LMFDB - Embedded newform 153.2.s.a.113.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			113.16
Character	$\chi$	$=$	153.113
Dual form			153.2.s.a.65.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.37615 - 0.312826i) q^{2} +(-1.39072 - 1.03242i) q^{3} +(3.61637 - 0.969004i) q^{4} +(-0.222937 - 0.452071i) q^{5} +(-3.62753 - 2.01814i) q^{6} +(-0.665919 - 0.328395i) q^{7} +(3.86148 - 1.59948i) q^{8} +(0.868203 + 2.87162i) q^{9} +O(q^{10})$	\(q+(2.37615 - 0.312826i) q^{2} +(-1.39072 - 1.03242i) q^{3} +(3.61637 - 0.969004i) q^{4} +(-0.222937 - 0.452071i) q^{5} +(-3.62753 - 2.01814i) q^{6} +(-0.665919 - 0.328395i) q^{7} +(3.86148 - 1.59948i) q^{8} +(0.868203 + 2.87162i) q^{9} +(-0.671150 - 1.00445i) q^{10} +(0.966772 - 0.328175i) q^{11} +(-6.02979 - 2.38602i) q^{12} +(1.39452 + 5.20440i) q^{13} +(-1.68505 - 0.571999i) q^{14} +(-0.156686 + 0.858869i) q^{15} +(2.19038 - 1.26462i) q^{16} +(-3.71857 + 1.78107i) q^{17} +(2.96130 + 6.55181i) q^{18} +(-3.37354 - 1.39737i) q^{19} +(-1.24428 - 1.41883i) q^{20} +(0.587064 + 1.14422i) q^{21} +(2.19453 - 1.08222i) q^{22} +(0.352872 - 0.402373i) q^{23} +(-7.02157 - 1.76226i) q^{24} +(2.88914 - 3.76520i) q^{25} +(4.94165 + 11.9302i) q^{26} +(1.75731 - 4.88998i) q^{27} +(-2.72643 - 0.542320i) q^{28} +(0.414188 - 6.31929i) q^{29} +(-0.103633 + 2.08982i) q^{30} +(-0.330507 + 0.973643i) q^{31} +(-1.82278 + 1.39867i) q^{32} +(-1.68332 - 0.541719i) q^{33} +(-8.27872 + 5.39536i) q^{34} +0.374254i q^{35} +(5.92236 + 9.54357i) q^{36} +(2.20919 + 11.1064i) q^{37} +(-8.45317 - 2.26502i) q^{38} +(3.43377 - 8.67759i) q^{39} +(-1.58394 - 1.38908i) q^{40} +(-6.68958 + 0.438458i) q^{41} +(1.75289 + 2.53518i) q^{42} +(2.33510 + 1.79179i) q^{43} +(3.17821 - 2.12361i) q^{44} +(1.10462 - 1.03268i) q^{45} +(0.712603 - 1.06649i) q^{46} +(3.06452 - 11.4370i) q^{47} +(-4.35183 - 0.502674i) q^{48} +(-3.92573 - 5.11610i) q^{49} +(5.68718 - 9.85048i) q^{50} +(7.01031 + 1.36217i) q^{51} +(10.0862 + 17.4698i) q^{52} +(3.30651 - 7.98262i) q^{53} +(2.64591 - 12.1690i) q^{54} +(-0.363887 - 0.363887i) q^{55} +(-3.09669 - 0.202968i) q^{56} +(3.24898 + 5.42627i) q^{57} +(-0.992666 - 15.1452i) q^{58} +(1.14780 - 8.71842i) q^{59} +(0.265612 + 3.25782i) q^{60} +(-2.81827 + 5.71489i) q^{61} +(-0.480754 + 2.41691i) q^{62} +(0.364874 - 2.19738i) q^{63} +(-7.47053 + 7.47053i) q^{64} +(2.04187 - 1.79067i) q^{65} +(-4.16930 - 0.760618i) q^{66} +(8.82398 + 5.09452i) q^{67} +(-11.7219 + 10.0443i) q^{68} +(-0.906165 + 0.195275i) q^{69} +(0.117076 + 0.889283i) q^{70} +(-4.19907 + 0.835247i) q^{71} +(7.94564 + 9.70004i) q^{72} +(2.65455 + 1.77371i) q^{73} +(8.72372 + 25.6993i) q^{74} +(-7.90527 + 2.25352i) q^{75} +(-13.5540 - 1.78442i) q^{76} +(-0.751563 - 0.0989451i) q^{77} +(5.44457 - 21.6934i) q^{78} +(-3.32914 - 9.80734i) q^{79} +(-1.06001 - 0.708279i) q^{80} +(-7.49245 + 4.98630i) q^{81} +(-15.7583 + 3.13452i) q^{82} +(-0.169437 - 1.28700i) q^{83} +(3.23179 + 3.56904i) q^{84} +(1.63418 + 1.28399i) q^{85} +(6.10907 + 3.52707i) q^{86} +(-7.10021 + 8.36075i) q^{87} +(3.20826 - 2.81357i) q^{88} +(-2.39586 + 2.39586i) q^{89} +(2.30170 - 2.79936i) q^{90} +(0.780465 - 3.92366i) q^{91} +(0.886215 - 1.79707i) q^{92} +(1.46485 - 1.01284i) q^{93} +(3.70399 - 28.1346i) q^{94} +(0.120377 + 1.83661i) q^{95} +(3.97899 - 0.0632744i) q^{96} +(15.9021 + 1.04228i) q^{97} +(-10.9286 - 10.9286i) q^{98} +(1.78175 + 2.49128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.37615	−	0.312826i	1.68019	−	0.221201i	0.770781	−	0.637101i	$-0.219866\pi$
$2$	2.37615	−	0.312826i	1.68019	−	0.221201i	0.909411	+	0.415899i	$0.136533\pi$
$3$	−1.39072	−	1.03242i	−0.802932	−	0.596070i
$3$	−1.39072	−	1.03242i	−0.802932	−	0.596070i
$4$	3.61637	−	0.969004i	1.80819	−	0.484502i
$5$	−0.222937	−	0.452071i	−0.0997003	−	0.202172i	0.841308	−	0.540557i	$-0.181786\pi$
$5$	−0.222937	−	0.452071i	−0.0997003	−	0.202172i	−0.941008	+	0.338384i	$0.890120\pi$
$6$	−3.62753	−	2.01814i	−1.48093	−	0.823902i
$7$	−0.665919	−	0.328395i	−0.251694	−	0.124122i	0.312066	−	0.950060i	$-0.398979\pi$
$7$	−0.665919	−	0.328395i	−0.251694	−	0.124122i	−0.563760	+	0.825939i	$0.690646\pi$
$8$	3.86148	−	1.59948i	1.36524	−	0.565500i
$9$	0.868203	+	2.87162i	0.289401	+	0.957208i
$10$	−0.671150	−	1.00445i	−0.212236	−	0.317634i
$11$	0.966772	−	0.328175i	0.291493	−	0.0989485i	−0.171863	−	0.985121i	$-0.554979\pi$
$11$	0.966772	−	0.328175i	0.291493	−	0.0989485i	0.463356	+	0.886172i	$0.346645\pi$
$12$	−6.02979	−	2.38602i	−1.74065	−	0.688784i
$13$	1.39452	+	5.20440i	0.386769	+	1.44344i	0.835360	+	0.549704i	$0.185259\pi$
$13$	1.39452	+	5.20440i	0.386769	+	1.44344i	−0.448591	+	0.893737i	$0.648074\pi$
$14$	−1.68505	−	0.571999i	−0.450349	−	0.152873i
$15$	−0.156686	+	0.858869i	−0.0404562	+	0.221759i
$16$	2.19038	−	1.26462i	0.547596	−	0.316155i
$17$	−3.71857	+	1.78107i	−0.901886	+	0.431973i
$17$	−3.71857	+	1.78107i	−0.901886	+	0.431973i
$18$	2.96130	+	6.55181i	0.697985	+	1.54428i
$19$	−3.37354	−	1.39737i	−0.773944	−	0.320578i	−0.0394751	−	0.999221i	$-0.512569\pi$
$19$	−3.37354	−	1.39737i	−0.773944	−	0.320578i	−0.734469	+	0.678643i	$0.762569\pi$
$20$	−1.24428	−	1.41883i	−0.278230	−	0.317260i
$21$	0.587064	+	1.14422i	0.128108	+	0.249688i
$22$	2.19453	−	1.08222i	0.467876	−	0.230731i
$23$	0.352872	−	0.402373i	0.0735788	−	0.0839006i	−0.713879	−	0.700269i	$-0.753063\pi$
$23$	0.352872	−	0.402373i	0.0735788	−	0.0839006i	0.787458	+	0.616368i	$0.211397\pi$
$24$	−7.02157	−	1.76226i	−1.43327	−	0.359719i
$25$	2.88914	−	3.76520i	0.577828	−	0.753040i
$26$	4.94165	+	11.9302i	0.969137	+	2.33970i
$27$	1.75731	−	4.88998i	0.338194	−	0.941077i
$28$	−2.72643	−	0.542320i	−0.515246	−	0.102489i
$29$	0.414188	−	6.31929i	0.0769129	−	1.17346i	−0.768679	−	0.639634i	$-0.779086\pi$
$29$	0.414188	−	6.31929i	0.0769129	−	1.17346i	0.845592	−	0.533829i	$-0.179247\pi$
$30$	−0.103633	+	2.08982i	−0.0189208	+	0.381547i
$31$	−0.330507	+	0.973643i	−0.0593609	+	0.174871i	−0.972565	−	0.232631i	$-0.925267\pi$
$31$	−0.330507	+	0.973643i	−0.0593609	+	0.174871i	0.913204	+	0.407502i	$0.133600\pi$
$32$	−1.82278	+	1.39867i	−0.322225	+	0.247252i
$33$	−1.68332	−	0.541719i	−0.293029	−	0.0943012i
$34$	−8.27872	+	5.39536i	−1.41979	+	0.925296i
$35$			0.374254i			0.0632604i
$36$	5.92236	+	9.54357i	0.987060	+	1.59060i
$37$	2.20919	+	11.1064i	0.363189	+	1.82587i	0.540045	+	0.841636i	$0.318407\pi$
$37$	2.20919	+	11.1064i	0.363189	+	1.82587i	−0.176856	+	0.984237i	$0.556593\pi$
$38$	−8.45317	−	2.26502i	−1.37129	−	0.367435i
$39$	3.43377	−	8.67759i	0.549843	−	1.38953i
$40$	−1.58394	−	1.38908i	−0.250443	−	0.219633i
$41$	−6.68958	+	0.438458i	−1.04474	+	0.0684757i	−0.578094	−	0.815970i	$-0.696203\pi$
$41$	−6.68958	+	0.438458i	−1.04474	+	0.0684757i	−0.466643	+	0.884446i	$0.654537\pi$
$42$	1.75289	+	2.53518i	0.270477	+	0.391187i
$43$	2.33510	+	1.79179i	0.356100	+	0.273245i	0.771282	−	0.636493i	$-0.219616\pi$
$43$	2.33510	+	1.79179i	0.356100	+	0.273245i	−0.415183	+	0.909738i	$0.636282\pi$
$44$	3.17821	−	2.12361i	0.479133	−	0.320146i
$45$	1.10462	−	1.03268i	0.164668	−	0.153943i
$46$	0.712603	−	1.06649i	0.105068	−	0.157245i
$47$	3.06452	−	11.4370i	0.447007	−	1.66825i	−0.263576	−	0.964639i	$-0.584902\pi$
$47$	3.06452	−	11.4370i	0.447007	−	1.66825i	0.710583	−	0.703614i	$-0.248431\pi$
$48$	−4.35183	−	0.502674i	−0.628133	−	0.0725547i
$49$	−3.92573	−	5.11610i	−0.560818	−	0.730872i
$50$	5.68718	−	9.85048i	0.804288	−	1.39307i
$51$	7.01031	+	1.36217i	0.981640	+	0.190742i
$52$	10.0862	+	17.4698i	1.39870	+	2.42262i
$53$	3.30651	−	7.98262i	0.454184	−	1.09650i	−0.516532	−	0.856268i	$-0.672777\pi$
$53$	3.30651	−	7.98262i	0.454184	−	1.09650i	0.970716	−	0.240230i	$-0.0772228\pi$
$54$	2.64591	−	12.1690i	0.360062	−	1.65600i
$55$	−0.363887	−	0.363887i	−0.0490666	−	0.0490666i
$56$	−3.09669	−	0.202968i	−0.413813	−	0.0271227i
$57$	3.24898	+	5.42627i	0.430338	+	0.718727i
$58$	−0.992666	−	15.1452i	−0.130343	−	1.98866i
$59$	1.14780	−	8.71842i	0.149431	−	1.13504i	−0.738232	−	0.674547i	$-0.764339\pi$
$59$	1.14780	−	8.71842i	0.149431	−	1.13504i	0.887663	−	0.460494i	$-0.152328\pi$
$60$	0.265612	+	3.25782i	0.0342904	+	0.420583i
$61$	−2.81827	+	5.71489i	−0.360843	+	0.731716i	−0.999279	−	0.0379579i	$-0.987915\pi$
$61$	−2.81827	+	5.71489i	−0.360843	+	0.731716i	0.638437	+	0.769674i	$0.279581\pi$
$62$	−0.480754	+	2.41691i	−0.0610558	+	0.306948i
$63$	0.364874	−	2.19738i	0.0459698	−	0.276844i
$64$	−7.47053	+	7.47053i	−0.933817	+	0.933817i
$65$	2.04187	−	1.79067i	0.253263	−	0.222105i
$66$	−4.16930	−	0.760618i	−0.513205	−	0.0936256i
$67$	8.82398	+	5.09452i	1.07802	+	0.622395i	0.930362	−	0.366643i	$-0.119493\pi$
$67$	8.82398	+	5.09452i	1.07802	+	0.622395i	0.147659	+	0.989038i	$0.452826\pi$
$68$	−11.7219	+	10.0443i	−1.42149	+	1.21805i
$69$	−0.906165	+	0.195275i	−0.109089	+	0.0235084i
$70$	0.117076	+	0.889283i	0.0139933	+	0.106290i
$71$	−4.19907	+	0.835247i	−0.498338	+	0.0991255i	−0.437858	−	0.899044i	$-0.644263\pi$
$71$	−4.19907	+	0.835247i	−0.498338	+	0.0991255i	−0.0604793	+	0.998169i	$0.519263\pi$
$72$	7.94564	+	9.70004i	0.936403	+	1.14316i
$73$	2.65455	+	1.77371i	0.310691	+	0.207597i	0.701133	−	0.713030i	$-0.252678\pi$
$73$	2.65455	+	1.77371i	0.310691	+	0.207597i	−0.390442	+	0.920627i	$0.627678\pi$
$74$	8.72372	+	25.6993i	1.01411	+	2.98748i
$75$	−7.90527	+	2.25352i	−0.912821	+	0.260214i
$76$	−13.5540	−	1.78442i	−1.55476	−	0.204687i
$77$	−0.751563	−	0.0989451i	−0.0856485	−	0.0112758i
$78$	5.44457	−	21.6934i	0.616476	−	2.45630i
$79$	−3.32914	−	9.80734i	−0.374558	−	1.10341i	−0.956887	−	0.290459i	$-0.906192\pi$
$79$	−3.32914	−	9.80734i	−0.374558	−	1.10341i	0.582330	−	0.812953i	$-0.302141\pi$
$80$	−1.06001	−	0.708279i	−0.118513	−	0.0791880i
$81$	−7.49245	+	4.98630i	−0.832494	+	0.554034i
$82$	−15.7583	+	3.13452i	−1.74021	+	0.346149i
$83$	−0.169437	−	1.28700i	−0.0185982	−	0.141267i	0.979627	−	0.200828i	$-0.0643633\pi$
$83$	−0.169437	−	1.28700i	−0.0185982	−	0.141267i	−0.998225	+	0.0595610i	$0.981030\pi$
$84$	3.23179	+	3.56904i	0.352618	+	0.389415i
$85$	1.63418	+	1.28399i	0.177251	+	0.139269i
$86$	6.10907	+	3.52707i	0.658758	+	0.380334i
$87$	−7.10021	+	8.36075i	−0.761222	+	0.896366i
$88$	3.20826	−	2.81357i	0.342002	−	0.299927i
$89$	−2.39586	+	2.39586i	−0.253961	+	0.253961i	−0.822592	−	0.568632i	$-0.807473\pi$
$89$	−2.39586	+	2.39586i	−0.253961	+	0.253961i	0.568632	+	0.822592i	$0.307473\pi$
$90$	2.30170	−	2.79936i	0.242621	−	0.295078i
$91$	0.780465	−	3.92366i	0.0818149	−	0.411311i
$92$	0.886215	−	1.79707i	0.0923943	−	0.187357i
$93$	1.46485	−	1.01284i	0.151898	−	0.105027i
$94$	3.70399	−	28.1346i	0.382037	−	2.90186i
$95$	0.120377	+	1.83661i	0.0123505	+	0.188432i
$96$	3.97899	−	0.0632744i	0.406104	−	0.00645791i
$97$	15.9021	+	1.04228i	1.61461	+	0.105827i	0.845746	−	0.533586i	$-0.179156\pi$
$97$	15.9021	+	1.04228i	1.61461	+	0.105827i	0.768863	+	0.639413i	$0.220823\pi$
$98$	−10.9286	−	10.9286i	−1.10395	−	1.10395i
$99$	1.78175	+	2.49128i	0.179073	+	0.250383i
$100$	6.79971	−	16.4160i	0.679971	−	1.64160i
$101$	6.54019	+	11.3279i	0.650773	+	1.12717i	0.982936	+	0.183949i	$0.0588883\pi$
$101$	6.54019	+	11.3279i	0.650773	+	1.12717i	−0.332163	+	0.943222i	$0.607778\pi$
$102$	17.0837	+	1.04371i	1.69154	+	0.103343i
$103$	−3.23969	+	5.61131i	−0.319216	+	0.552899i	−0.980325	−	0.197391i	$-0.936753\pi$
$103$	−3.23969	+	5.61131i	−0.319216	+	0.552899i	0.661108	+	0.750290i	$0.270086\pi$
$104$	13.7092	+	17.8662i	1.34430	+	1.75192i
$105$	0.386389	−	0.520482i	0.0377077	−	0.0507939i
$106$	5.35959	−	20.0023i	0.520570	−	1.94279i
$107$	−8.20002	+	12.2722i	−0.792726	+	1.18640i	0.186266	+	0.982499i	$0.440361\pi$
$107$	−8.20002	+	12.2722i	−0.792726	+	1.18640i	−0.978992	+	0.203899i	$0.934639\pi$
$108$	1.61666	−	19.3868i	0.155564	−	1.86550i
$109$	0.866335	−	0.578867i	0.0829798	−	0.0554454i	−0.513388	−	0.858156i	$-0.671610\pi$
$109$	0.866335	−	0.578867i	0.0829798	−	0.0554454i	0.596368	+	0.802711i	$0.296610\pi$
$110$	−0.978484	−	0.750817i	−0.0932948	−	0.0715876i
$111$	8.39409	−	17.7266i	0.796732	−	1.68254i
$112$	−1.87391	+	0.122823i	−0.177068	+	0.0116057i
$113$	3.58041	+	3.13993i	0.336817	+	0.295380i	0.811000	−	0.585046i	$-0.198923\pi$
$113$	3.58041	+	3.13993i	0.336817	+	0.295380i	−0.474184	+	0.880426i	$0.657257\pi$
$114$	9.41754	+	11.8773i	0.882033	+	1.11241i
$115$	−0.260569	−	0.0698193i	−0.0242982	−	0.00651068i
$116$	−4.62556	−	23.2543i	−0.429473	−	2.15911i
$117$	−13.7344	+	8.52300i	−1.26974	+	0.787952i
$118$		−	21.0753i		−	1.94014i
$119$	3.06116	+	0.0351111i	0.280616	+	0.00321863i
$120$	0.768700	+	3.56712i	0.0701724	+	0.325632i
$121$	−7.89994	+	6.06183i	−0.718176	+	0.551076i
$122$	−4.90887	+	14.4611i	−0.444428	+	1.30924i
$123$	9.75600	+	6.29671i	0.879669	+	0.567755i
$124$	−0.251773	+	3.84132i	−0.0226099	+	0.344961i
$125$	−4.81807	−	0.958374i	−0.430941	−	0.0857195i
$126$	0.179596	−	5.33545i	0.0159997	−	0.475320i
$127$	−2.87472	−	6.94019i	−0.255090	−	0.615843i	0.743510	−	0.668724i	$-0.233159\pi$
$127$	−2.87472	−	6.94019i	−0.255090	−	0.615843i	−0.998601	+	0.0528818i	$0.983159\pi$
$128$	−12.6168	+	16.4425i	−1.11518	+	1.45333i
$129$	−1.39759	−	4.90269i	−0.123051	−	0.431658i
$130$	4.29162	−	4.89365i	0.376400	−	0.429202i
$131$	3.94700	−	1.94645i	0.344851	−	0.170062i	−0.261612	−	0.965173i	$-0.584254\pi$
$131$	3.94700	−	1.94645i	0.344851	−	0.170062i	0.606464	+	0.795111i	$0.292588\pi$
$132$	−6.61246	−	0.327910i	−0.575541	−	0.0285409i
$133$	1.78762	+	2.03839i	0.155006	+	0.176751i
$134$	22.5608	+	9.34498i	1.94895	+	0.807284i
$135$	−2.60238	+	0.295729i	−0.223978	+	0.0254523i
$136$	−11.5104	+	12.8253i	−0.987009	+	1.09976i
$137$	5.46680	−	3.15626i	0.467060	−	0.269657i	−0.247948	−	0.968773i	$-0.579756\pi$
$137$	5.46680	−	3.15626i	0.467060	−	0.269657i	0.715008	+	0.699116i	$0.246423\pi$
$138$	−2.09210	+	0.747475i	−0.178091	+	0.0636293i
$139$	−14.3494	−	4.87096i	−1.21710	−	0.413149i	−0.362276	−	0.932071i	$-0.618000\pi$
$139$	−14.3494	−	4.87096i	−1.21710	−	0.413149i	−0.854822	+	0.518922i	$0.826334\pi$
$140$	0.362654	+	1.35344i	0.0306498	+	0.114387i
$141$	−16.0697	+	12.7417i	−1.35331	+	1.07305i
$142$	−9.71633	+	3.29825i	−0.815376	+	0.276783i
$143$	3.05613	+	4.57383i	0.255567	+	0.382483i
$144$	5.53321	+	5.19201i	0.461101	+	0.432668i
$145$	−2.94911	+	1.22156i	−0.244910	+	0.101445i
$146$	6.86246	+	3.38419i	0.567941	+	0.280078i
$147$	0.177596	+	11.1681i	0.0146479	+	0.921128i
$148$	18.7514	+	38.0240i	1.54135	+	3.12555i
$149$	−7.14890	+	1.91554i	−0.585661	+	0.156927i	−0.539469	−	0.842005i	$-0.681375\pi$
$149$	−7.14890	+	1.91554i	−0.585661	+	0.156927i	−0.0461915	+	0.998933i	$0.514708\pi$
$150$	−18.0791	+	7.82768i	−1.47615	+	0.639127i
$151$	2.43620	−	0.320732i	0.198255	−	0.0261008i	−0.0307447	−	0.999527i	$-0.509788\pi$
$151$	2.43620	−	0.320732i	0.198255	−	0.0261008i	0.229000	+	0.973427i	$0.426455\pi$
$152$	−15.2619			−1.23790
$153$	−8.34304	−	9.13201i	−0.674495	−	0.738279i
$154$	−1.81678			−0.146400
$155$	0.513838	−	0.0676480i	0.0412724	−	0.00543362i
$156$	4.00916	−	34.7088i	0.320990	−	2.77892i
$157$	9.25817	−	2.48072i	0.738883	−	0.197983i	0.130301	−	0.991474i	$-0.458406\pi$
$157$	9.25817	−	2.48072i	0.738883	−	0.197983i	0.608581	+	0.793491i	$0.291739\pi$
$158$	−10.9785	−	22.2623i	−0.873405	−	1.77109i
$159$	−12.8399	+	7.68787i	−1.01827	+	0.609688i
$160$	1.03866	+	0.512211i	0.0821133	+	0.0404938i
$161$	−0.367121	+	0.152067i	−0.0289332	+	0.0119845i
$162$	−16.2433	+	14.1920i	−1.27620	+	1.11503i
$163$	3.62885	+	5.43096i	0.284234	+	0.425386i	0.945922	−	0.324393i	$-0.105160\pi$
$163$	3.62885	+	5.43096i	0.284234	+	0.425386i	−0.661689	+	0.749779i	$0.730160\pi$
$164$	−23.7671	+	8.06786i	−1.85590	+	0.629994i
$165$	0.130379	+	0.881751i	0.0101500	+	0.0686442i
$166$	−0.805217	−	3.00511i	−0.0624970	−	0.233242i
$167$	3.86302	+	1.31132i	0.298929	+	0.101473i	0.466875	−	0.884323i	$-0.345380\pi$
$167$	3.86302	+	1.31132i	0.298929	+	0.101473i	−0.167945	+	0.985796i	$0.553713\pi$
$168$	4.09708	+	3.47937i	0.316097	+	0.268439i
$169$	−13.8828	+	8.01523i	−1.06791	+	0.616556i
$170$	4.28471	+	2.53974i	0.328623	+	0.194790i
$171$	1.08379	−	10.9007i	0.0828798	−	0.833601i
$172$	10.1809	+	4.21705i	0.776283	+	0.321547i
$173$	5.42802	+	6.18947i	0.412685	+	0.470577i	0.920417	−	0.390938i	$-0.127849\pi$
$173$	5.42802	+	6.18947i	0.412685	+	0.470577i	−0.507732	+	0.861515i	$0.669516\pi$
$174$	−14.2557	+	22.0875i	−1.08072	+	1.67445i
$175$	−3.16041	+	1.55854i	−0.238904	+	0.117815i
$176$	1.70259	−	1.94143i	0.128337	−	0.146341i
$177$	−10.5974	+	10.9399i	−0.796547	+	0.822290i
$178$	−4.94343	+	6.44241i	−0.370526	+	0.482879i
$179$	4.54443	+	10.9712i	0.339667	+	0.820028i	0.997748	+	0.0670807i	$0.0213685\pi$
$179$	4.54443	+	10.9712i	0.339667	+	0.820028i	−0.658081	+	0.752947i	$0.728631\pi$
$180$	2.99406	−	4.80494i	0.223164	−	0.358139i
$181$	17.5732	+	3.49554i	1.30621	+	0.259821i	0.798650	−	0.601796i	$-0.205548\pi$
$181$	17.5732	+	3.49554i	1.30621	+	0.259821i	0.507559	+	0.861617i	$0.330548\pi$
$182$	0.627077	−	9.56735i	0.0464821	−	0.709179i
$183$	9.81961	−	5.03816i	0.725886	−	0.372431i
$184$	0.719020	−	2.11816i	0.0530068	−	0.156153i
$185$	4.52835	−	3.47472i	0.332931	−	0.255467i
$186$	3.16387	−	2.86491i	0.231986	−	0.210065i
$187$	−3.01051	+	2.94223i	−0.220150	+	0.215157i
$188$		−	44.3299i		−	3.23309i
$189$	−2.77607	+	2.67924i	−0.201929	+	0.194886i
$190$	0.860573	+	4.32639i	0.0624325	+	0.313869i
$191$	−20.7356	−	5.55608i	−1.50037	−	0.402024i	−0.587148	−	0.809479i	$-0.699749\pi$
$191$	−20.7356	−	5.55608i	−1.50037	−	0.402024i	−0.913225	+	0.407456i	$0.866416\pi$
$192$	18.1022	−	2.67666i	1.30641	−	0.193172i
$193$	−6.77019	−	5.93730i	−0.487329	−	0.427376i	0.380094	−	0.924948i	$-0.375892\pi$
$193$	−6.77019	−	5.93730i	−0.487329	−	0.427376i	−0.867423	+	0.497572i	$0.834225\pi$
$194$	38.1117	−	2.49797i	2.73626	−	0.179344i
$195$	−4.68840	+	0.382248i	−0.335743	+	0.0273733i
$196$	−19.1544	−	14.6977i	−1.36817	−	1.04984i
$197$	15.1511	−	10.1237i	1.07947	−	0.721281i	0.117130	−	0.993117i	$-0.462631\pi$
$197$	15.1511	−	10.1237i	1.07947	−	0.721281i	0.962344	+	0.271836i	$0.0876307\pi$
$198$	5.01304	+	5.36228i	0.356261	+	0.381081i
$199$	13.9975	−	20.9487i	0.992255	−	1.48501i	0.121929	−	0.992539i	$-0.461092\pi$
$199$	13.9975	−	20.9487i	0.992255	−	1.48501i	0.870326	−	0.492476i	$-0.163908\pi$
$200$	5.13400	−	19.1603i	0.363029	−	1.35484i
$201$	−7.01197	−	16.1951i	−0.494586	−	1.14232i
$202$	19.0841	+	24.8709i	1.34275	+	1.74991i
$203$	−2.35104	+	4.07212i	−0.165011	+	0.285807i
$204$	26.6719	−	1.86690i	1.86740	−	0.130709i
$205$	1.68957	+	2.92642i	0.118004	+	0.204390i
$206$	−5.94263	+	14.3468i	−0.414043	+	0.999587i
$207$	1.46183	+	0.663973i	0.101604	+	0.0461493i
$208$	9.63611	+	9.63611i	0.668144	+	0.668144i
$209$	−3.72003	−	0.243824i	−0.257320	−	0.0168656i
$210$	0.755296	−	1.35762i	0.0521204	−	0.0936844i
$211$	0.988397	+	15.0800i	0.0680441	+	1.03815i	0.886244	+	0.463218i	$0.153305\pi$
$211$	0.988397	+	15.0800i	0.0680441	+	1.03815i	−0.818200	+	0.574934i	$0.805028\pi$
$212$	4.22238	−	32.0722i	0.289994	−	2.20273i
$213$	6.70206	+	3.17362i	0.459217	+	0.217453i
$214$	−15.6454	+	31.7258i	−1.06950	+	2.16873i
$215$	0.289435	−	1.45509i	0.0197393	−	0.0992361i
$216$	−1.03561	−	21.6933i	−0.0704642	−	1.47604i
$217$	0.539830	−	0.539830i	0.0366461	−	0.0366461i
$218$	1.87746	−	1.64649i	0.127157	−	0.111514i
$219$	−1.86051	−	5.20735i	−0.125722	−	0.351880i
$220$	−1.66856	−	0.963344i	−0.112494	−	0.0649487i
$221$	−14.4550	−	16.8692i	−0.972350	−	1.13475i
$222$	14.4003	−	44.7470i	0.966483	−	3.00322i
$223$	−2.01017	−	15.2687i	−0.134611	−	1.02247i	−0.916777	−	0.399400i	$-0.869218\pi$
$223$	−2.01017	−	15.2687i	−0.134611	−	1.02247i	0.782166	−	0.623070i	$-0.214115\pi$
$224$	1.67314	−	0.332808i	0.111791	−	0.0222366i
$225$	13.3206	+	5.02757i	0.888040	+	0.335171i
$226$	9.48984	+	6.34091i	0.631255	+	0.421791i
$227$	5.72342	+	16.8607i	0.379877	+	1.11908i	0.953870	+	0.300221i	$0.0970603\pi$
$227$	5.72342	+	16.8607i	0.379877	+	1.11908i	−0.573993	+	0.818860i	$0.694606\pi$
$228$	17.0076	+	16.4752i	1.12636	+	1.09109i
$229$	−7.87450	−	1.03670i	−0.520362	−	0.0685069i	−0.134229	−	0.990950i	$-0.542856\pi$
$229$	−7.87450	−	1.03670i	−0.520362	−	0.0685069i	−0.386132	+	0.922443i	$0.626189\pi$
$230$	−0.640993	−	0.0843883i	−0.0422658	−	0.00556440i
$231$	0.943060	+	0.913536i	0.0620488	+	0.0601063i
$232$	−8.50818	−	25.0643i	−0.558589	−	1.64555i
$233$	−15.3673	−	10.2681i	−1.00675	−	0.672687i	−0.0611841	−	0.998126i	$-0.519488\pi$
$233$	−15.3673	−	10.2681i	−1.00675	−	0.672687i	−0.945563	+	0.325440i	$0.894488\pi$
$234$	−29.9687	+	24.5484i	−1.95911	+	1.60478i
$235$	−5.85351	+	1.16434i	−0.381841	+	0.0759529i
$236$	−4.29731	−	32.6413i	−0.279731	−	2.12477i
$237$	−5.49542	+	17.0763i	−0.356966	+	1.10923i
$238$	7.28476	−	0.874182i	0.472201	−	0.0566648i
$239$	14.9969	+	8.65844i	0.970067	+	0.560068i	0.899257	−	0.437422i	$-0.144108\pi$
$239$	14.9969	+	8.65844i	0.970067	+	0.560068i	0.0708101	+	0.997490i	$0.477442\pi$
$240$	0.742939	+	2.07940i	0.0479565	+	0.134225i
$241$	9.34914	−	8.19898i	0.602231	−	0.528143i	−0.303039	−	0.952978i	$-0.598001\pi$
$241$	9.34914	−	8.19898i	0.602231	−	0.528143i	0.905271	+	0.424835i	$0.139668\pi$
$242$	−16.8751	+	16.8751i	−1.08477	+	1.08477i
$243$	15.5679	+	0.800828i	0.998680	+	0.0513731i
$244$	−4.65417	+	23.3981i	−0.297953	+	1.49791i
$245$	−1.43765	+	2.91527i	−0.0918483	+	0.186250i
$246$	25.1515	+	11.9100i	1.60360	+	0.759353i
$247$	2.56800	−	19.5059i	0.163398	−	1.24113i
$248$	0.281073	+	4.28834i	0.0178481	+	0.272310i
$249$	−1.09309	+	1.96479i	−0.0692720	+	0.124514i
$250$	−11.7483	−	0.770021i	−0.743025	−	0.0487004i
$251$	12.5986	+	12.5986i	0.795218	+	0.795218i	0.982337	−	0.187119i	$-0.0599151\pi$
$251$	12.5986	+	12.5986i	0.795218	+	0.795218i	−0.187119	+	0.982337i	$0.559915\pi$
$252$	−0.809753	−	8.30012i	−0.0510096	−	0.522858i
$253$	0.209098	−	0.504807i	0.0131459	−	0.0317369i
$254$	−9.00184	−	15.5916i	−0.564826	−	0.978307i
$255$	−0.947058	−	3.47284i	−0.0593071	−	0.217477i
$256$	−14.2708	+	24.7178i	−0.891925	+	1.54486i
$257$	−6.82292	−	8.89180i	−0.425602	−	0.554655i	0.530502	−	0.847684i	$-0.322004\pi$
$257$	−6.82292	−	8.89180i	−0.425602	−	0.554655i	−0.956104	+	0.293029i	$0.905337\pi$
$258$	−4.85457	−	11.2123i	−0.302232	−	0.698049i
$259$	2.17613	−	8.12142i	0.135218	−	0.504640i
$260$	5.64900	−	8.45432i	0.350336	−	0.524315i
$261$	18.5062	−	4.29704i	1.14551	−	0.265980i
$262$	8.76977	−	5.85977i	0.541798	−	0.362018i
$263$	13.2633	+	10.1773i	0.817853	+	0.627560i	0.930590	−	0.366064i	$-0.119295\pi$
$263$	13.2633	+	10.1773i	0.817853	+	0.627560i	−0.112737	+	0.993625i	$0.535962\pi$
$264$	−7.36659	+	0.600602i	−0.453382	+	0.0369645i
$265$	−4.34585	+	0.284842i	−0.266964	+	0.0174977i
$266$	4.88531	+	4.28430i	0.299537	+	0.262687i
$267$	5.80551	−	0.858427i	0.355291	−	0.0525349i
$268$	36.8474	+	9.87323i	2.25081	+	0.603104i
$269$	1.87839	+	9.44333i	0.114528	+	0.575770i	0.994847	+	0.101388i	$0.0323284\pi$
$269$	1.87839	+	9.44333i	0.114528	+	0.575770i	−0.880319	+	0.474382i	$0.842672\pi$
$270$	−6.09114	+	1.51679i	−0.370695	+	0.0923088i
$271$			21.5828i			1.31106i	0.755168	+	0.655531i	$0.227555\pi$
$271$			21.5828i			1.31106i	−0.755168	+	0.655531i	$0.772445\pi$
$272$	−5.89273	+	8.60381i	−0.357299	+	0.521682i
$273$	−5.13629	+	4.65094i	−0.310862	+	0.281488i
$274$	12.0026	−	9.20990i	0.725102	−	0.556390i
$275$	1.55750	−	4.58823i	0.0939205	−	0.276681i
$276$	−3.08781	+	1.58427i	−0.185864	+	0.0953616i
$277$	1.67954	−	25.6248i	0.100914	−	1.53964i	−0.584443	−	0.811435i	$-0.698687\pi$
$277$	1.67954	−	25.6248i	0.100914	−	1.53964i	0.685356	−	0.728208i	$-0.259647\pi$
$278$	−35.6200	−	7.08526i	−2.13635	−	0.424946i
$279$	−3.08288	−	0.103773i	−0.184567	−	0.00621272i
$280$	0.598610	+	1.44517i	0.0357738	+	0.0863656i
$281$	7.10351	−	9.25748i	0.423760	−	0.552255i	−0.531869	−	0.846826i	$-0.678510\pi$
$281$	7.10351	−	9.25748i	0.423760	−	0.552255i	0.955629	+	0.294572i	$0.0951769\pi$
$282$	−34.1980	+	35.3032i	−2.03646	+	2.10228i
$283$	0.720976	−	0.822116i	0.0428576	−	0.0488697i	−0.730014	−	0.683432i	$-0.760486\pi$
$283$	0.720976	−	0.822116i	0.0428576	−	0.0488697i	0.772871	+	0.634563i	$0.218820\pi$
$284$	−14.3760	+	7.08948i	−0.853061	+	0.420683i
$285$	1.72874	−	2.67848i	0.102402	−	0.158660i
$286$	8.69264	+	9.91206i	0.514007	+	0.586112i
$287$	4.59870	+	1.90485i	0.271453	+	0.112439i
$288$	−5.59898	−	4.02000i	−0.329923	−	0.236881i
$289$	10.6556	−	13.2461i	0.626798	−	0.779182i
$290$	−6.62538	+	3.82517i	−0.389056	+	0.224622i
$291$	−21.0392	−	17.8672i	−1.23334	−	1.04739i
$292$	11.3186	+	3.84213i	0.662369	+	0.224844i
$293$	0.611280	+	2.28133i	0.0357113	+	0.133276i	0.981480	−	0.191564i	$-0.0613560\pi$
$293$	0.611280	+	2.28133i	0.0357113	+	0.133276i	−0.945769	+	0.324841i	$0.894689\pi$
$294$	3.91566	+	26.4815i	0.228366	+	1.54443i
$295$	−4.19723	+	1.42477i	−0.244372	+	0.0829532i
$296$	26.2951	+	39.3534i	1.52837	+	2.28737i
$297$	0.0941461	−	5.30420i	0.00546291	−	0.307781i
$298$	−16.3876	+	6.78798i	−0.949310	+	0.393217i
$299$	2.58620	+	1.27537i	0.149564	+	0.0737566i
$300$	−26.4047	+	15.8098i	−1.52448	+	0.912780i
$301$	−0.966575	−	1.96002i	−0.0557125	−	0.112974i
$302$	5.68844	−	1.52421i	0.327333	−	0.0877086i
$303$	2.59966	−	22.5062i	0.149347	−	1.29295i
$304$	−9.15649	+	1.20547i	−0.525161	+	0.0691387i
$305$	3.21183			0.183909
$306$	−22.6810	−	19.0891i	−1.29659	−	1.09125i
$307$	−31.4910			−1.79729			−0.898644	−	0.438678i	$-0.855447\pi$
$307$	−31.4910			−1.79729			−0.898644	+	0.438678i	$0.855447\pi$
$308$	−2.81381	+	0.370445i	−0.160332	+	0.0211081i
$309$	10.2988	−	4.45903i	0.585876	−	0.253665i
$310$	1.19979	−	0.321484i	0.0681437	−	0.0182590i
$311$	−4.98640	−	10.1114i	−0.282753	−	0.573366i	0.708443	−	0.705768i	$-0.249398\pi$
$311$	−4.98640	−	10.1114i	−0.282753	−	0.573366i	−0.991196	+	0.132402i	$0.957731\pi$
$312$	−0.620192	−	39.0006i	−0.0351114	−	2.20797i
$313$	7.54591	+	3.72123i	0.426520	+	0.210336i	0.642863	−	0.765981i	$-0.277746\pi$
$313$	7.54591	+	3.72123i	0.426520	+	0.210336i	−0.216343	+	0.976317i	$0.569413\pi$
$314$	21.2228	−	8.79076i	1.19767	−	0.496091i
$315$	−1.07472	+	0.324928i	−0.0605534	+	0.0183076i
$316$	−21.5428	−	32.2411i	−1.21188	−	1.81370i
$317$	1.22576	−	0.416090i	0.0688456	−	0.0233699i	−0.286804	−	0.957989i	$-0.592593\pi$
$317$	1.22576	−	0.416090i	0.0688456	−	0.0233699i	0.355650	+	0.934619i	$0.384260\pi$
$318$	−28.1045	+	22.2842i	−1.57602	+	1.24963i
$319$	−1.67341	−	6.24524i	−0.0936929	−	0.349667i
$320$	5.04267	+	1.71175i	0.281894	+	0.0956900i
$321$	24.0740	−	8.60130i	1.34368	−	0.480077i
$322$	−0.824764	+	0.476178i	−0.0459623	+	0.0265364i
$323$	15.0336	−	0.812309i	0.836491	−	0.0451981i
$324$	−22.2637	+	25.2926i	−1.23687	+	1.40514i
$325$	23.6246	+	9.78561i	1.31045	+	0.542808i
$326$	10.3216	+	11.7696i	0.571663	+	0.651856i
$327$	−1.80246	−	0.0893836i	−0.0996765	−	0.00494292i
$328$	−25.1303	+	12.3929i	−1.38759	+	0.684284i
$329$	−5.79656	+	6.60972i	−0.319575	+	0.364405i
$330$	0.585636	+	2.05439i	0.0322382	+	0.113090i
$331$	4.04081	−	5.26609i	0.222103	−	0.289450i	−0.668990	−	0.743272i	$-0.733273\pi$
$331$	4.04081	−	5.26609i	0.222103	−	0.289450i	0.891093	+	0.453821i	$0.149940\pi$
$332$	−1.85986	−	4.49010i	−0.102073	−	0.246426i
$333$	−29.9752	+	15.9865i	−1.64263	+	0.876057i
$334$	9.58932	+	1.90744i	0.524705	+	0.104370i
$335$	0.335898	−	5.12482i	0.0183521	−	0.279999i
$336$	2.73289	+	1.76386i	0.149091	+	0.0962264i
$337$	−2.42739	+	7.15085i	−0.132228	+	0.389532i	−0.992798	−	0.119801i	$-0.961774\pi$
$337$	−2.42739	+	7.15085i	−0.132228	+	0.389532i	0.860570	+	0.509333i	$0.170108\pi$
$338$	−30.4802	+	23.3883i	−1.65790	+	1.27215i
$339$	−1.73760	−	8.06327i	−0.0943736	−	0.437937i
$340$	7.15399	+	3.05987i	0.387980	+	0.165945i
$341$			1.04976i			0.0568474i
$342$	−0.834781	−	26.2408i	−0.0451398	−	1.41894i
$343$	1.94808	+	9.79366i	0.105186	+	0.528808i
$344$	11.8829	+	3.18400i	0.640681	+	0.171670i
$345$	0.290296	+	0.366117i	0.0156290	+	0.0197111i
$346$	14.8340	+	13.0091i	0.797482	+	0.699373i
$347$	−27.3689	+	1.79386i	−1.46924	+	0.0962992i	−0.778884	−	0.627168i	$-0.784214\pi$
$347$	−27.3689	+	1.79386i	−1.46924	+	0.0962992i	−0.690358	+	0.723468i	$0.742547\pi$
$348$	−17.5754	+	37.1157i	−0.942141	+	1.98961i
$349$	−8.60687	−	6.60428i	−0.460715	−	0.353519i	0.352177	−	0.935933i	$-0.385442\pi$
$349$	−8.60687	−	6.60428i	−0.460715	−	0.353519i	−0.812892	+	0.582414i	$0.802108\pi$
$350$	−7.02204	+	4.69198i	−0.375344	+	0.250797i
$351$	27.9000	+	2.32658i	1.48919	+	0.124183i
$352$	−1.30320	+	1.95038i	−0.0694610	+	0.103956i
$353$	−1.82756	+	6.82053i	−0.0972710	+	0.363020i	−0.997354	−	0.0726982i	$-0.976839\pi$
$353$	−1.82756	+	6.82053i	−0.0972710	+	0.363020i	0.900083	+	0.435719i	$0.143506\pi$
$354$	−21.7587	+	29.3099i	−1.15646	+	1.55780i
$355$	1.31372	+	1.71207i	0.0697249	+	0.0908672i
$356$	−6.34272	+	10.9859i	−0.336164	+	0.582253i
$357$	−4.22097	−	3.20925i	−0.223397	−	0.169851i
$358$	14.2303	+	24.6477i	0.752096	+	1.30267i
$359$	1.46983	−	3.54849i	0.0775748	−	0.187282i	−0.880334	−	0.474354i	$-0.842682\pi$
$359$	1.46983	−	3.54849i	0.0775748	−	0.187282i	0.957909	+	0.287072i	$0.0926818\pi$
$360$	2.61373	−	5.75449i	0.137756	−	0.303288i
$361$	−4.00687	−	4.00687i	−0.210888	−	0.210888i
$362$	42.8501	+	2.80855i	2.25215	+	0.147614i
$363$	17.2450	−	0.274232i	0.905127	−	0.0143934i
$364$	−0.979593	−	14.9457i	−0.0513446	−	0.783367i
$365$	0.210047	−	1.59547i	0.0109944	−	0.0835106i
$366$	21.7568	−	15.0432i	1.13725	−	0.786323i
$367$	−6.58764	+	13.3584i	−0.343872	+	0.697303i	−0.998267	−	0.0588497i	$-0.981257\pi$
$367$	−6.58764	+	13.3584i	−0.343872	+	0.697303i	0.654395	+	0.756153i	$0.272923\pi$
$368$	0.264076	−	1.32760i	0.0137659	−	0.0692059i
$369$	−7.06700	−	18.8293i	−0.367893	−	0.980213i
$370$	9.67305	−	9.67305i	0.502878	−	0.502878i
$371$	−4.82332	+	4.22994i	−0.250414	+	0.219607i
$372$	4.31602	−	5.08226i	0.223775	−	0.263503i
$373$	3.87184	+	2.23541i	0.200476	+	0.115745i	0.596878	−	0.802332i	$-0.296408\pi$
$373$	3.87184	+	2.23541i	0.200476	+	0.115745i	−0.396401	+	0.918077i	$0.629741\pi$
$374$	−6.23301	+	7.93295i	−0.322302	+	0.410203i
$375$	5.71114	+	6.30712i	0.294922	+	0.325698i
$376$	−6.45956	−	49.0652i	−0.333126	−	2.53034i
$377$	33.4657	−	6.65675i	1.72357	−	0.342840i
$378$	−5.75821	+	7.23470i	−0.296171	+	0.372113i
$379$	−12.0411	−	8.04562i	−0.618511	−	0.413276i	0.206457	−	0.978456i	$-0.433807\pi$
$379$	−12.0411	−	8.04562i	−0.618511	−	0.413276i	−0.824968	+	0.565180i	$0.808807\pi$
$380$	2.21501	+	6.52520i	0.113628	+	0.334736i
$381$	−3.16729	+	12.6198i	−0.162265	+	0.646532i
$382$	−51.0089	−	6.71545i	−2.60984	−	0.343592i
$383$	1.46284	+	0.192586i	0.0747475	+	0.00984070i	0.167807	−	0.985820i	$-0.446331\pi$
$383$	1.46284	+	0.192586i	0.0747475	+	0.00984070i	−0.0930597	+	0.995661i	$0.529665\pi$
$384$	34.5221	−	9.84107i	1.76170	−	0.502200i
$385$	0.122821	+	0.361818i	0.00625952	+	0.0184400i
$386$	−17.9443	−	11.9900i	−0.913342	−	0.610276i
$387$	−3.11800	+	8.26117i	−0.158497	+	0.419939i
$388$	58.5178	−	11.6399i	2.97079	−	0.590927i
$389$	−4.98165	−	37.8394i	−0.252580	−	1.91854i	−0.376827	−	0.926284i	$-0.622985\pi$
$389$	−4.98165	−	37.8394i	−0.252580	−	1.91854i	0.124247	−	0.992251i	$-0.460348\pi$
$390$	−11.0208	+	2.37493i	−0.558058	+	0.120259i
$391$	−0.595524	+	2.12474i	−0.0301169	+	0.107453i
$392$	−23.3422	−	13.4766i	−1.17896	−	0.680672i
$393$	−7.49873	−	1.36802i	−0.378261	−	0.0690074i
$394$	32.8344	−	28.7950i	1.65417	−	1.45067i
$395$	−3.69142	+	3.69142i	−0.185736	+	0.185736i
$396$	8.85754	+	7.28289i	0.445108	+	0.365979i
$397$	−1.08068	+	5.43296i	−0.0542379	+	0.272673i	−0.998382	−	0.0568600i	$-0.981891\pi$
$397$	−1.08068	+	5.43296i	−0.0542379	+	0.272673i	0.944144	+	0.329533i	$0.106891\pi$
$398$	26.7068	−	54.1560i	1.33869	−	2.71460i
$399$	−0.381596	−	4.68040i	−0.0191037	−	0.234313i
$400$	1.56678	−	11.9009i	0.0783391	−	0.595045i
$401$	1.34048	+	20.4518i	0.0669404	+	1.02131i	0.890764	+	0.454467i	$0.150170\pi$
$401$	1.34048	+	20.4518i	0.0669404	+	1.02131i	−0.823823	+	0.566847i	$0.808163\pi$
$402$	−21.7277	−	36.2885i	−1.08368	−	1.80991i
$403$	−5.52813	−	0.362332i	−0.275376	−	0.0180491i
$404$	34.6286	+	34.6286i	1.72284	+	1.72284i
$405$	3.92450	+	2.27549i	0.195010	+	0.113070i
$406$	−4.31256	+	10.4114i	−0.214029	+	0.516711i
$407$	5.78061	+	10.0123i	0.286534	+	0.496292i
$408$	29.2489	−	5.95283i	1.44804	−	0.294709i
$409$	11.6707	−	20.2142i	0.577078	−	0.999528i	−0.418735	−	0.908109i	$-0.637526\pi$
$409$	11.6707	−	20.2142i	0.577078	−	0.999528i	0.995812	−	0.0914193i	$-0.0291404\pi$
$410$	4.93012	+	6.42506i	0.243481	+	0.317311i
$411$	−10.8614	−	1.25458i	−0.535753	−	0.0618840i
$412$	−6.27855	+	23.4319i	−0.309322	+	1.15441i
$413$	−3.62743	+	5.42883i	−0.178494	+	0.267135i
$414$	3.68123	+	1.12040i	0.180923	+	0.0550647i
$415$	−0.544044	+	0.363518i	−0.0267060	+	0.0178444i
$416$	−9.82111	−	7.53600i	−0.481520	−	0.369483i
$417$	14.9271	+	21.5888i	0.730982	+	1.05721i
$418$	−8.91562	+	0.584360i	−0.436077	+	0.0285820i
$419$	26.0377	+	22.8345i	1.27203	+	1.11554i	0.987625	+	0.156833i	$0.0501283\pi$
$419$	26.0377	+	22.8345i	1.27203	+	1.11554i	0.284402	+	0.958705i	$0.408205\pi$
$420$	0.892976	−	2.25667i	0.0435728	−	0.110114i
$421$	2.92019	+	0.782462i	0.142321	+	0.0381349i	0.329276	−	0.944234i	$-0.393195\pi$
$421$	2.92019	+	0.782462i	0.142321	+	0.0381349i	−0.186955	+	0.982368i	$0.559862\pi$
$422$	7.06601	+	35.5232i	0.343968	+	1.72924i
$423$	35.5033	−	1.12944i	1.72623	−	0.0549153i
$424$		−	36.1134i		−	1.75382i
$425$	−4.03739	+	19.1469i	−0.195842	+	0.928763i
$426$	16.9179	+	5.44443i	0.819674	+	0.263783i
$427$	3.75348	−	2.88015i	0.181644	−	0.139380i
$428$	−17.7625	+	52.3267i	−0.858584	+	2.52931i
$429$	0.471902	−	9.51613i	0.0227836	−	0.459443i
$430$	0.232551	−	3.54805i	0.0112146	−	0.171102i
$431$	−38.4058	−	7.63939i	−1.84994	−	0.367977i	−0.860098	−	0.510128i	$-0.829598\pi$
$431$	−38.4058	−	7.63939i	−1.84994	−	0.367977i	−0.989845	+	0.142151i	$0.954598\pi$
$432$	−2.33478	−	12.9332i	−0.112332	−	0.622251i
$433$	9.24045	+	22.3084i	0.444068	+	1.07207i	0.974508	+	0.224352i	$0.0720265\pi$
$433$	9.24045	+	22.3084i	0.444068	+	1.07207i	−0.530441	+	0.847722i	$0.677973\pi$
$434$	1.11384	−	1.45159i	0.0534663	−	0.0696786i
$435$	5.36255	+	1.34588i	0.257115	+	0.0645300i
$436$	2.57207	−	2.93288i	0.123180	−	0.140459i
$437$	−1.75269	+	0.864331i	−0.0838426	+	0.0413466i
$438$	−6.04984	−	11.7914i	−0.289073	−	0.563416i
$439$	−25.0661	−	28.5824i	−1.19634	−	1.36417i	−0.914440	−	0.404722i	$-0.867368\pi$
$439$	−25.0661	−	28.5824i	−1.19634	−	1.36417i	−0.281901	−	0.959443i	$-0.590965\pi$
$440$	−1.98717	−	0.823114i	−0.0947347	−	0.0392404i
$441$	11.2832	−	15.7150i	0.537295	−	0.748334i
$442$	−39.6244	−	35.5619i	−1.88474	−	1.69151i
$443$	−33.1913	+	19.1630i	−1.57697	+	0.910462i	−0.581687	+	0.813413i	$0.697607\pi$
$443$	−33.1913	+	19.1630i	−1.57697	+	0.910462i	−0.995280	+	0.0970494i	$0.969060\pi$
$444$	13.1790	−	72.2401i	0.625447	−	3.42836i
$445$	1.61722	+	0.548973i	0.0766637	+	0.0260238i
$446$	−9.55292	−	35.6520i	−0.452344	−	1.68817i
$447$	11.9198	+	4.71671i	0.563786	+	0.223093i
$448$	7.42805	−	2.52148i	0.350943	−	0.119129i
$449$	−8.96395	−	13.4155i	−0.423035	−	0.633116i	0.557334	−	0.830288i	$-0.311824\pi$
$449$	−8.96395	−	13.4155i	−0.423035	−	0.633116i	−0.980369	+	0.197172i	$0.936824\pi$
$450$	33.2245	+	7.77922i	1.56622	+	0.366716i
$451$	−6.32341	+	2.61924i	−0.297758	+	0.123335i
$452$	15.9907	+	7.88574i	0.752140	+	0.370914i
$453$	−3.71920	−	2.06914i	−0.174743	−	0.0972167i
$454$	18.8741	+	38.2730i	0.885808	+	1.79624i
$455$	−1.94777	+	0.521903i	−0.0913127	+	0.0244672i
$456$	21.2250	+	15.7568i	0.993954	+	0.737878i
$457$	−19.4616	+	2.56216i	−0.910374	+	0.119853i	−0.571143	−	0.820850i	$-0.693500\pi$
$457$	−19.4616	+	2.56216i	−0.910374	+	0.119853i	−0.339230	+	0.940703i	$0.610167\pi$
$458$	−19.0353			−0.889461
$459$	2.17473	+	21.3136i	0.101508	+	0.994835i
$460$	−1.00997			−0.0470901
$461$	−13.2905	+	1.74972i	−0.618999	+	0.0814927i	−0.433503	−	0.901152i	$-0.642723\pi$
$461$	−13.2905	+	1.74972i	−0.618999	+	0.0814927i	−0.185496	+	0.982645i	$0.559389\pi$
$462$	2.52663	+	1.87568i	0.117549	+	0.0872648i
$463$	−0.913894	+	0.244877i	−0.0424722	+	0.0113804i	−0.279993	−	0.960002i	$-0.590332\pi$
$463$	−0.913894	+	0.244877i	−0.0424722	+	0.0113804i	0.237520	+	0.971383i	$0.423665\pi$
$464$	−7.08427	−	14.3655i	−0.328879	−	0.666900i
$465$	−0.784446	−	0.436419i	−0.0363778	−	0.0202384i
$466$	−39.7272	−	19.5913i	−1.84033	−	0.907549i
$467$	−27.8933	+	11.5538i	−1.29075	+	0.534644i	−0.919208	−	0.393773i	$-0.871169\pi$
$467$	−27.8933	+	11.5538i	−1.29075	+	0.534644i	−0.371538	+	0.928418i	$0.621169\pi$
$468$	−41.4098	+	44.1310i	−1.91417	+	2.03996i
$469$	−4.20304	−	6.29029i	−0.194078	−	0.290459i
$470$	−13.5446	+	4.59777i	−0.624765	+	0.212079i
$471$	−15.4367	−	6.10837i	−0.711285	−	0.281459i
$472$	−9.51269	−	35.5018i	−0.437857	−	1.63410i
$473$	2.84553	+	0.965928i	0.130838	+	0.0444134i
$474$	−7.71602	+	42.2951i	−0.354409	+	1.94268i
$475$	−15.0080	+	8.66488i	−0.688614	+	0.397572i
$476$	11.1043	−	2.83931i	0.508966	−	0.130139i
$477$	25.7938	+	2.56452i	1.18102	+	0.117421i
$478$	38.3434	+	15.8823i	1.75379	+	0.726442i
$479$	−14.1926	−	16.1835i	−0.648476	−	0.739445i	0.330413	−	0.943836i	$-0.392812\pi$
$479$	−14.1926	−	16.1835i	−0.648476	−	0.739445i	−0.978889	+	0.204391i	$0.934479\pi$
$480$	−0.915667	−	1.78468i	−0.0417943	−	0.0814591i
$481$	−54.7212	+	26.9855i	−2.49507	+	1.23043i
$482$	19.6501	−	22.4067i	0.895038	−	1.02060i
$483$	0.667560	+	0.167543i	0.0303750	+	0.00762345i
$484$	−22.6952	+	29.5769i	−1.03160	+	1.34441i
$485$	−3.07397	−	7.42122i	−0.139582	−	0.336980i
$486$	37.2421	−	2.96715i	1.68934	−	0.134593i
$487$	−9.83269	−	1.95584i	−0.445562	−	0.0886277i	−0.0327900	−	0.999462i	$-0.510439\pi$
$487$	−9.83269	−	1.95584i	−0.445562	−	0.0886277i	−0.412772	+	0.910835i	$0.635439\pi$
$488$	−1.74186	+	26.5757i	−0.0788503	+	1.20302i
$489$	0.560336	−	11.2995i	0.0253393	−	0.510979i
$490$	−2.50411	+	7.37686i	−0.113124	+	0.333253i
$491$	−3.43095	+	2.63266i	−0.154837	+	0.118810i	−0.683274	−	0.730162i	$-0.739445\pi$
$491$	−3.43095	+	2.63266i	−0.154837	+	0.118810i	0.528438	+	0.848972i	$0.322778\pi$
$492$	41.3829	+	13.3176i	1.86568	+	0.600405i
$493$	9.71492	+	24.2365i	0.437538	+	1.09156i
$494$		−	47.1523i		−	2.12148i
$495$	0.729020	−	1.36088i	0.0327670	−	0.0611668i
$496$	0.507349	+	2.55062i	0.0227807	+	0.114526i
$497$	3.07053	+	0.822746i	0.137732	+	0.0369052i
$498$	−1.98272	+	5.01059i	−0.0888476	+	0.224530i
$499$	17.5954	+	15.4308i	0.787679	+	0.690776i	0.955483	−	0.295045i	$-0.0953345\pi$
$499$	17.5954	+	15.4308i	0.787679	+	0.690776i	−0.167805	+	0.985820i	$0.553668\pi$
$500$	−18.3526	+	1.20289i	−0.820754	+	0.0537950i
$501$	−4.01854	−	5.81195i	−0.179535	−	0.259659i
$502$	33.8774	+	25.9950i	1.51202	+	1.16022i
$503$	9.17711	−	6.13195i	0.409187	−	0.273410i	−0.333895	−	0.942610i	$-0.608363\pi$
$503$	9.17711	−	6.13195i	0.409187	−	0.273410i	0.743082	+	0.669200i	$0.233363\pi$
$504$	−2.10571	−	9.06875i	−0.0937957	−	0.403954i
$505$	3.66298	−	5.48204i	0.163001	−	0.243948i
$506$	0.338931	−	1.26491i	0.0150673	−	0.0562320i
$507$	27.5822	+	3.18598i	1.22497	+	0.141494i
$508$	−17.1211	−	22.3127i	−0.759628	−	0.989967i
$509$	13.6706	−	23.6782i	0.605939	−	1.04952i	−0.385963	−	0.922514i	$-0.626131\pi$
$509$	13.6706	−	23.6782i	0.605939	−	1.04952i	0.991902	−	0.127003i	$-0.0405358\pi$
$510$	−3.33674	−	7.95571i	−0.147754	−	0.352285i
$511$	−1.18523	−	2.05289i	−0.0524317	−	0.0908144i
$512$	−10.3147	+	24.9019i	−0.455850	+	1.10052i
$513$	−12.7614	+	14.0409i	−0.563431	+	0.619923i
$514$	−18.9939	−	18.9939i	−0.837783	−	0.837783i
$515$	3.25896	+	0.213603i	0.143607	+	0.00941249i
$516$	−9.80494	−	16.3757i	−0.431638	−	0.720899i
$517$	−0.790627	−	12.0626i	−0.0347717	−	0.530514i
$518$	2.63021	−	19.9784i	0.115565	−	0.877803i
$519$	−1.15870	−	14.2118i	−0.0508613	−	0.623831i
$520$	5.02050	−	10.1806i	0.220163	−	0.446447i
$521$	0.254038	−	1.27713i	0.0111296	−	0.0559523i	−0.974821	−	0.222987i	$-0.928419\pi$
$521$	0.254038	−	1.27713i	0.0111296	−	0.0559523i	0.985951	+	0.167035i	$0.0534192\pi$
$522$	42.6294	−	15.9996i	1.86584	−	0.700285i
$523$	−4.98904	+	4.98904i	−0.218155	+	0.218155i	−0.807721	−	0.589565i	$-0.799299\pi$
$523$	−4.98904	+	4.98904i	−0.218155	+	0.218155i	0.589565	+	0.807721i	$0.299299\pi$
$524$	12.3877	−	10.8637i	0.541160	−	0.474585i
$525$	6.00431	+	1.09539i	0.262050	+	0.0478065i
$526$	34.6994	+	20.0337i	1.51297	+	0.873511i
$527$	−0.505112	−	4.20922i	−0.0220030	−	0.183356i
$528$	−4.37220	+	0.942191i	−0.190275	+	0.0410036i
$529$	2.96472	+	22.5193i	0.128901	+	0.979098i
$530$	−10.2373	+	2.03632i	−0.444680	+	0.0884523i
$531$	26.0325	−	4.27330i	1.12972	−	0.185445i
$532$	8.43990	+	5.63936i	0.365916	+	0.244497i
$533$	−11.6106	−	34.2038i	−0.502912	−	1.48153i
$534$	13.5262	−	3.85586i	0.585337	−	0.166860i
$535$	7.37599	+	0.971068i	0.318892	+	0.0419829i
$536$	42.2221	+	5.55865i	1.82372	+	0.240097i
$537$	5.00692	−	19.9497i	0.216065	−	0.860892i
$538$	7.41746	+	21.8511i	0.319790	+	0.942070i
$539$	−5.47426	−	3.65778i	−0.235793	−	0.157552i
$540$	−9.12463	+	3.59119i	−0.392662	+	0.154540i
$541$	40.2772	−	8.01163i	1.73165	−	0.344447i	0.774178	−	0.632968i	$-0.218163\pi$
$541$	40.2772	−	8.01163i	1.73165	−	0.344447i	0.957474	+	0.288521i	$0.0931634\pi$
$542$	6.75166	+	51.2840i	0.290009	+	2.20284i
$543$	−20.8306	−	23.0043i	−0.893926	−	0.987211i
$544$	4.28701	−	8.44754i	0.183804	−	0.362185i
$545$	−0.454827	−	0.262594i	−0.0194826	−	0.0112483i
$546$	−10.7497	+	12.6581i	−0.460043	+	0.541717i
$547$	−27.5805	+	24.1874i	−1.17926	+	1.03418i	−0.180538	+	0.983568i	$0.557784\pi$
$547$	−27.5805	+	24.1874i	−1.17926	+	1.03418i	−0.998718	+	0.0506126i	$0.983883\pi$
$548$	16.7116	−	16.7116i	0.713883	−	0.713883i
$549$	−18.8578	−	3.13133i	−0.804833	−	0.133642i
$550$	2.26552	−	11.3896i	0.0966022	−	0.485652i
$551$	−10.2277	+	20.7396i	−0.435713	+	0.883538i
$552$	−3.18680	+	2.20344i	−0.135639	+	0.0937846i
$553$	−1.00374	+	7.62417i	−0.0426834	+	0.324213i
$554$	−4.02526	−	61.4137i	−0.171017	−	2.60922i
$555$	−9.88505	+	0.157193i	−0.419597	+	0.00667249i
$556$	−56.6127	−	3.71059i	−2.40091	−	0.157364i
$557$	−4.48661	−	4.48661i	−0.190104	−	0.190104i	0.605637	−	0.795741i	$-0.292918\pi$
$557$	−4.48661	−	4.48661i	−0.190104	−	0.190104i	−0.795741	+	0.605637i	$0.792918\pi$
$558$	−7.35785	+	0.717826i	−0.311483	+	0.0303880i
$559$	−6.06884	+	14.6515i	−0.256685	+	0.619692i
$560$	0.473288	+	0.819760i	0.0200001	+	0.0346412i
$561$	7.22441	−	0.983700i	0.305015	−	0.0415318i
$562$	13.9830	−	24.2193i	0.589838	−	1.02163i
$563$	11.5661	+	15.0732i	0.487452	+	0.635260i	0.970720	−	0.240212i	$-0.0772170\pi$
$563$	11.5661	+	15.0732i	0.487452	+	0.635260i	−0.483268	+	0.875472i	$0.660550\pi$
$564$	−45.7672	+	61.6504i	−1.92715	+	2.59595i
$565$	0.621268	−	2.31861i	0.0261370	−	0.0975445i
$566$	1.45597	−	2.17901i	0.0611989	−	0.0915906i
$567$	6.62684	−	0.859993i	0.278301	−	0.0361163i
$568$	−14.8786	+	9.94159i	−0.624294	+	0.417140i
$569$	15.2156	+	11.6753i	0.637869	+	0.489454i	0.876339	−	0.481696i	$-0.159979\pi$
$569$	15.2156	+	11.6753i	0.637869	+	0.489454i	−0.238469	+	0.971150i	$0.576646\pi$
$570$	3.26985	−	6.90527i	0.136959	−	0.289230i
$571$	28.0613	−	1.83924i	1.17433	−	0.0769696i	0.534283	−	0.845306i	$-0.320582\pi$
$571$	28.0613	−	1.83924i	1.17433	−	0.0769696i	0.640046	+	0.768336i	$0.278915\pi$
$572$	15.4842	+	13.5793i	0.647426	+	0.567777i
$573$	23.1011	+	29.1348i	0.965064	+	1.21713i
$574$	11.5231	+	3.08760i	0.480965	+	0.128874i
$575$	−0.495519	−	2.49114i	−0.0206646	−	0.103888i
$576$	−27.9385	−	14.9666i	−1.16410	−	0.623609i
$577$			44.0005i			1.83176i	0.401449	+	0.915881i	$0.368507\pi$
$577$			44.0005i			1.83176i	−0.401449	+	0.915881i	$0.631493\pi$
$578$	21.1755	−	34.8080i	0.880785	−	1.44782i
$579$	3.28563	+	15.2468i	0.136546	+	0.633637i
$580$	−9.48138	+	7.27532i	−0.393693	+	0.302091i
$581$	−0.309814	+	0.912683i	−0.0128533	+	0.0378645i
$582$	−55.5817	−	35.8735i	−2.30393	−	1.48700i
$583$	0.576946	−	8.80249i	0.0238947	−	0.364562i
$584$	13.0875	+	2.60326i	0.541564	+	0.107724i
$585$	6.91489	+	4.30882i	0.285896	+	0.178148i
$586$	2.16615	+	5.22955i	0.0894828	+	0.216031i
$587$	6.52486	−	8.50336i	0.269310	−	0.350971i	−0.639047	−	0.769168i	$-0.720671\pi$
$587$	6.52486	−	8.50336i	0.269310	−	0.350971i	0.908357	+	0.418196i	$0.137338\pi$
$588$	11.4642	+	40.2159i	0.472775	+	1.65847i
$589$	2.47552	−	2.82279i	0.102002	−	0.116311i
$590$	−9.52754	+	4.69846i	−0.392243	+	0.193433i
$591$	−31.5229	−	1.56321i	−1.29668	−	0.0643018i
$592$	18.8843	+	21.5334i	0.776139	+	0.885017i
$593$	−17.9488	−	7.43464i	−0.737069	−	0.305304i	−0.0176157	−	0.999845i	$-0.505608\pi$
$593$	−17.9488	−	7.43464i	−0.737069	−	0.305304i	−0.719453	+	0.694541i	$0.755608\pi$
$594$	−1.43559	−	12.6330i	−0.0589028	−	0.518339i
$595$	−0.666573	−	1.39169i	−0.0273268	−	0.0570537i
$596$	−23.9969	+	13.8546i	−0.982953	+	0.567508i
$597$	−41.0945	+	14.6825i	−1.68189	+	0.600913i
$598$	6.54416	+	2.22144i	0.267610	+	0.0908415i
$599$	4.18348	+	15.6130i	0.170932	+	0.637929i	0.997209	+	0.0746637i	$0.0237883\pi$
$599$	4.18348	+	15.6130i	0.170932	+	0.637929i	−0.826276	+	0.563265i	$0.809545\pi$
$600$	−26.9215	+	21.3462i	−1.09907	+	0.871455i
$601$	16.3911	−	5.56403i	0.668607	−	0.226962i	0.0335622	−	0.999437i	$-0.489315\pi$
$601$	16.3911	−	5.56403i	0.668607	−	0.226962i	0.635045	+	0.772475i	$0.280981\pi$
$602$	−2.90987	−	4.35493i	−0.118598	−	0.177494i
$603$	−6.96856	+	29.7622i	−0.283782	+	1.21201i
$604$	8.49941	−	3.52057i	0.345836	−	0.143250i
$605$	4.50157	+	2.21993i	0.183015	+	0.0902528i
$606$	−0.863349	−	54.2914i	−0.0350711	−	2.20544i
$607$	2.48444	+	5.03794i	0.100840	+	0.204484i	0.941446	−	0.337164i	$-0.109468\pi$
$607$	2.48444	+	5.03794i	0.100840	+	0.204484i	−0.840606	+	0.541647i	$0.817801\pi$
$608$	8.10367	−	2.17137i	0.328647	−	0.0880607i
$609$	7.47379	−	3.23591i	0.302853	−	0.131126i
$610$	7.63179	−	1.00474i	0.309002	−	0.0406809i
$611$	63.7961			2.58091
$612$	−39.0205	−	24.9403i	−1.57731	−	1.00815i
$613$	−24.3856			−0.984927			−0.492463	−	0.870333i	$-0.663903\pi$
$613$	−24.3856			−0.984927			−0.492463	+	0.870333i	$0.663903\pi$
$614$	−74.8274	+	9.85121i	−3.01979	+	0.397563i
$615$	0.671587	−	5.81417i	0.0270810	−	0.234450i
$616$	−3.06040	+	0.820033i	−0.123307	+	0.0330401i
$617$	8.14777	+	16.5220i	0.328017	+	0.665152i	0.996939	−	0.0781799i	$-0.0249109\pi$
$617$	8.14777	+	16.5220i	0.328017	+	0.665152i	−0.668922	+	0.743332i	$0.733244\pi$
$618$	23.0765	−	13.8170i	0.928272	−	0.555803i
$619$	8.35682	+	4.12113i	0.335889	+	0.165642i	0.602410	−	0.798187i	$-0.294207\pi$
$619$	8.35682	+	4.12113i	0.335889	+	0.165642i	−0.266521	+	0.963829i	$0.585874\pi$
$620$	1.79268	−	0.742552i	0.0719957	−	0.0298216i
$621$	−1.34749	−	2.43263i	−0.0540730	−	0.0976180i
$622$	−15.0115	−	22.4664i	−0.601908	−	0.900819i
$623$	2.38224	−	0.808660i	0.0954423	−	0.0323983i
$624$	−3.45258	−	23.3497i	−0.138214	−	0.934735i
$625$	−5.50082	−	20.5293i	−0.220033	−	0.821173i
$626$	19.0943	+	6.48164i	0.763162	+	0.259059i
$627$	4.92179	+	4.17974i	0.196557	+	0.166923i
$628$	31.0772	−	17.9424i	1.24011	−	0.715981i
$629$	−27.9962	−	37.3651i	−1.11628	−	1.48984i
$630$	−2.45204	+	1.10828i	−0.0976916	+	0.0441548i
$631$	−5.45994	−	2.26158i	−0.217357	−	0.0900321i	0.271348	−	0.962481i	$-0.412531\pi$
$631$	−5.45994	−	2.26158i	−0.217357	−	0.0900321i	−0.488705	+	0.872449i	$0.662531\pi$
$632$	−28.5420	−	32.5459i	−1.13534	−	1.29461i
$633$	14.1944	−	21.9925i	0.564177	−	0.874125i
$634$	2.78243	−	1.37214i	0.110504	−	0.0544947i
$635$	−2.49658	+	2.84680i	−0.0990737	+	0.112972i
$636$	−38.9842	+	40.2441i	−1.54582	+	1.59578i
$637$	21.1518	−	27.5655i	0.838064	−	1.09219i
$638$	−5.92994	−	14.3161i	−0.234769	−	0.566782i
$639$	−6.04416	−	11.3330i	−0.239103	−	0.448326i
$640$	10.2459	+	2.03804i	0.405006	+	0.0805607i
$641$	−1.02804	+	15.6849i	−0.0406052	+	0.619516i	0.928261	+	0.371930i	$0.121304\pi$
$641$	−1.02804	+	15.6849i	−0.0406052	+	0.619516i	−0.968866	+	0.247586i	$0.920363\pi$
$642$	54.5128	−	27.9689i	2.15145	−	1.10385i
$643$	−10.3410	+	30.4637i	−0.407810	+	1.20137i	0.528116	+	0.849172i	$0.322899\pi$
$643$	−10.3410	+	30.4637i	−0.407810	+	1.20137i	−0.935926	+	0.352197i	$0.885435\pi$
$644$	−1.18029	+	0.905672i	−0.0465101	+	0.0356885i
$645$	−1.90479	+	1.72480i	−0.0750010	+	0.0679139i
$646$	35.4679	−	6.63306i	1.39547	−	0.260974i
$647$			22.2315i			0.874010i	0.899459	+	0.437005i	$0.143961\pi$
$647$			22.2315i			0.874010i	−0.899459	+	0.437005i	$0.856039\pi$
$648$	−20.9564	+	31.2385i	−0.823247	+	1.22716i
$649$	−1.75150	−	8.80540i	−0.0687525	−	0.345642i
$650$	59.1967	+	15.8617i	2.32188	+	0.622147i
$651$	−1.30809	+	0.193419i	−0.0512679	+	0.00758069i
$652$	18.3859	+	16.1240i	0.720048	+	0.631465i
$653$	−3.61153	+	0.236712i	−0.141330	+	0.00926325i	−0.135904	−	0.990722i	$-0.543394\pi$
$653$	−3.61153	+	0.236712i	−0.141330	+	0.00926325i	−0.00542604	+	0.999985i	$0.501727\pi$
$654$	−4.31089	+	0.351469i	−0.168569	+	0.0137435i
$655$	−1.75986	−	1.35039i	−0.0687636	−	0.0527641i
$656$	−14.0983	+	9.42016i	−0.550445	+	0.367795i
$657$	−2.78875	+	9.16280i	−0.108799	+	0.357475i
$658$	−11.7058	+	17.5190i	−0.456340	+	0.682961i
$659$	−1.86369	+	6.95540i	−0.0725992	+	0.270944i	−0.992678	−	0.120789i	$-0.961458\pi$
$659$	−1.86369	+	6.95540i	−0.0725992	+	0.270944i	0.920079	+	0.391733i	$0.128124\pi$
$660$	1.32592	+	3.06240i	0.0516114	+	0.119204i
$661$	−15.2860	−	19.9211i	−0.594556	−	0.774841i	0.395048	−	0.918661i	$-0.370728\pi$
$661$	−15.2860	−	19.9211i	−0.594556	−	0.774841i	−0.989604	+	0.143820i	$0.954061\pi$
$662$	7.95420	−	13.7771i	0.309149	−	0.535461i
$663$	2.68670	+	38.3840i	0.104343	+	1.49071i
$664$	−2.71281	−	4.69873i	−0.105277	−	0.182346i
$665$	0.522970	−	1.26256i	0.0202799	−	0.0489600i
$666$	−66.2246	+	47.3634i	−2.56615	+	1.83530i
$667$	−2.39656	−	2.39656i	−0.0927951	−	0.0927951i
$668$	15.2408	+	0.998934i	0.589684	+	0.0386499i
$669$	−12.9682	+	23.3099i	−0.501381	+	0.901213i
$670$	−0.805032	−	12.2824i	−0.0311011	−	0.474511i
$671$	−0.849143	+	6.44988i	−0.0327808	+	0.248995i
$672$	−2.67046	−	1.26454i	−0.103015	−	0.0487808i
$673$	13.9828	−	28.3543i	0.538997	−	1.09298i	−0.441649	−	0.897188i	$-0.645606\pi$
$673$	13.9828	−	28.3543i	0.538997	−	1.09298i	0.980646	−	0.195790i	$-0.0627271\pi$
$674$	−3.53086	+	17.7508i	−0.136004	+	0.683737i
$675$	−13.3346	−	20.7444i	−0.513251	−	0.798454i
$676$	−42.4386	+	42.4386i	−1.63225	+	1.63225i
$677$	−30.8797	+	27.0808i	−1.18680	+	1.04080i	−0.188529	+	0.982068i	$0.560372\pi$
$677$	−30.8797	+	27.0808i	−1.18680	+	1.04080i	−0.998274	+	0.0587308i	$0.981295\pi$
$678$	−6.65120	−	18.6160i	−0.255438	−	0.714942i
$679$	−10.2472	−	5.91623i	−0.393252	−	0.227044i
$680$	8.36405	+	2.34428i	0.320747	+	0.0898990i
$681$	9.44766	−	29.3574i	0.362035	−	1.12498i
$682$	0.328391	+	2.49438i	0.0125747	+	0.0955146i
$683$	−37.3073	+	7.42089i	−1.42753	+	0.283953i	−0.847565	−	0.530692i	$-0.821932\pi$
$683$	−37.3073	+	7.42089i	−1.42753	+	0.283953i	−0.579961	+	0.814644i	$0.696932\pi$
$684$	−6.64347	−	40.4714i	−0.254019	−	1.54746i
$685$	−2.64560	−	1.76774i	−0.101083	−	0.0675417i
$686$	7.69264	+	22.6618i	0.293706	+	0.865231i
$687$	9.88091	+	9.57157i	0.376980	+	0.365178i
$688$	7.38070	+	0.971687i	0.281387	+	0.0370452i
$689$	46.1558	+	6.07652i	1.75839	+	0.231497i
$690$	0.804317	+	0.779136i	0.0306198	+	0.0296612i
$691$	−0.339026	−	0.998739i	−0.0128972	−	0.0379938i	0.940291	−	0.340372i	$-0.110553\pi$
$691$	−0.339026	−	0.998739i	−0.0128972	−	0.0379938i	−0.953188	+	0.302378i	$0.902220\pi$
$692$	25.6274	+	17.1237i	0.974207	+	0.650944i
$693$	−0.368376	−	2.24411i	−0.0139934	−	0.0852467i
$694$	−64.4715	+	12.8242i	−2.44731	+	0.486799i
$695$	0.996985	+	7.57285i	0.0378178	+	0.287255i
$696$	−14.0445	+	43.6415i	−0.532354	+	1.65423i
$697$	24.0948	−	13.5451i	0.912654	−	0.513056i
$698$	−22.5172	−	13.0003i	−0.852289	−	0.492069i
$699$	10.7706	+	30.1457i	0.407381	+	1.14021i
$700$	−9.91898	+	8.69871i	−0.374902	+	0.328780i
$701$	13.4241	−	13.4241i	0.507022	−	0.507022i	−0.406589	−	0.913611i	$-0.633282\pi$
$701$	13.4241	−	13.4241i	0.507022	−	0.507022i	0.913611	+	0.406589i	$0.133282\pi$
$702$	67.0224	−	3.19955i	2.52960	−	0.120759i
$703$	8.06685	−	40.5548i	0.304247	−	1.52955i
$704$	−4.77066	+	9.67395i	−0.179801	+	0.364601i
$705$	9.34268	+	4.42404i	0.351866	+	0.166619i
$706$	−2.20891	+	16.7783i	−0.0831333	+	0.631460i
$707$	−0.635198	−	9.69125i	−0.0238891	−	0.364477i
$708$	−27.7233	+	49.8315i	−1.04190	+	1.87278i
$709$	18.1644	+	1.19056i	0.682177	+	0.0447123i	0.402552	−	0.915397i	$-0.368123\pi$
$709$	18.1644	+	1.19056i	0.682177	+	0.0447123i	0.279625	+	0.960109i	$0.409790\pi$
$710$	3.65717	+	3.65717i	0.137251	+	0.137251i
$711$	25.2726	−	18.0748i	0.947797	−	0.677858i
$712$	−5.41943	+	13.0837i	−0.203102	+	0.490331i
$713$	0.275141	+	0.476558i	0.0103041	+	0.0178472i
$714$	−11.0336	−	6.30522i	−0.412922	−	0.235967i
$715$	1.38637	−	2.40126i	0.0518473	−	0.0898021i
$716$	27.0655	+	35.2725i	1.01149	+	1.31819i
$717$	−11.9173	−	27.5246i	−0.445058	−	1.02792i
$718$	2.38248	−	8.89154i	0.0889134	−	0.331829i
$719$	13.0787	−	19.5737i	0.487754	−	0.729976i	−0.503201	−	0.864170i	$-0.667844\pi$
$719$	13.0787	−	19.5737i	0.487754	−	0.729976i	0.990955	+	0.134193i	$0.0428444\pi$
$720$	1.11360	−	3.65889i	0.0415015	−	0.136359i
$721$	4.00010	−	2.67278i	0.148971	−	0.0995395i
$722$	−10.7744	−	8.26747i	−0.400981	−	0.307683i
$723$	−21.4669	+	1.75021i	−0.798361	+	0.0650908i
$724$	66.9386	−	4.38739i	2.48775	−	0.163056i
$725$	−22.5968	−	19.8168i	−0.839223	−	0.735978i
$726$	40.8909	−	6.04629i	1.51760	−	0.224399i
$727$	−4.15025	−	1.11206i	−0.153924	−	0.0412439i	0.181034	−	0.983477i	$-0.442056\pi$
$727$	−4.15025	−	1.11206i	−0.153924	−	0.0412439i	−0.334958	+	0.942233i	$0.608722\pi$
$728$	−3.26206	−	16.3995i	−0.120900	−	0.607804i
$729$	−20.8238	−	17.1864i	−0.771250	−	0.636532i
$730$		−	3.85678i		−	0.142746i
$731$	−11.8746	−	2.50391i	−0.439196	−	0.0926104i
$732$	30.6294	−	27.7351i	1.13209	−	1.02512i
$733$	8.51833	−	6.53634i	0.314632	−	0.241425i	−0.439357	−	0.898312i	$-0.644794\pi$
$733$	8.51833	−	6.53634i	0.314632	−	0.241425i	0.753989	+	0.656887i	$0.228127\pi$
$734$	−11.4744	+	33.8024i	−0.423526	+	1.24767i
$735$	5.00917	−	2.57006i	0.184766	−	0.0947981i
$736$	−0.0804209	+	1.22699i	−0.00296435	+	0.0452273i
$737$	10.2027	+	2.02944i	0.375820	+	0.0747553i
$738$	−22.6825	−	42.5304i	−0.834956	−	1.56557i
$739$	6.20725	+	14.9856i	0.228337	+	0.551255i	0.995975	−	0.0896286i	$-0.0285680\pi$
$739$	6.20725	+	14.9856i	0.228337	+	0.551255i	−0.767638	+	0.640884i	$0.778568\pi$
$740$	13.0092	−	16.9539i	0.478227	−	0.623237i
$741$	−23.7097	+	24.4760i	−0.870999	+	0.899148i
$742$	−10.1377	+	11.5598i	−0.372167	+	0.424375i
$743$	−15.3702	+	7.57977i	−0.563880	+	0.278075i	−0.701806	−	0.712368i	$-0.747623\pi$
$743$	−15.3702	+	7.57977i	−0.563880	+	0.278075i	0.137927	+	0.990442i	$0.455956\pi$
$744$	4.03649	−	6.25406i	0.147985	−	0.229285i
$745$	2.45971	+	2.80477i	0.0901169	+	0.102759i
$746$	9.89937	+	4.10045i	0.362442	+	0.150128i
$747$	3.54869	−	1.60394i	0.129840	−	0.0586851i
$748$	−8.03609	+	13.5574i	−0.293829	+	0.495708i
$749$	9.49068	−	5.47945i	0.346782	−	0.200215i
$750$	15.5435	+	13.2001i	0.567570	+	0.481998i
$751$	6.32030	+	2.14545i	0.230631	+	0.0782886i	0.434363	−	0.900738i	$-0.356974\pi$
$751$	6.32030	+	2.14545i	0.230631	+	0.0782886i	−0.203732	+	0.979027i	$0.565307\pi$
$752$	−7.75091	−	28.9268i	−0.282647	−	1.05485i
$753$	−4.51404	−	30.5283i	−0.164501	−	1.11251i
$754$	77.4372	−	26.2864i	2.82010	−	0.957293i
$755$	−0.688111	−	1.02983i	−0.0250429	−	0.0374794i
$756$	−7.44310	+	12.3791i	−0.270703	+	0.450225i
$757$	9.34496	−	3.87081i	0.339648	−	0.140687i	−0.206339	−	0.978481i	$-0.566155\pi$
$757$	9.34496	−	3.87081i	0.339648	−	0.140687i	0.545987	+	0.837794i	$0.316155\pi$
$758$	−31.1284	−	15.3508i	−1.13063	−	0.557567i
$759$	−0.811971	+	0.486167i	−0.0294727	+	0.0176468i
$760$	3.40244	+	6.89947i	0.123419	+	0.250270i
$761$	−11.8235	+	3.16811i	−0.428603	+	0.114844i	−0.466670	−	0.884431i	$-0.654546\pi$
$761$	−11.8235	+	3.16811i	−0.428603	+	0.114844i	0.0380675	+	0.999275i	$0.487880\pi$
$762$	−3.57815	+	30.9773i	−0.129623	+	1.12219i
$763$	−0.767006	+	0.100978i	−0.0277675	+	0.00365566i
$764$	−80.3714			−2.90774
$765$	−2.26835	+	5.80751i	−0.0820122	+	0.209971i
$766$	3.53617			0.127767
$767$	46.9748	−	6.18434i	1.69616	−	0.223304i
$768$	45.3659	−	19.6420i	1.63700	−	0.708768i
$769$	−21.6739	+	5.80750i	−0.781581	+	0.209424i	−0.627482	−	0.778631i	$-0.715914\pi$
$769$	−21.6739	+	5.80750i	−0.781581	+	0.209424i	−0.154099	+	0.988055i	$0.549248\pi$
$770$	0.405027	+	0.821313i	0.0145961	+	0.0295981i
$771$	0.308663	+	19.4101i	0.0111162	+	0.699039i
$772$	−30.2368	−	14.9111i	−1.08825	−	0.536664i
$773$	29.2000	−	12.0950i	1.05025	−	0.435029i	0.210270	−	0.977643i	$-0.432566\pi$
$773$	29.2000	−	12.0950i	1.05025	−	0.435029i	0.839982	+	0.542615i	$0.182566\pi$
$774$	−4.82452	+	20.6052i	−0.173414	+	0.740637i
$775$	2.71108	+	4.05742i	0.0973848	+	0.145747i
$776$	63.0725	−	21.4102i	2.26417	−	0.768583i
$777$	−11.4111	+	9.04793i	−0.409372	+	0.324593i
$778$	−23.6743	−	88.3537i	−0.848765	−	3.16763i
$779$	23.1803	+	7.86864i	0.830519	+	0.281923i
$780$	−16.5846	+	5.92543i	−0.593824	+	0.212165i
$781$	−3.78544	+	2.18552i	−0.135454	+	0.0782041i
$782$	−0.750379	+	5.23500i	−0.0268335	+	0.187203i
$783$	−30.1733	−	13.1303i	−1.07831	−	0.469239i
$784$	−15.0688	−	6.24169i	−0.538170	−	0.222917i
$785$	−3.18545	−	3.63231i	−0.113694	−	0.129643i
$786$	−18.2461	−	0.904816i	−0.650815	−	0.0322737i
$787$	25.7992	−	12.7228i	0.919642	−	0.453517i	0.0800845	−	0.996788i	$-0.474481\pi$
$787$	25.7992	−	12.7228i	0.919642	−	0.453517i	0.839557	+	0.543271i	$0.182814\pi$
$788$	44.9823	−	51.2925i	1.60243	−	1.82722i
$789$	−7.93829	−	27.8472i	−0.282610	−	0.991386i
$790$	−7.61660	+	9.92615i	−0.270987	+	0.353157i
$791$	−1.35312	−	3.26673i	−0.0481115	−	0.116152i
$792$	10.8649	+	6.77017i	0.386069	+	0.240567i
$793$	−33.6727	−	6.69791i	−1.19575	−	0.237850i
$794$	−0.868293	+	13.2476i	−0.0308146	+	0.470140i
$795$	6.33794	+	4.09063i	0.224784	+	0.145080i
$796$	30.3207	−	89.3220i	1.07469	−	3.16593i
$797$	20.2134	−	15.5103i	0.715994	−	0.549401i	−0.185262	−	0.982689i	$-0.559313\pi$
$797$	20.2134	−	15.5103i	0.715994	−	0.549401i	0.901256	+	0.433288i	$0.142647\pi$
$798$	−2.37088	−	11.0020i	−0.0839283	−	0.389465i
$799$	8.97439	+	47.9873i	0.317491	+	1.69767i
$800$			10.9041i			0.385517i
$801$	−8.96010	−	4.79991i	−0.316589	−	0.169597i
$802$	9.58303	+	48.1771i	0.338389	+	1.70119i
$803$	3.14843	+	0.843619i	0.111106	+	0.0297707i
$804$	−41.0511	−	51.7730i	−1.44776	−	1.82589i
$805$	0.150590	+	0.132064i	0.00530759	+	0.00465463i
$806$	−13.2490	+	0.868385i	−0.466676	+	0.0305876i
$807$	7.13719	−	15.0723i	0.251241	−	0.530571i
$808$	43.3735	+	33.2817i	1.52588	+	1.17085i
$809$	−1.47986	+	0.988813i	−0.0520292	+	0.0347648i	−0.581313	−	0.813680i	$-0.697461\pi$
$809$	−1.47986	+	0.988813i	−0.0520292	+	0.0347648i	0.529284	+	0.848445i	$0.322461\pi$
$810$	10.0370	+	4.17921i	0.352666	+	0.146842i
$811$	27.6326	−	41.3552i	0.970314	−	1.45218i	0.0800181	−	0.996793i	$-0.474502\pi$
$811$	27.6326	−	41.3552i	0.970314	−	1.45218i	0.890295	−	0.455383i	$-0.150498\pi$
$812$	−4.55634	+	17.0045i	−0.159896	+	0.596740i
$813$	22.2826	−	30.0156i	0.781485	−	1.05269i
$814$	16.8677	+	21.9824i	0.591213	+	0.770484i
$815$	1.64618	−	2.85126i	0.0576630	−	0.0998752i
$816$	17.0779	−	5.88169i	0.597846	−	0.205900i
$817$	−5.37378	−	9.30767i	−0.188005	−	0.325634i
$818$	21.4077	−	51.6828i	0.748504	−	1.80705i
$819$	11.9449	−	1.16533i	0.417388	−	0.0407200i
$820$	8.94581	+	8.94581i	0.312401	+	0.312401i
$821$	−36.8211	−	2.41338i	−1.28506	−	0.0842275i	−0.592492	−	0.805576i	$-0.701856\pi$
$821$	−36.8211	−	2.41338i	−1.28506	−	0.0842275i	−0.692572	+	0.721349i	$0.743523\pi$
$822$	−26.2007	+	0.416647i	−0.913856	+	0.0145322i
$823$	−0.722027	−	11.0160i	−0.0251683	−	0.383994i	−0.991798	−	0.127816i	$-0.959203\pi$
$823$	−0.722027	−	11.0160i	−0.0251683	−	0.383994i	0.966630	−	0.256178i	$-0.0824633\pi$
$824$	−3.53484	+	26.8498i	−0.123142	+	0.935356i
$825$	−6.90304	+	4.77295i	−0.240333	+	0.166173i
$826$	−6.92103	+	14.0345i	−0.240813	+	0.488321i
$827$	4.01743	−	20.1970i	0.139700	−	0.702318i	−0.845916	−	0.533316i	$-0.820946\pi$
$827$	4.01743	−	20.1970i	0.139700	−	0.702318i	0.985616	−	0.169002i	$-0.0540543\pi$
$828$	5.92991	+	0.984658i	0.206079	+	0.0342192i
$829$	−10.5506	+	10.5506i	−0.366437	+	0.366437i	−0.866176	−	0.499739i	$-0.833429\pi$
$829$	−10.5506	+	10.5506i	−0.366437	+	0.366437i	0.499739	+	0.866176i	$0.333429\pi$
$830$	−1.17901	+	1.03396i	−0.0409241	+	0.0358894i
$831$	−28.7914	+	33.9029i	−0.998762	+	1.17608i
$832$	−49.2974	−	28.4619i	−1.70908	−	0.986738i
$833$	23.7102	+	12.0326i	0.821511	+	0.416905i
$834$	42.2225	+	46.6286i	1.46204	+	1.61462i
$835$	−0.268400	−	2.03870i	−0.00928836	−	0.0705521i
$836$	−13.6893	+	2.72297i	−0.473454	+	0.0941758i
$837$	4.18029	+	3.32716i	0.144492	+	0.115004i
$838$	69.0128	+	46.1129i	2.38401	+	1.59294i
$839$	−7.12023	−	20.9755i	−0.245818	−	0.724155i	−0.997881	−	0.0650645i	$-0.979275\pi$
$839$	−7.12023	−	20.9755i	−0.245818	−	0.724155i	0.752063	−	0.659091i	$-0.229059\pi$
$840$	0.659531	−	2.62785i	0.0227560	−	0.0906694i
$841$	−11.0100	−	1.44950i	−0.379656	−	0.0499827i
$842$	7.18358	+	0.945736i	0.247562	+	0.0325922i
$843$	−19.4366	+	5.54072i	−0.669433	+	0.190833i
$844$	18.1870	+	53.5773i	0.626023	+	1.84421i
$845$	6.71844	+	4.48912i	0.231121	+	0.154430i
$846$	84.0078	−	13.7901i	2.88825	−	0.474112i
$847$	7.25139	−	1.44239i	0.249161	−	0.0495612i
$848$	−2.85245	−	21.6665i	−0.0979534	−	0.744030i
$849$	−1.85145	+	0.398980i	−0.0635415	+	0.0136930i
$850$	−3.60377	+	46.7590i	−0.123608	+	1.60382i
$851$	5.24846	+	3.03020i	0.179915	+	0.103874i
$852$	27.3124	+	4.98269i	0.935707	+	0.170704i
$853$	20.4168	−	17.9051i	0.699058	−	0.613057i	−0.234232	−	0.972181i	$-0.575258\pi$
$853$	20.4168	−	17.9051i	0.699058	−	0.613057i	0.933290	+	0.359123i	$0.116924\pi$
$854$	8.01784	−	8.01784i	0.274365	−	0.274365i
$855$	−5.16953	+	1.94022i	−0.176794	+	0.0663543i
$856$	−12.0351	+	60.5046i	−0.411351	+	2.06800i
$857$	14.7603	−	29.9309i	0.504202	−	1.02242i	−0.484815	−	0.874617i	$-0.661113\pi$
$857$	14.7603	−	29.9309i	0.504202	−	1.02242i	0.989017	−	0.147804i	$-0.0472204\pi$
$858$	−1.85558	−	22.7594i	−0.0633486	−	0.776992i
$859$	−1.82866	+	13.8901i	−0.0623931	+	0.473923i	0.931514	+	0.363705i	$0.118488\pi$
$859$	−1.82866	+	13.8901i	−0.0623931	+	0.473923i	−0.993907	+	0.110218i	$0.964845\pi$
$860$	−0.363281	−	5.54260i	−0.0123878	−	0.189001i
$861$	−4.42890	−	7.39692i	−0.150937	−	0.252086i
$862$	−93.6478	−	6.13800i	−3.18966	−	0.209061i
$863$	4.06464	+	4.06464i	0.138362	+	0.138362i	0.772895	−	0.634533i	$-0.218808\pi$
$863$	4.06464	+	4.06464i	0.138362	+	0.138362i	−0.634533	+	0.772895i	$0.718808\pi$
$864$	3.63627	+	11.3712i	0.123708	+	0.386857i
$865$	1.58798	−	3.83371i	0.0539928	−	0.130350i
$866$	28.9353	+	50.1175i	0.983263	+	1.70306i
$867$	−28.4945	+	7.42053i	−0.967723	+	0.252015i
$868$	1.42913	−	2.47533i	0.0485078	−	0.0840181i
$869$	−6.43705	−	8.38892i	−0.218362	−	0.284575i
$870$	13.1632	+	1.52047i	0.446276	+	0.0515487i
$871$	−14.2088	+	53.0279i	−0.481446	+	1.79678i
$872$	2.41945	−	3.62096i	0.0819329	−	0.122621i
$873$	10.8132	+	46.5696i	0.365971	+	1.57614i
$874$	−3.89427	+	2.60207i	−0.131726	+	0.0880163i
$875$	2.89372	+	2.22043i	0.0978255	+	0.0750642i
$876$	−11.7742	−	17.0289i	−0.397815	−	0.575353i
$877$	6.51572	−	0.427063i	0.220020	−	0.0144209i	0.0450057	−	0.998987i	$-0.485669\pi$
$877$	6.51572	−	0.427063i	0.220020	−	0.0144209i	0.175015	+	0.984566i	$0.444003\pi$
$878$	−68.5022	−	60.0748i	−2.31184	−	2.02743i
$879$	1.50518	−	3.80378i	0.0507683	−	0.128298i
$880$	−1.25723	−	0.336874i	−0.0423813	−	0.0113560i
$881$	5.82712	+	29.2949i	0.196321	+	0.986971i	0.945752	+	0.324889i	$0.105327\pi$
$881$	5.82712	+	29.2949i	0.196321	+	0.986971i	−0.749431	+	0.662082i	$0.769673\pi$
$882$	21.8945	−	40.8709i	0.737226	−	1.37620i
$883$		−	49.5960i		−	1.66904i	−0.550978	−	0.834520i	$-0.685745\pi$
$883$		−	49.5960i		−	1.66904i	0.550978	−	0.834520i	$-0.314255\pi$
$884$	−68.6211	−	46.9984i	−2.30798	−	1.58073i
$885$	7.30813	+	2.35187i	0.245660	+	0.0790571i
$886$	−72.8728	+	55.9173i	−2.44821	+	1.87858i
$887$	4.91600	−	14.4821i	0.165063	−	0.486261i	−0.832654	−	0.553794i	$-0.813180\pi$
$887$	4.91600	−	14.4821i	0.165063	−	0.486261i	0.997717	+	0.0675332i	$0.0215129\pi$
$888$	4.06026	−	81.8772i	0.136253	−	2.74762i
$889$	−0.364792	+	5.56565i	−0.0122347	+	0.186666i
$890$	4.01450	+	0.798533i	0.134566	+	0.0267669i
$891$	−5.60711	+	7.27945i	−0.187845	+	0.243871i
$892$	−22.0650	−	53.2696i	−0.738791	−	1.78360i
$893$	−26.3199	+	34.3008i	−0.880763	+	1.14783i
$894$	29.7987	+	7.47880i	0.996616	+	0.250128i
$895$	3.94665	−	4.50029i	0.131922	−	0.150428i
$896$	13.8014	−	6.80610i	0.461073	−	0.227376i
$897$	−2.27995	−	4.44373i	−0.0761253	−	0.148372i
$898$	−25.4964	−	29.0731i	−0.850825	−	0.970181i
$899$	6.01584	+	2.49184i	0.200640	+	0.0831077i
$900$	53.0440	+	5.27384i	1.76813	+	0.175795i
$901$	1.92212	+	35.5731i	0.0640351	+	1.18511i
$902$	−14.2060	+	8.20183i	−0.473008	+	0.273091i
$903$	−0.679336	+	3.72376i	−0.0226069	+	0.123919i
$904$	18.8479	+	6.39801i	0.626872	+	0.212794i
$905$	−2.33749	−	8.72364i	−0.0777008	−	0.289983i
$906$	−9.48465	−	3.75312i	−0.315107	−	0.124689i
$907$	0.302207	−	0.102585i	0.0100346	−	0.00340629i	−0.316418	−	0.948620i	$-0.602480\pi$
$907$	0.302207	−	0.102585i	0.0100346	−	0.00340629i	0.326452	+	0.945214i	$0.394147\pi$
$908$	37.0361	+	55.4284i	1.22909	+	1.83946i
$909$	−26.8514	+	28.6159i	−0.890603	+	0.949129i
$910$	−4.46492	+	1.84943i	−0.148011	+	0.0613080i
$911$	−14.5927	−	7.19632i	−0.483477	−	0.238425i	0.184181	−	0.982892i	$-0.441037\pi$
$911$	−14.5927	−	7.19632i	−0.483477	−	0.238425i	−0.667659	+	0.744468i	$0.732703\pi$
$912$	13.9787	+	7.77690i	0.462880	+	0.257519i
$913$	−0.586170	−	1.18864i	−0.0193994	−	0.0393381i
$914$	−45.4421	+	12.1762i	−1.50309	+	0.402752i
$915$	−4.46676	−	3.31597i	−0.147666	−	0.109623i
$916$	−29.4817	+	3.88134i	−0.974103	+	0.128243i
$917$	−3.26759			−0.107905
$918$	11.8349	+	49.9640i	0.390611	+	1.64906i
$919$	−32.6543			−1.07716			−0.538582	−	0.842573i	$-0.681040\pi$
$919$	−32.6543			−1.07716			−0.538582	+	0.842573i	$0.681040\pi$
$920$	−1.11786	+	0.147169i	−0.0368546	+	0.00485200i
$921$	43.7952	+	32.5121i	1.44310	+	1.07131i
$922$	−31.0328	+	8.31521i	−1.02201	+	0.273847i
$923$	−10.2026	−	20.6889i	−0.335823	−	0.680983i
$924$	4.29568	+	2.38986i	0.141317	+	0.0786206i
$925$	48.2003	+	23.7698i	1.58482	+	0.781545i
$926$	−2.09494	+	0.867754i	−0.0688441	+	0.0285162i
$927$	−18.9263	−	4.43142i	−0.621621	−	0.145547i
$928$	8.08361	+	12.0980i	0.265357	+	0.397136i
$929$	13.4095	−	4.55192i	0.439952	−	0.149344i	−0.0926698	−	0.995697i	$-0.529540\pi$
$929$	13.4095	−	4.55192i	0.439952	−	0.149344i	0.532622	+	0.846353i	$0.321207\pi$
$930$	−2.00048	−	0.791601i	−0.0655984	−	0.0259576i
$931$	6.09453	+	22.7451i	0.199740	+	0.745440i
$932$	−65.5238	−	22.2423i	−2.14630	−	0.728572i
$933$	−3.50458	+	19.2102i	−0.114735	+	0.628914i
$934$	−62.6642	+	36.1792i	−2.05044	+	1.18382i
$935$	2.00125	+	0.705032i	0.0654479	+	0.0230570i
$936$	−39.4026	+	54.8791i	−1.28791	+	1.79378i
$937$	−25.9564	−	10.7515i	−0.847959	−	0.351236i	−0.0839723	−	0.996468i	$-0.526761\pi$
$937$	−25.9564	−	10.7515i	−0.847959	−	0.351236i	−0.763987	+	0.645232i	$0.776761\pi$
$938$	−11.9548	−	13.6318i	−0.390338	−	0.445096i
$939$	−6.65236	−	12.9658i	−0.217092	−	0.423122i
$940$	−20.0402	+	9.88275i	−0.653641	+	0.322340i
$941$	−3.68514	+	4.20210i	−0.120132	+	0.136984i	−0.808780	−	0.588112i	$-0.799871\pi$
$941$	−3.68514	+	4.20210i	−0.120132	+	0.136984i	0.688647	+	0.725096i	$0.258205\pi$
$942$	−38.5907	−	9.68541i	−1.25735	−	0.315568i
$943$	−2.18414	+	2.84643i	−0.0711254	+	0.0926924i
$944$	−8.51135	−	20.5482i	−0.277021	−	0.668787i
$945$	1.83009	+	0.657678i	0.0595329	+	0.0213943i
$946$	7.06358	+	1.40503i	0.229657	+	0.0456816i
$947$	−1.86646	+	28.4767i	−0.0606518	+	0.925367i	0.853782	+	0.520631i	$0.174303\pi$
$947$	−1.86646	+	28.4767i	−0.0606518	+	0.925367i	−0.914434	+	0.404736i	$0.867363\pi$
$948$	−3.32645	+	67.0795i	−0.108038	+	2.17864i
$949$	−5.52930	+	16.2888i	−0.179489	+	0.528756i
$950$	−32.9507	+	25.2839i	−1.06906	+	0.820319i
$951$	−2.13427	−	0.686840i	−0.0692085	−	0.0222723i
$952$	11.8768	−	4.76068i	0.384928	−	0.154294i
$953$			37.4674i			1.21369i	0.794821	+	0.606844i	$0.207565\pi$
$953$			37.4674i			1.21369i	−0.794821	+	0.606844i	$0.792435\pi$
$954$	62.0922	−	1.97530i	2.01031	−	0.0639526i
$955$	2.11098	+	10.6126i	0.0683096	+	0.343416i
$956$	62.6243	+	16.7801i	2.02542	+	0.542709i
$957$	−4.12050	+	10.4131i	−0.133197	+	0.336606i
$958$	−38.7863	−	34.0147i	−1.25313	−	1.09897i
$959$	−4.67695	+	0.306543i	−0.151026	+	0.00989880i
$960$	−5.24568	−	7.58674i	−0.169304	−	0.244861i
$961$	23.7552	+	18.2280i	0.766297	+	0.588000i
$962$	−121.584	+	81.2398i	−3.92002	+	2.61927i
$963$	−42.3604	−	12.8926i	−1.36505	−	0.415459i
$964$	25.8651	−	38.7099i	0.833060	−	1.24676i
$965$	−1.17476	+	4.38425i	−0.0378167	+	0.141134i
$966$	1.63863	+	0.189276i	0.0527222	+	0.00608986i
$967$	−2.82928	−	3.68719i	−0.0909836	−	0.118572i	0.745643	−	0.666345i	$-0.232142\pi$
$967$	−2.82928	−	3.68719i	−0.0909836	−	0.118572i	−0.836627	+	0.547773i	$0.815476\pi$
$968$	−20.8097	+	36.0434i	−0.668848	+	1.15848i
$969$	−21.7461	−	14.3913i	−0.698587	−	0.462316i
$970$	−9.62576	−	16.6723i	−0.309065	−	0.535316i
$971$	17.1196	−	41.3304i	0.549394	−	1.32636i	−0.368536	−	0.929614i	$-0.620141\pi$
$971$	17.1196	−	41.3304i	0.549394	−	1.32636i	0.917930	−	0.396742i	$-0.129859\pi$
$972$	57.0753	−	12.1892i	1.83069	−	0.390970i
$973$	7.95592	+	7.95592i	0.255055	+	0.255055i
$974$	−23.9758	−	1.57146i	−0.768233	−	0.0503527i
$975$	−22.7522	−	37.9996i	−0.728655	−	1.21696i
$976$	1.05406	+	16.0818i	0.0337396	+	0.514767i
$977$	−3.87397	+	29.4257i	−0.123939	+	0.941411i	0.810612	+	0.585583i	$0.199134\pi$
$977$	−3.87397	+	29.4257i	−0.123939	+	0.941411i	−0.934551	+	0.355828i	$0.884199\pi$
$978$	−2.20332	−	27.0245i	−0.0704545	−	0.864148i
$979$	−1.52999	+	3.10251i	−0.0488987	+	0.0991567i
$980$	−2.37418	+	11.9358i	−0.0758404	+	0.381276i
$981$	2.41444	+	1.98521i	0.0770872	+	0.0633830i
$982$	−7.32889	+	7.32889i	−0.233874	+	0.233874i
$983$	21.7491	−	19.0734i	0.693688	−	0.608348i	−0.238148	−	0.971229i	$-0.576540\pi$
$983$	21.7491	−	19.0734i	0.693688	−	0.608348i	0.931835	+	0.362881i	$0.118207\pi$
$984$	47.7440	+	8.71009i	1.52202	+	0.277668i
$985$	−7.95436	−	4.59245i	−0.253447	−	0.146328i
$986$	30.6659	+	54.5504i	0.976601	+	1.73724i
$987$	14.8854	−	3.20775i	0.473808	−	0.102104i
$988$	−9.61446	−	73.0291i	−0.305877	−	2.32337i
$989$	1.54496	−	0.307311i	0.0491268	−	0.00977193i
$990$	1.30654	−	3.46170i	0.0415246	−	0.110020i
$991$	−15.8269	−	10.5752i	−0.502759	−	0.335933i	0.278191	−	0.960526i	$-0.410265\pi$
$991$	−15.8269	−	10.5752i	−0.502759	−	0.335933i	−0.780951	+	0.624593i	$0.785265\pi$
$992$	−0.759360	−	2.23700i	−0.0241097	−	0.0710249i
$993$	−11.0565	+	3.15182i	−0.350866	+	0.100020i
$994$	7.55341	+	0.994426i	0.239580	+	0.0315413i
$995$	−12.5909	−	1.65762i	−0.399157	−	0.0525500i
$996$	−2.04914	+	8.16464i	−0.0649296	+	0.258707i
$997$	−10.2998	−	30.3423i	−0.326199	−	0.960951i	−0.979077	−	0.203488i	$-0.934772\pi$
$997$	−10.2998	−	30.3423i	−0.326199	−	0.960951i	0.652879	−	0.757463i	$-0.273561\pi$
$998$	46.6365	+	31.1615i	1.47625	+	0.986400i
$999$	58.1920	+	8.71436i	1.84111	+	0.275710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.113.16	yes	256
3.2	odd	2		459.2.y.a.368.1		256
9.2	odd	6	inner	153.2.s.a.11.16	✓	256
9.7	even	3		459.2.y.a.62.1		256
17.14	odd	16	inner	153.2.s.a.14.16	yes	256
51.14	even	16		459.2.y.a.422.1		256
153.65	even	48	inner	153.2.s.a.65.16	yes	256
153.133	odd	48		459.2.y.a.116.1		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.16	✓	256	9.2	odd	6	inner
153.2.s.a.14.16	yes	256	17.14	odd	16	inner
153.2.s.a.65.16	yes	256	153.65	even	48	inner
153.2.s.a.113.16	yes	256	1.1	even	1	trivial
459.2.y.a.62.1		256	9.7	even	3
459.2.y.a.116.1		256	153.133	odd	48
459.2.y.a.368.1		256	3.2	odd	2
459.2.y.a.422.1		256	51.14	even	16

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.37615 - 0.312826i) q^{2} +(-1.39072 - 1.03242i) q^{3} +(3.61637 - 0.969004i) q^{4} +(-0.222937 - 0.452071i) q^{5} +(-3.62753 - 2.01814i) q^{6} +(-0.665919 - 0.328395i) q^{7} +(3.86148 - 1.59948i) q^{8} +(0.868203 + 2.87162i) q^{9} +O(q^{10})\)	\(q+(2.37615 - 0.312826i) q^{2} +(-1.39072 - 1.03242i) q^{3} +(3.61637 - 0.969004i) q^{4} +(-0.222937 - 0.452071i) q^{5} +(-3.62753 - 2.01814i) q^{6} +(-0.665919 - 0.328395i) q^{7} +(3.86148 - 1.59948i) q^{8} +(0.868203 + 2.87162i) q^{9} +(-0.671150 - 1.00445i) q^{10} +(0.966772 - 0.328175i) q^{11} +(-6.02979 - 2.38602i) q^{12} +(1.39452 + 5.20440i) q^{13} +(-1.68505 - 0.571999i) q^{14} +(-0.156686 + 0.858869i) q^{15} +(2.19038 - 1.26462i) q^{16} +(-3.71857 + 1.78107i) q^{17} +(2.96130 + 6.55181i) q^{18} +(-3.37354 - 1.39737i) q^{19} +(-1.24428 - 1.41883i) q^{20} +(0.587064 + 1.14422i) q^{21} +(2.19453 - 1.08222i) q^{22} +(0.352872 - 0.402373i) q^{23} +(-7.02157 - 1.76226i) q^{24} +(2.88914 - 3.76520i) q^{25} +(4.94165 + 11.9302i) q^{26} +(1.75731 - 4.88998i) q^{27} +(-2.72643 - 0.542320i) q^{28} +(0.414188 - 6.31929i) q^{29} +(-0.103633 + 2.08982i) q^{30} +(-0.330507 + 0.973643i) q^{31} +(-1.82278 + 1.39867i) q^{32} +(-1.68332 - 0.541719i) q^{33} +(-8.27872 + 5.39536i) q^{34} +0.374254i q^{35} +(5.92236 + 9.54357i) q^{36} +(2.20919 + 11.1064i) q^{37} +(-8.45317 - 2.26502i) q^{38} +(3.43377 - 8.67759i) q^{39} +(-1.58394 - 1.38908i) q^{40} +(-6.68958 + 0.438458i) q^{41} +(1.75289 + 2.53518i) q^{42} +(2.33510 + 1.79179i) q^{43} +(3.17821 - 2.12361i) q^{44} +(1.10462 - 1.03268i) q^{45} +(0.712603 - 1.06649i) q^{46} +(3.06452 - 11.4370i) q^{47} +(-4.35183 - 0.502674i) q^{48} +(-3.92573 - 5.11610i) q^{49} +(5.68718 - 9.85048i) q^{50} +(7.01031 + 1.36217i) q^{51} +(10.0862 + 17.4698i) q^{52} +(3.30651 - 7.98262i) q^{53} +(2.64591 - 12.1690i) q^{54} +(-0.363887 - 0.363887i) q^{55} +(-3.09669 - 0.202968i) q^{56} +(3.24898 + 5.42627i) q^{57} +(-0.992666 - 15.1452i) q^{58} +(1.14780 - 8.71842i) q^{59} +(0.265612 + 3.25782i) q^{60} +(-2.81827 + 5.71489i) q^{61} +(-0.480754 + 2.41691i) q^{62} +(0.364874 - 2.19738i) q^{63} +(-7.47053 + 7.47053i) q^{64} +(2.04187 - 1.79067i) q^{65} +(-4.16930 - 0.760618i) q^{66} +(8.82398 + 5.09452i) q^{67} +(-11.7219 + 10.0443i) q^{68} +(-0.906165 + 0.195275i) q^{69} +(0.117076 + 0.889283i) q^{70} +(-4.19907 + 0.835247i) q^{71} +(7.94564 + 9.70004i) q^{72} +(2.65455 + 1.77371i) q^{73} +(8.72372 + 25.6993i) q^{74} +(-7.90527 + 2.25352i) q^{75} +(-13.5540 - 1.78442i) q^{76} +(-0.751563 - 0.0989451i) q^{77} +(5.44457 - 21.6934i) q^{78} +(-3.32914 - 9.80734i) q^{79} +(-1.06001 - 0.708279i) q^{80} +(-7.49245 + 4.98630i) q^{81} +(-15.7583 + 3.13452i) q^{82} +(-0.169437 - 1.28700i) q^{83} +(3.23179 + 3.56904i) q^{84} +(1.63418 + 1.28399i) q^{85} +(6.10907 + 3.52707i) q^{86} +(-7.10021 + 8.36075i) q^{87} +(3.20826 - 2.81357i) q^{88} +(-2.39586 + 2.39586i) q^{89} +(2.30170 - 2.79936i) q^{90} +(0.780465 - 3.92366i) q^{91} +(0.886215 - 1.79707i) q^{92} +(1.46485 - 1.01284i) q^{93} +(3.70399 - 28.1346i) q^{94} +(0.120377 + 1.83661i) q^{95} +(3.97899 - 0.0632744i) q^{96} +(15.9021 + 1.04228i) q^{97} +(-10.9286 - 10.9286i) q^{98} +(1.78175 + 2.49128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

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