f.i.99.6		16	52.19	even	12
676.2.f.i.239.2		16	52.43	odd	6
676.2.f.i.239.6		16	13.4	even	6
676.2.l.i.319.3		16	13.5	odd	4
676.2.l.i.319.4		16	52.31	even	4
676.2.l.i.587.3		16	52.23	odd	6
676.2.l.i.587.4		16	13.10	even	6
676.2.l.k.19.1		16	13.12	even	2
676.2.l.k.19.4		16	52.51	odd	2
676.2.l.k.427.1		16	52.15	even	12
676.2.l.k.427.4		16	13.2	odd	12
676.2.l.m.319.1		16	52.47	even	4
676.2.l.m.319.2		16	13.8	odd	4
676.2.l.m.587.1		16	13.3	even	3
676.2.l.m.587.2		16	52.3	odd	6
832.2.bu.n.63.2		16	104.37	odd	12
832.2.bu.n.63.3		16	104.11	even	12
832.2.bu.n.383.2		16	8.3	odd	2
832.2.bu.n.383.3		16	8.5	even	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)

\(f(q)\)	\(=\)	\(q+(1.41419 + 0.00757716i) q^{2} +(-1.40004 - 0.808315i) q^{3} +(1.99989 + 0.0214311i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(-1.97381 - 1.15372i) q^{6} +(-1.97429 - 0.529008i) q^{7} +(2.82806 + 0.0454612i) q^{8} +(-0.193255 - 0.334727i) q^{9} +O(q^{10})\)	\(q+(1.41419 + 0.00757716i) q^{2} +(-1.40004 - 0.808315i) q^{3} +(1.99989 + 0.0214311i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(-1.97381 - 1.15372i) q^{6} +(-1.97429 - 0.529008i) q^{7} +(2.82806 + 0.0454612i) q^{8} +(-0.193255 - 0.334727i) q^{9} +(-2.17244 + 2.14928i) q^{10} +(1.12074 + 4.18264i) q^{11} +(-2.78260 - 1.64654i) q^{12} +(-2.92531 - 2.10774i) q^{13} +(-2.78801 - 0.763079i) q^{14} +(3.37433 - 0.904148i) q^{15} +(3.99908 + 0.0857196i) q^{16} +(4.14654 - 2.39401i) q^{17} +(-0.270763 - 0.474833i) q^{18} +(0.603848 - 2.25359i) q^{19} +(-3.08853 + 3.02304i) q^{20} +(2.33648 + 2.33648i) q^{21} +(1.55324 + 5.92356i) q^{22} +(2.45806 - 4.25748i) q^{23} +(-3.92266 - 2.34961i) q^{24} +0.330547i q^{25} +(-4.12098 - 3.00292i) q^{26} +5.47473i q^{27} +(-3.93701 - 1.10027i) q^{28} +(-2.94247 + 5.09651i) q^{29} +(4.77880 - 1.25307i) q^{30} +(0.420375 + 0.420375i) q^{31} +(5.65482 + 0.151526i) q^{32} +(1.81181 - 6.76178i) q^{33} +(5.88215 - 3.35417i) q^{34} +(3.82499 - 2.20836i) q^{35} +(-0.379313 - 0.673557i) q^{36} +(-1.86603 + 0.500000i) q^{37} +(0.871034 - 3.18244i) q^{38} +(2.39183 + 5.31550i) q^{39} +(-4.39069 + 4.25176i) q^{40} +(0.401924 + 1.50000i) q^{41} +(3.28653 + 3.32194i) q^{42} +(-5.59481 - 9.69049i) q^{43} +(2.15170 + 8.38882i) q^{44} +(0.806745 + 0.216167i) q^{45} +(3.50843 - 6.00228i) q^{46} +(-8.07035 + 8.07035i) q^{47} +(-5.52959 - 3.35253i) q^{48} +(-2.44422 - 1.41117i) q^{49} +(-0.00250460 + 0.467457i) q^{50} -7.74044 q^{51} +(-5.80510 - 4.27794i) q^{52} -1.33055 q^{53} +(-0.0414829 + 7.74233i) q^{54} +(-8.10346 - 4.67854i) q^{55} +(-5.55935 - 1.58582i) q^{56} +(-2.66702 + 2.66702i) q^{57} +(-4.19984 + 7.18515i) q^{58} +(6.48147 + 1.73670i) q^{59} +(6.76765 - 1.73588i) q^{60} +(0.358528 + 0.620988i) q^{61} +(0.591307 + 0.597677i) q^{62} +(0.204467 + 0.763079i) q^{63} +(7.99587 + 0.257134i) q^{64} +(7.69041 - 1.24922i) q^{65} +(2.61349 - 9.54874i) q^{66} +(6.84166 - 1.83322i) q^{67} +(8.34391 - 4.69887i) q^{68} +(-6.88277 + 3.97377i) q^{69} +(5.42600 - 3.09406i) q^{70} +(-0.454168 + 1.69498i) q^{71} +(-0.531319 - 0.955413i) q^{72} +(5.35696 + 5.35696i) q^{73} +(-2.64271 + 0.692957i) q^{74} +(0.267186 - 0.462779i) q^{75} +(1.25592 - 4.49398i) q^{76} -8.85061i q^{77} +(3.34223 + 7.53527i) q^{78} -1.11723i q^{79} +(-6.24150 + 5.97954i) q^{80} +(3.84554 - 6.66067i) q^{81} +(0.557032 + 2.12434i) q^{82} +(-2.45738 - 2.45738i) q^{83} +(4.62261 + 4.72276i) q^{84} +(-2.67784 + 9.99383i) q^{85} +(-7.83871 - 13.7466i) q^{86} +(8.23917 - 4.75689i) q^{87} +(2.97936 + 11.8797i) q^{88} +(1.88163 - 0.504180i) q^{89} +(1.13926 + 0.311814i) q^{90} +(4.66037 + 5.70880i) q^{91} +(5.00708 - 8.46180i) q^{92} +(-0.248748 - 0.928339i) q^{93} +(-11.4742 + 11.3519i) q^{94} +(2.52078 + 4.36612i) q^{95} +(-7.79451 - 4.78302i) q^{96} +(-1.32723 - 0.355630i) q^{97} +(-3.44591 - 2.01419i) q^{98} +(1.18345 - 1.18345i) 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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