LMFDB - Embedded newform 52.2.l.b.11.1

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			11.1
Root			$-0.00757716 - 1.41419i$ of defining polynomial
Character	$\chi$	$=$	52.11
Dual form			52.2.l.b.19.1

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

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

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 $

$2$	−1.22094	−	0.713659i	−0.863334	−	0.504633i
$2$	−1.22094	−	0.713659i	−0.863334	−	0.504633i
$3$	1.40004	−	0.808315i	0.808315	−	0.466681i	−0.0380556	−	0.999276i	$-0.512116\pi$
$3$	1.40004	−	0.808315i	0.808315	−	0.466681i	0.846370	+	0.532595i	$0.178783\pi$
$4$	0.981383	+	1.74267i	0.490691	+	0.871333i
$5$	−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	$0.910522\pi$
$6$	−2.28623	−	0.0122495i	−0.933348	−	0.00500082i
$7$	1.97429	−	0.529008i	0.746210	−	0.199946i	0.134374	−	0.990931i	$-0.457098\pi$
$7$	1.97429	−	0.529008i	0.746210	−	0.199946i	0.611836	+	0.790984i	$0.290431\pi$
$8$	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	0.562760	+	0.826620i	$0.309739\pi$
$11$	−1.12074	+	4.18264i	−0.337915	+	1.26111i	−0.900675	+	0.434494i	$0.856927\pi$
$12$	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	0.909925	−	0.414773i	$-0.136139\pi$
$17$	4.14654	+	2.39401i	1.00568	+	0.580632i	0.0957589	+	0.995405i	$0.469472\pi$
$18$	0.474833	−	0.270763i	0.111919	−	0.0638195i
$19$	−0.603848	−	2.25359i	−0.138532	−	0.517010i	−0.999958	−	0.00912654i	$-0.997095\pi$
$19$	−0.603848	−	2.25359i	−0.138532	−	0.517010i	0.861426	−	0.507883i	$-0.169572\pi$
$20$	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	−0.999894	−	0.0145418i	$-0.995371\pi$
$23$	−2.45806	−	4.25748i	−0.512541	−	0.887747i	0.487354	−	0.873205i	$-0.337962\pi$
$24$	−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	−0.998517	−	0.0544380i	$-0.982663\pi$
$29$	−2.94247	−	5.09651i	−0.546403	−	0.946398i	0.452114	−	0.891960i	$-0.350670\pi$
$30$	3.47459	+	3.51203i	0.634371	+	0.641206i
$31$	−0.420375	+	0.420375i	−0.0755017	+	0.0755017i	−0.743849	−	0.668348i	$-0.767002\pi$
$31$	−0.420375	+	0.420375i	−0.0755017	+	0.0755017i	0.668348	+	0.743849i	$0.267002\pi$
$32$	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	0.102149	−	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	$0.0446391\pi$
$42$	−4.52014	+	1.18525i	−0.697473	+	0.182888i
$43$	5.59481	−	9.69049i	0.853200	−	1.47779i	−0.0251051	−	0.999685i	$-0.507992\pi$
$43$	5.59481	−	9.69049i	0.853200	−	1.47779i	0.878305	−	0.478101i	$-0.158675\pi$
$44$	−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	0.980459	+	0.196722i	$0.0630296\pi$
$47$	8.07035	+	8.07035i	1.17718	+	1.17718i	0.196722	+	0.980459i	$0.436970\pi$
$48$	−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	−0.654732	−	0.755861i	$-0.727218\pi$
$59$	−6.48147	+	1.73670i	−0.843816	+	0.226100i	−0.189084	+	0.981961i	$0.560552\pi$
$60$	−1.73588	−	6.76765i	−0.224101	−	0.873699i
$61$	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	$0.152050\pi$
$62$	0.813257	−	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	−0.184581	−	0.982817i	$-0.559093\pi$
$67$	−6.84166	−	1.83322i	−0.835842	−	0.223963i	−0.651261	+	0.758854i	$0.725759\pi$
$68$	−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	0.987625	−	0.156834i	$-0.0501286\pi$
$71$	0.454168	+	1.69498i	0.0538999	+	0.201157i	−0.933725	+	0.357991i	$0.883462\pi$
$72$	0.937842	+	0.561753i	0.110526	+	0.0662032i
$73$	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	$0.103792\pi$
$74$	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	$-0.979981\pi$
$79$		−	1.11723i		−	0.125698i	0.998023	−	0.0628489i	$-0.0200186\pi$
$80$	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	−0.559260	−	0.828992i	$-0.688915\pi$
$83$	2.45738	−	2.45738i	0.269733	−	0.269733i	0.828992	+	0.559260i	$0.188915\pi$
$84$	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	0.357162	−	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
$94$	−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	−0.325568	−	0.945518i	$-0.605556\pi$
$97$	−1.32723	+	0.355630i	−0.134760	+	0.0361088i	0.190809	+	0.981627i	$0.438889\pi$
$98$	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	−0.462049	−	0.886855i	$-0.652885\pi$
$101$	0.753397	−	0.434974i	0.0749658	−	0.0432815i	0.537014	+	0.843573i	$0.319552\pi$
$102$	−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	−0.123222	−	0.992379i	$-0.539323\pi$
$107$	6.97804	−	4.02877i	0.674593	−	0.389476i	0.797815	+	0.602903i	$0.205989\pi$
$108$	−9.54063	+	5.37281i	−0.918048	+	0.516998i
$109$	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	$0.444953\pi$
$110$	−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	−0.995993	−	0.0894334i	$-0.971494\pi$
$113$	−4.47045	+	7.74305i	−0.420545	+	0.728405i	0.575448	+	0.817838i	$0.304828\pi$
$114$	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	0.829580	−	0.558388i	$-0.188580\pi$
$127$	−0.775200	−	1.34269i	−0.0687879	−	0.119144i	−0.898368	+	0.439244i	$0.855247\pi$
$128$	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	$0.0574485\pi$
$131$			4.10898i			0.359003i	−0.983758	+	0.179502i	$0.942552\pi$
$132$	−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	−0.964222	−	0.265096i	$-0.914596\pi$
$137$	−3.06346	−	11.4330i	−0.261729	−	0.976786i	0.702493	−	0.711691i	$-0.252070\pi$
$138$	5.56753	+	9.76368i	0.473939	+	0.831140i
$139$	7.30191	+	4.21576i	0.619340	+	0.357576i	0.776612	−	0.629979i	$-0.216937\pi$
$139$	7.30191	+	4.21576i	0.619340	+	0.357576i	−0.157272	+	0.987555i	$0.550270\pi$
$140$	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	−0.314276	−	0.949332i	$-0.601762\pi$
$149$	−1.36446	+	0.365606i	−0.111781	+	0.0299516i	0.202495	+	0.979283i	$0.435095\pi$
$150$	−0.00404902	+	0.755704i	−0.000330601	+	0.0617030i
$151$	6.88689	+	6.88689i	0.560447	+	0.560447i	0.929435	−	0.368987i	$-0.120295\pi$
$151$	6.88689	+	6.88689i	0.560447	+	0.560447i	−0.368987	+	0.929435i	$0.620295\pi$
$152$	−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	0.617461	−	0.786601i	$-0.288161\pi$
$163$	19.7316	−	5.28707i	1.54550	−	0.414115i	0.928038	+	0.372486i	$0.121495\pi$
$164$	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	−0.727867	−	0.685719i	$-0.759488\pi$
$167$	3.17054	−	11.8326i	0.245344	−	0.915635i	0.973210	−	0.229917i	$-0.0738453\pi$
$168$	−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	0.705864	−	0.708348i	$-0.250559\pi$
$173$	5.85764	+	3.38191i	0.445348	+	0.257122i	−0.260515	+	0.965470i	$0.583893\pi$
$174$	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	0.686084	−	0.727522i	$-0.259328\pi$
$179$	−3.83994	−	6.65097i	−0.287011	−	0.497117i	−0.973095	+	0.230405i	$0.925995\pi$
$180$	1.16843	+	1.19375i	0.0870898	+	0.0889766i
$181$			10.6994i			0.795283i	0.917541	+	0.397642i	$0.130171\pi$
$181$			10.6994i			0.795283i	−0.917541	+	0.397642i	$0.869829\pi$
$182$	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	0.879060	−	0.476712i	$-0.158171\pi$
$191$	12.5176	+	7.22707i	0.905745	+	0.522932i	0.0266854	+	0.999644i	$0.491505\pi$
$192$	−11.4024	+	6.10318i	−0.822897	+	0.440459i
$193$	−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	$0.0531559\pi$
$198$	0.600343	+	2.28951i	0.0426645	+	0.162708i
$199$	−8.28694	+	14.3534i	−0.587445	+	1.01749i	0.407120	+	0.913374i	$0.366533\pi$
$199$	−8.28694	+	14.3534i	−0.587445	+	1.01749i	−0.994566	+	0.104111i	$0.966800\pi$
$200$	−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	−0.669815	+	0.742528i	$0.733627\pi$
$211$	−23.9352	+	13.8190i	−1.64777	+	0.951341i	−0.977956	+	0.208812i	$0.933040\pi$
$212$	−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	0.159178	−	0.987250i	$-0.449116\pi$
$223$	−2.93579	−	0.786643i	−0.196595	−	0.0526775i	−0.355773	+	0.934572i	$0.615782\pi$
$224$	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	0.998339	+	0.0576122i	$0.0183487\pi$
$227$	2.44919	+	9.14049i	0.162558	+	0.606675i	−0.835781	+	0.549063i	$0.814985\pi$
$228$	2.03036	−	7.26511i	0.134464	−	0.481144i
$229$	−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	$0.302216\pi$
$230$	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	$-0.753906\pi$
$233$		−	21.3205i		−	1.39675i	0.715731	−	0.698376i	$-0.246094\pi$
$234$	−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	−0.487271	−	0.873251i	$-0.662007\pi$
$239$	5.96711	−	5.96711i	0.385981	−	0.385981i	0.873251	+	0.487271i	$0.162007\pi$
$240$	10.0902	−	9.66671i	0.651319	−	0.623983i
$241$	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	$0.683815\pi$
$242$	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	−0.757466	−	0.652875i	$-0.773563\pi$
$251$	2.95746	−	5.12248i	0.186673	−	0.323328i	0.944139	+	0.329547i	$0.106896\pi$
$252$	−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	0.527884	−	0.849316i	$-0.322986\pi$
$257$	24.4854	−	14.1366i	1.52736	−	0.881819i	0.999472	−	0.0325029i	$-0.0103478\pi$
$258$	−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	−0.813020	−	0.582236i	$-0.802178\pi$
$263$	−11.6002	+	6.69738i	−0.715299	+	0.412978i	0.0977210	+	0.995214i	$0.468845\pi$
$264$	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	0.269733	+	0.962935i	$0.413065\pi$
$269$	−11.4654	+	19.8587i	−0.699060	+	1.21081i	−0.968793	+	0.247872i	$0.920269\pi$
$270$	−16.1835	+	4.24354i	−0.984894	+	0.258254i
$271$	2.48442	−	9.27197i	0.150918	−	0.563232i	−0.848503	−	0.529191i	$-0.822496\pi$
$271$	2.48442	−	9.27197i	0.150918	−	0.563232i	0.999420	−	0.0340411i	$-0.0108377\pi$
$272$	−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	0.471106	−	0.882076i	$-0.343855\pi$
$277$	−0.952681	−	0.550031i	−0.0572411	−	0.0330482i	−0.528347	+	0.849028i	$0.677188\pi$
$278$	−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	−0.476634	−	0.879102i	$-0.658143\pi$
$281$	6.74660	−	6.74660i	0.402469	−	0.402469i	0.879102	+	0.476634i	$0.158143\pi$
$282$	−18.3518	−	18.5495i	−1.09283	−	1.10461i
$283$	10.5772	+	18.3202i	0.628746	+	1.08902i	0.987804	+	0.155705i	$0.0497650\pi$
$283$	10.5772	+	18.3202i	0.628746	+	1.08902i	−0.359057	+	0.933316i	$0.616902\pi$
$284$	−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	−0.956594	−	0.291425i	$-0.905871\pi$
$293$	−4.68793	−	17.4956i	−0.273872	−	1.02210i	0.682722	−	0.730678i	$-0.260796\pi$
$294$	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	0.468869	−	0.883268i	$-0.344662\pi$
$307$	−7.26086	−	7.26086i	−0.414399	−	0.414399i	−0.883268	+	0.468869i	$0.844662\pi$
$308$	−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	0.157343	−	0.987544i	$-0.449707\pi$
$317$	−14.7813	−	14.7813i	−0.830201	−	0.830201i	−0.987544	+	0.157343i	$0.949707\pi$
$318$	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	−0.996894	−	0.0787555i	$-0.974905\pi$
$331$	−3.14630	−	11.7421i	−0.172936	−	0.645407i	0.823958	−	0.566651i	$-0.191761\pi$
$332$	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	$0.170837\pi$
$337$			18.7726i			1.02261i	−0.859401	+	0.511303i	$0.829163\pi$
$338$	−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	0.302698	−	0.953086i	$-0.402113\pi$
$347$	−6.91748	−	3.99381i	−0.371350	−	0.214399i	−0.674048	+	0.738688i	$0.735446\pi$
$348$	0.203891	−	19.0265i	0.0109297	−	1.01992i
$349$	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	$0.123484\pi$
$354$	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	−0.866894	−	0.498492i	$-0.833887\pi$
$359$	−25.8704	−	25.8704i	−1.36539	−	1.36539i	−0.498492	−	0.866894i	$-0.666113\pi$
$360$	−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	−0.884348	−	0.466828i	$-0.845397\pi$
$367$	−17.6675	+	10.2004i	−0.922238	+	0.532454i	−0.0378895	+	0.999282i	$0.512063\pi$
$368$	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	−0.464718	−	0.885459i	$-0.653844\pi$
$373$	10.3223	−	17.8788i	0.534471	−	0.925731i	0.999189	−	0.0402718i	$-0.0128224\pi$
$374$	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	0.592996	−	0.805205i	$-0.297945\pi$
$379$	13.7043	+	3.67206i	0.703943	+	0.188621i	0.110947	+	0.993826i	$0.464612\pi$
$380$	−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	0.989438	+	0.144954i	$0.0463035\pi$
$383$	4.01265	+	14.9754i	0.205037	+	0.765207i	−0.784402	+	0.620253i	$0.787030\pi$
$384$	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	$0.323705\pi$
$389$			33.5493i			1.70102i	−0.525963	+	0.850508i	$0.676295\pi$
$390$	−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	−0.998428	−	0.0560542i	$-0.982148\pi$
$397$	−3.22366	−	12.0309i	−0.161791	−	0.603813i	0.836637	−	0.547758i	$-0.184519\pi$
$398$	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	−0.110317	−	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
$406$	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	−0.690316	−	0.723508i	$-0.742528\pi$
$409$	−18.7351	+	5.02006i	−0.926393	+	0.248226i	−0.236077	+	0.971734i	$0.575862\pi$
$410$	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	−0.560826	−	0.827934i	$-0.689516\pi$
$419$	−2.54287	+	1.46812i	−0.124227	+	0.0717226i	0.436599	+	0.899656i	$0.356183\pi$
$420$	−7.00726	−	12.4430i	−0.341919	−	0.607155i
$421$	−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	$0.800002\pi$
$422$	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	−0.210967	−	0.977493i	$-0.567661\pi$
$431$	−18.3194	−	4.90868i	−0.882417	−	0.236443i	−0.671450	+	0.741050i	$0.734328\pi$
$432$	−18.7260	−	11.3534i	−0.900956	−	0.546239i
$433$	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	$0.628545\pi$
$434$	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	−0.775137	−	0.631793i	$-0.782319\pi$
$439$	−19.5845	−	33.9214i	−0.934717	−	1.61898i	−0.159580	−	0.987185i	$-0.551014\pi$
$440$	−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	$0.361512\pi$
$443$			38.1735i			1.81368i	−0.421477	+	0.906839i	$0.638488\pi$
$444$	−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	0.944086	−	0.329699i	$-0.106947\pi$
$449$	−0.812961	−	3.03401i	−0.0383660	−	0.143184i	−0.982452	+	0.186515i	$0.940281\pi$
$450$	−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	0.380125	+	0.924935i	$0.375881\pi$
$457$	−8.79773	+	32.8336i	−0.411541	+	1.53589i	−0.791665	+	0.610955i	$0.790786\pi$
$458$	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	−0.749678	−	0.661803i	$-0.769792\pi$
$461$	−22.9313	+	6.14442i	−1.06802	+	0.286174i	−0.318339	+	0.947977i	$0.603125\pi$
$462$	0.108415	−	20.2345i	0.00504393	−	0.941394i
$463$	24.4048	+	24.4048i	1.13419	+	1.13419i	0.989474	+	0.144713i	$0.0462258\pi$
$463$	24.4048	+	24.4048i	1.13419	+	1.13419i	0.144713	+	0.989474i	$0.453774\pi$
$464$	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	−0.996881	−	0.0789246i	$-0.974851\pi$
$479$	−2.05936	+	7.68562i	−0.0940943	+	0.351165i	0.902786	+	0.430090i	$0.141518\pi$
$480$	−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	−0.961295	−	0.275520i	$-0.911150\pi$
$487$	−5.88223	−	21.9528i	−0.266549	−	0.994775i	0.694746	−	0.719255i	$-0.255517\pi$
$488$	−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	0.866693	−	0.498843i	$-0.166241\pi$
$491$	0.0296046	+	0.0512767i	0.00133604	+	0.00231409i	−0.865357	+	0.501157i	$0.832908\pi$
$492$	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	0.165836	−	0.986153i	$-0.446968\pi$
$499$	25.7335	−	25.7335i	1.15199	−	1.15199i	0.986153	−	0.165836i	$-0.0530323\pi$
$500$	−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	0.789510	−	0.613738i	$-0.210335\pi$
$503$	14.6397	+	8.45225i	0.652753	+	0.376867i	−0.136757	+	0.990605i	$0.543668\pi$
$504$	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	−0.748772	−	0.662827i	$-0.769356\pi$
$509$	5.21379	−	19.4581i	0.231097	−	0.862466i	0.979870	−	0.199639i	$-0.0639769\pi$
$510$	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	−0.143426	−	0.989661i	$-0.545812\pi$
$523$	14.6805	−	8.47577i	0.641932	−	0.370620i	0.785358	+	0.619041i	$0.212479\pi$
$524$	−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	−0.807760	−	0.589512i	$-0.799320\pi$
$541$	−5.07631	+	5.07631i	−0.218248	+	0.218248i	0.589512	+	0.807760i	$0.299320\pi$
$542$	−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	$-0.759779\pi$
$547$		−	32.0440i		−	1.37010i	0.728494	−	0.685052i	$-0.240221\pi$
$548$	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	0.570107	−	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
$562$	−13.0520	+	3.42242i	−0.550564	+	0.144366i
$563$	2.79472	−	4.84060i	0.117783	−	0.204007i	−0.801106	−	0.598523i	$-0.795754\pi$
$563$	2.79472	−	4.84060i	0.117783	−	0.204007i	0.918889	+	0.394516i	$0.129088\pi$
$564$	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	0.184381	−	0.982855i	$-0.440972\pi$
$569$	26.9010	−	15.5313i	1.12775	−	0.651106i	0.943368	+	0.331749i	$0.107639\pi$
$570$	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	−0.975715	−	0.219044i	$-0.929706\pi$
$577$	−28.6991	−	28.6991i	−1.19476	−	1.19476i	−0.219044	−	0.975715i	$-0.570294\pi$
$578$	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	0.131161	−	0.991361i	$-0.458129\pi$
$587$	−6.07956	−	1.62901i	−0.250930	−	0.0672365i	−0.382091	+	0.924125i	$0.624796\pi$
$588$	−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	−0.999404	−	0.0345259i	$-0.989008\pi$
$593$	−23.4963	+	23.4963i	−0.964878	+	0.964878i	0.0345259	+	0.999404i	$0.489008\pi$
$594$	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	$0.162500\pi$
$599$			23.9175i			0.977241i	−0.872496	+	0.488621i	$0.837500\pi$
$600$	−1.32091	+	0.734579i	−0.0539261	+	0.0299891i
$601$	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	$0.636554\pi$
$602$	−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	−0.264645	−	0.964346i	$-0.585255\pi$
$607$	−30.3561	−	17.5261i	−1.23211	−	0.711362i	−0.967470	+	0.252984i	$0.918588\pi$
$608$	−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	−0.997070	−	0.0764895i	$-0.975629\pi$
$613$	−2.36044	+	8.80929i	−0.0953373	+	0.355804i	0.901733	+	0.432293i	$0.142295\pi$
$614$	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	−0.403612	−	0.914930i	$-0.632246\pi$
$617$	−7.34468	+	1.96800i	−0.295686	+	0.0792287i	0.107927	+	0.994159i	$0.465579\pi$
$618$	26.4615	+	0.141779i	1.06444	+	0.00570318i
$619$	25.6801	+	25.6801i	1.03217	+	1.03217i	0.999465	+	0.0327040i	$0.0104119\pi$
$619$	25.6801	+	25.6801i	1.03217	+	1.03217i	0.0327040	+	0.999465i	$0.489588\pi$
$620$	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	0.180904	−	0.983501i	$-0.442098\pi$
$631$	20.8323	−	5.58201i	0.829322	−	0.222216i	0.648418	+	0.761285i	$0.275431\pi$
$632$	−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	−0.975426	−	0.220327i	$-0.929287\pi$
$641$	−41.8746	−	24.1763i	−1.65395	−	0.954907i	−0.678522	−	0.734580i	$-0.737379\pi$
$642$	−16.0027	+	9.12521i	−0.631578	+	0.360143i
$643$	−0.0193750	−	0.0723085i	−0.000764075	−	0.00285157i	0.965543	−	0.260245i	$-0.0838032\pi$
$643$	−0.0193750	−	0.0723085i	−0.000764075	−	0.00285157i	−0.966307	+	0.257393i	$0.917137\pi$
$644$	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	0.900422	−	0.435018i	$-0.143258\pi$
$647$	1.86890	+	3.23703i	0.0734741	+	0.127261i	−0.826948	+	0.562279i	$0.809925\pi$
$648$	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	−0.925055	−	0.379833i	$-0.875981\pi$
$653$	−20.2252	−	35.0310i	−0.791473	−	1.37087i	0.133583	−	0.991038i	$-0.457352\pi$
$654$	−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	−0.329084	−	0.944301i	$-0.606740\pi$
$659$	−33.6653	−	19.4367i	−1.31141	−	0.757145i	−0.982330	+	0.187155i	$0.940073\pi$
$660$	30.2521	+	0.324187i	1.17756	+	0.0126190i
$661$	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
$666$	−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	−0.257134	−	0.966376i	$-0.582778\pi$
$673$	11.7053	−	6.75805i	0.451205	−	0.260504i	0.708339	+	0.705872i	$0.249445\pi$
$674$	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	−0.391736	−	0.920078i	$-0.628125\pi$
$683$	−7.08109	+	1.89737i	−0.270950	+	0.0726010i	0.120786	+	0.992679i	$0.461459\pi$
$684$	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	0.658579	−	0.752512i	$-0.271158\pi$
$691$	22.4140	+	6.00581i	0.852669	+	0.228472i	0.194090	+	0.980984i	$0.437825\pi$
$692$	−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	$0.0110396\pi$
$701$			1.83613i			0.0693497i	−0.999399	+	0.0346748i	$0.988960\pi$
$702$	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	0.986912	−	0.161261i	$-0.0515560\pi$
$709$	1.37371	+	5.12676i	0.0515908	+	0.192540i	−0.935321	+	0.353800i	$0.884889\pi$
$710$	−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	−0.365949	−	0.930635i	$-0.619255\pi$
$719$	16.7047	−	28.9333i	0.622979	−	1.07903i	0.988928	−	0.148397i	$-0.0474112\pi$
$720$	−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	0.985019	+	0.172445i	$0.0551668\pi$
$733$	31.3372	+	31.3372i	1.15746	+	1.15746i	0.172445	+	0.985019i	$0.444833\pi$
$734$	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	0.531488	+	0.847066i	$0.321633\pi$
$739$	−9.57785	+	35.7450i	−0.352327	+	1.31490i	−0.883815	+	0.467836i	$0.845034\pi$
$740$	−4.25176	+	7.18534i	−0.156298	+	0.264138i
$741$	13.4233	+	2.18045i	0.493116	+	0.0801010i
$742$	3.70958	+	1.01531i	0.136183	+	0.0372733i
$743$	−12.2084	−	3.27124i	−0.447884	−	0.120010i	0.0278251	−	0.999613i	$-0.491142\pi$
$743$	−12.2084	−	3.27124i	−0.447884	−	0.120010i	−0.475709	+	0.879603i	$0.657809\pi$
$744$	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	0.599109	−	0.800668i	$-0.295522\pi$
$751$	−10.7931	−	18.6941i	−0.393844	−	0.682159i	−0.992953	+	0.118509i	$0.962188\pi$
$752$	−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	0.925733	−	0.378179i	$-0.123449\pi$
$757$	3.72408	+	6.45030i	0.135354	+	0.234440i	−0.790379	+	0.612619i	$0.790116\pi$
$758$	−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	0.952847	+	0.303450i	$0.0981385\pi$
$761$	7.70710	+	28.7633i	0.279382	+	1.04267i	−0.673465	+	0.739219i	$0.735195\pi$
$762$	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	−0.276433	−	0.961033i	$-0.589152\pi$
$769$	12.2981	−	45.8972i	0.443482	−	1.65510i	0.719914	−	0.694063i	$-0.244181\pi$
$770$	−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	0.216732	−	0.976231i	$-0.430460\pi$
$773$	24.8153	−	6.64923i	0.892543	−	0.239156i	0.675811	+	0.737075i	$0.263794\pi$
$774$	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	−0.0477596	−	0.998859i	$-0.515208\pi$
$787$	11.5106	−	3.08426i	0.410309	−	0.109942i	0.458068	+	0.888917i	$0.348541\pi$
$788$	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	0.265717	−	0.964051i	$-0.414391\pi$
$797$	−12.3178	−	7.11167i	−0.436318	−	0.251908i	−0.702034	+	0.712143i	$0.747725\pi$
$798$	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	0.915560	−	0.402182i	$-0.131748\pi$
$809$	3.11393	+	5.39349i	0.109480	+	0.189625i	−0.806080	+	0.591807i	$0.798415\pi$
$810$	−16.7084	+	16.5303i	−0.587074	+	0.580816i
$811$	−8.66022	+	8.66022i	−0.304102	+	0.304102i	−0.842616	−	0.538515i	$-0.818986\pi$
$811$	−8.66022	+	8.66022i	−0.304102	+	0.304102i	0.538515	+	0.842616i	$0.318986\pi$
$812$	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	0.843046	+	0.537842i	$0.180760\pi$
$821$	−4.46914	+	16.6791i	−0.155974	+	0.582104i	−0.999020	+	0.0442618i	$0.985906\pi$
$822$	6.86372	+	26.1759i	0.239400	+	0.912990i
$823$	8.61216	−	14.9167i	0.300201	−	0.519963i	−0.675980	−	0.736920i	$-0.736280\pi$
$823$	8.61216	−	14.9167i	0.300201	−	0.519963i	0.976181	+	0.216956i	$0.0696130\pi$
$824$	−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	0.830855	−	0.556489i	$-0.187852\pi$
$827$	7.89012	+	7.89012i	0.274366	+	0.274366i	−0.556489	+	0.830855i	$0.687852\pi$
$828$	1.86475	+	3.31128i	0.0648045	+	0.115075i
$829$	−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	$0.450010\pi$
$830$	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	−0.513286	−	0.858218i	$-0.671572\pi$
$839$	−15.3139	+	4.10335i	−0.528695	+	0.141663i	−0.0154095	+	0.999881i	$0.504905\pi$
$840$	−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	−0.728343	−	0.685213i	$-0.759709\pi$
$853$	−1.25966	+	1.25966i	−0.0431300	+	0.0431300i	0.685213	+	0.728343i	$0.259709\pi$
$854$	−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	$-0.986983\pi$
$857$		−	2.39366i		−	0.0817658i	0.999164	−	0.0408829i	$-0.0130171\pi$
$858$	12.4811	+	33.4416i	0.426096	+	1.14168i
$859$		−	17.8687i		−	0.609673i	−0.952405	−	0.304837i	$-0.901398\pi$
$859$		−	17.8687i		−	0.609673i	0.952405	−	0.304837i	$-0.0986018\pi$
$860$	−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	−0.928322	−	0.371776i	$-0.878749\pi$
$863$	−16.3496	+	16.3496i	−0.556546	+	0.556546i	0.371776	+	0.928322i	$0.378749\pi$
$864$	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	−0.160702	−	0.987003i	$-0.551376\pi$
$877$	5.73412	−	1.53645i	0.193628	−	0.0518824i	0.354330	+	0.935121i	$0.384709\pi$
$878$	−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	−0.931625	−	0.363422i	$-0.881608\pi$
$881$	−32.1364	+	18.5540i	−1.08270	+	0.625099i	−0.151079	+	0.988522i	$0.548275\pi$
$882$	−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	0.147609	−	0.989046i	$-0.452842\pi$
$887$	32.1042	−	18.5354i	1.07795	−	0.622356i	0.930343	+	0.366689i	$0.119509\pi$
$888$	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	−0.998477	−	0.0551749i	$-0.982428\pi$
$907$	−16.4743	−	28.5344i	−0.547021	−	0.947468i	0.451456	−	0.892294i	$-0.350905\pi$
$908$	−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	$0.122543\pi$
$911$			22.6697i			0.751082i	−0.926806	+	0.375541i	$0.877457\pi$
$912$	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	0.618723	−	0.785610i	$-0.287651\pi$
$919$	7.50982	+	4.33579i	0.247726	+	0.143025i	−0.370997	+	0.928634i	$0.620984\pi$
$920$	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	−0.0280869	−	0.999605i	$-0.508942\pi$
$929$	13.6363	−	3.65383i	0.447392	−	0.119878i	0.475479	+	0.879727i	$0.342275\pi$
$930$	−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	0.771537	−	0.636184i	$-0.219488\pi$
$941$	4.15205	+	4.15205i	0.135353	+	0.135353i	−0.636184	+	0.771537i	$0.719488\pi$
$942$	−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	−0.976916	−	0.213623i	$-0.931474\pi$
$947$	−0.740729	+	2.76444i	−0.0240705	+	0.0898322i	0.952846	+	0.303455i	$0.0981403\pi$
$948$	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	0.618657	−	0.785661i	$-0.287677\pi$
$953$	7.64309	+	4.41274i	0.247584	+	0.142943i	−0.371074	+	0.928603i	$0.621010\pi$
$954$	−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	−0.00141655	+	0.999999i	$0.500451\pi$
$967$	−31.1406	+	31.1406i	−1.00142	+	1.00142i	−0.999999	+	0.00141655i	$0.999549\pi$
$968$	−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	0.700356	−	0.713794i	$-0.253025\pi$
$971$	13.4730	+	7.77866i	0.432370	+	0.249629i	−0.267986	+	0.963423i	$0.586358\pi$
$972$	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	0.490348	+	0.871526i	$0.336870\pi$
$977$	−11.5672	+	43.1696i	−0.370069	+	1.38112i	−0.860417	+	0.509590i	$0.829797\pi$
$978$	−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	0.282343	−	0.959314i	$-0.408888\pi$
$983$	−21.2250	−	21.2250i	−0.676971	−	0.676971i	−0.959314	+	0.282343i	$0.908888\pi$
$984$	−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	−0.732557	−	0.680706i	$-0.761673\pi$
$991$	−16.0337	+	9.25705i	−0.509327	+	0.294060i	0.223230	+	0.974766i	$0.428340\pi$
$992$	−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	−0.00423556	−	0.999991i	$-0.501348\pi$
$997$	27.2779	−	47.2467i	0.863900	−	1.49632i	0.868135	−	0.496327i	$-0.165318\pi$
$998$	−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.11.1	✓	16
3.2	odd	2		468.2.cb.f.271.4		16
4.3	odd	2	inner	52.2.l.b.11.4	yes	16
8.3	odd	2		832.2.bu.n.63.3		16
8.5	even	2		832.2.bu.n.63.2		16
12.11	even	2		468.2.cb.f.271.1		16
13.2	odd	12		676.2.f.h.239.3		16
13.3	even	3		676.2.f.h.99.7		16
13.4	even	6		676.2.l.i.319.3		16
13.5	odd	4		676.2.l.m.587.1		16
13.6	odd	12	inner	52.2.l.b.19.4	yes	16
13.7	odd	12		676.2.l.k.19.1		16
13.8	odd	4		676.2.l.i.587.4		16
13.9	even	3		676.2.l.m.319.2		16
13.10	even	6		676.2.f.i.99.2		16
13.11	odd	12		676.2.f.i.239.6		16
13.12	even	2		676.2.l.k.427.4		16
39.32	even	12		468.2.cb.f.19.1		16
52.3	odd	6		676.2.f.h.99.3		16
52.7	even	12		676.2.l.k.19.4		16
52.11	even	12		676.2.f.i.239.2		16
52.15	even	12		676.2.f.h.239.7		16
52.19	even	12	inner	52.2.l.b.19.1	yes	16
52.23	odd	6		676.2.f.i.99.6		16
52.31	even	4		676.2.l.m.587.2		16
52.35	odd	6		676.2.l.m.319.1		16
52.43	odd	6		676.2.l.i.319.4		16
52.47	even	4		676.2.l.i.587.3		16
52.51	odd	2		676.2.l.k.427.1		16
104.19	even	12		832.2.bu.n.383.2		16
104.45	odd	12		832.2.bu.n.383.3		16
156.71	odd	12		468.2.cb.f.19.4		16

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

\(f(q)\)	\(=\)	\(q+(-1.22094 - 0.713659i) q^{2} +(1.40004 - 0.808315i) q^{3} +(0.981383 + 1.74267i) q^{4} +(-1.52798 - 1.52798i) q^{5} +(-2.28623 - 0.0122495i) q^{6} +(1.97429 - 0.529008i) q^{7} +(0.0454612 - 2.82806i) q^{8} +(-0.193255 + 0.334727i) q^{9} +O(q^{10})\)	\(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

L-functions

Modular forms

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