LMFDB - Embedded newform 52.2.l.b.11.4

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			11.4
Root			$-0.713659 + 1.22094i$ of defining polynomial
Character	$\chi$	$=$	52.11
Dual form			52.2.l.b.19.4

$q$-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 $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	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	−0.846370	−	0.532595i	$-0.821217\pi$
$3$	−1.40004	+	0.808315i	−0.808315	+	0.466681i	0.0380556	+	0.999276i	$0.487884\pi$
$4$	1.99989	−	0.0214311i	0.999943	−	0.0107156i
$5$	−1.52798	−	1.52798i	−0.683334	−	0.683334i	0.277416	−	0.960750i	$-0.410522\pi$
$5$	−1.52798	−	1.52798i	−0.683334	−	0.683334i	−0.960750	+	0.277416i	$0.910522\pi$
$6$	−1.97381	+	1.15372i	−0.805803	+	0.471005i
$7$	−1.97429	+	0.529008i	−0.746210	+	0.199946i	−0.611836	−	0.790984i	$-0.709569\pi$
$7$	−1.97429	+	0.529008i	−0.746210	+	0.199946i	−0.134374	+	0.990931i	$0.542902\pi$
$8$	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	−0.562760	−	0.826620i	$-0.690261\pi$
$11$	1.12074	−	4.18264i	0.337915	−	1.26111i	0.900675	−	0.434494i	$-0.143073\pi$
$12$	−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	0.909925	−	0.414773i	$-0.136139\pi$
$17$	4.14654	+	2.39401i	1.00568	+	0.580632i	0.0957589	+	0.995405i	$0.469472\pi$
$18$	−0.270763	+	0.474833i	−0.0638195	+	0.111919i
$19$	0.603848	+	2.25359i	0.138532	+	0.517010i	0.999958	+	0.00912654i	$0.00290511\pi$
$19$	0.603848	+	2.25359i	0.138532	+	0.517010i	−0.861426	+	0.507883i	$0.830428\pi$
$20$	−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	0.999894	+	0.0145418i	$0.00462896\pi$
$23$	2.45806	+	4.25748i	0.512541	+	0.887747i	−0.487354	+	0.873205i	$0.662038\pi$
$24$	−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	−0.998517	−	0.0544380i	$-0.982663\pi$
$29$	−2.94247	−	5.09651i	−0.546403	−	0.946398i	0.452114	−	0.891960i	$-0.350670\pi$
$30$	4.77880	+	1.25307i	0.872486	+	0.228779i
$31$	0.420375	−	0.420375i	0.0755017	−	0.0755017i	−0.668348	−	0.743849i	$-0.732998\pi$
$31$	0.420375	−	0.420375i	0.0755017	−	0.0755017i	0.743849	+	0.668348i	$0.232998\pi$
$32$	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	0.102149	−	0.994769i	$-0.467428\pi$
$37$	−1.86603	−	0.500000i	−0.306773	−	0.0821995i	−0.408921	+	0.912570i	$0.634095\pi$
$38$	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	−0.927413	−	0.374039i	$-0.877972\pi$
$41$	0.401924	−	1.50000i	0.0627700	−	0.234261i	0.990183	+	0.139779i	$0.0446391\pi$
$42$	3.28653	−	3.32194i	0.507122	−	0.512586i
$43$	−5.59481	+	9.69049i	−0.853200	+	1.47779i	0.0251051	+	0.999685i	$0.492008\pi$
$43$	−5.59481	+	9.69049i	−0.853200	+	1.47779i	−0.878305	+	0.478101i	$0.841325\pi$
$44$	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	−0.980459	−	0.196722i	$-0.936970\pi$
$47$	−8.07035	−	8.07035i	−1.17718	−	1.17718i	−0.196722	−	0.980459i	$-0.563030\pi$
$48$	−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	0.189084	−	0.981961i	$-0.439448\pi$
$59$	6.48147	−	1.73670i	0.843816	−	0.226100i	0.654732	+	0.755861i	$0.272782\pi$
$60$	6.76765	+	1.73588i	0.873699	+	0.224101i
$61$	0.358528	−	0.620988i	0.0459048	−	0.0795094i	−0.842160	−	0.539228i	$-0.818716\pi$
$61$	0.358528	−	0.620988i	0.0459048	−	0.0795094i	0.888065	+	0.459718i	$0.152050\pi$
$62$	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	0.651261	−	0.758854i	$-0.274241\pi$
$67$	6.84166	+	1.83322i	0.835842	+	0.223963i	0.184581	+	0.982817i	$0.440907\pi$
$68$	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	0.933725	−	0.357991i	$-0.116538\pi$
$71$	−0.454168	−	1.69498i	−0.0538999	−	0.201157i	−0.987625	+	0.156834i	$0.949871\pi$
$72$	−0.531319	+	0.955413i	−0.0626165	+	0.112597i
$73$	5.35696	−	5.35696i	0.626985	−	0.626985i	−0.320323	−	0.947308i	$-0.603792\pi$
$73$	5.35696	−	5.35696i	0.626985	−	0.626985i	0.947308	+	0.320323i	$0.103792\pi$
$74$	−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	$0.0200186\pi$
$79$			1.11723i			0.125698i	−0.998023	+	0.0628489i	$0.979981\pi$
$80$	−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	−0.828992	−	0.559260i	$-0.811085\pi$
$83$	−2.45738	+	2.45738i	−0.269733	+	0.269733i	0.559260	+	0.828992i	$0.311085\pi$
$84$	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	0.357162	−	0.934042i	$-0.383744\pi$
$89$	1.88163	+	0.504180i	0.199452	+	0.0534430i	−0.157710	+	0.987485i	$0.550411\pi$
$90$	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	−0.325568	−	0.945518i	$-0.605556\pi$
$97$	−1.32723	+	0.355630i	−0.134760	+	0.0361088i	0.190809	+	0.981627i	$0.438889\pi$
$98$	−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	−0.462049	−	0.886855i	$-0.652885\pi$
$101$	0.753397	−	0.434974i	0.0749658	−	0.0432815i	0.537014	+	0.843573i	$0.319552\pi$
$102$	−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	−0.797815	−	0.602903i	$-0.794011\pi$
$107$	−6.97804	+	4.02877i	−0.674593	+	0.389476i	0.123222	+	0.992379i	$0.460677\pi$
$108$	−0.117330	−	10.9488i	−0.0112901	−	1.05355i
$109$	12.0811	+	12.0811i	1.15716	+	1.15716i	0.985084	+	0.172075i	$0.0550472\pi$
$109$	12.0811	+	12.0811i	1.15716	+	1.15716i	0.172075	+	0.985084i	$0.444953\pi$
$110$	−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	−0.995993	−	0.0894334i	$-0.971494\pi$
$113$	−4.47045	+	7.74305i	−0.420545	+	0.728405i	0.575448	+	0.817838i	$0.304828\pi$
$114$	−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	0.898368	−	0.439244i	$-0.144753\pi$
$127$	0.775200	+	1.34269i	0.0687879	+	0.119144i	−0.829580	+	0.558388i	$0.811420\pi$
$128$	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	$-0.942552\pi$
$131$		−	4.10898i		−	0.359003i	0.983758	−	0.179502i	$-0.0574485\pi$
$132$	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	−0.964222	−	0.265096i	$-0.914596\pi$
$137$	−3.06346	−	11.4330i	−0.261729	−	0.976786i	0.702493	−	0.711691i	$-0.252070\pi$
$138$	−9.76368	−	5.56753i	−0.831140	−	0.473939i
$139$	−7.30191	−	4.21576i	−0.619340	−	0.357576i	0.157272	−	0.987555i	$-0.449730\pi$
$139$	−7.30191	−	4.21576i	−0.619340	−	0.357576i	−0.776612	+	0.629979i	$0.783063\pi$
$140$	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	−0.314276	−	0.949332i	$-0.601762\pi$
$149$	−1.36446	+	0.365606i	−0.111781	+	0.0299516i	0.202495	+	0.979283i	$0.435095\pi$
$150$	0.381359	+	0.652435i	0.0311378	+	0.0532711i
$151$	−6.88689	−	6.88689i	−0.560447	−	0.560447i	0.368987	−	0.929435i	$-0.379705\pi$
$151$	−6.88689	−	6.88689i	−0.560447	−	0.560447i	−0.929435	+	0.368987i	$0.879705\pi$
$152$	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	−0.928038	−	0.372486i	$-0.878505\pi$
$163$	−19.7316	+	5.28707i	−1.54550	+	0.414115i	−0.617461	+	0.786601i	$0.711839\pi$
$164$	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	0.727867	+	0.685719i	$0.240512\pi$
$167$	−3.17054	+	11.8326i	−0.245344	+	0.915635i	−0.973210	+	0.229917i	$0.926155\pi$
$168$	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	0.705864	−	0.708348i	$-0.250559\pi$
$173$	5.85764	+	3.38191i	0.445348	+	0.257122i	−0.260515	+	0.965470i	$0.583893\pi$
$174$	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	0.973095	−	0.230405i	$-0.0740052\pi$
$179$	3.83994	+	6.65097i	0.287011	+	0.497117i	−0.686084	+	0.727522i	$0.740672\pi$
$180$	1.60877	−	0.449598i	0.119910	−	0.0335111i
$181$			10.6994i			0.795283i	0.917541	+	0.397642i	$0.130171\pi$
$181$			10.6994i			0.795283i	−0.917541	+	0.397642i	$0.869829\pi$
$182$	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	−0.0266854	−	0.999644i	$-0.508495\pi$
$191$	−12.5176	−	7.22707i	−0.905745	−	0.522932i	−0.879060	+	0.476712i	$0.841829\pi$
$192$	−10.9867	+	6.82318i	−0.792897	+	0.492420i
$193$	−18.9062	−	5.06589i	−1.36089	−	0.364651i	−0.496750	−	0.867894i	$-0.665473\pi$
$193$	−18.9062	−	5.06589i	−1.36089	−	0.364651i	−0.864145	+	0.503243i	$0.832140\pi$
$194$	−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	−0.937088	−	0.349094i	$-0.886489\pi$
$197$	0.687766	−	2.56678i	0.0490013	−	0.182875i	0.986089	+	0.166219i	$0.0531559\pi$
$198$	1.68260	+	1.66467i	0.119577	+	0.118303i
$199$	8.28694	−	14.3534i	0.587445	−	1.01749i	−0.407120	−	0.913374i	$-0.633467\pi$
$199$	8.28694	−	14.3534i	0.587445	−	1.01749i	0.994566	−	0.104111i	$-0.0331996\pi$
$200$	−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	0.669815	−	0.742528i	$-0.266373\pi$
$211$	23.9352	−	13.8190i	1.64777	−	0.951341i	0.977956	−	0.208812i	$-0.0669598\pi$
$212$	−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	0.355773	−	0.934572i	$-0.384218\pi$
$223$	2.93579	+	0.786643i	0.196595	+	0.0526775i	−0.159178	+	0.987250i	$0.550884\pi$
$224$	−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	−0.998339	−	0.0576122i	$-0.981651\pi$
$227$	−2.44919	−	9.14049i	−0.162558	−	0.606675i	0.835781	−	0.549063i	$-0.185015\pi$
$228$	−5.39090	−	5.27659i	−0.357021	−	0.349450i
$229$	−3.49493	+	3.49493i	−0.230952	+	0.230952i	−0.813090	−	0.582138i	$-0.802216\pi$
$229$	−3.49493	+	3.49493i	−0.230952	+	0.230952i	0.582138	+	0.813090i	$0.302216\pi$
$230$	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	$-0.753906\pi$
$233$		−	21.3205i		−	1.39675i	0.715731	−	0.698376i	$-0.246094\pi$
$234$	−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	−0.873251	−	0.487271i	$-0.837993\pi$
$239$	−5.96711	+	5.96711i	−0.385981	+	0.385981i	0.487271	+	0.873251i	$0.337993\pi$
$240$	13.5717	+	3.32652i	0.876050	+	0.214726i
$241$	5.36803	+	20.0338i	0.345785	+	1.29049i	0.891692	+	0.452643i	$0.149519\pi$
$241$	5.36803	+	20.0338i	0.345785	+	1.29049i	−0.545906	+	0.837846i	$0.683815\pi$
$242$	−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	−0.944139	−	0.329547i	$-0.893104\pi$
$251$	−2.95746	+	5.12248i	−0.186673	+	0.323328i	0.757466	+	0.652875i	$0.226437\pi$
$252$	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	0.527884	−	0.849316i	$-0.322986\pi$
$257$	24.4854	−	14.1366i	1.52736	−	0.881819i	0.999472	−	0.0325029i	$-0.0103478\pi$
$258$	−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	−0.0977210	−	0.995214i	$-0.531155\pi$
$263$	11.6002	−	6.69738i	0.715299	−	0.412978i	0.813020	+	0.582236i	$0.197822\pi$
$264$	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	0.269733	+	0.962935i	$0.413065\pi$
$269$	−11.4654	+	19.8587i	−0.699060	+	1.21081i	−0.968793	+	0.247872i	$0.920269\pi$
$270$	−11.7667	+	11.8935i	−0.716101	+	0.723816i
$271$	−2.48442	+	9.27197i	−0.150918	+	0.563232i	0.848503	+	0.529191i	$0.177504\pi$
$271$	−2.48442	+	9.27197i	−0.150918	+	0.563232i	−0.999420	+	0.0340411i	$0.989162\pi$
$272$	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	0.471106	−	0.882076i	$-0.343855\pi$
$277$	−0.952681	−	0.550031i	−0.0572411	−	0.0330482i	−0.528347	+	0.849028i	$0.677188\pi$
$278$	−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	−0.476634	−	0.879102i	$-0.658143\pi$
$281$	6.74660	−	6.74660i	0.402469	−	0.402469i	0.879102	+	0.476634i	$0.158143\pi$
$282$	25.2402	+	6.61836i	1.50303	+	0.394118i
$283$	−10.5772	−	18.3202i	−0.628746	−	1.08902i	−0.987804	−	0.155705i	$-0.950235\pi$
$283$	−10.5772	−	18.3202i	−0.628746	−	1.08902i	0.359057	−	0.933316i	$-0.383098\pi$
$284$	−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	−0.956594	−	0.291425i	$-0.905871\pi$
$293$	−4.68793	−	17.4956i	−0.273872	−	1.02210i	0.682722	−	0.730678i	$-0.260796\pi$
$294$	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	0.883268	−	0.468869i	$-0.155338\pi$
$307$	7.26086	+	7.26086i	0.414399	+	0.414399i	−0.468869	+	0.883268i	$0.655338\pi$
$308$	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	0.157343	−	0.987544i	$-0.449707\pi$
$317$	−14.7813	−	14.7813i	−0.830201	−	0.830201i	−0.987544	+	0.157343i	$0.949707\pi$
$318$	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	0.996894	+	0.0787555i	$0.0250946\pi$
$331$	3.14630	+	11.7421i	0.172936	+	0.645407i	−0.823958	+	0.566651i	$0.808239\pi$
$332$	−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	$0.170837\pi$
$337$			18.7726i			1.02261i	−0.859401	+	0.511303i	$0.829163\pi$
$338$	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	0.674048	−	0.738688i	$-0.264554\pi$
$347$	6.91748	+	3.99381i	0.371350	+	0.214399i	−0.302698	+	0.953086i	$0.597887\pi$
$348$	16.5793	+	9.33665i	0.888746	+	0.500497i
$349$	9.90639	+	2.65441i	0.530277	+	0.142087i	0.514016	−	0.857781i	$-0.328157\pi$
$349$	9.90639	+	2.65441i	0.530277	+	0.142087i	0.0162607	+	0.999868i	$0.494824\pi$
$350$	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	−0.990812	−	0.135246i	$-0.956817\pi$
$353$	−1.22350	+	4.56617i	−0.0651204	+	0.243033i	0.925692	+	0.378279i	$0.123484\pi$
$354$	−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	0.866894	+	0.498492i	$0.166113\pi$
$359$	25.8704	+	25.8704i	1.36539	+	1.36539i	0.498492	+	0.866894i	$0.333887\pi$
$360$	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	0.0378895	−	0.999282i	$-0.487937\pi$
$367$	17.6675	−	10.2004i	0.922238	−	0.532454i	0.884348	+	0.466828i	$0.154603\pi$
$368$	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	−0.464718	−	0.885459i	$-0.653844\pi$
$373$	10.3223	−	17.8788i	0.534471	−	0.925731i	0.999189	−	0.0402718i	$-0.0128224\pi$
$374$	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	−0.110947	−	0.993826i	$-0.535388\pi$
$379$	−13.7043	−	3.67206i	−0.703943	−	0.188621i	−0.592996	+	0.805205i	$0.702055\pi$
$380$	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	−0.989438	−	0.144954i	$-0.953697\pi$
$383$	−4.01265	−	14.9754i	−0.205037	−	0.765207i	0.784402	−	0.620253i	$-0.212970\pi$
$384$	−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	$0.323705\pi$
$389$			33.5493i			1.70102i	−0.525963	+	0.850508i	$0.676295\pi$
$390$	−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	−0.998428	−	0.0560542i	$-0.982148\pi$
$397$	−3.22366	−	12.0309i	−0.161791	−	0.603813i	0.836637	−	0.547758i	$-0.184519\pi$
$398$	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	−0.110317	−	0.993896i	$-0.535187\pi$
$401$	−14.0736	−	3.77101i	−0.702802	−	0.188315i	−0.592485	+	0.805581i	$0.701853\pi$
$402$	−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	−0.690316	−	0.723508i	$-0.742528\pi$
$409$	−18.7351	+	5.02006i	−0.926393	+	0.248226i	−0.236077	+	0.971734i	$0.575862\pi$
$410$	−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	−0.436599	−	0.899656i	$-0.643817\pi$
$419$	2.54287	−	1.46812i	0.124227	−	0.0717226i	0.560826	+	0.827934i	$0.310484\pi$
$420$	−14.2796	+	0.153022i	−0.696771	+	0.00746673i
$421$	−4.53947	−	4.53947i	−0.221240	−	0.221240i	0.587780	−	0.809021i	$-0.300002\pi$
$421$	−4.53947	−	4.53947i	−0.221240	−	0.221240i	−0.809021	+	0.587780i	$0.800002\pi$
$422$	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	0.671450	−	0.741050i	$-0.265672\pi$
$431$	18.3194	+	4.90868i	0.882417	+	0.236443i	0.210967	+	0.977493i	$0.432339\pi$
$432$	−0.469292	−	21.8939i	−0.0225788	−	1.05337i
$433$	4.30614	+	2.48615i	0.206940	+	0.119477i	0.599888	−	0.800084i	$-0.295212\pi$
$433$	4.30614	+	2.48615i	0.206940	+	0.119477i	−0.392949	+	0.919560i	$0.628545\pi$
$434$	−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	0.775137	+	0.631793i	$0.217681\pi$
$439$	19.5845	+	33.9214i	0.934717	+	1.61898i	0.159580	+	0.987185i	$0.448986\pi$
$440$	−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	$-0.638488\pi$
$443$		−	38.1735i		−	1.81368i	0.421477	−	0.906839i	$-0.361512\pi$
$444$	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	0.944086	−	0.329699i	$-0.106947\pi$
$449$	−0.812961	−	3.03401i	−0.0383660	−	0.143184i	−0.982452	+	0.186515i	$0.940281\pi$
$450$	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	0.380125	+	0.924935i	$0.375881\pi$
$457$	−8.79773	+	32.8336i	−0.411541	+	1.53589i	−0.791665	+	0.610955i	$0.790786\pi$
$458$	−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	−0.749678	−	0.661803i	$-0.769792\pi$
$461$	−22.9313	+	6.14442i	−1.06802	+	0.286174i	−0.318339	+	0.947977i	$0.603125\pi$
$462$	−10.2111	−	17.4694i	−0.475065	−	0.812749i
$463$	−24.4048	−	24.4048i	−1.13419	−	1.13419i	−0.989474	−	0.144713i	$-0.953774\pi$
$463$	−24.4048	−	24.4048i	−1.13419	−	1.13419i	−0.144713	−	0.989474i	$-0.546226\pi$
$464$	−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	−0.902786	−	0.430090i	$-0.858482\pi$
$479$	2.05936	−	7.68562i	0.0940943	−	0.351165i	0.996881	+	0.0789246i	$0.0251487\pi$
$480$	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	0.961295	+	0.275520i	$0.0888500\pi$
$487$	5.88223	+	21.9528i	0.266549	+	0.994775i	−0.694746	+	0.719255i	$0.744483\pi$
$488$	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	0.865357	−	0.501157i	$-0.167092\pi$
$491$	−0.0296046	−	0.0512767i	−0.00133604	−	0.00231409i	−0.866693	+	0.498843i	$0.833759\pi$
$492$	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	−0.165836	+	0.986153i	$0.553032\pi$
$499$	−25.7335	+	25.7335i	−1.15199	+	1.15199i	−0.986153	+	0.165836i	$0.946968\pi$
$500$	−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	0.136757	−	0.990605i	$-0.456332\pi$
$503$	−14.6397	−	8.45225i	−0.652753	−	0.376867i	−0.789510	+	0.613738i	$0.789665\pi$
$504$	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	−0.748772	−	0.662827i	$-0.769356\pi$
$509$	5.21379	−	19.4581i	0.231097	−	0.862466i	0.979870	−	0.199639i	$-0.0639769\pi$
$510$	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	−0.785358	−	0.619041i	$-0.787521\pi$
$523$	−14.6805	+	8.47577i	−0.641932	+	0.370620i	0.143426	+	0.989661i	$0.454188\pi$
$524$	−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	−0.807760	−	0.589512i	$-0.799320\pi$
$541$	−5.07631	+	5.07631i	−0.218248	+	0.218248i	0.589512	+	0.807760i	$0.299320\pi$
$542$	−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	$0.240221\pi$
$547$			32.0440i			1.37010i	−0.728494	+	0.685052i	$0.759779\pi$
$548$	−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	0.570107	−	0.821570i	$-0.306902\pi$
$557$	15.4125	+	4.12977i	0.653049	+	0.174984i	0.0829418	+	0.996554i	$0.473568\pi$
$558$	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	−0.918889	−	0.394516i	$-0.870912\pi$
$563$	−2.79472	+	4.84060i	−0.117783	+	0.204007i	0.801106	+	0.598523i	$0.204246\pi$
$564$	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	0.184381	−	0.982855i	$-0.440972\pi$
$569$	26.9010	−	15.5313i	1.12775	−	0.651106i	0.943368	+	0.331749i	$0.107639\pi$
$570$	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	−0.975715	−	0.219044i	$-0.929706\pi$
$577$	−28.6991	−	28.6991i	−1.19476	−	1.19476i	−0.219044	−	0.975715i	$-0.570294\pi$
$578$	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	0.382091	−	0.924125i	$-0.375204\pi$
$587$	6.07956	+	1.62901i	0.250930	+	0.0672365i	−0.131161	+	0.991361i	$0.541871\pi$
$588$	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	−0.999404	−	0.0345259i	$-0.989008\pi$
$593$	−23.4963	+	23.4963i	−0.964878	+	0.964878i	0.0345259	+	0.999404i	$0.489008\pi$
$594$	−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	$-0.837500\pi$
$599$		−	23.9175i		−	0.977241i	0.872496	−	0.488621i	$-0.162500\pi$
$600$	0.776656	+	1.29662i	0.0317069	+	0.0529344i
$601$	14.2083	+	24.6095i	0.579569	+	1.00384i	0.995529	+	0.0944594i	$0.0301123\pi$
$601$	14.2083	+	24.6095i	0.579569	+	1.00384i	−0.415960	+	0.909383i	$0.636554\pi$
$602$	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	0.967470	−	0.252984i	$-0.0814120\pi$
$607$	30.3561	+	17.5261i	1.23211	+	0.711362i	0.264645	+	0.964346i	$0.414745\pi$
$608$	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	−0.997070	−	0.0764895i	$-0.975629\pi$
$613$	−2.36044	+	8.80929i	−0.0953373	+	0.355804i	0.901733	+	0.432293i	$0.142295\pi$
$614$	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	−0.403612	−	0.914930i	$-0.632246\pi$
$617$	−7.34468	+	1.96800i	−0.295686	+	0.0792287i	0.107927	+	0.994159i	$0.465579\pi$
$618$	−22.8454	+	13.3535i	−0.918978	+	0.537157i
$619$	−25.6801	−	25.6801i	−1.03217	−	1.03217i	−0.999465	−	0.0327040i	$-0.989588\pi$
$619$	−25.6801	−	25.6801i	−1.03217	−	1.03217i	−0.0327040	−	0.999465i	$-0.510412\pi$
$620$	−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	−0.648418	−	0.761285i	$-0.724569\pi$
$631$	−20.8323	+	5.58201i	−0.829322	+	0.222216i	−0.180904	+	0.983501i	$0.557902\pi$
$632$	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	−0.975426	−	0.220327i	$-0.929287\pi$
$641$	−41.8746	−	24.1763i	−1.65395	−	0.954907i	−0.678522	−	0.734580i	$-0.737379\pi$
$642$	9.12521	−	16.0027i	0.360143	−	0.631578i
$643$	0.0193750	+	0.0723085i	0.000764075	+	0.00285157i	0.966307	−	0.257393i	$-0.0828635\pi$
$643$	0.0193750	+	0.0723085i	0.000764075	+	0.00285157i	−0.965543	+	0.260245i	$0.916197\pi$
$644$	−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	0.826948	−	0.562279i	$-0.190075\pi$
$647$	−1.86890	−	3.23703i	−0.0734741	−	0.127261i	−0.900422	+	0.435018i	$0.856742\pi$
$648$	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	−0.925055	−	0.379833i	$-0.875981\pi$
$653$	−20.2252	−	35.0310i	−0.791473	−	1.37087i	0.133583	−	0.991038i	$-0.457352\pi$
$654$	−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	0.982330	−	0.187155i	$-0.0599268\pi$
$659$	33.6653	+	19.4367i	1.31141	+	0.757145i	0.329084	+	0.944301i	$0.393260\pi$
$660$	14.8453	−	26.3612i	0.577852	−	1.02611i
$661$	39.1027	+	10.4775i	1.52092	+	0.407529i	0.920044	−	0.391815i	$-0.128153\pi$
$661$	39.1027	+	10.4775i	1.52092	+	0.407529i	0.600874	+	0.799344i	$0.294819\pi$
$662$	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	−0.257134	−	0.966376i	$-0.582778\pi$
$673$	11.7053	−	6.75805i	0.451205	−	0.260504i	0.708339	+	0.705872i	$0.249445\pi$
$674$	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	−0.120786	−	0.992679i	$-0.538541\pi$
$683$	7.08109	−	1.89737i	0.270950	−	0.0726010i	0.391736	+	0.920078i	$0.371875\pi$
$684$	−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	−0.194090	−	0.980984i	$-0.562175\pi$
$691$	−22.4140	−	6.00581i	−0.852669	−	0.228472i	−0.658579	+	0.752512i	$0.728842\pi$
$692$	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	$0.0110396\pi$
$701$			1.83613i			0.0693497i	−0.999399	+	0.0346748i	$0.988960\pi$
$702$	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	0.986912	−	0.161261i	$-0.0515560\pi$
$709$	1.37371	+	5.12676i	0.0515908	+	0.192540i	−0.935321	+	0.353800i	$0.884889\pi$
$710$	−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	0.365949	+	0.930635i	$0.380745\pi$
$719$	−16.7047	+	28.9333i	−0.622979	+	1.07903i	−0.988928	+	0.148397i	$0.952589\pi$
$720$	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	0.985019	+	0.172445i	$0.0551668\pi$
$733$	31.3372	+	31.3372i	1.15746	+	1.15746i	0.172445	+	0.985019i	$0.444833\pi$
$734$	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	−0.531488	−	0.847066i	$-0.678367\pi$
$739$	9.57785	−	35.7450i	0.352327	−	1.31490i	0.883815	−	0.467836i	$-0.154966\pi$
$740$	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	0.475709	−	0.879603i	$-0.342191\pi$
$743$	12.2084	+	3.27124i	0.447884	+	0.120010i	−0.0278251	+	0.999613i	$0.508858\pi$
$744$	−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	0.992953	−	0.118509i	$-0.0378115\pi$
$751$	10.7931	+	18.6941i	0.393844	+	0.682159i	−0.599109	+	0.800668i	$0.704478\pi$
$752$	−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	0.925733	−	0.378179i	$-0.123449\pi$
$757$	3.72408	+	6.45030i	0.135354	+	0.234440i	−0.790379	+	0.612619i	$0.790116\pi$
$758$	−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	0.952847	+	0.303450i	$0.0981385\pi$
$761$	7.70710	+	28.7633i	0.279382	+	1.04267i	−0.673465	+	0.739219i	$0.735195\pi$
$762$	−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	−0.276433	−	0.961033i	$-0.589152\pi$
$769$	12.2981	−	45.8972i	0.443482	−	1.65510i	0.719914	−	0.694063i	$-0.244181\pi$
$770$	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	0.216732	−	0.976231i	$-0.430460\pi$
$773$	24.8153	−	6.64923i	0.892543	−	0.239156i	0.675811	+	0.737075i	$0.263794\pi$
$774$	−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	−0.458068	−	0.888917i	$-0.651459\pi$
$787$	−11.5106	+	3.08426i	−0.410309	+	0.109942i	0.0477596	+	0.998859i	$0.484792\pi$
$788$	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	0.265717	−	0.964051i	$-0.414391\pi$
$797$	−12.3178	−	7.11167i	−0.436318	−	0.251908i	−0.702034	+	0.712143i	$0.747725\pi$
$798$	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	0.915560	−	0.402182i	$-0.131748\pi$
$809$	3.11393	+	5.39349i	0.109480	+	0.189625i	−0.806080	+	0.591807i	$0.798415\pi$
$810$	5.96147	−	22.7351i	0.209465	−	0.798829i
$811$	8.66022	−	8.66022i	0.304102	−	0.304102i	−0.538515	−	0.842616i	$-0.681014\pi$
$811$	8.66022	−	8.66022i	0.304102	−	0.304102i	0.842616	+	0.538515i	$0.181014\pi$
$812$	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	0.843046	+	0.537842i	$0.180760\pi$
$821$	−4.46914	+	16.6791i	−0.155974	+	0.582104i	−0.999020	+	0.0442618i	$0.985906\pi$
$822$	19.2372	+	19.0321i	0.670973	+	0.663821i
$823$	−8.61216	+	14.9167i	−0.300201	+	0.519963i	−0.976181	−	0.216956i	$-0.930387\pi$
$823$	−8.61216	+	14.9167i	−0.300201	+	0.519963i	0.675980	+	0.736920i	$0.263720\pi$
$824$	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	0.556489	−	0.830855i	$-0.312148\pi$
$827$	−7.89012	−	7.89012i	−0.274366	−	0.274366i	−0.830855	+	0.556489i	$0.812148\pi$
$828$	−3.80003	+	0.0407218i	−0.132060	+	0.00141518i
$829$	−17.8732	+	10.3191i	−0.620761	+	0.358396i	−0.777165	−	0.629297i	$-0.783343\pi$
$829$	−17.8732	+	10.3191i	−0.620761	+	0.358396i	0.156404	+	0.987693i	$0.450010\pi$
$830$	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	0.0154095	−	0.999881i	$-0.495095\pi$
$839$	15.3139	−	4.10335i	0.528695	−	0.141663i	0.513286	+	0.858218i	$0.328428\pi$
$840$	−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	−0.728343	−	0.685213i	$-0.759709\pi$
$853$	−1.25966	+	1.25966i	−0.0431300	+	0.0431300i	0.685213	+	0.728343i	$0.259709\pi$
$854$	−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	$-0.986983\pi$
$857$		−	2.39366i		−	0.0817658i	0.999164	−	0.0408829i	$-0.0130171\pi$
$858$	−27.7716	−	22.4244i	−0.948106	−	0.765557i
$859$			17.8687i			0.609673i	0.952405	+	0.304837i	$0.0986018\pi$
$859$			17.8687i			0.609673i	−0.952405	+	0.304837i	$0.901398\pi$
$860$	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	−0.371776	−	0.928322i	$-0.621251\pi$
$863$	16.3496	−	16.3496i	0.556546	−	0.556546i	0.928322	+	0.371776i	$0.121251\pi$
$864$	−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	−0.160702	−	0.987003i	$-0.551376\pi$
$877$	5.73412	−	1.53645i	0.193628	−	0.0518824i	0.354330	+	0.935121i	$0.384709\pi$
$878$	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	−0.931625	−	0.363422i	$-0.881608\pi$
$881$	−32.1364	+	18.5540i	−1.08270	+	0.625099i	−0.151079	+	0.988522i	$0.548275\pi$
$882$	−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	−0.930343	−	0.366689i	$-0.880491\pi$
$887$	−32.1042	+	18.5354i	−1.07795	+	0.622356i	−0.147609	+	0.989046i	$0.547158\pi$
$888$	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	0.998477	+	0.0551749i	$0.0175716\pi$
$907$	16.4743	+	28.5344i	0.547021	+	0.947468i	−0.451456	+	0.892294i	$0.649095\pi$
$908$	−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	$-0.877457\pi$
$911$		−	22.6697i		−	0.751082i	0.926806	−	0.375541i	$-0.122543\pi$
$912$	−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	0.370997	−	0.928634i	$-0.379016\pi$
$919$	−7.50982	−	4.33579i	−0.247726	−	0.143025i	−0.618723	+	0.785610i	$0.712349\pi$
$920$	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	−0.0280869	−	0.999605i	$-0.508942\pi$
$929$	13.6363	−	3.65383i	0.447392	−	0.119878i	0.475479	+	0.879727i	$0.342275\pi$
$930$	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	0.771537	−	0.636184i	$-0.219488\pi$
$941$	4.15205	+	4.15205i	0.135353	+	0.135353i	−0.636184	+	0.771537i	$0.719488\pi$
$942$	−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	−0.952846	−	0.303455i	$-0.901860\pi$
$947$	0.740729	−	2.76444i	0.0240705	−	0.0898322i	0.976916	+	0.213623i	$0.0685264\pi$
$948$	−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	0.618657	−	0.785661i	$-0.287677\pi$
$953$	7.64309	+	4.41274i	0.247584	+	0.142943i	−0.371074	+	0.928603i	$0.621010\pi$
$954$	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	0.00141655	−	0.999999i	$-0.499549\pi$
$967$	31.1406	−	31.1406i	1.00142	−	1.00142i	0.999999	−	0.00141655i	$-0.000450902\pi$
$968$	−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	0.267986	−	0.963423i	$-0.413642\pi$
$971$	−13.4730	−	7.77866i	−0.432370	−	0.249629i	−0.700356	+	0.713794i	$0.746975\pi$
$972$	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	0.490348	+	0.871526i	$0.336870\pi$
$977$	−11.5672	+	43.1696i	−0.370069	+	1.38112i	−0.860417	+	0.509590i	$0.829797\pi$
$978$	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	0.959314	−	0.282343i	$-0.0911115\pi$
$983$	21.2250	+	21.2250i	0.676971	+	0.676971i	−0.282343	+	0.959314i	$0.591112\pi$
$984$	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	−0.223230	−	0.974766i	$-0.571660\pi$
$991$	16.0337	−	9.25705i	0.509327	−	0.294060i	0.732557	+	0.680706i	$0.238327\pi$
$992$	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	−0.00423556	−	0.999991i	$-0.501348\pi$
$997$	27.2779	−	47.2467i	0.863900	−	1.49632i	0.868135	−	0.496327i	$-0.165318\pi$
$998$	−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.11.4	yes	16
3.2	odd	2		468.2.cb.f.271.1		16
4.3	odd	2	inner	52.2.l.b.11.1	✓	16
8.3	odd	2		832.2.bu.n.63.2		16
8.5	even	2		832.2.bu.n.63.3		16
12.11	even	2		468.2.cb.f.271.4		16
13.2	odd	12		676.2.f.h.239.7		16
13.3	even	3		676.2.f.h.99.3		16
13.4	even	6		676.2.l.i.319.4		16
13.5	odd	4		676.2.l.m.587.2		16
13.6	odd	12	inner	52.2.l.b.19.1	yes	16
13.7	odd	12		676.2.l.k.19.4		16
13.8	odd	4		676.2.l.i.587.3		16
13.9	even	3		676.2.l.m.319.1		16
13.10	even	6		676.2.f.i.99.6		16
13.11	odd	12		676.2.f.i.239.2		16
13.12	even	2		676.2.l.k.427.1		16
39.32	even	12		468.2.cb.f.19.4		16
52.3	odd	6		676.2.f.h.99.7		16
52.7	even	12		676.2.l.k.19.1		16
52.11	even	12		676.2.f.i.239.6		16
52.15	even	12		676.2.f.h.239.3		16
52.19	even	12	inner	52.2.l.b.19.4	yes	16
52.23	odd	6		676.2.f.i.99.2		16
52.31	even	4		676.2.l.m.587.1		16
52.35	odd	6		676.2.l.m.319.2		16
52.43	odd	6		676.2.l.i.319.3		16
52.47	even	4		676.2.l.i.587.4		16
52.51	odd	2		676.2.l.k.427.4		16
104.19	even	12		832.2.bu.n.383.3		16
104.45	odd	12		832.2.bu.n.383.2		16
156.71	odd	12		468.2.cb.f.19.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.11.1	✓	16	4.3	odd	2	inner
52.2.l.b.11.4	yes	16	1.1	even	1	trivial
52.2.l.b.19.1	yes	16	13.6	odd	12	inner
52.2.l.b.19.4	yes	16	52.19	even	12	inner
468.2.cb.f.19.1		16	156.71	odd	12
468.2.cb.f.19.4		16	39.32	even	12
468.2.cb.f.271.1		16	3.2	odd	2
468.2.cb.f.271.4		16	12.11	even	2
676.2.f.h.99.3		16	13.3	even	3
676.2.f.h.99.7		16	52.3	odd	6
676.2.f.h.239.3		16	52.15	even	12
676.2.f.h.239.7		16	13.2	odd	12
676.2.f.i.99.2		16	52.23	odd	6
676.2.f.i.99.6		16	13.10	even	6
676.2.f.i.239.2		16	13.11	odd	12
676.2.f.i.239.6		16	52.11	even	12
676.2.l.i.319.3		16	52.43	odd	6
676.2.l.i.319.4		16	13.4	even	6
676.2.l.i.587.3		16	13.8	odd	4
676.2.l.i.587.4		16	52.47	even	4
676.2.l.k.19.1		16	52.7	even	12
676.2.l.k.19.4		16	13.7	odd	12
676.2.l.k.427.1		16	13.12	even	2
676.2.l.k.427.4		16	52.51	odd	2
676.2.l.m.319.1		16	13.9	even	3
676.2.l.m.319.2		16	52.35	odd	6
676.2.l.m.587.1		16	52.31	even	4
676.2.l.m.587.2		16	13.5	odd	4
832.2.bu.n.63.2		16	8.3	odd	2
832.2.bu.n.63.3		16	8.5	even	2
832.2.bu.n.383.2		16	104.45	odd	12
832.2.bu.n.383.3		16	104.19	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.41419 - 0.00757716i) q^{2} +(-1.40004 + 0.808315i) q^{3} +(1.99989 - 0.0214311i) q^{4} +(-1.52798 - 1.52798i) q^{5} +(-1.97381 + 1.15372i) q^{6} +(-1.97429 + 0.529008i) q^{7} +(2.82806 - 0.0454612i) q^{8} +(-0.193255 + 0.334727i) q^{9} +O(q^{10})\)	\(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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