LMFDB - Embedded newform 52.2.l.b.19.1

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			19.1
Root			$-0.00757716 + 1.41419i$ of defining polynomial
Character	$\chi$	$=$	52.19
Dual form			52.2.l.b.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22094 + 0.713659i) q^{2} +(1.40004 + 0.808315i) q^{3} +(0.981383 - 1.74267i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(-2.28623 + 0.0122495i) q^{6} +(1.97429 + 0.529008i) q^{7} +(0.0454612 + 2.82806i) q^{8} +(-0.193255 - 0.334727i) q^{9} +O(q^{10})$	\(q+(-1.22094 + 0.713659i) q^{2} +(1.40004 + 0.808315i) q^{3} +(0.981383 - 1.74267i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(-2.28623 + 0.0122495i) q^{6} +(1.97429 + 0.529008i) q^{7} +(0.0454612 + 2.82806i) q^{8} +(-0.193255 - 0.334727i) q^{9} +(0.775114 - 2.95603i) 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} +(-2.07378 - 3.42045i) q^{16} +(4.14654 - 2.39401i) q^{17} +(0.474833 + 0.270763i) q^{18} +(-0.603848 + 2.25359i) q^{19} +(1.16323 + 4.16230i) q^{20} +(2.33648 + 2.33648i) q^{21} +(4.35333 + 4.30693i) q^{22} +(-2.45806 + 4.25748i) q^{23} +(-2.22232 + 3.99615i) q^{24} +0.330547i q^{25} +(5.07583 + 0.485758i) q^{26} -5.47473i q^{27} +(2.85942 - 2.92136i) q^{28} +(-2.94247 + 5.09651i) q^{29} +(3.47459 - 3.51203i) q^{30} +(-0.420375 - 0.420375i) q^{31} +(4.97298 + 2.69619i) q^{32} +(1.81181 - 6.76178i) q^{33} +(-3.35417 + 5.88215i) q^{34} +(-3.82499 + 2.20836i) q^{35} +(-0.772974 + 0.00828333i) 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} +(-4.52014 - 1.18525i) q^{42} +(5.59481 + 9.69049i) q^{43} +(-8.38882 - 2.15170i) q^{44} +(0.806745 + 0.216167i) q^{45} +(-0.0372502 - 6.95234i) q^{46} +(8.07035 - 8.07035i) q^{47} +(-0.138577 - 6.46503i) q^{48} +(-2.44422 - 1.41117i) q^{49} +(-0.235897 - 0.403577i) q^{50} +7.74044 q^{51} +(-6.54394 + 3.02933i) q^{52} -1.33055 q^{53} +(3.90709 + 6.68431i) q^{54} +(8.10346 + 4.67854i) q^{55} +(-1.40631 + 5.60745i) q^{56} +(-2.66702 + 2.66702i) q^{57} +(-0.0445911 - 8.32245i) q^{58} +(-6.48147 - 1.73670i) q^{59} +(-1.73588 + 6.76765i) q^{60} +(0.358528 + 0.620988i) q^{61} +(0.813257 + 0.213248i) 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} +(-0.102613 - 9.57548i) q^{68} +(-6.88277 + 3.97377i) q^{69} +(3.09406 - 5.42600i) q^{70} +(0.454168 - 1.69498i) q^{71} +(0.937842 - 0.561753i) q^{72} +(5.35696 + 5.35696i) q^{73} +(1.92147 - 1.94217i) q^{74} +(-0.267186 + 0.462779i) q^{75} +(3.33465 + 3.26394i) q^{76} -8.85061i q^{77} +(6.71373 + 4.78295i) q^{78} +1.11723i q^{79} +(8.39507 + 2.05769i) q^{80} +(3.84554 - 6.66067i) q^{81} +(-1.56121 - 1.54457i) q^{82} +(2.45738 + 2.45738i) q^{83} +(6.36468 - 1.77872i) q^{84} +(-2.67784 + 9.99383i) q^{85} +(-13.7466 - 7.83871i) q^{86} +(-8.23917 + 4.75689i) q^{87} +(11.7778 - 3.35966i) 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} +(-4.09393 + 15.6129i) q^{94} +(-2.52078 - 4.36612i) q^{95} +(4.78302 + 7.79451i) q^{96} +(-1.32723 - 0.355630i) q^{97} +(3.99134 - 0.0213854i) 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 $

$2$	−1.22094	+	0.713659i	−0.863334	+	0.504633i
$2$	−1.22094	+	0.713659i	−0.863334	+	0.504633i
$3$	1.40004	+	0.808315i	0.808315	+	0.466681i	0.846370	−	0.532595i	$-0.178783\pi$
$3$	1.40004	+	0.808315i	0.808315	+	0.466681i	−0.0380556	+	0.999276i	$0.512116\pi$
$4$	0.981383	−	1.74267i	0.490691	−	0.871333i
$5$	−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	$0.410522\pi$
$6$	−2.28623	+	0.0122495i	−0.933348	+	0.00500082i
$7$	1.97429	+	0.529008i	0.746210	+	0.199946i	0.611836	−	0.790984i	$-0.290431\pi$
$7$	1.97429	+	0.529008i	0.746210	+	0.199946i	0.134374	+	0.990931i	$0.457098\pi$
$8$	0.0454612	+	2.82806i	0.0160730	+	0.999871i
$9$	−0.193255	−	0.334727i	−0.0644182	−	0.111576i
$10$	0.775114	−	2.95603i	0.245113	−	0.934778i
$11$	−1.12074	−	4.18264i	−0.337915	−	1.26111i	−0.900675	−	0.434494i	$-0.856927\pi$
$11$	−1.12074	−	4.18264i	−0.337915	−	1.26111i	0.562760	−	0.826620i	$-0.309739\pi$
$12$	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
$16$	−2.07378	−	3.42045i	−0.518444	−	0.855112i
$17$	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	$0.136139\pi$
$18$	0.474833	+	0.270763i	0.111919	+	0.0638195i
$19$	−0.603848	+	2.25359i	−0.138532	+	0.517010i	0.861426	+	0.507883i	$0.169572\pi$
$19$	−0.603848	+	2.25359i	−0.138532	+	0.517010i	−0.999958	+	0.00912654i	$0.997095\pi$
$20$	1.16323	+	4.16230i	0.260106	+	0.930718i
$21$	2.33648	+	2.33648i	0.509861	+	0.509861i
$22$	4.35333	+	4.30693i	0.928133	+	0.918240i
$23$	−2.45806	+	4.25748i	−0.512541	+	0.887747i	0.487354	+	0.873205i	$0.337962\pi$
$23$	−2.45806	+	4.25748i	−0.512541	+	0.887747i	−0.999894	+	0.0145418i	$0.995371\pi$
$24$	−2.22232	+	3.99615i	−0.453628	+	0.815711i
$25$			0.330547i			0.0661093i
$26$	5.07583	+	0.485758i	0.995452	+	0.0952650i
$27$		−	5.47473i		−	1.05361i
$28$	2.85942	−	2.92136i	0.540379	−	0.552086i
$29$	−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	$0.982663\pi$
$30$	3.47459	−	3.51203i	0.634371	−	0.641206i
$31$	−0.420375	−	0.420375i	−0.0755017	−	0.0755017i	0.668348	−	0.743849i	$-0.267002\pi$
$31$	−0.420375	−	0.420375i	−0.0755017	−	0.0755017i	−0.743849	+	0.668348i	$0.767002\pi$
$32$	4.97298	+	2.69619i	0.879108	+	0.476623i
$33$	1.81181	−	6.76178i	0.315396	−	1.17708i
$34$	−3.35417	+	5.88215i	−0.575235	+	1.00878i
$35$	−3.82499	+	2.20836i	−0.646541	+	0.373280i
$36$	−0.772974	+	0.00828333i	−0.128829	+	0.00138055i
$37$	−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	$0.877972\pi$
$42$	−4.52014	−	1.18525i	−0.697473	−	0.182888i
$43$	5.59481	+	9.69049i	0.853200	+	1.47779i	0.878305	+	0.478101i	$0.158675\pi$
$43$	5.59481	+	9.69049i	0.853200	+	1.47779i	−0.0251051	+	0.999685i	$0.507992\pi$
$44$	−8.38882	−	2.15170i	−1.26466	−	0.324382i
$45$	0.806745	+	0.216167i	0.120263	+	0.0322242i
$46$	−0.0372502	−	6.95234i	−0.00549224	−	1.02507i
$47$	8.07035	−	8.07035i	1.17718	−	1.17718i	0.196722	−	0.980459i	$-0.436970\pi$
$47$	8.07035	−	8.07035i	1.17718	−	1.17718i	0.980459	−	0.196722i	$-0.0630296\pi$
$48$	−0.138577	−	6.46503i	−0.0200018	−	0.933147i
$49$	−2.44422	−	1.41117i	−0.349175	−	0.201596i
$50$	−0.235897	−	0.403577i	−0.0333609	−	0.0570744i
$51$	7.74044			1.08388
$52$	−6.54394	+	3.02933i	−0.907481	+	0.420092i
$53$	−1.33055			−0.182765			−0.0913823	−	0.995816i	$-0.529129\pi$
$53$	−1.33055			−0.182765			−0.0913823	+	0.995816i	$0.529129\pi$
$54$	3.90709	+	6.68431i	0.531687	+	0.909619i
$55$	8.10346	+	4.67854i	1.09267	+	0.630854i
$56$	−1.40631	+	5.60745i	−0.187927	+	0.749327i
$57$	−2.66702	+	2.66702i	−0.353256	+	0.353256i
$58$	−0.0445911	−	8.32245i	−0.00585510	−	1.09279i
$59$	−6.48147	−	1.73670i	−0.843816	−	0.226100i	−0.189084	−	0.981961i	$-0.560552\pi$
$59$	−6.48147	−	1.73670i	−0.843816	−	0.226100i	−0.654732	+	0.755861i	$0.727218\pi$
$60$	−1.73588	+	6.76765i	−0.224101	+	0.873699i
$61$	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	$0.818716\pi$
$62$	0.813257	+	0.213248i	0.103284	+	0.0270825i
$63$	−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	$-0.725759\pi$
$67$	−6.84166	+	1.83322i	−0.835842	+	0.223963i	−0.184581	+	0.982817i	$0.559093\pi$
$68$	−0.102613	−	9.57548i	−0.0124436	−	1.16120i
$69$	−6.88277	+	3.97377i	−0.828588	+	0.478386i
$70$	3.09406	−	5.42600i	0.369811	−	0.648531i
$71$	0.454168	−	1.69498i	0.0538999	−	0.201157i	−0.933725	−	0.357991i	$-0.883462\pi$
$71$	0.454168	−	1.69498i	0.0538999	−	0.201157i	0.987625	+	0.156834i	$0.0501286\pi$
$72$	0.937842	−	0.561753i	0.110526	−	0.0662032i
$73$	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	$0.603792\pi$
$74$	1.92147	−	1.94217i	0.223367	−	0.225773i
$75$	−0.267186	+	0.462779i	−0.0308519	+	0.0534371i
$76$	3.33465	+	3.26394i	0.382511	+	0.374400i
$77$		−	8.85061i		−	1.00862i
$78$	6.71373	+	4.78295i	0.760180	+	0.541562i
$79$			1.11723i			0.125698i	0.998023	+	0.0628489i	$0.0200186\pi$
$79$			1.11723i			0.125698i	−0.998023	+	0.0628489i	$0.979981\pi$
$80$	8.39507	+	2.05769i	0.938597	+	0.230056i
$81$	3.84554	−	6.66067i	0.427282	−	0.740075i
$82$	−1.56121	−	1.54457i	−0.172407	−	0.170569i
$83$	2.45738	+	2.45738i	0.269733	+	0.269733i	0.828992	−	0.559260i	$-0.188915\pi$
$83$	2.45738	+	2.45738i	0.269733	+	0.269733i	−0.559260	+	0.828992i	$0.688915\pi$
$84$	6.36468	−	1.77872i	0.694444	−	0.194075i
$85$	−2.67784	+	9.99383i	−0.290453	+	1.08398i
$86$	−13.7466	−	7.83871i	−1.48234	−	0.845270i
$87$	−8.23917	+	4.75689i	−0.883332	+	0.509992i
$88$	11.7778	−	3.35966i	1.25552	−	0.358141i
$89$	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
$94$	−4.09393	+	15.6129i	−0.422256	+	1.61035i
$95$	−2.52078	−	4.36612i	−0.258626	−	0.447954i
$96$	4.78302	+	7.79451i	0.488165	+	0.795524i
$97$	−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	$0.605556\pi$
$98$	3.99134	−	0.0213854i	0.403186	−	0.00216025i
$99$	−1.18345	+	1.18345i	−0.118942	+	0.118942i
$100$	0.576033	+	0.324393i	0.0576033	+	0.0324393i
$101$	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	$0.652885\pi$
$102$	−9.45061	+	5.52403i	−0.935750	+	0.546961i
$103$	−11.5743			−1.14045			−0.570225	−	0.821489i	$-0.693144\pi$
$103$	−11.5743			−1.14045			−0.570225	+	0.821489i	$0.693144\pi$
$104$	5.82784	−	8.36876i	0.571467	−	0.820625i
$105$	−7.14019			−0.696811
$106$	1.62452	−	0.949556i	0.157787	−	0.0922290i
$107$	6.97804	+	4.02877i	0.674593	+	0.389476i	0.797815	−	0.602903i	$-0.205989\pi$
$107$	6.97804	+	4.02877i	0.674593	+	0.389476i	−0.123222	+	0.992379i	$0.539323\pi$
$108$	−9.54063	−	5.37281i	−0.918048	−	0.516998i
$109$	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	$-0.0550472\pi$
$110$	−13.2327	+	0.0709000i	−1.26169	+	0.00676005i
$111$	−3.01667	−	0.808315i	−0.286330	−	0.0767218i
$112$	−2.28478	−	7.84998i	−0.215892	−	0.741754i
$113$	−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	$0.971494\pi$
$114$	1.35293	−	5.15962i	0.126713	−	0.483243i
$115$	−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
$120$	−2.71039	−	9.50170i	−0.247424	−	0.867383i
$121$	−6.71217	+	3.87527i	−0.610197	+	0.352298i
$122$	−0.880914	−	0.502322i	−0.0797542	−	0.0454781i
$123$	−0.649762	+	2.42494i	−0.0585871	+	0.218650i
$124$	−1.14512	+	0.320025i	−0.102835	+	0.0287391i
$125$	−8.14498	−	8.14498i	−0.728509	−	0.728509i
$126$	0.794219	+	0.785754i	0.0707547	+	0.0700005i
$127$	−0.775200	+	1.34269i	−0.0687879	+	0.119144i	−0.898368	−	0.439244i	$-0.855247\pi$
$127$	−0.775200	+	1.34269i	−0.0687879	+	0.119144i	0.829580	+	0.558388i	$0.188580\pi$
$128$	9.57896	−	6.02026i	0.846668	−	0.532121i
$129$			18.0895i			1.59269i
$130$	−8.49800	+	7.01354i	−0.745324	+	0.615128i
$131$		−	4.10898i		−	0.359003i	−0.983758	−	0.179502i	$-0.942552\pi$
$131$		−	4.10898i		−	0.359003i	0.983758	−	0.179502i	$-0.0574485\pi$
$132$	−10.0055	−	9.79329i	−0.870863	−	0.852396i
$133$	−2.38434	+	4.12979i	−0.206748	+	0.358099i
$134$	7.04495	−	7.12085i	0.608591	−	0.615148i
$135$	8.36529	+	8.36529i	0.719969	+	0.719969i
$136$	6.95891	+	11.6178i	0.596721	+	0.996222i
$137$	−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	$0.914596\pi$
$138$	5.56753	−	9.76368i	0.473939	−	0.831140i
$139$	7.30191	−	4.21576i	0.619340	−	0.357576i	−0.157272	−	0.987555i	$-0.550270\pi$
$139$	7.30191	−	4.21576i	0.619340	−	0.357576i	0.776612	+	0.629979i	$0.216937\pi$
$140$	0.0946552	+	8.83292i	0.00799982	+	0.746518i
$141$	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
$146$	−10.3636	−	2.71748i	−0.857695	−	0.224900i
$147$	−2.28134	−	3.95140i	−0.188162	−	0.325906i
$148$	−0.959952	+	3.74255i	−0.0789075	+	0.307636i
$149$	−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	$0.601762\pi$
$150$	−0.00404902	−	0.755704i	−0.000330601	−	0.0617030i
$151$	6.88689	−	6.88689i	0.560447	−	0.560447i	−0.368987	−	0.929435i	$-0.620295\pi$
$151$	6.88689	−	6.88689i	0.560447	−	0.560447i	0.929435	+	0.368987i	$0.120295\pi$
$152$	−6.40075	−	1.60527i	−0.519169	−	0.130205i
$153$	−1.60268	−	0.925305i	−0.129569	−	0.0748065i
$154$	6.31631	+	10.8061i	0.508983	+	0.870777i
$155$	1.28465			0.103186
$156$	−11.6104	−	1.04838i	−0.929580	−	0.0839373i
$157$	14.0877			1.12432			0.562162	−	0.827027i	$-0.309970\pi$
$157$	14.0877			1.12432			0.562162	+	0.827027i	$0.309970\pi$
$158$	−0.797318	−	1.36406i	−0.0634312	−	0.108519i
$159$	−1.86282	−	1.07550i	−0.147731	−	0.0852927i
$160$	−11.7184	+	3.47890i	−0.926417	+	0.275031i
$161$	−7.10515	+	7.10515i	−0.559965	+	0.559965i
$162$	0.0582765	+	10.8767i	0.00457864	+	0.854553i
$163$	19.7316	+	5.28707i	1.54550	+	0.414115i	0.928038	−	0.372486i	$-0.121495\pi$
$163$	19.7316	+	5.28707i	1.54550	+	0.414115i	0.617461	+	0.786601i	$0.288161\pi$
$164$	3.00844	+	0.771655i	0.234920	+	0.0602561i
$165$	7.56346	+	13.1003i	0.588815	+	1.01986i
$166$	−4.75404	−	1.24658i	−0.368985	−	0.0967534i
$167$	3.17054	+	11.8326i	0.245344	+	0.915635i	0.973210	+	0.229917i	$0.0738453\pi$
$167$	3.17054	+	11.8326i	0.245344	+	0.915635i	−0.727867	+	0.685719i	$0.759488\pi$
$168$	−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
$172$	22.3779	−	0.239806i	1.70630	−	0.0182850i
$173$	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	$0.250559\pi$
$174$	6.66473	−	11.6878i	0.505252	−	0.886051i
$175$	−0.174862	+	0.652593i	−0.0132183	+	0.0493314i
$176$	−11.9823	+	12.5073i	−0.903204	+	0.942772i
$177$	−7.67053	−	7.67053i	−0.576552	−	0.576552i
$178$	−1.93754	+	1.95841i	−0.145225	+	0.146789i
$179$	−3.83994	+	6.65097i	−0.287011	+	0.497117i	−0.973095	−	0.230405i	$-0.925995\pi$
$179$	−3.83994	+	6.65097i	−0.287011	+	0.497117i	0.686084	+	0.727522i	$0.259328\pi$
$180$	1.16843	−	1.19375i	0.0870898	−	0.0889766i
$181$		−	10.6994i		−	0.795283i	−0.917541	−	0.397642i	$-0.869829\pi$
$181$		−	10.6994i		−	0.795283i	0.917541	−	0.397642i	$-0.130171\pi$
$182$	9.76417	+	3.64418i	0.723768	+	0.270125i
$183$			1.15921i			0.0856915i
$184$	−12.1522	−	6.75799i	−0.895870	−	0.498206i
$185$	2.08726	−	3.61524i	0.153458	−	0.265798i
$186$	0.966223	+	0.955924i	0.0708469	+	0.0700918i
$187$	−14.6605	−	14.6605i	−1.07208	−	1.07208i
$188$	−6.14383	−	21.9840i	−0.448085	−	1.60335i
$189$	2.89618	−	10.8087i	0.210666	−	0.786216i
$190$	6.19363	+	3.53178i	0.449333	+	0.256223i
$191$	12.5176	−	7.22707i	0.905745	−	0.522932i	0.0266854	−	0.999644i	$-0.491505\pi$
$191$	12.5176	−	7.22707i	0.905745	−	0.522932i	0.879060	+	0.476712i	$0.158171\pi$
$192$	−11.4024	−	6.10318i	−0.822897	−	0.440459i
$193$	−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	$0.886489\pi$
$198$	0.600343	−	2.28951i	0.0426645	−	0.162708i
$199$	−8.28694	−	14.3534i	−0.587445	−	1.01749i	−0.994566	−	0.104111i	$-0.966800\pi$
$199$	−8.28694	−	14.3534i	−0.587445	−	1.01749i	0.407120	−	0.913374i	$-0.366533\pi$
$200$	−0.934806	+	0.0150270i	−0.0661008	+	0.00106257i
$201$	−11.0604	−	2.96363i	−0.780142	−	0.209039i
$202$	−1.23027	+	0.00659173i	−0.0865618	+	0.000463793i
$203$	−8.50538	+	8.50538i	−0.596960	+	0.596960i
$204$	7.59634	−	13.4890i	0.531850	−	0.944420i
$205$	−2.90610	−	1.67784i	−0.202971	−	0.117185i
$206$	14.1315	−	8.26010i	0.984589	−	0.575509i
$207$	1.90012			0.132068
$208$	−1.14300	+	14.3768i	−0.0792528	+	0.996855i
$209$	10.1027			0.698820
$210$	8.71773	−	5.09566i	0.601581	−	0.351634i
$211$	−23.9352	−	13.8190i	−1.64777	−	0.951341i	−0.977956	−	0.208812i	$-0.933040\pi$
$211$	−23.9352	−	13.8190i	−1.64777	−	0.951341i	−0.669815	−	0.742528i	$-0.733627\pi$
$212$	−1.30578	+	2.31870i	−0.0896810	+	0.159249i
$213$	2.00593	−	2.00593i	0.137444	−	0.137444i
$214$	−11.3949	+	0.0610533i	−0.778942	+	0.00417352i
$215$	−23.3556	−	6.25813i	−1.59284	−	0.426801i
$216$	15.4829	−	0.248888i	1.05348	−	0.0169347i
$217$	−0.607559	−	1.05232i	−0.0412438	−	0.0714364i
$218$	−6.12850	+	23.3721i	−0.415074	+	1.58296i
$219$	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	$-0.615782\pi$
$223$	−2.93579	+	0.786643i	−0.196595	+	0.0526775i	0.159178	+	0.987250i	$0.449116\pi$
$224$	8.39179	+	7.95379i	0.560700	+	0.531435i
$225$	0.110643	−	0.0638796i	0.00737618	−	0.00425864i
$226$	10.9840	+	6.26341i	0.730648	+	0.416636i
$227$	2.44919	−	9.14049i	0.162558	−	0.606675i	−0.835781	−	0.549063i	$-0.814985\pi$
$227$	2.44919	−	9.14049i	0.162558	−	0.606675i	0.998339	−	0.0576122i	$-0.0183487\pi$
$228$	2.03036	+	7.26511i	0.134464	+	0.481144i
$229$	−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	$0.802216\pi$
$230$	10.6800	+	10.5661i	0.704216	+	0.696710i
$231$	7.15408	−	12.3912i	0.470704	−	0.815283i
$232$	−14.5470	−	8.08980i	−0.955058	−	0.531121i
$233$			21.3205i			1.39675i	0.715731	+	0.698376i	$0.246094\pi$
$233$			21.3205i			1.39675i	−0.715731	+	0.698376i	$0.753906\pi$
$234$	−0.818331	−	1.79289i	−0.0534960	−	0.117205i
$235$			24.6627i			1.60882i
$236$	−9.38730	+	9.59067i	−0.611061	+	0.624300i
$237$	−0.903070	+	1.56416i	−0.0586607	+	0.101603i
$238$	−9.73379	+	9.83866i	−0.630948	+	0.637746i
$239$	5.96711	+	5.96711i	0.385981	+	0.385981i	0.873251	−	0.487271i	$-0.162007\pi$
$239$	5.96711	+	5.96711i	0.385981	+	0.385981i	−0.487271	+	0.873251i	$0.662007\pi$
$240$	10.0902	+	9.66671i	0.651319	+	0.623983i
$241$	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	$-0.149519\pi$
$242$	5.42953	−	9.52167i	0.349023	−	0.612076i
$243$	−3.45593	+	1.99528i	−0.221698	+	0.127997i
$244$	1.43403	−	0.0153673i	0.0918043	−	0.000983791i
$245$	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
$250$	15.7572	+	4.13178i	0.996576	+	0.261317i
$251$	2.95746	+	5.12248i	0.186673	+	0.323328i	0.944139	−	0.329547i	$-0.106896\pi$
$251$	2.95746	+	5.12248i	0.186673	+	0.323328i	−0.757466	+	0.652875i	$0.773563\pi$
$252$	−1.53045	−	0.392556i	−0.0964095	−	0.0247287i
$253$	20.5624	+	5.50967i	1.29274	+	0.346390i
$254$	−0.0117476	−	2.19257i	−0.000737112	−	0.137574i
$255$	−11.8273	+	11.8273i	−0.740651	+	0.740651i
$256$	−7.39891	+	14.1865i	−0.462432	+	0.886655i
$257$	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	$0.322986\pi$
$258$	−12.9097	−	22.0861i	−0.803723	−	1.37502i
$259$	−3.94857			−0.245352
$260$	5.37026	−	14.6278i	0.333050	−	0.907176i
$261$	2.27458			0.140793
$262$	2.93241	+	5.01681i	0.181165	+	0.309940i
$263$	−11.6002	−	6.69738i	−0.715299	−	0.412978i	0.0977210	−	0.995214i	$-0.468845\pi$
$263$	−11.6002	−	6.69738i	−0.715299	−	0.412978i	−0.813020	+	0.582236i	$0.802178\pi$
$264$	19.2051	+	4.81652i	1.18199	+	0.296437i
$265$	2.03305	−	2.03305i	0.124889	−	0.124889i
$266$	−0.0361330	−	6.74383i	−0.00221546	−	0.413491i
$267$	3.04189	+	0.815072i	0.186161	+	0.0498816i
$268$	−3.51960	+	13.7218i	−0.214994	+	0.838193i
$269$	−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	$-0.413065\pi$
$270$	−16.1835	−	4.24354i	−0.984894	−	0.258254i
$271$	2.48442	+	9.27197i	0.150918	+	0.563232i	0.999420	+	0.0340411i	$0.0108377\pi$
$271$	2.48442	+	9.27197i	0.150918	+	0.563232i	−0.848503	+	0.529191i	$0.822496\pi$
$272$	−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
$276$	0.170325	+	15.8942i	0.0102523	+	0.956717i
$277$	−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	$0.343855\pi$
$278$	−5.90657	+	10.3582i	−0.354252	+	0.621247i
$279$	−0.0594714	+	0.221950i	−0.00356046	+	0.0132878i
$280$	−6.41926	−	10.7169i	−0.383624	−	0.640457i
$281$	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	$0.658143\pi$
$282$	−18.3518	+	18.5495i	−1.09283	+	1.10461i
$283$	10.5772	−	18.3202i	0.628746	−	1.08902i	−0.359057	−	0.933316i	$-0.616902\pi$
$283$	10.5772	−	18.3202i	0.628746	−	1.08902i	0.987804	−	0.155705i	$-0.0497650\pi$
$284$	−2.50807	−	2.45489i	−0.148827	−	0.145671i
$285$		−	8.15033i		−	0.482784i
$286$	−3.65691	−	21.7748i	−0.216238	−	1.28757i
$287$			3.17405i			0.187358i
$288$	−0.0585661	−	2.18564i	−0.00345104	−	0.128790i
$289$	2.96254	−	5.13126i	0.174267	−	0.301839i
$290$	12.7847	+	12.6484i	0.750742	+	0.742740i
$291$	−1.57072	−	1.57072i	−0.0920770	−	0.0920770i
$292$	14.5926	−	4.07817i	0.853969	−	0.238657i
$293$	−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	$0.905871\pi$
$294$	5.60533	+	3.19632i	0.326910	+	0.186413i
$295$	12.5572	−	7.24991i	0.731109	−	0.422106i
$296$	−1.49886	−	5.25450i	−0.0871196	−	0.305412i
$297$	−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
$302$	−3.49358	+	13.3234i	−0.201033	+	0.766674i
$303$	0.703192	+	1.21796i	0.0403973	+	0.0699702i
$304$	8.96054	−	2.60802i	0.513922	−	0.149580i
$305$	−1.49668	−	0.401035i	−0.0856998	−	0.0229632i
$306$	2.61712	−	0.0140224i	0.149611	−	0.000801605i
$307$	−7.26086	+	7.26086i	−0.414399	+	0.414399i	−0.883268	−	0.468869i	$-0.844662\pi$
$307$	−7.26086	+	7.26086i	−0.414399	+	0.414399i	0.468869	+	0.883268i	$0.344662\pi$
$308$	−15.4237	−	8.68584i	−0.878845	−	0.494921i
$309$	−16.2045	−	9.35568i	−0.921843	−	0.532226i
$310$	−1.56848	+	0.916803i	−0.0890837	+	0.0520709i
$311$	9.77167			0.554101			0.277050	−	0.960855i	$-0.410643\pi$
$311$	9.77167			0.554101			0.277050	+	0.960855i	$0.410643\pi$
$312$	14.9238	−	7.00589i	0.844895	−	0.396630i
$313$	−31.6333			−1.78802			−0.894010	−	0.448047i	$-0.852120\pi$
$313$	−31.6333			−1.78802			−0.894010	+	0.448047i	$0.852120\pi$
$314$	−17.2003	+	10.0538i	−0.970667	+	0.567370i
$315$	1.47839	+	0.853550i	0.0832980	+	0.0480921i
$316$	1.94695	+	1.09643i	0.109525	+	0.0616788i
$317$	−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	$0.449707\pi$
$318$	3.04193	−	0.0162985i	0.170583	−	0.000913973i
$319$	24.6146	+	6.59547i	1.37815	+	0.369275i
$320$	11.8246	−	12.6104i	0.661017	−	0.704944i
$321$	6.51304	+	11.2809i	0.363522	+	0.629639i
$322$	3.60430	−	13.7456i	0.200860	−	0.766013i
$323$	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
$328$	−4.22382	+	1.20486i	−0.233221	+	0.0665271i
$329$	20.2025	−	11.6639i	1.11380	−	0.643051i
$330$	−18.5837	−	10.5969i	−1.02300	−	0.583342i
$331$	−3.14630	+	11.7421i	−0.172936	+	0.645407i	0.823958	+	0.566651i	$0.191761\pi$
$331$	−3.14630	+	11.7421i	−0.172936	+	0.645407i	−0.996894	+	0.0787555i	$0.974905\pi$
$332$	6.69403	−	1.87077i	0.367382	−	0.102672i
$333$	0.527981	+	0.527981i	0.0289332	+	0.0289332i
$334$	−12.3155	−	12.1842i	−0.673873	−	0.666691i
$335$	7.65280	−	13.2550i	0.418117	−	0.724201i
$336$	3.14647	−	12.8371i	0.171654	−	0.700323i
$337$		−	18.7726i		−	1.02261i	−0.859401	−	0.511303i	$-0.829163\pi$
$337$		−	18.7726i		−	1.02261i	0.859401	−	0.511303i	$-0.170837\pi$
$338$	−13.8245	−	12.1195i	−0.751953	−	0.659216i
$339$		−	14.4541i		−	0.785041i
$340$	14.7879	+	14.4744i	0.801989	+	0.784982i
$341$	−1.28715	+	2.22941i	−0.0697031	+	0.120729i
$342$	−0.896916	+	0.906579i	−0.0484997	+	0.0490222i
$343$	−14.1960	−	14.1960i	−0.766513	−	0.766513i
$344$	−27.1510	+	16.2630i	−1.46388	+	0.876842i
$345$	4.44490	−	16.5886i	0.239305	−	0.893100i
$346$	−4.73829	+	8.30946i	−0.254732	+	0.446719i
$347$	−6.91748	+	3.99381i	−0.371350	+	0.214399i	−0.674048	−	0.738688i	$-0.735446\pi$
$347$	−6.91748	+	3.99381i	−0.371350	+	0.214399i	0.302698	+	0.953086i	$0.402113\pi$
$348$	0.203891	+	19.0265i	0.0109297	+	1.01992i
$349$	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	$0.956817\pi$
$354$	14.8394	+	3.89111i	0.788704	+	0.206810i
$355$	1.89594	+	3.28386i	0.100626	+	0.174289i
$356$	0.967977	−	3.77384i	0.0513027	−	0.200013i
$357$	15.2818	+	4.09476i	0.808801	+	0.216718i
$358$	−0.0581916	−	10.8608i	−0.00307552	−	0.574013i
$359$	−25.8704	+	25.8704i	−1.36539	+	1.36539i	−0.498492	+	0.866894i	$0.666113\pi$
$359$	−25.8704	+	25.8704i	−1.36539	+	1.36539i	−0.866894	+	0.498492i	$0.833887\pi$
$360$	−0.574657	+	2.29135i	−0.0302871	+	0.120765i
$361$	11.7404	+	6.77834i	0.617918	+	0.356755i
$362$	7.63575	+	13.0634i	0.401326	+	0.686595i
$363$	−12.5298			−0.657642
$364$	−14.5222	+	2.51896i	−0.761168	+	0.132029i
$365$	−16.3707			−0.856880
$366$	−0.827283	−	1.41533i	−0.0432428	−	0.0739804i
$367$	−17.6675	−	10.2004i	−0.922238	−	0.532454i	−0.0378895	−	0.999282i	$-0.512063\pi$
$367$	−17.6675	−	10.2004i	−0.922238	−	0.532454i	−0.884348	+	0.466828i	$0.845397\pi$
$368$	19.6600	−	0.421408i	1.02485	−	0.0219674i
$369$	0.424416	−	0.424416i	0.0220942	−	0.0220942i
$370$	0.0316310	+	5.90358i	0.00164442	+	0.306913i
$371$	−2.62688	−	0.703870i	−0.136381	−	0.0365431i
$372$	−1.86190	−	0.477572i	−0.0965352	−	0.0247609i
$373$	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	$0.653844\pi$
$374$	28.3621	+	7.43695i	1.46657	+	0.384556i
$375$	−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	$-0.464612\pi$
$379$	13.7043	−	3.67206i	0.703943	−	0.188621i	0.592996	+	0.805205i	$0.297945\pi$
$380$	−10.0825	+	0.108046i	−0.517223	+	0.00554266i
$381$	−2.17063	+	1.25321i	−0.111205	+	0.0642040i
$382$	−10.1256	+	17.7571i	−0.518072	+	0.908534i
$383$	4.01265	−	14.9754i	0.205037	−	0.765207i	−0.784402	−	0.620253i	$-0.787030\pi$
$383$	4.01265	−	14.9754i	0.205037	−	0.765207i	0.989438	−	0.144954i	$-0.0463035\pi$
$384$	18.2772	−	0.685812i	0.932705	−	0.0349977i
$385$	13.5236	+	13.5236i	0.689225	+	0.689225i
$386$	19.4679	−	19.6777i	0.990892	−	1.00157i
$387$	2.16244	−	3.74546i	0.109923	−	0.190393i
$388$	−1.92226	+	1.96391i	−0.0975882	+	0.0997024i
$389$		−	33.5493i		−	1.70102i	−0.525963	−	0.850508i	$-0.676295\pi$
$389$		−	33.5493i		−	1.70102i	0.525963	−	0.850508i	$-0.323705\pi$
$390$	−17.5667	+	2.95020i	−0.889525	+	0.149389i
$391$			23.5384i			1.19039i
$392$	3.87977	−	6.97657i	0.195958	−	0.352370i
$393$	3.32135	−	5.75274i	0.167540	−	0.290187i
$394$	−2.67152	−	2.64305i	−0.134589	−	0.133155i
$395$	−1.70710	−	1.70710i	−0.0858935	−	0.0858935i
$396$	0.900946	+	3.22379i	0.0452742	+	0.162002i
$397$	−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	$0.982148\pi$
$398$	20.3613	+	11.6106i	1.02062	+	0.581985i
$399$	−6.67635	+	3.85459i	−0.334235	+	0.192971i
$400$	1.13062	−	0.685480i	0.0565308	−	0.0342740i
$401$	−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
$406$	4.31461	−	16.4545i	0.214130	−	0.816622i
$407$	4.18264	+	7.24455i	0.207326	+	0.359099i
$408$	0.351890	+	21.8905i	0.0174211	+	1.08374i
$409$	−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	$0.742528\pi$
$410$	4.74558	−	0.0254265i	0.234367	−	0.00125573i
$411$	−13.5304	+	13.5304i	−0.667407	+	0.667407i
$412$	−11.3588	+	20.1702i	−0.559609	+	0.993712i
$413$	−11.8775	−	6.85750i	−0.584456	−	0.337436i
$414$	−2.31994	+	1.35604i	−0.114019	+	0.0666457i
$415$	−7.50966			−0.368635
$416$	−8.86462	−	18.3690i	−0.434624	−	0.900612i
$417$	13.6306			0.667495
$418$	−12.3348	+	7.20990i	−0.603315	+	0.352648i
$419$	−2.54287	−	1.46812i	−0.124227	−	0.0717226i	0.436599	−	0.899656i	$-0.356183\pi$
$419$	−2.54287	−	1.46812i	−0.124227	−	0.0717226i	−0.560826	+	0.827934i	$0.689516\pi$
$420$	−7.00726	+	12.4430i	−0.341919	+	0.607155i
$421$	−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	$0.300002\pi$
$422$	39.0855	−	0.209418i	1.90265	−	0.0101943i
$423$	−4.26099	−	1.14173i	−0.207177	−	0.0555128i
$424$	−0.0604883	−	3.76287i	−0.00293757	−	0.182741i
$425$	0.791331	+	1.37063i	0.0383852	+	0.0664851i
$426$	−1.01757	+	3.88067i	−0.0493014	+	0.188019i
$427$	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	$-0.734328\pi$
$431$	−18.3194	+	4.90868i	−0.882417	+	0.236443i	−0.210967	+	0.977493i	$0.567661\pi$
$432$	−18.7260	+	11.3534i	−0.900956	+	0.546239i
$433$	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	$0.295212\pi$
$434$	1.49279	+	0.851233i	0.0716563	+	0.0408605i
$435$	5.32086	−	19.8577i	0.255116	−	0.952105i
$436$	−9.19715	−	32.9095i	−0.440463	−	1.57608i
$437$	−8.11034	−	8.11034i	−0.387970	−	0.387970i
$438$	−12.3128	−	12.1816i	−0.588331	−	0.582060i
$439$	−19.5845	+	33.9214i	−0.934717	+	1.61898i	−0.159580	+	0.987185i	$0.551014\pi$
$439$	−19.5845	+	33.9214i	−0.934717	+	1.61898i	−0.775137	+	0.631793i	$0.782319\pi$
$440$	−12.8628	+	23.1298i	−0.613210	+	1.10267i
$441$			1.09086i			0.0519458i
$442$	22.2100	−	10.1374i	1.05642	−	0.482185i
$443$		−	38.1735i		−	1.81368i	−0.421477	−	0.906839i	$-0.638488\pi$
$443$		−	38.1735i		−	1.81368i	0.421477	−	0.906839i	$-0.361512\pi$
$444$	−4.36913	+	4.46379i	−0.207350	+	0.211842i
$445$	−2.10471	+	3.64547i	−0.0997729	+	0.172812i
$446$	3.02303	−	3.05559i	0.143144	−	0.144687i
$447$	−1.61478	−	1.61478i	−0.0763763	−	0.0763763i
$448$	−15.9222	−	3.72222i	−0.752251	−	0.175859i
$449$	−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	$0.106947\pi$
$450$	−0.0894998	+	0.156954i	−0.00421906	+	0.00739890i
$451$	5.82351	−	3.36221i	0.274219	−	0.158320i
$452$	−17.8808	+	0.191614i	−0.841041	+	0.00901275i
$453$	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	$-0.375881\pi$
$458$	6.76128	+	1.77291i	0.315934	+	0.0828426i
$459$	−13.1065	−	22.7012i	−0.611761	−	1.05960i
$460$	−20.5802	−	5.27875i	−0.959556	−	0.246123i
$461$	−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	$0.769792\pi$
$462$	0.108415	+	20.2345i	0.00504393	+	0.941394i
$463$	24.4048	−	24.4048i	1.13419	−	1.13419i	0.144713	−	0.989474i	$-0.453774\pi$
$463$	24.4048	−	24.4048i	1.13419	−	1.13419i	0.989474	−	0.144713i	$-0.0462258\pi$
$464$	23.5344	−	0.504455i	1.09256	−	0.0234187i
$465$	1.79857	+	1.03840i	0.0834065	+	0.0481548i
$466$	−15.2156	−	26.0310i	−0.704847	−	1.20586i
$467$	17.7779			0.822661			0.411331	−	0.911486i	$-0.365064\pi$
$467$	17.7779			0.822661			0.411331	+	0.911486i	$0.365064\pi$
$468$	2.27864	+	1.60500i	0.105330	+	0.0741912i
$469$	−14.4772			−0.668494
$470$	−17.6007	−	30.1116i	−0.811861	−	1.38895i
$471$	19.7234	+	11.3873i	0.908807	+	0.524700i
$472$	4.61685	−	18.4090i	0.212508	−	0.847341i
$473$	34.2615	−	34.2615i	1.57535	−	1.57535i
$474$	−0.0136854	−	2.55423i	−0.000628592	−	0.117320i
$475$	−0.744917	−	0.199600i	−0.0341791	−	0.00915828i
$476$	4.86292	−	18.9590i	0.222892	−	0.868985i
$477$	0.257134	+	0.445369i	0.0117734	+	0.0203921i
$478$	−11.5440	−	3.02700i	−0.528009	−	0.138452i
$479$	−2.05936	−	7.68562i	−0.0940943	−	0.351165i	0.902786	−	0.430090i	$-0.141518\pi$
$479$	−2.05936	−	7.68562i	−0.0940943	−	0.351165i	−0.996881	+	0.0789246i	$0.974851\pi$
$480$	−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
$484$	0.166103	+	15.5002i	0.00755014	+	0.704555i
$485$	2.57138	−	1.48459i	0.116760	−	0.0674115i
$486$	2.79552	−	4.90247i	0.126808	−	0.222380i
$487$	−5.88223	+	21.9528i	−0.266549	+	0.994775i	0.694746	+	0.719255i	$0.255517\pi$
$487$	−5.88223	+	21.9528i	−0.266549	+	0.994775i	−0.961295	+	0.275520i	$0.911150\pi$
$488$	−1.73989	+	1.04217i	−0.0787613	+	0.0471768i
$489$	23.3515	+	23.3515i	1.05599	+	1.05599i
$490$	−6.06602	+	6.13137i	−0.274035	+	0.276987i
$491$	0.0296046	−	0.0512767i	0.00133604	−	0.00231409i	−0.865357	−	0.501157i	$-0.832908\pi$
$491$	0.0296046	−	0.0512767i	0.00133604	−	0.00231409i	0.866693	+	0.498843i	$0.166241\pi$
$492$	3.58821	+	3.51212i	0.161769	+	0.158338i
$493$			28.1772i			1.26904i
$494$	−4.15973	+	11.1455i	−0.187155	+	0.501461i
$495$		−	3.61659i		−	0.162554i
$496$	−0.566107	+	2.30964i	−0.0254190	+	0.103706i
$497$	1.79332	−	3.10611i	0.0804412	−	0.139328i
$498$	−5.64823	−	5.58803i	−0.253103	−	0.250405i
$499$	25.7335	+	25.7335i	1.15199	+	1.15199i	0.986153	+	0.165836i	$0.0530323\pi$
$499$	25.7335	+	25.7335i	1.15199	+	1.15199i	0.165836	+	0.986153i	$0.446968\pi$
$500$	−22.1873	+	6.20064i	−0.992247	+	0.277301i
$501$	−5.12559	+	19.1290i	−0.228994	+	0.854619i
$502$	−7.26658	−	4.14361i	−0.324323	−	0.184938i
$503$	14.6397	−	8.45225i	0.652753	−	0.376867i	−0.136757	−	0.990605i	$-0.543668\pi$
$503$	14.6397	−	8.45225i	0.652753	−	0.376867i	0.789510	+	0.613738i	$0.210335\pi$
$504$	2.14874	−	0.612934i	0.0957125	−	0.0273023i
$505$	−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	$0.769356\pi$
$510$	5.99973	−	22.8810i	0.265672	−	1.01319i
$511$	7.74230	+	13.4101i	0.342499	+	0.593226i
$512$	−1.09069	−	22.6011i	−0.0482023	−	0.998838i
$513$	12.3378	+	3.30591i	0.544728	+	0.145959i
$514$	−39.9839	+	0.214231i	−1.76361	+	0.00944933i
$515$	17.6853	−	17.6853i	0.779308	−	0.779308i
$516$	31.5239	+	17.7527i	1.38776	+	0.781518i
$517$	−42.8001	−	24.7107i	−1.88235	−	1.08677i
$518$	4.82096	−	2.81793i	0.211821	−	0.123813i
$519$	10.9346			0.479975
$520$	3.88248	+	21.6922i	0.170258	+	0.951264i
$521$	4.77166			0.209050			0.104525	−	0.994522i	$-0.466668\pi$
$521$	4.77166			0.209050			0.104525	+	0.994522i	$0.466668\pi$
$522$	−2.77713	+	1.62328i	−0.121552	+	0.0710489i
$523$	14.6805	+	8.47577i	0.641932	+	0.370620i	0.785358	−	0.619041i	$-0.212479\pi$
$523$	14.6805	+	8.47577i	0.641932	+	0.370620i	−0.143426	+	0.989661i	$0.545812\pi$
$524$	−7.16058	−	4.03248i	−0.312811	−	0.176160i
$525$	−0.772315	+	0.772315i	−0.0337066	+	0.0337066i
$526$	18.9428	−	0.101494i	0.825944	−	0.00442536i
$527$	−2.74949	−	0.736723i	−0.119769	−	0.0320921i
$528$	−26.8856	+	7.82521i	−1.17005	+	0.340549i
$529$	−0.584106	−	1.01170i	−0.0253959	−	0.0439870i
$530$	−1.03133	+	3.93313i	−0.0447979	+	0.170844i
$531$	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
$536$	−5.49548	−	19.2653i	−0.237369	−	0.832134i
$537$	−10.7522	+	6.20776i	−0.463990	+	0.267885i
$538$	28.1709	+	16.0639i	1.21454	+	0.692562i
$539$	−3.16310	+	11.8049i	−0.136245	+	0.508471i
$540$	22.7875	−	6.36836i	0.980616	−	0.274051i
$541$	−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	$0.799320\pi$
$542$	−9.65034	−	9.54748i	−0.414517	−	0.410099i
$543$	8.64852	−	14.9797i	0.371143	−	0.642839i
$544$	27.0754	−	0.725507i	1.16085	−	0.0311059i
$545$			36.9194i			1.58145i
$546$	10.7246	+	12.9945i	0.458971	+	0.556114i
$547$			32.0440i			1.37010i	0.728494	+	0.685052i	$0.240221\pi$
$547$			32.0440i			1.37010i	−0.728494	+	0.685052i	$0.759779\pi$
$548$	16.9175	+	16.5587i	0.722678	+	0.707354i
$549$	0.138574	−	0.240018i	0.00591421	−	0.0102437i
$550$	−1.42364	+	1.43898i	−0.0607042	+	0.0613582i
$551$	−9.70865	−	9.70865i	−0.413602	−	0.413602i
$552$	−11.5510	−	19.2843i	−0.491642	−	0.820792i
$553$	−0.591022	+	2.20572i	−0.0251328	+	0.0937969i
$554$	0.770631	−	1.35144i	0.0327410	−	0.0574173i
$555$	5.84451	−	3.37433i	0.248086	−	0.143232i
$556$	−0.180697	−	16.8621i	−0.00766325	−	0.715111i
$557$	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
$562$	−13.0520	−	3.42242i	−0.550564	−	0.144366i
$563$	2.79472	+	4.84060i	0.117783	+	0.204007i	0.918889	−	0.394516i	$-0.129088\pi$
$563$	2.79472	+	4.84060i	0.117783	+	0.204007i	−0.801106	+	0.598523i	$0.795754\pi$
$564$	9.16840	−	35.7447i	0.386059	−	1.50512i
$565$	18.6620	+	5.00047i	0.785116	+	0.210371i
$566$	0.160289	+	29.9163i	0.00673747	+	1.25747i
$567$	11.1157	−	11.1157i	0.466818	−	0.466818i
$568$	4.81415	+	1.20736i	0.201997	+	0.0506597i
$569$	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	$0.440972\pi$
$570$	5.81655	+	9.95105i	0.243629	+	0.416804i
$571$	−9.21948			−0.385823			−0.192912	−	0.981216i	$-0.561793\pi$
$571$	−9.21948			−0.385823			−0.192912	+	0.981216i	$0.561793\pi$
$572$	20.0046	+	23.9759i	0.836436	+	1.00248i
$573$	23.3670			0.976169
$574$	−2.26519	−	3.87532i	−0.0945471	−	0.161753i
$575$	−1.40730	−	0.812503i	−0.0586883	−	0.0338837i
$576$	1.63131	+	2.62674i	0.0679711	+	0.109447i
$577$	−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	$0.929706\pi$
$578$	0.0448952	+	8.37920i	0.00186739	+	0.348529i
$579$	−30.5642	−	8.18966i	−1.27021	−	0.340351i
$580$	−24.6360	−	6.31904i	−1.02295	−	0.262384i
$581$	3.55160	+	6.15155i	0.147345	+	0.255209i
$582$	3.03870	+	0.796793i	0.125958	+	0.0330281i
$583$	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	$-0.624796\pi$
$587$	−6.07956	+	1.62901i	−0.250930	+	0.0672365i	0.131161	+	0.991361i	$0.458129\pi$
$588$	−9.12485	+	0.0977835i	−0.376303	+	0.00403253i
$589$	1.20120	−	0.693512i	0.0494945	−	0.0285757i
$590$	−10.1576	+	17.8133i	−0.418183	+	0.733361i
$591$	−1.11186	+	4.14953i	−0.0457359	+	0.170689i
$592$	5.57994	+	5.34575i	0.229334	+	0.219709i
$593$	−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	$0.989008\pi$
$594$	23.5793	−	23.8333i	0.967469	−	0.977892i
$595$	−10.5736	+	18.3141i	−0.433477	+	0.750804i
$596$	−1.97619	+	2.01900i	−0.0809477	+	0.0827014i
$597$		−	26.7938i		−	1.09660i
$598$	−14.5448	+	20.4162i	−0.594781	+	0.834882i
$599$		−	23.9175i		−	0.977241i	−0.872496	−	0.488621i	$-0.837500\pi$
$599$		−	23.9175i		−	0.977241i	0.872496	−	0.488621i	$-0.162500\pi$
$600$	−1.32091	−	0.734579i	−0.0539261	−	0.0299891i
$601$	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	$-0.0301123\pi$
$602$	−22.9930	−	22.7479i	−0.937125	−	0.927136i
$603$	1.93581	+	1.93581i	0.0788322	+	0.0788322i
$604$	−5.24288	−	18.7602i	−0.213330	−	0.763343i
$605$	4.33473	−	16.1774i	0.176232	−	0.657706i
$606$	−1.72776	−	0.985221i	−0.0701856	−	0.0400218i
$607$	−30.3561	+	17.5261i	−1.23211	+	0.711362i	−0.967470	−	0.252984i	$-0.918588\pi$
$607$	−30.3561	+	17.5261i	−1.23211	+	0.711362i	−0.264645	+	0.964346i	$0.585255\pi$
$608$	−9.07903	+	9.57899i	−0.368203	+	0.388479i
$609$	−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	$0.975629\pi$
$614$	3.68329	−	14.0468i	0.148645	−	0.566884i
$615$	−2.71245	−	4.69809i	−0.109376	−	0.189445i
$616$	25.0301	−	0.402359i	1.00849	−	0.0162115i
$617$	−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	$0.632246\pi$
$618$	26.4615	−	0.141779i	1.06444	−	0.00570318i
$619$	25.6801	−	25.6801i	1.03217	−	1.03217i	0.0327040	−	0.999465i	$-0.489588\pi$
$619$	25.6801	−	25.6801i	1.03217	−	1.03217i	0.999465	−	0.0327040i	$-0.0104119\pi$
$620$	1.26073	−	2.23872i	0.0506323	−	0.0899092i
$621$	23.3086	+	13.4572i	0.935341	+	0.540019i
$622$	−11.9306	+	6.97364i	−0.478374	+	0.279617i
$623$	3.98158			0.159519
$624$	−13.2213	+	19.2043i	−0.529274	+	0.768786i
$625$	23.2380			0.929520
$626$	38.6223	−	22.5754i	1.54366	−	0.902294i
$627$	14.1442	+	8.16618i	0.564867	+	0.326126i
$628$	13.8255	−	24.5502i	0.551696	−	0.979661i
$629$	−6.54055	+	6.54055i	−0.260789	+	0.260789i
$630$	−2.41417	+	0.0129350i	−0.0961828	+	0.000515341i
$631$	20.8323	+	5.58201i	0.829322	+	0.222216i	0.648418	−	0.761285i	$-0.275431\pi$
$631$	20.8323	+	5.58201i	0.829322	+	0.222216i	0.180904	+	0.983501i	$0.442098\pi$
$632$	−3.15958	+	0.0507904i	−0.125681	+	0.00202033i
$633$	−22.3402	−	38.6944i	−0.887945	−	1.53797i
$634$	7.49826	−	28.5959i	0.297794	−	1.13569i
$635$	−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
$640$	−5.43762	+	23.8353i	−0.214941	+	0.942174i
$641$	−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	$0.929287\pi$
$642$	−16.0027	−	9.12521i	−0.631578	−	0.360143i
$643$	−0.0193750	+	0.0723085i	−0.000764075	+	0.00285157i	−0.966307	−	0.257393i	$-0.917137\pi$
$643$	−0.0193750	+	0.0723085i	−0.000764075	+	0.00285157i	0.965543	+	0.260245i	$0.0838032\pi$
$644$	5.40904	+	19.3548i	0.213146	+	0.762686i
$645$	−27.6403	−	27.6403i	−1.08834	−	1.08834i
$646$	−11.2306	−	11.1109i	−0.441860	−	0.437151i
$647$	1.86890	−	3.23703i	0.0734741	−	0.127261i	−0.826948	−	0.562279i	$-0.809925\pi$
$647$	1.86890	−	3.23703i	0.0734741	−	0.127261i	0.900422	+	0.435018i	$0.143258\pi$
$648$	19.0116	+	10.5726i	0.746847	+	0.415332i
$649$			29.0561i			1.14055i
$650$	−0.160566	+	1.67780i	−0.00629790	+	0.0658087i
$651$		−	1.96440i		−	0.0769908i
$652$	28.5779	−	29.1970i	1.11920	−	1.14344i
$653$	−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	$0.875981\pi$
$654$	−27.4721	+	27.7681i	−1.07425	+	1.08582i
$655$	6.27844	+	6.27844i	0.245319	+	0.245319i
$656$	4.29717	−	4.48542i	0.167776	−	0.175126i
$657$	0.757861	−	2.82838i	0.0295670	−	0.110345i
$658$	−16.3419	+	28.6586i	−0.637074	+	1.11723i
$659$	−33.6653	+	19.4367i	−1.31141	+	0.757145i	−0.982330	−	0.187155i	$-0.940073\pi$
$659$	−33.6653	+	19.4367i	−1.31141	+	0.757145i	−0.329084	+	0.944301i	$0.606740\pi$
$660$	30.2521	−	0.324187i	1.17756	−	0.0126190i
$661$	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
$666$	−1.02143	−	0.267834i	−0.0395797	−	0.0103784i
$667$	−14.4655	−	25.0550i	−0.560108	−	0.970135i
$668$	23.7318	+	6.08713i	0.918212	+	0.235518i
$669$	−4.74609	−	1.27171i	−0.183494	−	0.0491671i
$670$	0.115973	+	21.6451i	0.00448043	+	0.836223i
$671$	2.19556	−	2.19556i	0.0847586	−	0.0847586i
$672$	5.31969	+	17.9189i	0.205211	+	0.691235i
$673$	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	$0.582778\pi$
$674$	13.3972	+	22.9201i	0.516041	+	0.882851i
$675$	1.80965			0.0696536
$676$	25.5281	+	4.93125i	0.981849	+	0.189663i
$677$	40.3341			1.55017			0.775083	−	0.631860i	$-0.217708\pi$
$677$	40.3341			1.55017			0.775083	+	0.631860i	$0.217708\pi$
$678$	10.3153	+	17.6476i	0.396157	+	0.677752i
$679$	−2.43220	−	1.40423i	−0.0933392	−	0.0538894i
$680$	−28.3849	−	7.11876i	−1.08851	−	0.272992i
$681$	10.8174	−	10.8174i	0.414522	−	0.414522i
$682$	−0.0195059	−	3.64056i	−0.000746919	−	0.139404i
$683$	−7.08109	−	1.89737i	−0.270950	−	0.0726010i	0.120786	−	0.992679i	$-0.461459\pi$
$683$	−7.08109	−	1.89737i	−0.270950	−	0.0726010i	−0.391736	+	0.920078i	$0.628125\pi$
$684$	0.448092	−	1.74697i	0.0171332	−	0.0667971i
$685$	−12.7885	−	22.1503i	−0.488623	−	0.846320i
$686$	27.4636	+	7.20136i	1.04856	+	0.274949i
$687$	−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	$-0.437825\pi$
$691$	22.4140	−	6.00581i	0.852669	−	0.228472i	0.658579	+	0.752512i	$0.271158\pi$
$692$	−0.144956	−	13.5269i	−0.00551041	−	0.514214i
$693$	−2.96254	+	1.71042i	−0.112537	+	0.0649735i
$694$	5.59560	−	9.81291i	0.212406	−	0.372493i
$695$	−4.71558	+	17.5988i	−0.178872	+	0.667560i
$696$	−13.8273	−	23.0846i	−0.524124	−	0.875020i
$697$	5.25760	+	5.25760i	0.199146	+	0.199146i
$698$	−10.2008	+	10.3106i	−0.386104	+	0.390264i
$699$	−17.2337	+	29.8496i	−0.651838	+	1.12902i
$700$	0.965647	+	0.945170i	0.0364980	+	0.0357241i
$701$		−	1.83613i		−	0.0693497i	−0.999399	−	0.0346748i	$-0.988960\pi$
$701$		−	1.83613i		−	0.0693497i	0.999399	−	0.0346748i	$-0.0110396\pi$
$702$	2.65939	−	27.7888i	0.100372	−	1.04882i
$703$		−	4.50718i		−	0.169992i
$704$	10.0368	+	33.1557i	0.378274	+	1.24960i
$705$	−19.9352	+	34.5288i	−0.750803	+	1.30043i
$706$	4.75251	+	4.70185i	0.178863	+	0.176957i
$707$	1.25732	+	1.25732i	0.0472863	+	0.0472863i
$708$	−20.8949	+	5.83945i	−0.785278	+	0.219460i
$709$	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	$0.0515560\pi$
$710$	−4.65837	−	2.65634i	−0.174826	−	0.0996906i
$711$	0.373965	−	0.215909i	0.0140248	−	0.00809722i
$712$	1.51139	+	5.29843i	0.0566419	+	0.198567i
$713$	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
$718$	13.1235	−	50.0488i	0.489766	−	1.86780i
$719$	16.7047	+	28.9333i	0.622979	+	1.07903i	0.988928	+	0.148397i	$0.0474112\pi$
$719$	16.7047	+	28.9333i	0.622979	+	1.07903i	−0.365949	+	0.930635i	$0.619255\pi$
$720$	−0.933622	−	3.20771i	−0.0347941	−	0.119544i
$721$	−22.8510	−	6.12290i	−0.851015	−	0.228029i
$722$	−19.1718	+	0.102721i	−0.713500	+	0.00382289i
$723$	23.7091	−	23.7091i	0.881750	−	0.881750i
$724$	−18.6456	−	10.5002i	−0.692957	−	0.390239i
$725$	−1.68463	−	0.972624i	−0.0625657	−	0.0361223i
$726$	15.2981	−	8.94198i	0.567765	−	0.331868i
$727$	−23.0787			−0.855941			−0.427970	−	0.903793i	$-0.640771\pi$
$727$	−23.0787			−0.855941			−0.427970	+	0.903793i	$0.640771\pi$
$728$	15.9330	−	13.4394i	0.590515	−	0.498096i
$729$	−29.5245			−1.09350
$730$	19.9876	−	11.6831i	0.739774	−	0.432410i
$731$	46.3982	+	26.7880i	1.71610	+	0.990790i
$732$	2.02012	+	1.13763i	0.0746659	+	0.0420481i
$733$	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	$-0.0551668\pi$
$734$	28.8505	−	0.154579i	1.06489	−	0.00570563i
$735$	9.52352	+	2.55182i	0.351280	+	0.0941253i
$736$	−23.7029	+	14.5450i	−0.873699	+	0.536136i
$737$	15.3354	+	26.5617i	0.564886	+	0.978411i
$738$	−0.215298	+	0.821075i	−0.00792523	+	0.0302242i
$739$	−9.57785	−	35.7450i	−0.352327	−	1.31490i	−0.883815	−	0.467836i	$-0.845034\pi$
$739$	−9.57785	−	35.7450i	−0.352327	−	1.31490i	0.531488	−	0.847066i	$-0.321633\pi$
$740$	−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	$-0.657809\pi$
$743$	−12.2084	+	3.27124i	−0.447884	+	0.120010i	0.0278251	+	0.999613i	$0.491142\pi$
$744$	2.61409	−	0.745677i	0.0958373	−	0.0273379i
$745$	2.64351	−	1.52623i	0.0968506	−	0.0559167i
$746$	−25.3623	−	14.4623i	−0.928581	−	0.529503i
$747$	0.347651	−	1.29745i	0.0127199	−	0.0474712i
$748$	−39.9358	+	11.1608i	−1.46020	+	0.408078i
$749$	11.6454	+	11.6454i	0.425513	+	0.425513i
$750$	18.7210	+	18.5215i	0.683595	+	0.676309i
$751$	−10.7931	+	18.6941i	−0.393844	+	0.682159i	−0.992953	−	0.118509i	$-0.962188\pi$
$751$	−10.7931	+	18.6941i	−0.393844	+	0.682159i	0.599109	+	0.800668i	$0.295522\pi$
$752$	−44.3403	−	10.8681i	−1.61692	−	0.396319i
$753$			9.56224i			0.348467i
$754$	−17.4112	+	24.4397i	−0.634077	+	0.890041i
$755$			21.0461i			0.765946i
$756$	−15.9937	−	15.6545i	−0.581684	−	0.569350i
$757$	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	$0.123449\pi$
$758$	−14.1115	+	14.2636i	−0.512554	+	0.518076i
$759$	24.3346	+	24.3346i	0.883291	+	0.883291i
$760$	12.2330	−	7.32740i	0.443739	−	0.265793i
$761$	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	$-0.0981385\pi$
$762$	1.75584	−	3.07918i	0.0636072	−	0.111547i
$763$	30.2425	−	17.4605i	1.09485	−	0.632114i
$764$	−0.309768	−	28.9066i	−0.0112070	−	1.04580i
$765$	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	$0.589152\pi$
$770$	−26.1627	−	6.86024i	−0.942837	−	0.247226i
$771$	22.8537	+	39.5838i	0.823056	+	1.42558i
$772$	−9.72602	+	37.9187i	−0.350047	+	1.36472i
$773$	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	$0.430460\pi$
$774$	0.0327703	+	6.11623i	0.00117791	+	0.219843i
$775$	0.138954	−	0.138954i	0.00499136	−	0.00499136i
$776$	0.945406	−	3.76965i	0.0339381	−	0.135323i
$777$	−5.52817	−	3.19169i	−0.198322	−	0.114501i
$778$	23.9427	+	40.9616i	0.858388	+	1.46854i
$779$	−3.62309			−0.129811
$780$	19.3424	−	16.1386i	0.692571	−	0.577856i
$781$	−7.59850			−0.271896
$782$	−16.7984	−	28.7390i	−0.600710	−	1.02770i
$783$	27.9020	+	16.1092i	0.997137	+	0.575697i
$784$	0.241930	+	11.2868i	0.00864037	+	0.403100i
$785$	−21.5258	+	21.5258i	−0.768288	+	0.768288i
$786$	0.0503327	+	9.39405i	0.00179531	+	0.335075i
$787$	11.5106	+	3.08426i	0.410309	+	0.109942i	0.458068	−	0.888917i	$-0.348541\pi$
$787$	11.5106	+	3.08426i	0.410309	+	0.109942i	−0.0477596	+	0.998859i	$0.515208\pi$
$788$	5.14800	+	1.32044i	0.183390	+	0.0470389i
$789$	−10.8272	−	18.7532i	−0.385458	−	0.667633i
$790$	3.30255	+	0.865978i	0.117500	+	0.0308101i
$791$	−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
$796$	−33.1458	+	0.355197i	−1.17482	+	0.0125896i
$797$	−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	$0.414391\pi$
$798$	5.40055	−	9.47085i	0.191177	−	0.335265i
$799$	14.1436	−	52.7845i	0.500363	−	1.86738i
$800$	−0.891215	+	1.64380i	−0.0315092	+	0.0581172i
$801$	−0.532395	−	0.532395i	−0.0188113	−	0.0188113i
$802$	14.4918	−	14.6479i	0.511723	−	0.517236i
$803$	16.4025	−	28.4100i	0.578832	−	1.00257i
$804$	−16.0191	+	16.3662i	−0.564951	+	0.577191i
$805$		−	21.7131i		−	0.765286i
$806$	−1.92955	−	2.33795i	−0.0679656	−	0.0823509i
$807$		−	37.0707i		−	1.30495i
$808$	−1.19588	+	2.15043i	−0.0420710	+	0.0756518i
$809$	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	$0.131748\pi$
$810$	−16.7084	−	16.5303i	−0.587074	−	0.580816i
$811$	−8.66022	−	8.66022i	−0.304102	−	0.304102i	0.538515	−	0.842616i	$-0.318986\pi$
$811$	−8.66022	−	8.66022i	−0.304102	−	0.304102i	−0.842616	+	0.538515i	$0.818986\pi$
$812$	6.47501	+	23.1691i	0.227228	+	0.813075i
$813$	−4.01638	+	14.9893i	−0.140861	+	0.525699i
$814$	−10.2769	−	5.86017i	−0.360205	−	0.205399i
$815$	−38.2281	+	22.0710i	−1.33907	+	0.773113i
$816$	−16.0519	−	26.4758i	−0.561931	−	0.926837i
$817$	−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	$-0.180760\pi$
$822$	6.86372	−	26.1759i	0.239400	−	0.912990i
$823$	8.61216	+	14.9167i	0.300201	+	0.519963i	0.976181	−	0.216956i	$-0.0696130\pi$
$823$	8.61216	+	14.9167i	0.300201	+	0.519963i	−0.675980	+	0.736920i	$0.736280\pi$
$824$	−0.526182	−	32.7328i	−0.0183304	−	1.14030i
$825$	2.23508	+	0.598889i	0.0778157	+	0.0208506i
$826$	19.3957	−	0.103921i	0.674862	−	0.00361587i
$827$	7.89012	−	7.89012i	0.274366	−	0.274366i	−0.556489	−	0.830855i	$-0.687852\pi$
$827$	7.89012	−	7.89012i	0.274366	−	0.274366i	0.830855	+	0.556489i	$0.187852\pi$
$828$	1.86475	−	3.31128i	0.0648045	−	0.115075i
$829$	−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	$0.783343\pi$
$830$	9.16884	−	5.35934i	0.318255	−	0.186025i
$831$	−1.77839			−0.0616917
$832$	23.9323	+	16.1011i	0.829704	+	0.558204i
$833$	−13.5134			−0.468213
$834$	−16.6422	+	9.72762i	−0.576271	+	0.336840i
$835$	−22.9245	−	13.2355i	−0.793336	−	0.458033i
$836$	9.91464	−	17.6057i	0.342905	−	0.608905i
$837$	−2.30144	+	2.30144i	−0.0795495	+	0.0795495i
$838$	4.15242	−	0.0222484i	0.143443	−	0.000768559i
$839$	−15.3139	−	4.10335i	−0.528695	−	0.141663i	−0.0154095	−	0.999881i	$-0.504905\pi$
$839$	−15.3139	−	4.10335i	−0.528695	−	0.141663i	−0.513286	+	0.858218i	$0.671572\pi$
$840$	−0.324602	−	20.1929i	−0.0111998	−	0.696721i
$841$	−2.81628	−	4.87794i	−0.0971130	−	0.168205i
$842$	2.30278	−	8.78205i	0.0793592	−	0.302650i
$843$	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
$848$	2.75926	+	4.55106i	0.0947532	+	0.156284i
$849$	29.6169	−	17.0993i	1.01645	−	0.586848i
$850$	−1.94432	−	1.10871i	−0.0666898	−	0.0380284i
$851$	2.45806	−	9.17360i	0.0842612	−	0.314467i
$852$	−1.52708	−	5.46426i	−0.0523170	−	0.187202i
$853$	−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	$0.759709\pi$
$854$	−1.47344	−	1.45774i	−0.0504202	−	0.0498828i
$855$	−0.974304	+	1.68754i	−0.0333205	+	0.0577128i
$856$	−11.0764	+	19.9175i	−0.378583	+	0.680766i
$857$			2.39366i			0.0817658i	0.999164	+	0.0408829i	$0.0130171\pi$
$857$			2.39366i			0.0817658i	−0.999164	+	0.0408829i	$0.986983\pi$
$858$	12.4811	−	33.4416i	0.426096	−	1.14168i
$859$			17.8687i			0.609673i	0.952405	+	0.304837i	$0.0986018\pi$
$859$			17.8687i			0.609673i	−0.952405	+	0.304837i	$0.901398\pi$
$860$	−33.8267	+	34.5595i	−1.15348	+	1.17847i
$861$	−2.56563	+	4.44380i	−0.0874365	+	0.151444i
$862$	18.8638	−	19.0670i	0.642504	−	0.649426i
$863$	−16.3496	−	16.3496i	−0.556546	−	0.556546i	0.371776	−	0.928322i	$-0.378749\pi$
$863$	−16.3496	−	16.3496i	−0.556546	−	0.556546i	−0.928322	+	0.371776i	$0.878749\pi$
$864$	14.7609	−	27.2257i	0.502176	−	0.926239i
$865$	−3.78287	+	14.1179i	−0.128621	+	0.480022i
$866$	−3.48327	+	6.10855i	−0.118366	+	0.207577i
$867$	8.29535	−	4.78932i	0.281725	−	0.162654i
$868$	−2.43010	+	0.0260414i	−0.0824829	+	0.000883901i
$869$	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
$874$	15.6902	+	4.11421i	0.530730	+	0.139165i
$875$	−11.7717	−	20.3893i	−0.397958	−	0.689283i
$876$	23.7267	+	6.08583i	0.801652	+	0.205621i
$877$	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	$0.551376\pi$
$878$	−0.296790	−	55.3925i	−0.0100162	−	1.86941i
$879$	−20.7052	+	20.7052i	−0.698370	+	0.698370i
$880$	−0.802085	−	37.4197i	−0.0270383	−	1.26142i
$881$	−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	$0.881608\pi$
$882$	−0.778503	−	1.33188i	−0.0262136	−	0.0448466i
$883$	−31.7405			−1.06815			−0.534077	−	0.845436i	$-0.679341\pi$
$883$	−31.7405			−1.06815			−0.534077	+	0.845436i	$0.679341\pi$
$884$	−19.8825	+	28.2275i	−0.668720	+	0.949393i
$885$	23.4408			0.787955
$886$	27.2429	+	46.6075i	0.915242	+	1.56581i
$887$	32.1042	+	18.5354i	1.07795	+	0.622356i	0.930343	−	0.366689i	$-0.119509\pi$
$887$	32.1042	+	18.5354i	1.07795	+	0.622356i	0.147609	+	0.989046i	$0.452842\pi$
$888$	2.14882	−	8.56808i	0.0721098	−	0.287526i
$889$	−2.24076	+	2.24076i	−0.0751526	+	0.0751526i
$890$	−0.0318955	−	5.95294i	−0.00106914	−	0.199543i
$891$	−32.1691	−	8.61967i	−1.07770	−	0.288770i
$892$	−1.51028	+	5.88810i	−0.0505678	+	0.197148i
$893$	13.3140	+	23.0605i	0.445536	+	0.771692i
$894$	3.12394	+	0.819144i	0.104480	+	0.0273963i
$895$	−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
$900$	−0.00273803	−	0.255504i	−9.12675e−5	−	0.00851680i
$901$	−5.51717	+	3.18534i	−0.183803	+	0.106119i
$902$	−4.71069	+	8.26105i	−0.156849	+	0.275063i
$903$	−9.56947	+	35.7138i	−0.318452	+	1.18848i
$904$	21.6946	−	12.9947i	0.721552	−	0.432198i
$905$	16.3485	+	16.3485i	0.543444	+	0.543444i
$906$	−15.6606	+	15.8294i	−0.520290	+	0.525895i
$907$	−16.4743	+	28.5344i	−0.547021	+	0.947468i	0.451456	+	0.892294i	$0.350905\pi$
$907$	−16.4743	+	28.5344i	−0.547021	+	0.947468i	−0.998477	+	0.0551749i	$0.982428\pi$
$908$	−13.5252	−	13.2384i	−0.448851	−	0.439333i
$909$		−	0.336243i		−	0.0111525i
$910$	−20.4877	+	9.35122i	−0.679161	+	0.309990i
$911$		−	22.6697i		−	0.751082i	−0.926806	−	0.375541i	$-0.877457\pi$
$911$		−	22.6697i		−	0.751082i	0.926806	−	0.375541i	$-0.122543\pi$
$912$	14.6532	+	3.59160i	0.485217	+	0.118930i
$913$	7.52427	−	13.0324i	0.249017	−	0.431310i
$914$	34.1735	+	33.8092i	1.13036	+	1.11831i
$915$	−1.77126	−	1.77126i	−0.0585559	−	0.0585559i
$916$	−9.52037	+	2.66064i	−0.314562	+	0.0879099i
$917$	2.17368	−	8.11230i	0.0717813	−	0.267892i
$918$	32.2032	+	18.3632i	1.06286	+	0.606075i
$919$	7.50982	−	4.33579i	0.247726	−	0.143025i	−0.370997	−	0.928634i	$-0.620984\pi$
$919$	7.50982	−	4.33579i	0.247726	−	0.143025i	0.618723	+	0.785610i	$0.287651\pi$
$920$	28.8944	−	8.24220i	0.952619	−	0.271737i
$921$	−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
$926$	−12.3801	+	47.2134i	−0.406834	+	1.55153i
$927$	2.23679	+	3.87423i	0.0734657	+	0.127246i
$928$	−28.3740	+	17.4114i	−0.931423	+	0.571558i
$929$	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	$0.508942\pi$
$930$	−2.93700	+	0.0157363i	−0.0963082	+	0.000516013i
$931$	4.65615	−	4.65615i	0.152599	−	0.152599i
$932$	37.1545	+	20.9236i	1.21704	+	0.685375i
$933$	13.6807	+	7.89858i	0.447888	+	0.258588i
$934$	−21.7057	+	12.6873i	−0.710232	+	0.415142i
$935$	44.8018			1.46518
$936$	−3.92751	−	0.333433i	−0.128375	−	0.0108986i
$937$	−8.23591			−0.269055			−0.134528	−	0.990910i	$-0.542952\pi$
$937$	−8.23591			−0.269055			−0.134528	+	0.990910i	$0.542952\pi$
$938$	17.6757	−	10.3318i	0.577133	−	0.337344i
$939$	−44.2880	−	25.5697i	−1.44528	−	0.834434i
$940$	42.9788	+	24.2035i	1.40182	+	0.789432i
$941$	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	$0.219488\pi$
$942$	−32.2077	+	0.172567i	−1.04938	+	0.00562254i
$943$	−7.37418	−	1.97590i	−0.240136	−	0.0643443i
$944$	7.50081	+	25.7711i	0.244131	+	0.838776i
$945$	12.0902	+	20.9408i	0.393293	+	0.681203i
$946$	−17.3802	+	66.2823i	−0.565079	+	2.15502i
$947$	−0.740729	−	2.76444i	−0.0240705	−	0.0898322i	0.952846	−	0.303455i	$-0.0981403\pi$
$947$	−0.740729	−	2.76444i	−0.0240705	−	0.0898322i	−0.976916	+	0.213623i	$0.931474\pi$
$948$	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
$952$	7.59293	+	26.6183i	0.246088	+	0.862703i
$953$	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	$0.287677\pi$
$954$	−0.631787	−	0.360263i	−0.0204549	−	0.0116639i
$955$	−8.08391	+	30.1695i	−0.261589	+	0.976264i
$956$	16.2547	−	4.54267i	0.525715	−	0.146920i
$957$	29.1303	+	29.1303i	0.941648	+	0.941648i
$958$	7.99926	+	7.91399i	0.258444	+	0.255690i
$959$	−12.0963	+	20.9514i	−0.390610	+	0.676556i
$960$	26.7482	−	8.09711i	0.863294	−	0.261333i
$961$		−	30.6466i		−	0.988599i
$962$	−9.71450	+	1.63148i	−0.313208	+	0.0526010i
$963$		−	3.11432i		−	0.100357i
$964$	−29.6441	−	29.0155i	−0.954772	−	0.934526i
$965$	21.1477	−	36.6288i	0.680767	−	1.17912i
$966$	16.1570	−	16.3310i	0.519842	−	0.525442i
$967$	−31.1406	−	31.1406i	−1.00142	−	1.00142i	−0.999999	−	0.00141655i	$-0.999549\pi$
$967$	−31.1406	−	31.1406i	−1.00142	−	1.00142i	−0.00141655	−	0.999999i	$-0.500451\pi$
$968$	−11.2647	−	18.8063i	−0.362060	−	0.604456i
$969$	−4.67405	+	17.4438i	−0.150152	+	0.560376i
$970$	−2.08001	+	3.64767i	−0.0667850	+	0.117120i
$971$	13.4730	−	7.77866i	0.432370	−	0.249629i	−0.267986	−	0.963423i	$-0.586358\pi$
$971$	13.4730	−	7.77866i	0.432370	−	0.249629i	0.700356	+	0.713794i	$0.253025\pi$
$972$	0.0855222	+	7.98066i	0.00274313	+	0.255980i
$973$	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	$-0.336870\pi$
$978$	−45.1757	−	11.8457i	−1.44456	−	0.378785i
$979$	−4.21761	−	7.30512i	−0.134795	−	0.233473i
$980$	3.03053	−	11.8151i	0.0968068	−	0.377419i
$981$	−6.37859	−	1.70914i	−0.203653	−	0.0545686i
$982$	0.000448638		0.0837333i	1.43166e−5		0.00267204i
$983$	−21.2250	+	21.2250i	−0.676971	+	0.676971i	−0.959314	−	0.282343i	$-0.908888\pi$
$983$	−21.2250	+	21.2250i	−0.676971	+	0.676971i	0.282343	+	0.959314i	$0.408888\pi$
$984$	−6.88743	−	1.72733i	−0.219563	−	0.0550651i
$985$	−4.97288	−	2.87109i	−0.158449	−	0.0914807i
$986$	−20.1089	−	34.4026i	−0.640398	−	1.09560i
$987$	37.7124			1.20040
$988$	−2.87532	−	16.5766i	−0.0914762	−	0.527373i
$989$	−55.0094			−1.74920
$990$	2.58101	+	4.41564i	0.0820300	+	0.140338i
$991$	−16.0337	−	9.25705i	−0.509327	−	0.294060i	0.223230	−	0.974766i	$-0.428340\pi$
$991$	−16.0337	−	9.25705i	−0.509327	−	0.294060i	−0.732557	+	0.680706i	$0.761673\pi$
$992$	−0.957110	−	3.22393i	−0.0303883	−	0.102360i
$993$	−13.8963	+	13.8963i	−0.440986	+	0.440986i
$994$	0.0271765	+	5.07219i	0.000861986	+	0.160880i
$995$	34.5940	+	9.26943i	1.09670	+	0.293861i
$996$	10.8841	+	2.79173i	0.344875	+	0.0884594i
$997$	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	$0.501348\pi$
$998$	−49.7840	−	13.0541i	−1.57588	−	0.413220i
$999$	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.19.1	yes	16
3.2	odd	2		468.2.cb.f.19.4		16
4.3	odd	2	inner	52.2.l.b.19.4	yes	16
8.3	odd	2		832.2.bu.n.383.3		16
8.5	even	2		832.2.bu.n.383.2		16
12.11	even	2		468.2.cb.f.19.1		16
13.2	odd	12		676.2.l.k.427.1		16
13.3	even	3		676.2.l.m.587.2		16
13.4	even	6		676.2.f.i.239.2		16
13.5	odd	4		676.2.l.i.319.4		16
13.6	odd	12		676.2.f.i.99.6		16
13.7	odd	12		676.2.f.h.99.3		16
13.8	odd	4		676.2.l.m.319.1		16
13.9	even	3		676.2.f.h.239.7		16
13.10	even	6		676.2.l.i.587.3		16
13.11	odd	12	inner	52.2.l.b.11.4	yes	16
13.12	even	2		676.2.l.k.19.4		16
39.11	even	12		468.2.cb.f.271.1		16
52.3	odd	6		676.2.l.m.587.1		16
52.7	even	12		676.2.f.h.99.7		16
52.11	even	12	inner	52.2.l.b.11.1	✓	16
52.15	even	12		676.2.l.k.427.4		16
52.19	even	12		676.2.f.i.99.2		16
52.23	odd	6		676.2.l.i.587.4		16
52.31	even	4		676.2.l.i.319.3		16
52.35	odd	6		676.2.f.h.239.3		16
52.43	odd	6		676.2.f.i.239.6		16
52.47	even	4		676.2.l.m.319.2		16
52.51	odd	2		676.2.l.k.19.1		16
104.11	even	12		832.2.bu.n.63.2		16
104.37	odd	12		832.2.bu.n.63.3		16
156.11	odd	12		468.2.cb.f.271.4		16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.22094 + 0.713659i) q^{2} +(1.40004 + 0.808315i) q^{3} +(0.981383 - 1.74267i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(-2.28623 + 0.0122495i) q^{6} +(1.97429 + 0.529008i) q^{7} +(0.0454612 + 2.82806i) q^{8} +(-0.193255 - 0.334727i) q^{9} +O(q^{10})\)	\(q+(-1.22094 + 0.713659i) q^{2} +(1.40004 + 0.808315i) q^{3} +(0.981383 - 1.74267i) q^{4} +(-1.52798 + 1.52798i) q^{5} +(-2.28623 + 0.0122495i) q^{6} +(1.97429 + 0.529008i) q^{7} +(0.0454612 + 2.82806i) q^{8} +(-0.193255 - 0.334727i) q^{9} +(0.775114 - 2.95603i) 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} +(-2.07378 - 3.42045i) q^{16} +(4.14654 - 2.39401i) q^{17} +(0.474833 + 0.270763i) q^{18} +(-0.603848 + 2.25359i) q^{19} +(1.16323 + 4.16230i) q^{20} +(2.33648 + 2.33648i) q^{21} +(4.35333 + 4.30693i) q^{22} +(-2.45806 + 4.25748i) q^{23} +(-2.22232 + 3.99615i) q^{24} +0.330547i q^{25} +(5.07583 + 0.485758i) q^{26} -5.47473i q^{27} +(2.85942 - 2.92136i) q^{28} +(-2.94247 + 5.09651i) q^{29} +(3.47459 - 3.51203i) q^{30} +(-0.420375 - 0.420375i) q^{31} +(4.97298 + 2.69619i) q^{32} +(1.81181 - 6.76178i) q^{33} +(-3.35417 + 5.88215i) q^{34} +(-3.82499 + 2.20836i) q^{35} +(-0.772974 + 0.00828333i) 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} +(-4.52014 - 1.18525i) q^{42} +(5.59481 + 9.69049i) q^{43} +(-8.38882 - 2.15170i) q^{44} +(0.806745 + 0.216167i) q^{45} +(-0.0372502 - 6.95234i) q^{46} +(8.07035 - 8.07035i) q^{47} +(-0.138577 - 6.46503i) q^{48} +(-2.44422 - 1.41117i) q^{49} +(-0.235897 - 0.403577i) q^{50} +7.74044 q^{51} +(-6.54394 + 3.02933i) q^{52} -1.33055 q^{53} +(3.90709 + 6.68431i) q^{54} +(8.10346 + 4.67854i) q^{55} +(-1.40631 + 5.60745i) q^{56} +(-2.66702 + 2.66702i) q^{57} +(-0.0445911 - 8.32245i) q^{58} +(-6.48147 - 1.73670i) q^{59} +(-1.73588 + 6.76765i) q^{60} +(0.358528 + 0.620988i) q^{61} +(0.813257 + 0.213248i) 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} +(-0.102613 - 9.57548i) q^{68} +(-6.88277 + 3.97377i) q^{69} +(3.09406 - 5.42600i) q^{70} +(0.454168 - 1.69498i) q^{71} +(0.937842 - 0.561753i) q^{72} +(5.35696 + 5.35696i) q^{73} +(1.92147 - 1.94217i) q^{74} +(-0.267186 + 0.462779i) q^{75} +(3.33465 + 3.26394i) q^{76} -8.85061i q^{77} +(6.71373 + 4.78295i) q^{78} +1.11723i q^{79} +(8.39507 + 2.05769i) q^{80} +(3.84554 - 6.66067i) q^{81} +(-1.56121 - 1.54457i) q^{82} +(2.45738 + 2.45738i) q^{83} +(6.36468 - 1.77872i) q^{84} +(-2.67784 + 9.99383i) q^{85} +(-13.7466 - 7.83871i) q^{86} +(-8.23917 + 4.75689i) q^{87} +(11.7778 - 3.35966i) 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} +(-4.09393 + 15.6129i) q^{94} +(-2.52078 - 4.36612i) q^{95} +(4.78302 + 7.79451i) q^{96} +(-1.32723 - 0.355630i) q^{97} +(3.99134 - 0.0213854i) 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

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