LMFDB - Embedded newform 153.2.s.a.113.4

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			113.4
Character	$\chi$	$=$	153.113
Dual form			153.2.s.a.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68890 + 0.222348i) q^{2} +(1.30958 + 1.13358i) q^{3} +(0.871097 - 0.233410i) q^{4} +(-0.431798 - 0.875600i) q^{5} +(-2.46380 - 1.62332i) q^{6} +(2.92393 + 1.44192i) q^{7} +(1.72831 - 0.715890i) q^{8} +(0.429989 + 2.96903i) q^{9} +O(q^{10})$	\(q+(-1.68890 + 0.222348i) q^{2} +(1.30958 + 1.13358i) q^{3} +(0.871097 - 0.233410i) q^{4} +(-0.431798 - 0.875600i) q^{5} +(-2.46380 - 1.62332i) q^{6} +(2.92393 + 1.44192i) q^{7} +(1.72831 - 0.715890i) q^{8} +(0.429989 + 2.96903i) q^{9} +(0.923953 + 1.38279i) q^{10} +(-3.22699 + 1.09542i) q^{11} +(1.40536 + 0.681791i) q^{12} +(0.485696 + 1.81264i) q^{13} +(-5.25883 - 1.78513i) q^{14} +(0.427090 - 1.63615i) q^{15} +(-4.32178 + 2.49518i) q^{16} +(3.35545 + 2.39603i) q^{17} +(-1.38637 - 4.91878i) q^{18} +(1.65080 + 0.683785i) q^{19} +(-0.580512 - 0.661947i) q^{20} +(2.19458 + 5.20282i) q^{21} +(5.20650 - 2.56756i) q^{22} +(-2.05951 + 2.34842i) q^{23} +(3.07488 + 1.02167i) q^{24} +(2.46358 - 3.21060i) q^{25} +(-1.22333 - 2.95338i) q^{26} +(-2.80253 + 4.37560i) q^{27} +(2.88358 + 0.573580i) q^{28} +(0.427734 - 6.52595i) q^{29} +(-0.357520 + 2.85825i) q^{30} +(0.365730 - 1.07741i) q^{31} +(3.77599 - 2.89742i) q^{32} +(-5.46774 - 2.22352i) q^{33} +(-6.19977 - 3.30059i) q^{34} -3.18281i q^{35} +(1.06756 + 2.48594i) q^{36} +(-1.75772 - 8.83664i) q^{37} +(-2.94008 - 0.787793i) q^{38} +(-1.41872 + 2.92437i) q^{39} +(-1.37312 - 1.20419i) q^{40} +(4.80798 - 0.315131i) q^{41} +(-4.86326 - 8.29909i) q^{42} +(-8.86751 - 6.80428i) q^{43} +(-2.55534 + 1.70742i) q^{44} +(2.41401 - 1.65852i) q^{45} +(2.95614 - 4.42418i) q^{46} +(0.942428 - 3.51719i) q^{47} +(-8.48820 - 1.63145i) q^{48} +(2.20889 + 2.87868i) q^{49} +(-3.44687 + 5.97016i) q^{50} +(1.67812 + 6.94146i) q^{51} +(0.846177 + 1.46562i) q^{52} +(0.730606 - 1.76384i) q^{53} +(3.76029 - 8.01309i) q^{54} +(2.35256 + 2.35256i) q^{55} +(6.08572 + 0.398879i) q^{56} +(1.38673 + 2.76679i) q^{57} +(0.728633 + 11.1168i) q^{58} +(-0.828213 + 6.29090i) q^{59} +(-0.00985512 - 1.52493i) q^{60} +(-2.95443 + 5.99099i) q^{61} +(-0.378123 + 1.90095i) q^{62} +(-3.02385 + 9.30123i) q^{63} +(1.32440 - 1.32440i) q^{64} +(1.37743 - 1.20797i) q^{65} +(9.72886 + 2.53957i) q^{66} +(4.41090 + 2.54663i) q^{67} +(3.48218 + 1.30398i) q^{68} +(-5.35922 + 0.740820i) q^{69} +(0.707692 + 5.37545i) q^{70} +(16.3403 - 3.25028i) q^{71} +(2.86865 + 4.82358i) q^{72} +(-13.5589 - 9.05977i) q^{73} +(4.93342 + 14.5334i) q^{74} +(6.86573 - 1.41186i) q^{75} +(1.59761 + 0.210330i) q^{76} +(-11.0150 - 1.45015i) q^{77} +(1.74585 - 5.25443i) q^{78} +(-0.357632 - 1.05355i) q^{79} +(4.05092 + 2.70674i) q^{80} +(-8.63022 + 2.55329i) q^{81} +(-8.05013 + 1.60127i) q^{82} +(-1.10682 - 8.40712i) q^{83} +(3.12608 + 4.01992i) q^{84} +(0.649091 - 3.97263i) q^{85} +(16.4893 + 9.52008i) q^{86} +(7.95785 - 8.06137i) q^{87} +(-4.79305 + 4.20339i) q^{88} +(-9.18621 + 9.18621i) q^{89} +(-3.70826 + 3.33782i) q^{90} +(-1.19355 + 6.00038i) q^{91} +(-1.24589 + 2.52641i) q^{92} +(1.70028 - 0.996363i) q^{93} +(-0.809628 + 6.14973i) q^{94} +(-0.114092 - 1.74070i) q^{95} +(8.22941 + 0.485994i) q^{96} +(13.2223 + 0.866637i) q^{97} +(-4.37066 - 4.37066i) q^{98} +(-4.63989 - 9.11000i) 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 $

$2$	−1.68890	+	0.222348i	−1.19423	+	0.157224i	−0.701315	−	0.712852i	$-0.747403\pi$
$2$	−1.68890	+	0.222348i	−1.19423	+	0.157224i	−0.492919	+	0.870075i	$0.664070\pi$
$3$	1.30958	+	1.13358i	0.756085	+	0.654473i
$3$	1.30958	+	1.13358i	0.756085	+	0.654473i
$4$	0.871097	−	0.233410i	0.435548	−	0.116705i
$5$	−0.431798	−	0.875600i	−0.193106	−	0.391580i	0.778688	−	0.627411i	$-0.215886\pi$
$5$	−0.431798	−	0.875600i	−0.193106	−	0.391580i	−0.971794	+	0.235831i	$0.924219\pi$
$6$	−2.46380	−	1.62332i	−1.00584	−	0.662719i
$7$	2.92393	+	1.44192i	1.10514	+	0.544995i	0.900944	−	0.433935i	$-0.142875\pi$
$7$	2.92393	+	1.44192i	1.10514	+	0.544995i	0.204197	+	0.978930i	$0.434542\pi$
$8$	1.72831	−	0.715890i	0.611051	−	0.253105i
$9$	0.429989	+	2.96903i	0.143330	+	0.989675i
$10$	0.923953	+	1.38279i	0.292180	+	0.437278i
$11$	−3.22699	+	1.09542i	−0.972974	+	0.330280i	−0.762262	−	0.647268i	$-0.775911\pi$
$11$	−3.22699	+	1.09542i	−0.972974	+	0.330280i	−0.210712	+	0.977548i	$0.567578\pi$
$12$	1.40536	+	0.681791i	0.405692	+	0.196816i
$13$	0.485696	+	1.81264i	0.134708	+	0.502737i	0.999999	+	0.00146700i	$0.000466960\pi$
$13$	0.485696	+	1.81264i	0.134708	+	0.502737i	−0.865291	+	0.501270i	$0.832866\pi$
$14$	−5.25883	−	1.78513i	−1.40548	−	0.477097i
$15$	0.427090	−	1.63615i	0.110274	−	0.422451i
$16$	−4.32178	+	2.49518i	−1.08045	+	0.623795i
$17$	3.35545	+	2.39603i	0.813815	+	0.581123i
$17$	3.35545	+	2.39603i	0.813815	+	0.581123i
$18$	−1.38637	−	4.91878i	−0.326769	−	1.15937i
$19$	1.65080	+	0.683785i	0.378720	+	0.156871i	0.563919	−	0.825830i	$-0.309293\pi$
$19$	1.65080	+	0.683785i	0.378720	+	0.156871i	−0.185199	+	0.982701i	$0.559293\pi$
$20$	−0.580512	−	0.661947i	−0.129806	−	0.148016i
$21$	2.19458	+	5.20282i	0.478896	+	1.13535i
$22$	5.20650	−	2.56756i	1.11003	−	0.547406i
$23$	−2.05951	+	2.34842i	−0.429438	+	0.489680i	−0.925575	−	0.378564i	$-0.876418\pi$
$23$	−2.05951	+	2.34842i	−0.429438	+	0.489680i	0.496137	+	0.868244i	$0.334751\pi$
$24$	3.07488	+	1.02167i	0.627657	+	0.208547i
$25$	2.46358	−	3.21060i	0.492716	−	0.642120i
$26$	−1.22333	−	2.95338i	−0.239915	−	0.579206i
$27$	−2.80253	+	4.37560i	−0.539346	+	0.842084i
$28$	2.88358	+	0.573580i	0.544946	+	0.108396i
$29$	0.427734	−	6.52595i	0.0794281	−	1.21184i	−0.753119	−	0.657884i	$-0.771451\pi$
$29$	0.427734	−	6.52595i	0.0794281	−	1.21184i	0.832547	−	0.553954i	$-0.186882\pi$
$30$	−0.357520	+	2.85825i	−0.0652739	+	0.521843i
$31$	0.365730	−	1.07741i	0.0656871	−	0.193508i	−0.909131	−	0.416511i	$-0.863253\pi$
$31$	0.365730	−	1.07741i	0.0656871	−	0.193508i	0.974818	+	0.223003i	$0.0715860\pi$
$32$	3.77599	−	2.89742i	0.667507	−	0.512196i
$33$	−5.46774	−	2.22352i	−0.951811	−	0.387066i
$34$	−6.19977	−	3.30059i	−1.06325	−	0.566046i
$35$		−	3.18281i		−	0.537993i
$36$	1.06756	+	2.48594i	0.177927	+	0.414324i
$37$	−1.75772	−	8.83664i	−0.288967	−	1.45273i	−0.803521	−	0.595277i	$-0.797042\pi$
$37$	−1.75772	−	8.83664i	−0.288967	−	1.45273i	0.514554	−	0.857458i	$-0.327958\pi$
$38$	−2.94008	−	0.787793i	−0.476944	−	0.127797i
$39$	−1.41872	+	2.92437i	−0.227177	+	0.468275i
$40$	−1.37312	−	1.20419i	−0.217109	−	0.190399i
$41$	4.80798	−	0.315131i	0.750880	−	0.0492153i	0.314843	−	0.949144i	$-0.398048\pi$
$41$	4.80798	−	0.315131i	0.750880	−	0.0492153i	0.436037	+	0.899929i	$0.356382\pi$
$42$	−4.86326	−	8.29909i	−0.750417	−	1.28058i
$43$	−8.86751	−	6.80428i	−1.35228	−	1.03764i	−0.994598	−	0.103800i	$-0.966900\pi$
$43$	−8.86751	−	6.80428i	−1.35228	−	1.03764i	−0.357684	−	0.933843i	$-0.616433\pi$
$44$	−2.55534	+	1.70742i	−0.385232	+	0.257404i
$45$	2.41401	−	1.65852i	0.359860	−	0.247237i
$46$	2.95614	−	4.42418i	0.435860	−	0.652310i
$47$	0.942428	−	3.51719i	0.137467	−	0.513035i	−0.862508	−	0.506043i	$-0.831108\pi$
$47$	0.942428	−	3.51719i	0.137467	−	0.513035i	0.999976	−	0.00699191i	$-0.00222561\pi$
$48$	−8.48820	−	1.63145i	−1.22517	−	0.235480i
$49$	2.20889	+	2.87868i	0.315555	+	0.411240i
$50$	−3.44687	+	5.97016i	−0.487462	+	0.844308i
$51$	1.67812	+	6.94146i	0.234984	+	0.971999i
$52$	0.846177	+	1.46562i	0.117344	+	0.203245i
$53$	0.730606	−	1.76384i	0.100356	−	0.242282i	−0.865725	−	0.500520i	$-0.833142\pi$
$53$	0.730606	−	1.76384i	0.100356	−	0.242282i	0.966081	+	0.258238i	$0.0831420\pi$
$54$	3.76029	−	8.01309i	0.511710	−	1.09044i
$55$	2.35256	+	2.35256i	0.317218	+	0.317218i
$56$	6.08572	+	0.398879i	0.813238	+	0.0533025i
$57$	1.38673	+	2.76679i	0.183677	+	0.366470i
$58$	0.728633	+	11.1168i	0.0956742	+	1.45971i
$59$	−0.828213	+	6.29090i	−0.107824	+	0.819006i	0.849011	+	0.528375i	$0.177199\pi$
$59$	−0.828213	+	6.29090i	−0.107824	+	0.819006i	−0.956835	+	0.290631i	$0.906135\pi$
$60$	−0.00985512	−	1.52493i	−0.00127229	−	0.196867i
$61$	−2.95443	+	5.99099i	−0.378276	+	0.767068i	−0.999868	−	0.0162737i	$-0.994820\pi$
$61$	−2.95443	+	5.99099i	−0.378276	+	0.767068i	0.621592	+	0.783341i	$0.286486\pi$
$62$	−0.378123	+	1.90095i	−0.0480217	+	0.241421i
$63$	−3.02385	+	9.30123i	−0.380969	+	1.17184i
$64$	1.32440	−	1.32440i	0.165550	−	0.165550i
$65$	1.37743	−	1.20797i	0.170849	−	0.149831i
$66$	9.72886	+	2.53957i	1.19754	+	0.312599i
$67$	4.41090	+	2.54663i	0.538877	+	0.311121i	0.744624	−	0.667485i	$-0.232629\pi$
$67$	4.41090	+	2.54663i	0.538877	+	0.311121i	−0.205747	+	0.978605i	$0.565962\pi$
$68$	3.48218	+	1.30398i	0.422276	+	0.158131i
$69$	−5.35922	+	0.740820i	−0.645174	+	0.0891842i
$70$	0.707692	+	5.37545i	0.0845854	+	0.642490i
$71$	16.3403	−	3.25028i	1.93923	−	0.385737i	0.940257	−	0.340465i	$-0.110585\pi$
$71$	16.3403	−	3.25028i	1.93923	−	0.385737i	0.998975	−	0.0452718i	$-0.0144154\pi$
$72$	2.86865	+	4.82358i	0.338074	+	0.568464i
$73$	−13.5589	−	9.05977i	−1.58695	−	1.06037i	−0.959500	−	0.281709i	$-0.909099\pi$
$73$	−13.5589	−	9.05977i	−1.58695	−	1.06037i	−0.627450	−	0.778657i	$-0.715901\pi$
$74$	4.93342	+	14.5334i	0.573498	+	1.68947i
$75$	6.86573	−	1.41186i	0.792786	−	0.163028i
$76$	1.59761	+	0.210330i	0.183259	+	0.0241265i
$77$	−11.0150	−	1.45015i	−1.25527	−	0.165260i
$78$	1.74585	−	5.25443i	0.197679	−	0.594947i
$79$	−0.357632	−	1.05355i	−0.0402367	−	0.118533i	0.924955	−	0.380076i	$-0.124102\pi$
$79$	−0.357632	−	1.05355i	−0.0402367	−	0.118533i	−0.965192	+	0.261543i	$0.915769\pi$
$80$	4.05092	+	2.70674i	0.452906	+	0.302622i
$81$	−8.63022	+	2.55329i	−0.958913	+	0.283699i
$82$	−8.05013	+	1.60127i	−0.888988	+	0.176831i
$83$	−1.10682	−	8.40712i	−0.121489	−	0.922802i	−0.938282	−	0.345871i	$-0.887584\pi$
$83$	−1.10682	−	8.40712i	−0.121489	−	0.922802i	0.816793	−	0.576931i	$-0.195750\pi$
$84$	3.12608	+	4.01992i	0.341083	+	0.438610i
$85$	0.649091	−	3.97263i	0.0704038	−	0.430893i
$86$	16.4893	+	9.52008i	1.77808	+	1.02658i
$87$	7.95785	−	8.06137i	0.853171	−	0.864270i
$88$	−4.79305	+	4.20339i	−0.510941	+	0.448083i
$89$	−9.18621	+	9.18621i	−0.973736	+	0.973736i	−0.999664	−	0.0259279i	$-0.991746\pi$
$89$	−9.18621	+	9.18621i	−0.973736	+	0.973736i	0.0259279	+	0.999664i	$0.491746\pi$
$90$	−3.70826	+	3.33782i	−0.390885	+	0.351838i
$91$	−1.19355	+	6.00038i	−0.125118	+	0.629010i
$92$	−1.24589	+	2.52641i	−0.129893	+	0.263397i
$93$	1.70028	−	0.996363i	0.176311	−	0.103318i
$94$	−0.809628	+	6.14973i	−0.0835067	+	0.634297i
$95$	−0.114092	−	1.74070i	−0.0117056	−	0.178592i
$96$	8.22941	+	0.485994i	0.839911	+	0.0496016i
$97$	13.2223	+	0.866637i	1.34252	+	0.0879937i	0.719655	−	0.694332i	$-0.244300\pi$
$97$	13.2223	+	0.866637i	1.34252	+	0.0879937i	0.622869	+	0.782326i	$0.285967\pi$
$98$	−4.37066	−	4.37066i	−0.441503	−	0.441503i
$99$	−4.63989	−	9.11000i	−0.466326	−	0.915589i
$100$	1.39663	−	3.37177i	0.139663	−	0.337177i
$101$	−2.84476	−	4.92726i	−0.283064	−	0.490281i	0.689074	−	0.724691i	$-0.258017\pi$
$101$	−2.84476	−	4.92726i	−0.283064	−	0.490281i	−0.972138	+	0.234410i	$0.924684\pi$
$102$	−4.37760	−	11.3503i	−0.433447	−	1.12385i
$103$	−1.85005	+	3.20438i	−0.182291	+	0.315737i	−0.942660	−	0.333754i	$-0.891685\pi$
$103$	−1.85005	+	3.20438i	−0.182291	+	0.315737i	0.760369	+	0.649491i	$0.225018\pi$
$104$	2.13709	+	2.78511i	0.209559	+	0.273102i
$105$	3.60797	−	4.16814i	0.352102	−	0.406769i
$106$	−0.841735	+	3.14140i	−0.0817565	+	0.305120i
$107$	−8.47713	+	12.6869i	−0.819516	+	1.22649i	0.151732	+	0.988422i	$0.451515\pi$
$107$	−8.47713	+	12.6869i	−0.819516	+	1.22649i	−0.971248	+	0.238070i	$0.923485\pi$
$108$	−1.41997	+	4.46570i	−0.136636	+	0.429713i
$109$	3.45215	−	2.30665i	0.330656	−	0.220937i	−0.379149	−	0.925336i	$-0.623783\pi$
$109$	3.45215	−	2.30665i	0.330656	−	0.220937i	0.709805	+	0.704398i	$0.248783\pi$
$110$	−4.49632	−	3.45015i	−0.428707	−	0.328959i
$111$	7.71518	−	13.5648i	0.732292	−	1.28751i
$112$	−16.2344	+	1.06406i	−1.53401	+	0.100544i
$113$	−8.71078	−	7.63915i	−0.819441	−	0.718630i	0.143117	−	0.989706i	$-0.454287\pi$
$113$	−8.71078	−	7.63915i	−0.819441	−	0.718630i	−0.962558	+	0.271075i	$0.912621\pi$
$114$	−2.95724	−	4.36450i	−0.276971	−	0.408773i
$115$	2.94557	+	0.789264i	0.274676	+	0.0735993i
$116$	−1.15062	−	5.78457i	−0.106833	−	0.537084i
$117$	−5.17294	+	2.22146i	−0.478239	+	0.205374i
$118$		−	10.8089i		−	0.995037i
$119$	6.35619	+	11.8441i	0.582671	+	1.08575i
$120$	−0.433155	−	3.13352i	−0.0395415	−	0.286050i
$121$	0.486644	−	0.373415i	0.0442404	−	0.0339469i
$122$	3.65765	−	10.7751i	0.331148	−	0.975532i
$123$	6.65365	+	5.03754i	0.599939	+	0.454220i
$124$	0.0671093	−	1.02389i	0.00602659	−	0.0919480i
$125$	−8.66259	−	1.72310i	−0.774805	−	0.154118i
$126$	3.03887	−	16.3812i	0.270724	−	1.45935i
$127$	1.80127	+	4.34866i	0.159837	+	0.385881i	0.983427	−	0.181305i	$-0.0580321\pi$
$127$	1.80127	+	4.34866i	0.159837	+	0.385881i	−0.823590	+	0.567186i	$0.808032\pi$
$128$	−7.73714	+	10.0832i	−0.683873	+	0.891241i
$129$	−3.89949	−	18.9628i	−0.343331	−	1.66958i
$130$	−2.05775	+	2.34641i	−0.180477	+	0.205794i
$131$	11.5130	−	5.67756i	1.00589	−	0.496051i	0.136745	−	0.990606i	$-0.456336\pi$
$131$	11.5130	−	5.67756i	1.00589	−	0.496051i	0.869146	+	0.494555i	$0.164669\pi$
$132$	−5.28192	−	0.660681i	−0.459732	−	0.0575049i
$133$	3.84087	+	4.37967i	0.333045	+	0.379765i
$134$	−8.01581	−	3.32026i	−0.692460	−	0.286826i
$135$	5.04140	+	0.564518i	0.433895	+	0.0485860i
$136$	7.51456	+	1.73896i	0.644368	+	0.149115i
$137$	0.453041	−	0.261563i	0.0387059	−	0.0223469i	−0.480522	−	0.876983i	$-0.659553\pi$
$137$	0.453041	−	0.261563i	0.0387059	−	0.0223469i	0.519228	+	0.854636i	$0.326220\pi$
$138$	8.88647	−	2.44278i	0.756467	−	0.207944i
$139$	−13.5019	−	4.58328i	−1.14522	−	0.388749i	−0.316597	−	0.948560i	$-0.602540\pi$
$139$	−13.5019	−	4.58328i	−1.14522	−	0.388749i	−0.828620	+	0.559812i	$0.810874\pi$
$140$	−0.742899	−	2.77254i	−0.0627864	−	0.234322i
$141$	5.22120	−	3.53772i	0.439705	−	0.297929i
$142$	−26.8744	+	9.12262i	−2.25525	+	0.765554i
$143$	−3.55294	−	5.31734i	−0.297111	−	0.444659i
$144$	−9.26657	−	11.7586i	−0.772214	−	0.979881i
$145$	−5.89882	+	2.44337i	−0.489870	+	0.202911i
$146$	24.9141	+	12.2863i	2.06190	+	1.01682i
$147$	−0.370504	+	6.27380i	−0.0305587	+	0.517455i
$148$	−3.59370	−	7.28730i	−0.295400	−	0.599012i
$149$	−8.40704	+	2.25266i	−0.688731	+	0.184545i	−0.586178	−	0.810183i	$-0.699368\pi$
$149$	−8.40704	+	2.25266i	−0.688731	+	0.184545i	−0.102553	+	0.994727i	$0.532701\pi$
$150$	−11.2816	+	3.91108i	−0.921140	+	0.319338i
$151$	10.3804	−	1.36661i	0.844745	−	0.111213i	0.304283	−	0.952582i	$-0.401583\pi$
$151$	10.3804	−	1.36661i	0.844745	−	0.111213i	0.540461	+	0.841369i	$0.318250\pi$
$152$	3.34262			0.271122
$153$	−5.67108	+	10.9927i	−0.458480	+	0.888705i
$154$	18.9257			1.52507
$155$	−1.10130	+	0.144989i	−0.0884585	+	0.0116458i
$156$	−0.553266	+	2.87856i	−0.0442967	+	0.230469i
$157$	18.7548	−	5.02535i	1.49680	−	0.401066i	0.584773	−	0.811197i	$-0.301184\pi$
$157$	18.7548	−	5.02535i	1.49680	−	0.401066i	0.912027	+	0.410131i	$0.134517\pi$
$158$	0.838259	+	1.69982i	0.0666883	+	0.135230i
$159$	2.95624	−	1.48168i	0.234445	−	0.117505i
$160$	−4.16745	−	2.05516i	−0.329466	−	0.162474i
$161$	−9.40811	+	3.89697i	−0.741463	+	0.307124i
$162$	14.0079	−	6.23117i	1.10056	−	0.489567i
$163$	5.74447	+	8.59721i	0.449942	+	0.673385i	0.985221	−	0.171290i	$-0.0547936\pi$
$163$	5.74447	+	8.59721i	0.449942	+	0.673385i	−0.535279	+	0.844675i	$0.679794\pi$
$164$	4.11466	−	1.39674i	0.321301	−	0.109067i
$165$	0.414043	+	5.74767i	0.0322332	+	0.447455i
$166$	3.73861	+	13.9527i	0.290173	+	1.08294i
$167$	2.51434	+	0.853502i	0.194565	+	0.0660460i	0.417021	−	0.908897i	$-0.363074\pi$
$167$	2.51434	+	0.853502i	0.194565	+	0.0660460i	−0.222456	+	0.974943i	$0.571407\pi$
$168$	7.51756	+	7.42102i	0.579992	+	0.572544i
$169$	8.20855	−	4.73921i	0.631427	−	0.364555i
$170$	−0.212944	+	6.85371i	−0.0163320	+	0.525656i
$171$	−1.32035	+	5.19530i	−0.100970	+	0.397294i
$172$	−9.31264	−	3.85742i	−0.710082	−	0.294126i
$173$	−2.08047	−	2.37232i	−0.158175	−	0.180364i	0.667324	−	0.744768i	$-0.267440\pi$
$173$	−2.08047	−	2.37232i	−0.158175	−	0.180364i	−0.825499	+	0.564403i	$0.809106\pi$
$174$	−11.6476	+	15.3843i	−0.883001	+	1.16628i
$175$	11.8328	−	5.83528i	0.894473	−	0.441105i
$176$	11.2131	−	12.7861i	0.845218	−	0.963786i
$177$	−8.21586	+	7.29958i	−0.617542	+	0.548670i
$178$	13.4721	−	17.5571i	1.00977	−	1.31596i
$179$	0.762947	+	1.84192i	0.0570253	+	0.137671i	0.949824	−	0.312784i	$-0.101262\pi$
$179$	0.762947	+	1.84192i	0.0570253	+	0.137671i	−0.892799	+	0.450455i	$0.851262\pi$
$180$	1.71572	−	2.00818i	0.127882	−	0.149681i
$181$	−6.98647	−	1.38970i	−0.519300	−	0.103295i	−0.0715206	−	0.997439i	$-0.522785\pi$
$181$	−6.98647	−	1.38970i	−0.519300	−	0.103295i	−0.447780	+	0.894144i	$0.647785\pi$
$182$	0.681614	−	10.3994i	0.0505246	−	0.770857i
$183$	−10.6603	+	4.49658i	−0.788034	+	0.332397i
$184$	−1.87827	+	5.53319i	−0.138468	+	0.407913i
$185$	−6.97839	+	5.35470i	−0.513061	+	0.393686i
$186$	−2.65006	+	2.06081i	−0.194312	+	0.151106i
$187$	−13.4526	−	4.05637i	−0.983755	−	0.296631i
$188$		−	3.28378i		−	0.239495i
$189$	−14.5037	+	8.75291i	−1.05499	+	0.636680i
$190$	0.579731	+	2.91451i	0.0420581	+	0.211440i
$191$	−5.75287	−	1.54148i	−0.416263	−	0.111537i	0.0446078	−	0.999005i	$-0.485796\pi$
$191$	−5.75287	−	1.54148i	−0.416263	−	0.111537i	−0.460871	+	0.887467i	$0.652463\pi$
$192$	3.23572	−	0.233090i	0.233518	−	0.0168218i
$193$	−18.5796	−	16.2939i	−1.33739	−	1.17286i	−0.970086	−	0.242760i	$-0.921947\pi$
$193$	−18.5796	−	16.2939i	−1.33739	−	1.17286i	−0.367305	−	0.930101i	$-0.619719\pi$
$194$	−22.5239	+	1.47629i	−1.61712	+	0.105992i
$195$	3.17318	−	0.0205073i	0.227236	−	0.00146856i
$196$	2.59607	+	1.99203i	0.185433	+	0.142288i
$197$	11.5848	−	7.74071i	0.825383	−	0.551503i	−0.0696150	−	0.997574i	$-0.522177\pi$
$197$	11.5848	−	7.74071i	0.825383	−	0.551503i	0.894998	+	0.446071i	$0.147177\pi$
$198$	9.86190	+	14.3542i	0.700855	+	1.02011i
$199$	−8.45329	+	12.6512i	−0.599237	+	0.896822i	−0.999811	−	0.0194424i	$-0.993811\pi$
$199$	−8.45329	+	12.6512i	−0.599237	+	0.896822i	0.400573	+	0.916265i	$0.368811\pi$
$200$	1.95940	−	7.31258i	0.138550	−	0.517077i
$201$	2.88960	+	8.33512i	0.203817	+	0.587914i
$202$	5.90008	+	7.68913i	0.415128	+	0.541005i
$203$	10.6606	−	18.4647i	0.748226	−	1.29596i
$204$	3.08201	+	5.65500i	0.215784	+	0.395929i
$205$	−2.35201	−	4.07379i	−0.164271	−	0.284526i
$206$	2.41206	−	5.82324i	0.168056	−	0.405724i
$207$	−7.85809	−	5.10495i	−0.546175	−	0.354818i
$208$	−6.62195	−	6.62195i	−0.459149	−	0.459149i
$209$	−6.07616	−	0.398252i	−0.420297	−	0.0275477i
$210$	−5.16673	+	7.84180i	−0.356539	+	0.541136i
$211$	−0.364857	−	5.56664i	−0.0251178	−	0.383223i	−0.991848	−	0.127426i	$-0.959329\pi$
$211$	−0.364857	−	5.56664i	−0.0251178	−	0.383223i	0.966730	−	0.255798i	$-0.0823381\pi$
$212$	0.224731	−	1.70700i	0.0154346	−	0.117238i
$213$	25.0833	+	14.2665i	1.71868	+	0.977525i
$214$	11.4961	−	23.3118i	0.785859	−	1.59356i
$215$	−2.12885	+	10.7025i	−0.145187	+	0.729902i
$216$	−1.71119	+	9.56870i	−0.116432	+	0.651068i
$217$	2.62290	−	2.62290i	0.178054	−	0.178054i
$218$	−5.31746	+	4.66329i	−0.360144	+	0.315838i
$219$	−7.48646	−	27.2346i	−0.505888	−	1.84034i
$220$	2.59841	+	1.50019i	0.175185	+	0.101143i
$221$	−2.71343	+	7.24597i	−0.182525	+	0.487417i
$222$	−10.0141	+	24.6250i	−0.672101	+	1.65272i
$223$	3.10404	+	23.5776i	0.207862	+	1.57887i	0.703727	+	0.710471i	$0.251518\pi$
$223$	3.10404	+	23.5776i	0.207862	+	1.57887i	−0.495865	+	0.868400i	$0.665149\pi$
$224$	15.2186	−	3.02716i	1.01683	−	0.202261i
$225$	10.5917	+	5.93391i	0.706111	+	0.395594i
$226$	16.4102	+	10.9649i	1.09159	+	0.729377i
$227$	−0.299561	−	0.882477i	−0.0198825	−	0.0585720i	0.936536	−	0.350572i	$-0.114013\pi$
$227$	−0.299561	−	0.882477i	−0.0198825	−	0.0585720i	−0.956418	+	0.292000i	$0.905679\pi$
$228$	1.85377	+	2.08647i	0.122769	+	0.138180i
$229$	28.4118	+	3.74049i	1.87751	+	0.247179i	0.980739	−	0.195322i	$-0.0625752\pi$
$229$	28.4118	+	3.74049i	1.87751	+	0.247179i	0.896768	+	0.442501i	$0.145909\pi$
$230$	−5.15028	−	0.678047i	−0.339599	−	0.0447091i
$231$	−12.7811	−	14.3855i	−0.840936	−	0.946494i
$232$	−3.93261	−	11.5851i	−0.258188	−	0.760599i
$233$	−12.9650	−	8.66292i	−0.849364	−	0.567527i	0.0529546	−	0.998597i	$-0.483136\pi$
$233$	−12.9650	−	8.66292i	−0.849364	−	0.567527i	−0.902318	+	0.431070i	$0.858136\pi$
$234$	8.24265	−	4.90202i	0.538839	−	0.320455i
$235$	−3.48659	+	0.693526i	−0.227440	+	0.0452407i
$236$	0.746904	+	5.67330i	0.0486193	+	0.369300i
$237$	0.725936	−	1.78511i	0.0471546	−	0.115955i
$238$	−13.3685	−	18.5903i	−0.866551	−	1.20503i
$239$	23.4527	+	13.5404i	1.51703	+	0.875856i	0.999800	+	0.0200072i	$0.00636890\pi$
$239$	23.4527	+	13.5404i	1.51703	+	0.875856i	0.517227	+	0.855848i	$0.326964\pi$
$240$	2.23669	+	8.13673i	0.144378	+	0.525224i
$241$	−12.7820	+	11.2095i	−0.823359	+	0.722066i	−0.963397	−	0.268080i	$-0.913611\pi$
$241$	−12.7820	+	11.2095i	−0.823359	+	0.722066i	0.140038	+	0.990146i	$0.455278\pi$
$242$	−0.738866	+	0.738866i	−0.0474961	+	0.0474961i
$243$	−14.1963	−	6.43932i	−0.910694	−	0.413082i
$244$	−1.17524	+	5.90833i	−0.0752370	+	0.378242i
$245$	1.56678	−	3.17711i	0.100098	−	0.202978i
$246$	−12.3574	−	7.02848i	−0.787882	−	0.448120i
$247$	−0.437670	+	3.32443i	−0.0278483	+	0.211528i
$248$	−0.139209	−	2.12392i	−0.00883977	−	0.134869i
$249$	8.08069	−	12.2644i	0.512093	−	0.777228i
$250$	15.0134	+	0.984029i	0.949530	+	0.0622355i
$251$	8.24414	+	8.24414i	0.520366	+	0.520366i	0.917682	−	0.397316i	$-0.130058\pi$
$251$	8.24414	+	8.24414i	0.520366	+	0.520366i	−0.397316	+	0.917682i	$0.630058\pi$
$252$	−0.463067	+	8.80806i	−0.0291704	+	0.554856i
$253$	4.07353	−	9.83436i	0.256100	−	0.618281i
$254$	−4.00909	−	6.94394i	−0.251553	−	0.435702i
$255$	5.35334	−	4.46668i	0.335239	−	0.279714i
$256$	8.95229	−	15.5058i	0.559518	−	0.969114i
$257$	−4.03284	−	5.25570i	−0.251562	−	0.327841i	0.650453	−	0.759546i	$-0.274579\pi$
$257$	−4.03284	−	5.25570i	−0.251562	−	0.327841i	−0.902015	+	0.431705i	$0.857912\pi$
$258$	10.8022	+	31.1592i	0.672515	+	1.93989i
$259$	7.60231	−	28.3722i	0.472384	−	1.76296i
$260$	0.917921	−	1.37377i	0.0569271	−	0.0851974i
$261$	19.5596	−	1.53613i	1.21071	−	0.0950843i
$262$	−18.1818	+	12.1487i	−1.12328	+	0.750551i
$263$	13.3457	+	10.2405i	0.822930	+	0.631457i	0.931952	−	0.362583i	$-0.118105\pi$
$263$	13.3457	+	10.2405i	0.822930	+	0.631457i	−0.109021	+	0.994039i	$0.534772\pi$
$264$	−11.0418	+	0.0713593i	−0.679573	+	0.00439186i
$265$	−1.85989	+	0.121904i	−0.114252	+	0.00748849i
$266$	−7.46065	−	6.54282i	−0.457442	−	0.401166i
$267$	−22.4434	+	1.61674i	−1.37351	+	0.0989432i
$268$	4.43673	+	1.18882i	0.271016	+	0.0726186i
$269$	−2.87257	−	14.4414i	−0.175144	−	0.880506i	−0.963995	−	0.265922i	$-0.914324\pi$
$269$	−2.87257	−	14.4414i	−0.175144	−	0.880506i	0.788851	−	0.614584i	$-0.210676\pi$
$270$	−8.63995	+	0.167530i	−0.525810	+	0.0101956i
$271$			29.5435i			1.79464i	0.441381	+	0.897320i	$0.354489\pi$
$271$			29.5435i			1.79464i	−0.441381	+	0.897320i	$0.645511\pi$
$272$	−20.4800	−	1.98268i	−1.24178	−	0.120218i
$273$	−8.36496	+	6.50498i	−0.506270	+	0.393699i
$274$	−0.706983	+	0.542487i	−0.0427104	+	0.0327729i
$275$	−4.43301	+	13.0592i	−0.267321	+	0.787501i
$276$	−4.49548	+	1.89622i	−0.270596	+	0.114139i
$277$	−0.659393	+	10.0604i	−0.0396191	+	0.604470i	0.931177	+	0.364566i	$0.118783\pi$
$277$	−0.659393	+	10.0604i	−0.0396191	+	0.604470i	−0.970797	+	0.239904i	$0.922884\pi$
$278$	23.8225	+	4.73858i	1.42878	+	0.284201i
$279$	3.35611	+	0.622590i	0.200925	+	0.0372735i
$280$	−2.27854	−	5.50089i	−0.136169	−	0.328741i
$281$	−10.8464	+	14.1353i	−0.647043	+	0.843243i	−0.995567	−	0.0940567i	$-0.970017\pi$
$281$	−10.8464	+	14.1353i	−0.647043	+	0.843243i	0.348523	+	0.937300i	$0.386683\pi$
$282$	−8.03149	+	7.13578i	−0.478268	+	0.424929i
$283$	−4.01860	+	4.58233i	−0.238881	+	0.272392i	−0.858841	−	0.512241i	$-0.828815\pi$
$283$	−4.01860	+	4.58233i	−0.238881	+	0.272392i	0.619961	+	0.784633i	$0.287149\pi$
$284$	13.4753	−	6.64528i	0.799612	−	0.394325i
$285$	1.82381	−	2.40892i	0.108033	−	0.142692i
$286$	7.18286	+	8.19048i	0.424731	+	0.484313i
$287$	14.5126	+	6.01130i	0.856650	+	0.354836i
$288$	10.2261	+	9.96515i	0.602581	+	0.587202i
$289$	5.51805	+	16.0795i	0.324591	+	0.945854i
$290$	9.41925	−	5.43820i	0.553117	−	0.319342i
$291$	16.3333	+	16.1235i	0.957473	+	0.945177i
$292$	−13.9258	−	4.72716i	−0.814943	−	0.276636i
$293$	1.45697	+	5.43750i	0.0851173	+	0.317662i	0.995336	−	0.0964649i	$-0.0307536\pi$
$293$	1.45697	+	5.43750i	0.0851173	+	0.317662i	−0.910219	+	0.414127i	$0.864087\pi$
$294$	−0.769223	−	10.6782i	−0.0448620	−	0.622766i
$295$	5.86594	−	1.99122i	0.341528	−	0.115933i
$296$	−9.36395	−	14.0141i	−0.544269	−	0.814556i
$297$	4.25063	−	17.1899i	0.246647	−	0.997461i
$298$	13.6978	−	5.67381i	0.793491	−	0.328675i
$299$	−5.25715	−	2.59254i	−0.304029	−	0.149931i
$300$	5.65117	−	2.83240i	0.326270	−	0.163529i
$301$	−16.1167	−	32.6815i	−0.928952	−	1.88373i
$302$	−17.2276	+	4.61612i	−0.991337	+	0.265628i
$303$	1.86002	−	9.67739i	0.106855	−	0.555952i
$304$	−8.84058	+	1.16388i	−0.507042	+	0.0667533i
$305$	6.52143			0.373416
$306$	7.13369	−	19.8265i	0.407806	−	1.13341i
$307$	4.09589			0.233765			0.116882	−	0.993146i	$-0.462710\pi$
$307$	4.09589			0.233765			0.116882	+	0.993146i	$0.462710\pi$
$308$	−9.93360	+	1.30778i	−0.566020	+	0.0745179i
$309$	−6.05521	+	2.09921i	−0.344469	+	0.119420i
$310$	1.82775	−	0.489743i	0.103809	−	0.0278156i
$311$	−8.34205	−	16.9160i	−0.473034	−	0.959219i	−0.994380	−	0.105873i	$-0.966236\pi$
$311$	−8.34205	−	16.9160i	−0.473034	−	0.959219i	0.521345	−	0.853346i	$-0.325430\pi$
$312$	−0.358462	+	6.06988i	−0.0202939	+	0.343639i
$313$	18.5700	+	9.15772i	1.04964	+	0.517625i	0.883478	−	0.468473i	$-0.155196\pi$
$313$	18.5700	+	9.15772i	1.04964	+	0.517625i	0.166162	+	0.986098i	$0.446863\pi$
$314$	−30.5577	+	12.6574i	−1.72447	+	0.714299i
$315$	9.44985	−	1.36857i	0.532439	−	0.0771103i
$316$	−0.557440	−	0.834268i	−0.0313585	−	0.0469312i
$317$	−5.93584	+	2.01495i	−0.333390	+	0.113171i	−0.483115	−	0.875557i	$-0.660495\pi$
$317$	−5.93584	+	2.01495i	−0.333390	+	0.113171i	0.149725	+	0.988728i	$0.452161\pi$
$318$	−4.66335	+	3.15973i	−0.261508	+	0.177189i
$319$	5.76834	+	21.5277i	0.322965	+	1.20532i
$320$	−1.73152	−	0.587771i	−0.0967948	−	0.0328574i
$321$	−25.4831	+	7.00500i	−1.42233	+	0.390981i
$322$	15.0229	−	8.67346i	0.837192	−	0.483353i
$323$	3.90081	+	6.24979i	0.217047	+	0.347747i
$324$	−6.92179	+	4.23854i	−0.384544	+	0.235475i
$325$	7.01623	+	2.90622i	0.389190	+	0.161208i
$326$	−11.6134	−	13.2426i	−0.643207	−	0.733437i
$327$	7.13564	+	0.892550i	0.394602	+	0.0493581i
$328$	8.08409	−	3.98663i	0.446369	−	0.220125i
$329$	7.82710	−	8.92510i	0.431522	−	0.492057i
$330$	−1.97726	−	9.61518i	−0.108845	−	0.529298i
$331$	−12.2921	+	16.0194i	−0.675637	+	0.880508i	−0.997808	−	0.0661739i	$-0.978921\pi$
$331$	−12.2921	+	16.0194i	−0.675637	+	0.880508i	0.322171	+	0.946682i	$0.395587\pi$
$332$	−2.92645	−	7.06507i	−0.160610	−	0.387746i
$333$	25.4804	−	9.01836i	1.39632	−	0.494203i
$334$	−4.43624	−	0.882423i	−0.242740	−	0.0482840i
$335$	0.325214	−	4.96181i	0.0177684	−	0.271093i
$336$	−22.4664	−	17.0096i	−1.22565	−	0.927948i
$337$	1.45748	−	4.29358i	0.0793937	−	0.233886i	−0.899984	−	0.435922i	$-0.856422\pi$
$337$	1.45748	−	4.29358i	0.0793937	−	0.233886i	0.979378	+	0.202036i	$0.0647557\pi$
$338$	−12.8097	+	9.82921i	−0.696755	+	0.534639i
$339$	−2.74785	−	19.8784i	−0.149243	−	1.07965i
$340$	−0.361830	−	3.61205i	−0.0196230	−	0.195891i
$341$			3.87741i			0.209973i
$342$	1.07477	−	9.06792i	0.0581172	−	0.490337i
$343$	−2.14435	−	10.7804i	−0.115784	−	0.582086i
$344$	−20.1969	−	5.41175i	−1.08895	−	0.291782i
$345$	2.96276	+	4.37265i	0.159510	+	0.235416i
$346$	4.04119	+	3.54403i	0.217256	+	0.190528i
$347$	−33.8281	+	2.21721i	−1.81599	+	0.119026i	−0.935120	−	0.354332i	$-0.884708\pi$
$347$	−33.8281	+	2.21721i	−1.81599	+	0.119026i	−0.880870	+	0.473358i	$0.843042\pi$
$348$	5.05045	−	8.87967i	0.270733	−	0.476001i
$349$	19.8508	+	15.2321i	1.06259	+	0.815355i	0.983390	−	0.181504i	$-0.0580965\pi$
$349$	19.8508	+	15.2321i	1.06259	+	0.815355i	0.0792008	+	0.996859i	$0.474763\pi$
$350$	−18.6869	+	12.4862i	−0.998858	+	0.667415i
$351$	−9.29257	−	2.95477i	−0.496001	−	0.157714i
$352$	−9.01120	+	13.4862i	−0.480299	+	0.718818i
$353$	8.03648	−	29.9926i	0.427739	−	1.59634i	−0.330130	−	0.943935i	$-0.607093\pi$
$353$	8.03648	−	29.9926i	0.427739	−	1.59634i	0.757869	−	0.652407i	$-0.226241\pi$
$354$	12.2527	−	14.1551i	0.651225	−	0.752333i
$355$	−9.90164	−	12.9041i	−0.525525	−	0.684877i
$356$	−5.85793	+	10.1462i	−0.310469	+	0.537749i
$357$	−5.10234	+	22.7161i	−0.270044	+	1.20226i
$358$	−1.69809	−	2.94118i	−0.0897468	−	0.155446i
$359$	11.5446	−	27.8711i	0.609301	−	1.47098i	−0.254461	−	0.967083i	$-0.581898\pi$
$359$	11.5446	−	27.8711i	0.609301	−	1.47098i	0.863762	−	0.503900i	$-0.168102\pi$
$360$	2.98485	−	4.59461i	0.157315	−	0.242157i
$361$	−11.1774	−	11.1774i	−0.588286	−	0.588286i
$362$	12.1085	+	0.793630i	0.636406	+	0.0417123i
$363$	1.06060	+	0.0626343i	0.0556668	+	0.00328745i
$364$	0.360849	+	5.50549i	0.0189136	+	0.288566i
$365$	−2.07803	+	15.7842i	−0.108769	+	0.826182i
$366$	17.0044	−	9.96459i	0.888836	−	0.520857i
$367$	−3.69416	+	7.49102i	−0.192834	+	0.391028i	−0.971720	−	0.236137i	$-0.924118\pi$
$367$	−3.69416	+	7.49102i	−0.192834	+	0.391028i	0.778886	+	0.627166i	$0.215785\pi$
$368$	3.04102	−	15.2882i	0.158524	−	0.796954i
$369$	3.00301	+	14.1395i	0.156330	+	0.736073i
$370$	10.5952	−	10.5952i	0.550818	−	0.550818i
$371$	4.67956	−	4.10386i	0.242950	−	0.213062i
$372$	1.24855	−	1.26479i	0.0647342	−	0.0655763i
$373$	−30.1560	−	17.4105i	−1.56142	−	0.901484i	−0.997114	−	0.0759155i	$-0.975812\pi$
$373$	−30.1560	−	17.4105i	−1.56142	−	0.901484i	−0.564302	−	0.825569i	$-0.690855\pi$
$374$	23.6221	+	3.85963i	1.22147	+	0.199577i
$375$	−9.39106	−	12.0763i	−0.484952	−	0.623616i
$376$	−0.889112	−	6.75348i	−0.0458525	−	0.348284i
$377$	12.0370	−	2.39430i	0.619936	−	0.123313i
$378$	22.5490	−	18.0077i	1.15980	−	0.926214i
$379$	−9.53627	−	6.37193i	−0.489845	−	0.327304i	0.285998	−	0.958230i	$-0.407675\pi$
$379$	−9.53627	−	6.37193i	−0.489845	−	0.327304i	−0.775843	+	0.630926i	$0.782675\pi$
$380$	−0.505682	−	1.48969i	−0.0259409	−	0.0764195i
$381$	−2.57065	+	7.73680i	−0.131698	+	0.396368i
$382$	10.0588	+	1.32426i	0.514652	+	0.0677552i
$383$	5.17214	+	0.680926i	0.264284	+	0.0347937i	0.261504	−	0.965202i	$-0.415782\pi$
$383$	5.17214	+	0.680926i	0.264284	+	0.0347937i	0.00278044	+	0.999996i	$0.499115\pi$
$384$	−21.5626	+	4.43411i	−1.10036	+	0.226277i
$385$	3.48650	+	10.2709i	0.177689	+	0.523454i
$386$	35.0021	+	23.3876i	1.78156	+	1.19040i
$387$	16.3891	−	29.2536i	0.833107	−	1.48704i
$388$	11.7202	−	2.33129i	0.595003	−	0.118354i
$389$	1.44651	+	10.9873i	0.0733410	+	0.557081i	0.988184	+	0.153271i	$0.0489808\pi$
$389$	1.44651	+	10.9873i	0.0733410	+	0.557081i	−0.914843	+	0.403809i	$0.867686\pi$
$390$	−5.35464	+	0.740186i	−0.271143	+	0.0374808i
$391$	−12.5375	+	2.94535i	−0.634048	+	0.148953i
$392$	5.87846	+	3.39393i	0.296907	+	0.171419i
$393$	21.5131	+	5.61566i	1.08519	+	0.283272i
$394$	−17.8444	+	15.6492i	−0.898990	+	0.788393i
$395$	−0.768063	+	0.768063i	−0.0386454	+	0.0386454i
$396$	−6.16815	−	6.85270i	−0.309961	−	0.344361i
$397$	5.03515	−	25.3134i	0.252707	−	1.27044i	−0.620930	−	0.783866i	$-0.713245\pi$
$397$	5.03515	−	25.3134i	0.252707	−	1.27044i	0.873637	−	0.486578i	$-0.161755\pi$
$398$	11.4638	−	23.2463i	0.574628	−	1.16523i
$399$	0.0652049	+	10.0895i	0.00326433	+	0.505104i
$400$	−2.63602	+	20.0226i	−0.131801	+	1.00113i
$401$	1.03342	+	15.7670i	0.0516067	+	0.787366i	0.942720	+	0.333585i	$0.108258\pi$
$401$	1.03342	+	15.7670i	0.0516067	+	0.787366i	−0.891113	+	0.453781i	$0.850075\pi$
$402$	−6.73354	−	13.4347i	−0.335839	−	0.670062i
$403$	2.13059	+	0.139646i	0.106132	+	0.00695627i
$404$	−3.62813	−	3.62813i	−0.180506	−	0.180506i
$405$	5.96218	+	6.45412i	0.296263	+	0.320708i
$406$	−13.8991	+	33.5553i	−0.689800	+	1.66532i
$407$	15.3519	+	26.5903i	0.760967	+	1.31803i
$408$	7.86965	+	10.7957i	0.389606	+	0.534465i
$409$	−14.5112	+	25.1342i	−0.717533	+	1.24280i	0.244441	+	0.969664i	$0.421396\pi$
$409$	−14.5112	+	25.1342i	−0.717533	+	1.24280i	−0.961974	+	0.273140i	$0.911938\pi$
$410$	4.87811	+	6.35727i	0.240912	+	0.313963i
$411$	0.889796	+	0.171021i	0.0438904	+	0.00843585i
$412$	−0.863639	+	3.22315i	−0.0425485	+	0.158793i
$413$	−11.4926	+	17.1999i	−0.565515	+	0.846353i
$414$	14.4066	+	6.87452i	0.708047	+	0.337864i
$415$	−6.88336	+	4.59931i	−0.337891	+	0.225771i
$416$	7.08597	+	5.43726i	0.347418	+	0.266584i
$417$	−12.4863	−	21.3077i	−0.611456	−	1.04344i
$418$	10.3506	−	0.678413i	0.506263	−	0.0331823i
$419$	10.2682	+	9.00496i	0.501634	+	0.439921i	0.872391	−	0.488809i	$-0.162568\pi$
$419$	10.2682	+	9.00496i	0.501634	+	0.439921i	−0.370757	+	0.928730i	$0.620902\pi$
$420$	2.17001	−	4.47299i	0.105886	−	0.218260i
$421$	−13.2644	−	3.55418i	−0.646467	−	0.173220i	−0.0793358	−	0.996848i	$-0.525280\pi$
$421$	−13.2644	−	3.55418i	−0.646467	−	0.173220i	−0.567131	+	0.823628i	$0.691947\pi$
$422$	1.85394	+	9.32038i	0.0902483	+	0.453709i
$423$	10.8479	+	1.28574i	0.527441	+	0.0625149i
$424$		−	3.57150i		−	0.173447i
$425$	15.9591	−	4.87018i	0.774131	−	0.236238i
$426$	−45.5353	−	18.5175i	−2.20619	−	0.897176i
$427$	−17.2771	+	13.2572i	−0.836096	+	0.641559i
$428$	−4.42315	+	13.0302i	−0.213801	+	0.629838i
$429$	1.37479	−	10.9910i	0.0663757	−	0.530651i
$430$	1.21575	−	18.5488i	0.0586286	−	0.894500i
$431$	11.4427	+	2.27609i	0.551173	+	0.109635i	0.462817	−	0.886454i	$-0.346839\pi$
$431$	11.4427	+	2.27609i	0.551173	+	0.109635i	0.0883562	+	0.996089i	$0.471839\pi$
$432$	1.19400	−	25.9032i	0.0574463	−	1.24627i
$433$	1.20512	+	2.90941i	0.0579142	+	0.139817i	0.950188	−	0.311678i	$-0.100891\pi$
$433$	1.20512	+	2.90941i	0.0579142	+	0.139817i	−0.892274	+	0.451495i	$0.850891\pi$
$434$	−3.84663	+	5.01302i	−0.184644	+	0.240633i
$435$	−10.4947	−	3.48701i	−0.503184	−	0.167189i
$436$	2.46876	−	2.81509i	0.118232	−	0.134818i
$437$	−5.00567	+	2.46852i	−0.239454	+	0.118085i
$438$	18.6994	+	44.3319i	0.893494	+	2.11826i
$439$	−16.5220	−	18.8397i	−0.788552	−	0.899171i	0.208332	−	0.978058i	$-0.433197\pi$
$439$	−16.5220	−	18.8397i	−0.788552	−	0.899171i	−0.996884	+	0.0788873i	$0.974863\pi$
$440$	5.75012	+	2.38178i	0.274126	+	0.113547i
$441$	−7.59707	+	7.79604i	−0.361765	+	0.371240i
$442$	2.97158	−	12.8411i	0.141344	−	0.610787i
$443$	−19.8871	+	11.4818i	−0.944863	+	0.545517i	−0.891481	−	0.453057i	$-0.850333\pi$
$443$	−19.8871	+	11.4818i	−0.944863	+	0.545517i	−0.0533814	+	0.998574i	$0.517000\pi$
$444$	3.55452	−	13.6170i	0.168690	−	0.646236i
$445$	12.0100	+	4.07686i	0.569330	+	0.193262i
$446$	−10.4849	−	39.1300i	−0.496472	−	1.85286i
$447$	−13.5632	−	6.58002i	−0.641519	−	0.311224i
$448$	5.78213	−	1.96277i	0.273180	−	0.0927321i
$449$	12.2538	+	18.3391i	0.578292	+	0.865476i	0.999132	−	0.0416595i	$-0.0132645\pi$
$449$	12.2538	+	18.3391i	0.578292	+	0.865476i	−0.420840	+	0.907135i	$0.638264\pi$
$450$	−19.2077	−	7.66675i	−0.905458	−	0.361414i
$451$	−15.1701	+	6.28366i	−0.714332	+	0.295886i
$452$	−9.37098	−	4.62126i	−0.440774	−	0.217366i
$453$	15.1431	+	9.97734i	0.711485	+	0.468776i
$454$	0.702145	+	1.42381i	0.0329533	+	0.0668227i
$455$	5.76930	−	1.54588i	0.270469	−	0.0724720i
$456$	4.37742	+	3.78913i	0.204992	+	0.177442i
$457$	5.83440	−	0.768114i	0.272922	−	0.0359308i	0.00717699	−	0.999974i	$-0.497715\pi$
$457$	5.83440	−	0.768114i	0.272922	−	0.0359308i	0.265745	+	0.964043i	$0.414382\pi$
$458$	−48.8165			−2.28104
$459$	−19.8878	+	7.96713i	−0.928283	+	0.371874i
$460$	2.75010			0.128224
$461$	−5.60904	+	0.738445i	−0.261239	+	0.0343928i	−0.260008	−	0.965606i	$-0.583725\pi$
$461$	−5.60904	+	0.738445i	−0.261239	+	0.0343928i	−0.00123115	+	0.999999i	$0.500392\pi$
$462$	24.7846	+	21.4538i	1.15309	+	0.998120i
$463$	−14.9975	+	4.01856i	−0.696991	+	0.186758i	−0.589882	−	0.807489i	$-0.700826\pi$
$463$	−14.9975	+	4.01856i	−0.696991	+	0.186758i	−0.107108	+	0.994247i	$0.534159\pi$
$464$	14.4349	+	29.2710i	0.670122	+	1.35887i
$465$	−1.60659	−	1.05854i	−0.0745040	−	0.0490885i
$466$	23.8227	+	11.7481i	1.10357	+	0.544219i
$467$	6.42801	−	2.66257i	0.297453	−	0.123209i	−0.228966	−	0.973434i	$-0.573534\pi$
$467$	6.42801	−	2.66257i	0.297453	−	0.123209i	0.526419	+	0.850225i	$0.323534\pi$
$468$	−3.98762	+	3.14252i	−0.184328	+	0.145263i
$469$	9.22510	+	13.8063i	0.425975	+	0.637517i
$470$	5.73430	−	1.94653i	0.264504	−	0.0897869i
$471$	30.2576	+	14.6791i	1.39420	+	0.676375i
$472$	3.07219	+	11.4656i	0.141409	+	0.527745i
$473$	36.0689	+	12.2437i	1.65845	+	0.562967i
$474$	−0.829119	+	3.17628i	−0.0380827	+	0.145891i
$475$	6.26225	−	3.61551i	0.287332	−	0.165891i
$476$	8.30139	+	8.83378i	0.380494	+	0.404896i
$477$	5.55103	+	1.41076i	0.254164	+	0.0645941i
$478$	−42.6199	−	17.6537i	−1.94939	−	0.807463i
$479$	2.96427	+	3.38010i	0.135441	+	0.154441i	0.815584	−	0.578638i	$-0.196416\pi$
$479$	2.96427	+	3.38010i	0.135441	+	0.154441i	−0.680143	+	0.733079i	$0.738082\pi$
$480$	−3.12791	−	7.41553i	−0.142769	−	0.338471i
$481$	15.1640	−	7.47804i	0.691417	−	0.340969i
$482$	19.0951	−	21.7738i	0.869757	−	0.991767i
$483$	−16.7382	−	5.56147i	−0.761613	−	0.253056i
$484$	0.336756	−	0.438868i	0.0153071	−	0.0199486i
$485$	−4.95055	−	11.9517i	−0.224793	−	0.542698i
$486$	25.4079	+	7.71884i	1.15253	+	0.350134i
$487$	−5.53777	−	1.10153i	−0.250941	−	0.0499152i	0.0680171	−	0.997684i	$-0.478333\pi$
$487$	−5.53777	−	1.10153i	−0.250941	−	0.0499152i	−0.318958	+	0.947769i	$0.603333\pi$
$488$	−0.817285	+	12.4694i	−0.0369967	+	0.564461i
$489$	−2.22280	+	17.7705i	−0.100518	+	0.803611i
$490$	−1.93971	+	5.71419i	−0.0876271	+	0.258141i
$491$	3.30948	−	2.53946i	0.149355	−	0.114604i	−0.531381	−	0.847133i	$-0.678327\pi$
$491$	3.30948	−	2.53946i	0.149355	−	0.114604i	0.680736	+	0.732529i	$0.261660\pi$
$492$	6.97178	+	2.83516i	0.314312	+	0.127819i
$493$	17.0716	−	20.8726i	0.768868	−	0.940056i
$494$		−	5.71195i		−	0.256993i
$495$	−5.97322	+	7.99637i	−0.268476	+	0.359410i
$496$	1.10772	+	5.56888i	0.0497380	+	0.250050i
$497$	52.4644	+	14.0578i	2.35335	+	0.630578i
$498$	−10.9205	+	22.5102i	−0.489360	+	1.00870i
$499$	−2.15551	−	1.89034i	−0.0964941	−	0.0846231i	0.609740	−	0.792602i	$-0.291274\pi$
$499$	−2.15551	−	1.89034i	−0.0964941	−	0.0846231i	−0.706234	+	0.707979i	$0.749607\pi$
$500$	−7.94814	+	0.520949i	−0.355452	+	0.0232975i
$501$	2.32521	+	3.96793i	0.103883	+	0.177274i
$502$	−15.7566	−	12.0905i	−0.703252	−	0.539624i
$503$	−4.49269	+	3.00192i	−0.200319	+	0.133849i	−0.651684	−	0.758490i	$-0.725937\pi$
$503$	−4.49269	+	3.00192i	−0.200319	+	0.133849i	0.451365	+	0.892339i	$0.350937\pi$
$504$	1.43251	+	18.2402i	0.0638090	+	0.812482i
$505$	−3.08595	+	4.61845i	−0.137323	+	0.205518i
$506$	−4.69313	+	17.5150i	−0.208635	+	0.778637i
$507$	16.1220	+	3.09869i	0.716004	+	0.137618i
$508$	2.58410	+	3.36767i	0.114651	+	0.149416i
$509$	−1.74709	+	3.02606i	−0.0774386	+	0.134128i	−0.902144	−	0.431435i	$-0.858008\pi$
$509$	−1.74709	+	3.02606i	−0.0774386	+	0.134128i	0.824706	+	0.565562i	$0.191341\pi$
$510$	−8.04810	+	8.73408i	−0.356376	+	0.386751i
$511$	−26.5818	−	46.0410i	−1.17591	−	2.03673i
$512$	−1.94431	+	4.69398i	−0.0859271	+	0.207446i
$513$	−7.61839	+	5.30692i	−0.336360	+	0.234306i
$514$	7.97966	+	7.97966i	0.351968	+	0.351968i
$515$	3.60461	+	0.236258i	0.158838	+	0.0104108i
$516$	−7.82293	−	15.6082i	−0.344385	−	0.687114i
$517$	0.811578	+	12.3823i	0.0356932	+	0.544572i
$518$	−6.53104	+	49.6082i	−0.286957	+	2.17966i
$519$	−0.0353193	−	5.46512i	−0.00155035	−	0.239892i
$520$	1.51585	−	3.07384i	0.0664745	−	0.134797i
$521$	6.43957	−	32.3739i	0.282123	−	1.41833i	−0.536454	−	0.843930i	$-0.680236\pi$
$521$	6.43957	−	32.3739i	0.282123	−	1.41833i	0.818577	−	0.574397i	$-0.194764\pi$
$522$	−32.6927	+	6.94343i	−1.43092	+	0.303905i
$523$	5.80763	−	5.80763i	0.253950	−	0.253950i	−0.568638	−	0.822588i	$-0.692529\pi$
$523$	5.80763	−	5.80763i	0.253950	−	0.253950i	0.822588	+	0.568638i	$0.192529\pi$
$524$	8.70370	−	7.63294i	0.380223	−	0.333447i
$525$	22.1107	+	5.77165i	0.964990	+	0.251896i
$526$	−24.8165	−	14.3278i	−1.08205	−	0.624722i
$527$	3.80869	−	2.73888i	0.165909	−	0.119307i
$528$	29.1785	−	4.03342i	1.26983	−	0.175532i
$529$	1.72860	+	13.1300i	0.0751565	+	0.570870i
$530$	3.11407	−	0.619427i	0.135267	−	0.0269062i
$531$	−19.0340	+	0.246031i	−0.826004	+	0.0106768i
$532$	4.36802	+	2.91862i	0.189378	+	0.126538i
$533$	2.90644	+	8.56209i	0.125892	+	0.370865i
$534$	37.5451	−	7.72076i	1.62474	−	0.334110i
$535$	14.7691	+	1.94439i	0.638524	+	0.0840632i
$536$	9.44652	+	1.24366i	0.408027	+	0.0537178i
$537$	−1.08882	+	3.27700i	−0.0469862	+	0.141413i
$538$	8.06250	+	23.7513i	0.347599	+	1.02399i
$539$	−10.2814	−	6.86981i	−0.442851	−	0.295904i
$540$	4.52331	−	0.684962i	0.194652	−	0.0294761i
$541$	−25.8949	+	5.15082i	−1.11331	+	0.221451i	−0.717279	−	0.696786i	$-0.754613\pi$
$541$	−25.8949	+	5.15082i	−1.11331	+	0.221451i	−0.396031	+	0.918237i	$0.629613\pi$
$542$	−6.56894	−	49.8960i	−0.282160	−	2.14322i
$543$	−7.57400	−	9.73965i	−0.325031	−	0.417968i
$544$	19.6124	−	0.674738i	0.840877	−	0.0289291i
$545$	−3.51034	−	2.02670i	−0.150366	−	0.0868141i
$546$	12.6812	−	12.8462i	0.542706	−	0.549766i
$547$	−22.4870	+	19.7206i	−0.961476	+	0.843192i	−0.987684	−	0.156465i	$-0.949990\pi$
$547$	−22.4870	+	19.7206i	−0.961476	+	0.843192i	0.0262075	+	0.999657i	$0.491657\pi$
$548$	0.333591	−	0.333591i	0.0142503	−	0.0142503i
$549$	−19.0578	−	6.19572i	−0.813366	−	0.264427i
$550$	4.58322	−	23.0414i	0.195429	−	0.982489i
$551$	5.16845	−	10.4806i	0.220184	−	0.446488i
$552$	−8.73206	+	5.11698i	−0.371661	+	0.217793i
$553$	0.473446	−	3.59618i	0.0201330	−	0.152925i
$554$	−1.12326	−	17.1376i	−0.0477227	−	0.728108i
$555$	−15.2087	−	0.898163i	−0.645575	−	0.0381249i
$556$	−12.8312	−	0.841005i	−0.544166	−	0.0356665i
$557$	−14.2778	−	14.2778i	−0.604969	−	0.604969i	0.336658	−	0.941627i	$-0.390703\pi$
$557$	−14.2778	−	14.2778i	−0.604969	−	0.604969i	−0.941627	+	0.336658i	$0.890703\pi$
$558$	−5.80656	−	0.305269i	−0.245811	−	0.0129230i
$559$	8.02681	−	19.3784i	0.339498	−	0.819621i
$560$	7.94169	+	13.7554i	0.335598	+	0.581272i
$561$	−13.0191	−	20.5618i	−0.549666	−	0.868120i
$562$	15.1756	−	26.2849i	0.640143	−	1.10876i
$563$	−21.6095	−	28.1621i	−0.910734	−	1.18689i	−0.981895	−	0.189427i	$-0.939337\pi$
$563$	−21.6095	−	28.1621i	−0.910734	−	1.18689i	0.0711610	−	0.997465i	$-0.477330\pi$
$564$	3.72244	−	4.30037i	0.156743	−	0.181078i
$565$	−2.92754	+	10.9257i	−0.123163	+	0.459649i
$566$	5.76814	−	8.63264i	0.242453	−	0.362857i
$567$	−28.9158	−	4.97845i	−1.21435	−	0.209075i
$568$	25.9142	−	17.3153i	1.08734	−	0.726535i
$569$	−2.41954	−	1.85658i	−0.101432	−	0.0778317i	0.556800	−	0.830646i	$-0.312029\pi$
$569$	−2.41954	−	1.85658i	−0.101432	−	0.0778317i	−0.658232	+	0.752815i	$0.728696\pi$
$570$	−2.54462	+	4.47394i	−0.106583	+	0.187393i
$571$	−6.94350	+	0.455101i	−0.290577	+	0.0190454i	−0.209994	−	0.977703i	$-0.567345\pi$
$571$	−6.94350	+	0.455101i	−0.290577	+	0.0190454i	−0.0805821	+	0.996748i	$0.525678\pi$
$572$	−4.33607	−	3.80263i	−0.181300	−	0.158996i
$573$	−5.78644	−	8.54003i	−0.241732	−	0.356765i
$574$	−25.8469	−	6.92566i	−1.07883	−	0.289071i
$575$	2.46608	+	12.3978i	0.102842	+	0.517024i
$576$	4.50165	+	3.36270i	0.187569	+	0.140112i
$577$			21.0815i			0.877634i	0.898576	+	0.438817i	$0.144602\pi$
$577$			21.0815i			0.877634i	−0.898576	+	0.438817i	$0.855398\pi$
$578$	−12.8947	−	25.9298i	−0.536348	−	1.07854i
$579$	−5.86102	−	42.3996i	−0.243576	−	1.76207i
$580$	−4.56814	+	3.50526i	−0.189682	+	0.145548i
$581$	8.88615	−	26.1778i	0.368660	−	1.08604i
$582$	−31.1703	−	23.5993i	−1.29205	−	0.978224i
$583$	−0.425522	+	6.49221i	−0.0176233	+	0.268880i
$584$	−29.9198	−	5.95142i	−1.23809	−	0.246272i
$585$	4.17878	+	3.57021i	0.172771	+	0.147610i
$586$	−3.66970	−	8.85945i	−0.151594	−	0.365980i
$587$	10.9876	−	14.3193i	0.453506	−	0.591020i	−0.509510	−	0.860465i	$-0.670173\pi$
$587$	10.9876	−	14.3193i	0.453506	−	0.591020i	0.963016	+	0.269444i	$0.0868401\pi$
$588$	1.14162	+	5.55157i	0.0470797	+	0.228943i
$589$	1.34046	−	1.52851i	0.0552328	−	0.0629810i
$590$	−9.46425	+	4.66725i	−0.389637	+	0.192148i
$591$	23.9459	+	2.99524i	0.985004	+	0.123208i
$592$	29.6455	+	33.8042i	1.21842	+	1.38934i
$593$	−17.5477	−	7.26851i	−0.720599	−	0.298482i	−0.00791660	−	0.999969i	$-0.502520\pi$
$593$	−17.5477	−	7.26851i	−0.720599	−	0.298482i	−0.712683	+	0.701487i	$0.752520\pi$
$594$	−3.35674	+	29.9772i	−0.137729	+	1.22998i
$595$	7.62612	−	10.6798i	0.312641	−	0.437827i
$596$	−6.79755	+	3.92457i	−0.278438	+	0.160757i
$597$	−25.4114	+	6.98530i	−1.04002	+	0.285889i
$598$	9.45526	+	3.20963i	0.386654	+	0.131251i
$599$	−2.25647	−	8.42126i	−0.0921968	−	0.344083i	0.904383	−	0.426722i	$-0.140332\pi$
$599$	−2.25647	−	8.42126i	−0.0921968	−	0.344083i	−0.996580	+	0.0826390i	$0.973665\pi$
$600$	10.8554	−	7.35525i	0.443169	−	0.300277i
$601$	17.4883	−	5.93647i	0.713361	−	0.242153i	0.0589160	−	0.998263i	$-0.481236\pi$
$601$	17.4883	−	5.93647i	0.713361	−	0.242153i	0.654445	+	0.756109i	$0.272902\pi$
$602$	34.4862	+	51.6122i	1.40555	+	2.10356i
$603$	−5.66438	+	14.1911i	−0.230671	+	0.577906i
$604$	8.72335	−	3.61333i	0.354948	−	0.147024i
$605$	−0.537095	−	0.264866i	−0.0218360	−	0.0107683i
$606$	−0.989641	+	16.7577i	−0.0402014	+	0.680736i
$607$	−18.2780	−	37.0642i	−0.741882	−	1.50439i	−0.859392	−	0.511317i	$-0.829158\pi$
$607$	−18.2780	−	37.0642i	−0.741882	−	1.50439i	0.117510	−	0.993072i	$-0.462509\pi$
$608$	8.21463	−	2.20110i	0.333147	−	0.0892665i
$609$	34.8920	−	12.0963i	1.41390	−	0.490166i
$610$	−11.0141	+	1.45003i	−0.445946	+	0.0587099i
$611$	6.83315			0.276439
$612$	−2.37426	+	10.8994i	−0.0959739	+	0.440581i
$613$	−1.39251			−0.0562429			−0.0281214	−	0.999605i	$-0.508953\pi$
$613$	−1.39251			−0.0562429			−0.0281214	+	0.999605i	$0.508953\pi$
$614$	−6.91756	+	0.910714i	−0.279170	+	0.0367534i
$615$	1.53784	−	8.00114i	0.0620117	−	0.322637i
$616$	−20.0755	+	5.37921i	−0.808865	+	0.216735i
$617$	7.10499	+	14.4075i	0.286036	+	0.580024i	0.991708	−	0.128515i	$-0.0410211\pi$
$617$	7.10499	+	14.4075i	0.286036	+	0.580024i	−0.705671	+	0.708539i	$0.749354\pi$
$618$	9.75990	−	4.89171i	0.392601	−	0.196774i
$619$	−8.62952	−	4.25561i	−0.346850	−	0.171047i	0.260516	−	0.965469i	$-0.416107\pi$
$619$	−8.62952	−	4.25561i	−0.346850	−	0.171047i	−0.607366	+	0.794422i	$0.707774\pi$
$620$	−0.925496	+	0.383353i	−0.0371688	+	0.0153958i
$621$	−4.50392	−	15.5931i	−0.180736	−	0.625730i
$622$	17.8501	+	26.7146i	0.715725	+	1.07116i
$623$	−40.1056	+	13.6140i	−1.60680	+	0.545434i
$624$	−1.16544	−	16.1785i	−0.0466550	−	0.647657i
$625$	−3.00529	−	11.2159i	−0.120212	−	0.448636i
$626$	−33.3991	−	11.3375i	−1.33490	−	0.453137i
$627$	−7.50575	−	7.40936i	−0.299751	−	0.295901i
$628$	15.1643	−	8.75513i	0.605122	−	0.349368i
$629$	15.2750	−	33.8624i	0.609053	−	1.35018i
$630$	−15.6556	+	4.41254i	−0.623732	+	0.175800i
$631$	3.54388	+	1.46792i	0.141079	+	0.0584370i	0.452106	−	0.891964i	$-0.350673\pi$
$631$	3.54388	+	1.46792i	0.141079	+	0.0584370i	−0.311027	+	0.950401i	$0.600673\pi$
$632$	−1.37232	−	1.56484i	−0.0545881	−	0.0622458i
$633$	5.83243	−	7.70354i	0.231818	−	0.306188i
$634$	9.57703	−	4.72287i	0.380352	−	0.187569i
$635$	3.02990	−	3.45494i	0.120238	−	0.137105i
$636$	2.22933	−	1.98070i	0.0883987	−	0.0785400i
$637$	−4.14517	+	5.40209i	−0.164238	+	0.214038i
$638$	−14.5288	−	35.0756i	−0.575201	−	1.38866i
$639$	16.6763	+	47.1171i	0.659704	+	1.86392i
$640$	12.1698	+	2.42072i	0.481052	+	0.0956873i
$641$	−0.954442	+	14.5620i	−0.0376982	+	0.575163i	0.936671	+	0.350210i	$0.113890\pi$
$641$	−0.954442	+	14.5620i	−0.0376982	+	0.575163i	−0.974369	+	0.224954i	$0.927777\pi$
$642$	41.4809	−	17.4969i	1.63712	−	0.690547i
$643$	5.56426	−	16.3918i	0.219433	−	0.646429i	−0.780345	−	0.625349i	$-0.784956\pi$
$643$	5.56426	−	16.3918i	0.219433	−	0.646429i	0.999778	−	0.0210793i	$-0.00671023\pi$
$644$	−7.28578	+	5.59058i	−0.287100	+	0.220300i
$645$	−14.9200	+	11.6025i	−0.587475	+	0.456847i
$646$	−7.97771	−	9.68793i	−0.313879	−	0.381167i
$647$			8.67540i			0.341065i	0.985352	+	0.170533i	$0.0545488\pi$
$647$			8.67540i			0.341065i	−0.985352	+	0.170533i	$0.945451\pi$
$648$	−13.0878	+	10.5912i	−0.514139	+	0.416061i
$649$	−4.21852	−	21.2079i	−0.165591	−	0.832484i
$650$	−12.4959	−	3.34827i	−0.490130	−	0.131330i
$651$	6.40817	−	0.461623i	0.251156	−	0.0180924i
$652$	7.01066	+	6.14818i	0.274559	+	0.240781i
$653$	−17.0952	+	1.12048i	−0.668986	+	0.0438477i	−0.396112	−	0.918202i	$-0.629641\pi$
$653$	−17.0952	+	1.12048i	−0.668986	+	0.0438477i	−0.272874	+	0.962050i	$0.587974\pi$
$654$	−12.2499	+	0.0791668i	−0.479007	+	0.00309567i
$655$	−9.94255	−	7.62919i	−0.388488	−	0.298097i
$656$	−19.9927	+	13.3587i	−0.780584	+	0.521570i
$657$	21.0685	−	44.1523i	0.821961	−	1.72255i
$658$	−11.2347	+	16.8140i	−0.437975	+	0.655476i
$659$	−11.2755	+	42.0808i	−0.439232	+	1.63924i	0.291499	+	0.956571i	$0.405846\pi$
$659$	−11.2755	+	42.0808i	−0.439232	+	1.63924i	−0.730731	+	0.682666i	$0.760821\pi$
$660$	1.70223	+	4.91013i	0.0662593	+	0.191127i
$661$	13.2570	+	17.2768i	0.515636	+	0.671990i	0.976509	−	0.215476i	$-0.0691304\pi$
$661$	13.2570	+	17.2768i	0.515636	+	0.671990i	−0.460873	+	0.887466i	$0.652464\pi$
$662$	17.1983	−	29.7884i	0.668432	−	1.15776i
$663$	−11.7673	+	6.41328i	−0.457006	+	0.249071i
$664$	−7.93151	−	13.7378i	−0.307802	−	0.533129i
$665$	2.17636	−	5.25420i	0.0843956	−	0.203749i
$666$	−41.0287	+	20.8966i	−1.58983	+	0.809728i
$667$	14.4448	+	14.4448i	0.559304	+	0.559304i
$668$	2.38945	+	0.156613i	0.0924504	+	0.00605952i
$669$	−22.6621	+	34.3953i	−0.876167	+	1.32980i
$670$	0.553995	+	8.45232i	0.0214027	+	0.326542i
$671$	2.97129	−	22.5692i	0.114705	−	0.871274i
$672$	23.3614	+	13.2872i	0.901187	+	0.512564i
$673$	3.06323	−	6.21162i	0.118079	−	0.239440i	−0.829807	−	0.558051i	$-0.811549\pi$
$673$	3.06323	−	6.21162i	0.118079	−	0.239440i	0.947886	+	0.318610i	$0.103216\pi$
$674$	−1.50686	+	7.57550i	−0.0580421	+	0.291798i
$675$	7.14404	+	19.7774i	0.274974	+	0.761234i
$676$	6.04427	−	6.04427i	0.232472	−	0.232472i
$677$	−10.3195	+	9.04997i	−0.396611	+	0.347819i	−0.834303	−	0.551307i	$-0.814129\pi$
$677$	−10.3195	+	9.04997i	−0.396611	+	0.347819i	0.437692	+	0.899125i	$0.355796\pi$
$678$	9.06078	+	32.9617i	0.347977	+	1.26589i
$679$	37.4115	+	21.5995i	1.43572	+	0.828914i
$680$	−1.72214	−	7.33063i	−0.0660410	−	0.281117i
$681$	0.608061	−	1.49525i	0.0233010	−	0.0572980i
$682$	−0.862134	−	6.54856i	−0.0330128	−	0.250757i
$683$	−16.4867	+	3.27942i	−0.630848	+	0.125483i	−0.500150	−	0.865939i	$-0.666722\pi$
$683$	−16.4867	+	3.27942i	−0.630848	+	0.125483i	−0.130698	+	0.991422i	$0.541722\pi$
$684$	0.0624811	+	4.83379i	0.00238902	+	0.184825i
$685$	−0.424647	−	0.283740i	−0.0162249	−	0.0108412i
$686$	6.01859	+	17.7302i	0.229791	+	0.676942i
$687$	32.9674	+	37.1056i	1.25778	+	1.41567i
$688$	55.3013	+	7.28056i	2.10834	+	0.277569i
$689$	3.55206	+	0.467638i	0.135323	+	0.0178156i
$690$	−5.97607	−	6.72621i	−0.227505	−	0.256062i
$691$	11.4939	+	33.8598i	0.437247	+	1.28809i	0.912802	+	0.408403i	$0.133914\pi$
$691$	11.4939	+	33.8598i	0.437247	+	1.28809i	−0.475554	+	0.879686i	$0.657753\pi$
$692$	−2.36602	−	1.58092i	−0.0899424	−	0.0600976i
$693$	−0.430786	−	33.3273i	−0.0163642	−	1.26600i
$694$	56.6394	−	11.2663i	2.15000	−	0.427662i
$695$	1.81698	+	13.8013i	0.0689219	+	0.523514i
$696$	7.98258	−	19.6295i	0.302579	−	0.744055i
$697$	16.8880	+	10.4627i	0.639678	+	0.396302i
$698$	−36.9129	−	21.3117i	−1.39717	−	0.806659i
$699$	−7.15853	−	26.0416i	−0.270760	−	0.984984i
$700$	8.94548	−	7.84497i	0.338107	−	0.296512i
$701$	−21.6865	+	21.6865i	−0.819088	+	0.819088i	−0.985976	−	0.166888i	$-0.946628\pi$
$701$	−21.6865	+	21.6865i	−0.819088	+	0.819088i	0.166888	+	0.985976i	$0.446628\pi$
$702$	16.3512	+	2.92413i	0.617137	+	0.110364i
$703$	3.14072	−	15.7895i	0.118454	−	0.595511i
$704$	−2.82306	+	5.72459i	−0.106398	+	0.215754i
$705$	−5.35213	−	3.04411i	−0.201573	−	0.114648i
$706$	−6.90404	+	52.4414i	−0.259837	+	1.97366i
$707$	−1.21314	−	18.5089i	−0.0456246	−	0.696098i
$708$	−5.45302	+	8.27630i	−0.204937	+	0.311043i
$709$	−13.2172	−	0.866300i	−0.496382	−	0.0325346i	−0.184843	−	0.982768i	$-0.559178\pi$
$709$	−13.2172	−	0.866300i	−0.496382	−	0.0325346i	−0.311539	+	0.950234i	$0.600844\pi$
$710$	19.5921	+	19.5921i	0.735278	+	0.735278i
$711$	2.97423	−	1.51483i	0.111543	−	0.0568106i
$712$	−9.30032	+	22.4530i	−0.348544	+	0.841460i
$713$	1.77698	+	3.07782i	0.0665484	+	0.115265i
$714$	3.56648	−	39.4997i	0.133472	−	1.47824i
$715$	−3.12172	+	5.40697i	−0.116746	+	0.202209i
$716$	1.09452	+	1.42641i	0.0409042	+	0.0533074i
$717$	15.3639	+	44.3177i	0.573777	+	1.65507i
$718$	−13.3006	+	49.6385i	−0.496374	+	1.85249i
$719$	−3.43802	+	5.14536i	−0.128217	+	0.191890i	−0.890024	−	0.455914i	$-0.849312\pi$
$719$	−3.43802	+	5.14536i	−0.128217	+	0.191890i	0.761807	+	0.647804i	$0.224312\pi$
$720$	−6.29452	+	13.1911i	−0.234583	+	0.491605i
$721$	−10.0299	+	6.70175i	−0.373532	+	0.249586i
$722$	21.3629	+	16.3923i	0.795044	+	0.610058i
$723$	−29.4458	+	0.190299i	−1.09510	+	0.00707729i
$724$	−6.41026	+	0.420151i	−0.238236	+	0.0156148i
$725$	−19.8985	−	17.4505i	−0.739011	−	0.648095i
$726$	−1.80517	+	0.130038i	−0.0669960	+	0.00482617i
$727$	−4.46370	−	1.19605i	−0.165550	−	0.0443589i	0.175092	−	0.984552i	$-0.443978\pi$
$727$	−4.46370	−	1.19605i	−0.165550	−	0.0443589i	−0.340642	+	0.940193i	$0.610644\pi$
$728$	2.23279	+	11.2250i	0.0827526	+	0.416025i
$729$	−11.2917	−	24.5255i	−0.418211	−	0.908350i
$730$		−	27.1200i		−	1.00375i
$731$	−13.4512	−	44.0782i	−0.497510	−	1.63029i
$732$	−8.23663	+	6.40518i	−0.304435	+	0.236742i
$733$	33.0483	−	25.3588i	1.22067	−	0.936650i	0.221408	−	0.975181i	$-0.428935\pi$
$733$	33.0483	−	25.3588i	1.22067	−	0.936650i	0.999257	+	0.0385314i	$0.0122680\pi$
$734$	4.57346	−	13.4730i	0.168810	−	0.497297i
$735$	5.65333	−	2.38460i	0.208526	−	0.0879574i
$736$	−0.972330	+	14.8349i	−0.0358406	+	0.546821i
$737$	−17.0235	−	3.38619i	−0.627070	−	0.124732i
$738$	−8.21568	−	23.2125i	−0.302423	−	0.854464i
$739$	−2.24893	−	5.42939i	−0.0827282	−	0.199723i	0.877103	−	0.480303i	$-0.159473\pi$
$739$	−2.24893	−	5.42939i	−0.0827282	−	0.199723i	−0.959831	+	0.280580i	$0.909473\pi$
$740$	−4.82901	+	6.29329i	−0.177518	+	0.231346i
$741$	−4.34167	+	3.85747i	−0.159495	+	0.141708i
$742$	−6.99082	+	7.97151i	−0.256641	+	0.292643i
$743$	11.9997	−	5.91758i	0.440225	−	0.217095i	−0.208649	−	0.977990i	$-0.566907\pi$
$743$	11.9997	−	5.91758i	0.440225	−	0.217095i	0.648874	+	0.760896i	$0.275240\pi$
$744$	2.22533	−	2.93924i	0.0815845	−	0.107758i
$745$	5.60257	+	6.38851i	0.205262	+	0.234057i
$746$	54.8016	+	22.6996i	2.00643	+	0.831091i
$747$	24.4850	−	6.90114i	0.895861	−	0.252499i
$748$	−12.6654	−	0.393511i	−0.463091	−	0.0143882i
$749$	−43.0801	+	24.8723i	−1.57411	+	0.908814i
$750$	18.5457	+	18.3075i	0.677194	+	0.668497i
$751$	38.9263	+	13.2137i	1.42044	+	0.482174i	0.922824	−	0.385223i	$-0.125875\pi$
$751$	38.9263	+	13.2137i	1.42044	+	0.482174i	0.497616	+	0.867397i	$0.334209\pi$
$752$	4.70306	+	17.5520i	0.171503	+	0.640057i
$753$	1.45094	+	20.1417i	0.0528753	+	0.734006i
$754$	−19.7969	+	6.72014i	−0.720960	+	0.244733i
$755$	−5.67884	−	8.49898i	−0.206674	−	0.309310i
$756$	−10.5911	+	11.0099i	−0.385194	+	0.400427i
$757$	50.5570	−	20.9414i	1.83752	−	0.761128i	0.878540	−	0.477669i	$-0.158518\pi$
$757$	50.5570	−	20.9414i	1.83752	−	0.761128i	0.958985	−	0.283458i	$-0.0914818\pi$
$758$	17.5226	+	8.64119i	0.636450	+	0.313862i
$759$	16.4826	−	8.26119i	0.598282	−	0.299862i
$760$	−1.44334	−	2.92680i	−0.0523554	−	0.106166i
$761$	32.5267	−	8.71551i	1.17909	−	0.315937i	0.384527	−	0.923114i	$-0.374365\pi$
$761$	32.5267	−	8.71551i	1.17909	−	0.315937i	0.794567	+	0.607177i	$0.207698\pi$
$762$	2.62131	−	13.6383i	0.0949600	−	0.494062i
$763$	13.4199	−	1.76676i	0.485832	−	0.0639609i
$764$	−5.37110			−0.194320
$765$	12.0740	+	0.218981i	0.436535	+	0.00791728i
$766$	−8.88664			−0.321087
$767$	−11.8054	+	1.55421i	−0.426269	+	0.0561194i
$768$	29.3008	−	10.1579i	1.05730	−	0.366543i
$769$	−1.18623	+	0.317848i	−0.0427764	+	0.0114619i	−0.280144	−	0.959958i	$-0.590382\pi$
$769$	−1.18623	+	0.317848i	−0.0427764	+	0.0114619i	0.237367	+	0.971420i	$0.423715\pi$
$770$	−8.17207	−	16.5713i	−0.294501	−	0.597189i
$771$	0.676442	−	11.4543i	0.0243615	−	0.412516i
$772$	−19.9878	−	9.85690i	−0.719377	−	0.354758i
$773$	−30.7766	+	12.7481i	−1.10696	+	0.458517i	−0.859889	−	0.510481i	$-0.829467\pi$
$773$	−30.7766	+	12.7481i	−1.10696	+	0.458517i	−0.247068	+	0.968998i	$0.579467\pi$
$774$	−21.1752	+	53.0505i	−0.761125	+	1.90686i
$775$	−2.55812	−	3.82849i	−0.0918902	−	0.137523i
$776$	23.4727	−	7.96792i	0.842622	−	0.286032i
$777$	42.1180	−	28.5378i	1.51097	−	1.02379i
$778$	−4.88603	−	18.2349i	−0.175173	−	0.653753i
$779$	8.15251	+	2.76740i	0.292094	+	0.0991525i
$780$	2.75936	−	0.758516i	0.0988011	−	0.0271592i
$781$	−49.1694	+	28.3880i	−1.75942	+	1.01580i
$782$	20.5197	−	7.76209i	0.733782	−	0.277572i
$783$	27.3562	+	20.1607i	0.977631	+	0.720486i
$784$	−16.7291	−	6.92944i	−0.597469	−	0.247480i
$785$	−12.4985	−	14.2518i	−0.446091	−	0.508669i
$786$	−37.5821	−	4.70090i	−1.34051	−	0.167675i
$787$	−17.3365	+	8.54942i	−0.617980	+	0.304754i	−0.724201	−	0.689588i	$-0.757791\pi$
$787$	−17.3365	+	8.54942i	−0.617980	+	0.304754i	0.106221	+	0.994343i	$0.466125\pi$
$788$	8.28472	−	9.44692i	0.295131	−	0.336532i
$789$	5.86878	+	28.5392i	0.208934	+	1.01602i
$790$	1.12640	−	1.46796i	0.0400757	−	0.0522277i
$791$	−14.4546	−	34.8966i	−0.513948	−	1.24078i
$792$	−14.5409	−	12.4233i	−0.516690	−	0.441442i
$793$	−12.2945	−	2.44553i	−0.436590	−	0.0868432i
$794$	−2.87549	+	43.8714i	−0.102047	+	1.55694i
$795$	−2.57386	−	1.94870i	−0.0912855	−	0.0691131i
$796$	−4.41071	+	12.9935i	−0.156333	+	0.460543i
$797$	−22.2902	+	17.1039i	−0.789559	+	0.605850i	−0.922820	−	0.385231i	$-0.874122\pi$
$797$	−22.2902	+	17.1039i	−0.789559	+	0.605850i	0.133261	+	0.991081i	$0.457455\pi$
$798$	−2.35349	−	17.0256i	−0.0833128	−	0.602699i
$799$	11.5896	−	9.54365i	0.410010	−	0.337630i
$800$		−	19.2612i		−	0.680987i
$801$	−31.2240	−	23.3241i	−1.10325	−	0.824117i
$802$	−5.25111	−	26.3991i	−0.185423	−	0.932185i
$803$	53.6787	+	14.3832i	1.89428	+	0.507571i
$804$	4.46262	+	6.58624i	0.157384	+	0.232279i
$805$	7.47459	+	6.55504i	0.263445	+	0.231035i
$806$	−3.62940	+	0.237884i	−0.127840	+	0.00837909i
$807$	12.6086	−	22.1684i	0.443844	−	0.780364i
$808$	−8.44400	−	6.47931i	−0.297059	−	0.227941i
$809$	−20.2201	+	13.5107i	−0.710903	+	0.475010i	−0.857696	−	0.514157i	$-0.828105\pi$
$809$	−20.2201	+	13.5107i	−0.710903	+	0.475010i	0.146793	+	0.989167i	$0.453105\pi$
$810$	−11.5046	−	9.57468i	−0.404230	−	0.336420i
$811$	8.90598	−	13.3287i	0.312731	−	0.468035i	−0.641492	−	0.767129i	$-0.721684\pi$
$811$	8.90598	−	13.3287i	0.312731	−	0.468035i	0.954224	+	0.299094i	$0.0966844\pi$
$812$	4.97656	−	18.5728i	0.174643	−	0.651777i
$813$	−33.4899	+	38.6895i	−1.17454	+	1.35690i
$814$	−31.8402	−	41.4950i	−1.11600	−	1.45440i
$815$	5.04726	−	8.74212i	0.176798	−	0.306223i
$816$	−24.5727	−	25.8123i	−0.860216	−	0.903610i
$817$	−9.98585	−	17.2960i	−0.349361	−	0.605110i
$818$	18.9195	−	45.6757i	0.661504	−	1.59701i
$819$	−18.3285	−	0.963584i	−0.640449	−	0.0336703i
$820$	−2.99969	−	2.99969i	−0.104754	−	0.104754i
$821$	−3.86062	−	0.253038i	−0.134737	−	0.00883110i	−0.00211438	−	0.999998i	$-0.500673\pi$
$821$	−3.86062	−	0.253038i	−0.134737	−	0.00883110i	−0.132622	+	0.991167i	$0.542340\pi$
$822$	−1.54080	−	0.0909933i	−0.0537417	−	0.00317376i
$823$	1.46336	+	22.3266i	0.0510095	+	0.778255i	0.944364	+	0.328902i	$0.106679\pi$
$823$	1.46336	+	22.3266i	0.0510095	+	0.778255i	−0.893354	+	0.449353i	$0.851655\pi$
$824$	−0.903479	+	6.86261i	−0.0314742	+	0.239070i
$825$	−20.6091	+	12.0769i	−0.717515	+	0.420464i
$826$	15.5855	−	31.6043i	0.542290	−	1.09966i
$827$	−3.13912	+	15.7814i	−0.109158	+	0.548774i	0.887043	+	0.461687i	$0.152756\pi$
$827$	−3.13912	+	15.7814i	−0.109158	+	0.548774i	−0.996201	+	0.0870870i	$0.972244\pi$
$828$	−8.03671	−	2.61275i	−0.279295	−	0.0907993i
$829$	5.87342	−	5.87342i	0.203992	−	0.203992i	−0.597716	−	0.801708i	$-0.703925\pi$
$829$	5.87342	−	5.87342i	0.203992	−	0.203992i	0.801708	+	0.597716i	$0.203925\pi$
$830$	10.6027	−	9.29828i	0.368024	−	0.322748i
$831$	−12.2678	+	12.4274i	−0.425565	+	0.431101i
$832$	3.04392	+	1.75741i	0.105529	+	0.0609272i
$833$	0.514396	+	14.9518i	0.0178227	+	0.518050i
$834$	25.8258	+	33.2102i	0.894275	+	1.14998i
$835$	−0.338359	−	2.57009i	−0.0117094	−	0.0889418i
$836$	−5.38588	+	1.07132i	−0.186274	+	0.0370523i
$837$	3.68933	+	4.61975i	0.127522	+	0.159682i
$838$	−19.3442	−	12.9254i	−0.668234	−	0.446499i
$839$	−13.0057	−	38.3136i	−0.449007	−	1.32273i	−0.902199	−	0.431320i	$-0.858048\pi$
$839$	−13.0057	−	38.3136i	−0.449007	−	1.32273i	0.453191	−	0.891413i	$-0.350285\pi$
$840$	3.25178	−	9.78676i	0.112197	−	0.337675i
$841$	−13.6532	−	1.79748i	−0.470800	−	0.0619820i
$842$	23.1925	+	3.05335i	0.799266	+	0.105225i
$843$	−30.2278	+	6.21602i	−1.04110	+	0.214091i
$844$	−1.61713	−	4.76392i	−0.0556640	−	0.163981i
$845$	−7.69409	−	5.14103i	−0.264685	−	0.176857i
$846$	−18.6068	+	0.240510i	−0.639716	+	0.00826891i
$847$	1.96135	−	0.390137i	0.0673927	−	0.0134052i
$848$	1.24358	+	9.44592i	0.0427047	+	0.324374i
$849$	−10.4571	+	1.44552i	−0.358887	+	0.0496100i
$850$	−25.8705	+	11.7737i	−0.887351	+	0.403836i
$851$	24.3722	+	14.0713i	0.835469	+	0.482358i
$852$	25.1799	+	6.57283i	0.862650	+	0.225181i
$853$	35.6048	−	31.2245i	1.21908	−	1.06911i	0.223551	−	0.974692i	$-0.428235\pi$
$853$	35.6048	−	31.2245i	1.21908	−	1.06911i	0.995533	−	0.0944153i	$-0.0300982\pi$
$854$	26.2316	−	26.2316i	0.897626	−	0.897626i
$855$	5.11913	−	1.08722i	0.175071	−	0.0371822i
$856$	−5.56869	+	27.9957i	−0.190334	+	0.956872i
$857$	10.9290	−	22.1619i	0.373328	−	0.757035i	−0.626419	−	0.779486i	$-0.715480\pi$
$857$	10.9290	−	22.1619i	0.373328	−	0.757035i	0.999748	+	0.0224509i	$0.00714695\pi$
$858$	0.121941	+	18.8684i	0.00416298	+	0.644157i
$859$	−3.19216	+	24.2468i	−0.108915	+	0.827292i	0.846575	+	0.532269i	$0.178661\pi$
$859$	−3.19216	+	24.2468i	−0.108915	+	0.827292i	−0.955490	+	0.295023i	$0.904673\pi$
$860$	0.643622	+	9.81978i	0.0219473	+	0.334852i
$861$	12.1910	+	24.3234i	0.415470	+	0.828941i
$862$	−19.8316	−	1.29983i	−0.675467	−	0.0442724i
$863$	11.5923	+	11.5923i	0.394607	+	0.394607i	0.876326	−	0.481719i	$-0.159987\pi$
$863$	11.5923	+	11.5923i	0.394607	+	0.394607i	−0.481719	+	0.876326i	$0.659987\pi$
$864$	2.09562	+	24.6423i	0.0712946	+	0.838348i
$865$	−1.17886	+	2.84603i	−0.0400825	+	0.0967678i
$866$	−2.68223	−	4.64575i	−0.0911458	−	0.157869i
$867$	−11.0011	+	27.3125i	−0.373618	+	0.927583i
$868$	1.67259	−	2.89701i	0.0567715	−	0.0983311i
$869$	2.30815	+	3.00804i	0.0782985	+	0.102041i
$870$	18.4999	+	3.55573i	0.627205	+	0.120550i
$871$	−2.47378	+	9.23227i	−0.0838208	+	0.312824i
$872$	4.31509	−	6.45798i	0.146127	−	0.218695i
$873$	3.11238	+	39.6301i	0.105338	+	1.34127i
$874$	7.90521	−	5.28209i	0.267398	−	0.178669i
$875$	−22.8442	−	17.5290i	−0.772275	−	0.592588i
$876$	−12.8782	−	21.9766i	−0.435116	−	0.742519i
$877$	0.285089	−	0.0186857i	0.00962676	−	0.000630971i	−0.0605890	−	0.998163i	$-0.519298\pi$
$877$	0.285089	−	0.0186857i	0.00962676	−	0.000630971i	0.0702157	+	0.997532i	$0.477631\pi$
$878$	32.0930	+	28.1448i	1.08309	+	0.949841i
$879$	−4.25583	+	8.77243i	−0.143545	+	0.295887i
$880$	−16.0373	−	4.29718i	−0.540617	−	0.144858i
$881$	4.52996	+	22.7737i	0.152618	+	0.767264i	0.978953	+	0.204085i	$0.0654219\pi$
$881$	4.52996	+	22.7737i	0.152618	+	0.767264i	−0.826335	+	0.563179i	$0.809578\pi$
$882$	11.0973	−	14.8559i	0.373664	−	0.500225i
$883$			39.9852i			1.34561i	0.739821	+	0.672804i	$0.234910\pi$
$883$			39.9852i			1.34561i	−0.739821	+	0.672804i	$0.765090\pi$
$884$	−0.672376	+	6.94529i	−0.0226145	+	0.233595i
$885$	9.93911	+	4.04186i	0.334100	+	0.135866i
$886$	31.0343	−	23.8135i	1.04262	−	0.800029i
$887$	−11.4866	+	33.8385i	−0.385683	+	1.13618i	0.564752	+	0.825260i	$0.308972\pi$
$887$	−11.4866	+	33.8385i	−0.385683	+	1.13618i	−0.950435	+	0.310924i	$0.899362\pi$
$888$	3.62334	−	28.9674i	0.121591	−	0.972083i
$889$	−1.00363	+	15.3125i	−0.0336607	+	0.513563i
$890$	−21.1902	−	4.21500i	−0.710299	−	0.141287i
$891$	25.0527	−	17.6931i	0.839298	−	0.592742i
$892$	8.20715	+	19.8138i	0.274796	+	0.663416i
$893$	3.96077	−	5.16177i	0.132542	−	0.172732i
$894$	24.3700	+	8.09725i	0.815056	+	0.270813i
$895$	1.28334	−	1.46337i	0.0428975	−	0.0489152i
$896$	−37.1621	+	18.3263i	−1.24150	+	0.612239i
$897$	−3.94580	−	9.35454i	−0.131746	−	0.312339i
$898$	−24.7731	−	28.2483i	−0.826689	−	0.942659i
$899$	−6.87467	−	2.84758i	−0.229283	−	0.0949721i
$900$	10.6114	+	2.69681i	0.353713	+	0.0898938i
$901$	6.67773	−	4.16791i	0.222467	−	0.138853i
$902$	24.2236	−	13.9855i	0.806559	−	0.465667i
$903$	15.9410	−	61.0685i	0.530483	−	2.03223i
$904$	−20.5237	−	6.96687i	−0.682609	−	0.231715i
$905$	1.79993	+	6.71743i	0.0598317	+	0.223295i
$906$	−27.7936	−	13.4837i	−0.923382	−	0.447966i
$907$	27.5751	−	9.36050i	0.915617	−	0.310810i	0.176432	−	0.984313i	$-0.443544\pi$
$907$	27.5751	−	9.36050i	0.915617	−	0.310810i	0.739185	+	0.673503i	$0.235211\pi$
$908$	−0.466925	−	0.698802i	−0.0154954	−	0.0231906i
$909$	13.4059	−	10.5648i	0.444647	−	0.350413i
$910$	−9.40006	+	3.89363i	−0.311609	+	0.129073i
$911$	−7.82237	−	3.85757i	−0.259167	−	0.127807i	0.308064	−	0.951365i	$-0.400319\pi$
$911$	−7.82237	−	3.85757i	−0.259167	−	0.127807i	−0.567231	+	0.823559i	$0.691985\pi$
$912$	−12.8968	−	8.49731i	−0.427055	−	0.281374i
$913$	12.7810	+	25.9173i	0.422989	+	0.857737i
$914$	−9.68294	+	2.59454i	−0.320283	+	0.0858196i
$915$	8.54032	+	7.39257i	0.282334	+	0.244391i
$916$	25.6225	−	3.37327i	0.846592	−	0.111456i
$917$	41.8497			1.38200
$918$	31.8171	−	17.8777i	1.05012	−	0.590053i
$919$	20.8860			0.688965			0.344483	−	0.938793i	$-0.388054\pi$
$919$	20.8860			0.688965			0.344483	+	0.938793i	$0.388054\pi$
$920$	5.65590	−	0.744613i	0.186469	−	0.0245492i
$921$	5.36389	+	4.64303i	0.176746	+	0.152993i
$922$	9.30893	−	2.49432i	0.306573	−	0.0821460i
$923$	13.8280	+	28.0404i	0.455154	+	0.922962i
$924$	−14.4913	−	9.54790i	−0.476729	−	0.314103i
$925$	−32.7012	−	16.1265i	−1.07521	−	0.530234i
$926$	24.4357	−	10.1216i	0.803007	−	0.332616i
$927$	−10.3094	−	4.11500i	−0.338605	−	0.135154i
$928$	−17.2933	−	25.8813i	−0.567680	−	0.849594i
$929$	38.1002	−	12.9333i	1.25003	−	0.424327i	0.383538	−	0.923525i	$-0.374705\pi$
$929$	38.1002	−	12.9333i	1.25003	−	0.424327i	0.866488	+	0.499198i	$0.166372\pi$
$930$	2.94874	+	1.43054i	0.0966930	+	0.0469093i
$931$	1.67804	+	6.26254i	0.0549956	+	0.205246i
$932$	−13.3158	−	4.52009i	−0.436172	−	0.148060i
$933$	8.25110	−	31.6092i	0.270129	−	1.03484i
$934$	−10.2643	+	5.92607i	−0.335857	+	0.193907i
$935$	2.25707	+	13.5307i	0.0738142	+	0.442500i
$936$	−7.35014	+	7.54264i	−0.240247	+	0.246539i
$937$	5.85654	+	2.42586i	0.191325	+	0.0792493i	0.476289	−	0.879289i	$-0.341982\pi$
$937$	5.85654	+	2.42586i	0.191325	+	0.0792493i	−0.284964	+	0.958538i	$0.591982\pi$
$938$	−18.6501	−	21.2664i	−0.608947	−	0.694371i
$939$	13.9379	+	33.0434i	0.454845	+	1.07833i
$940$	−2.87528	+	1.41793i	−0.0937814	+	0.0462479i
$941$	−11.9566	+	13.6339i	−0.389775	+	0.444453i	−0.913134	−	0.407659i	$-0.866345\pi$
$941$	−11.9566	+	13.6339i	−0.389775	+	0.444453i	0.523359	+	0.852112i	$0.324679\pi$
$942$	−54.3659	−	18.0638i	−1.77134	−	0.588549i
$943$	−9.16202	+	11.9402i	−0.298357	+	0.388826i
$944$	−12.1176	−	29.2544i	−0.394394	−	0.952151i
$945$	13.9267	+	8.91991i	0.453036	+	0.290165i
$946$	−63.6391	−	12.6586i	−2.06909	−	0.411567i
$947$	2.18456	−	33.3300i	0.0709888	−	1.08308i	−0.802633	−	0.596473i	$-0.796568\pi$
$947$	2.18456	−	33.3300i	0.0709888	−	1.08308i	0.873622	−	0.486606i	$-0.161765\pi$
$948$	0.215699	−	1.72444i	0.00700558	−	0.0560073i
$949$	9.83663	−	28.9778i	0.319310	−	0.940658i
$950$	−9.77242	+	7.49864i	−0.317059	+	0.243288i
$951$	−10.0575	−	4.09003i	−0.326138	−	0.132628i
$952$	19.4646	+	15.9200i	0.630851	+	0.515970i
$953$			50.5808i			1.63847i	0.573455	+	0.819237i	$0.305603\pi$
$953$			50.5808i			1.63847i	−0.573455	+	0.819237i	$0.694397\pi$
$954$	−9.68883	−	1.14837i	−0.313687	−	0.0371798i
$955$	1.13436	+	5.70282i	0.0367071	+	0.184539i
$956$	23.5900	+	6.32092i	0.762955	+	0.204433i
$957$	−16.8493	+	34.7311i	−0.544662	+	1.12270i
$958$	−5.75792	−	5.04956i	−0.186030	−	0.163144i
$959$	1.70181	−	0.111543i	0.0549544	−	0.00360190i
$960$	−1.60127	−	2.73255i	−0.0516808	−	0.0881926i
$961$	23.5669	+	18.0835i	0.760223	+	0.583339i
$962$	−23.9477	+	16.0013i	−0.772105	+	0.515904i
$963$	−41.3129	−	19.7136i	−1.33129	−	0.635262i
$964$	−8.51793	+	12.7480i	−0.274344	+	0.410585i
$965$	−6.24429	+	23.3040i	−0.201011	+	0.750183i
$966$	29.5057	+	5.67107i	0.949331	+	0.182464i
$967$	−0.0825454	−	0.107575i	−0.00265448	−	0.00345939i	0.792024	−	0.610490i	$-0.209027\pi$
$967$	−0.0825454	−	0.107575i	−0.00265448	−	0.00345939i	−0.794679	+	0.607030i	$0.792361\pi$
$968$	0.573749	−	0.993762i	0.0184410	−	0.0319407i
$969$	−1.97622	+	12.6065i	−0.0634854	+	0.404978i
$970$	11.0184	+	19.0845i	0.353780	+	0.612766i
$971$	−10.9066	+	26.3310i	−0.350011	+	0.845001i	0.646607	+	0.762824i	$0.276188\pi$
$971$	−10.9066	+	26.3310i	−0.350011	+	0.845001i	−0.996618	+	0.0821778i	$0.973812\pi$
$972$	−13.8694	−	2.29571i	−0.444860	−	0.0736350i
$973$	−32.8699	−	32.8699i	−1.05376	−	1.05376i
$974$	9.59768	+	0.629065i	0.307529	+	0.0201565i
$975$	5.89387	+	11.7594i	0.188755	+	0.376602i
$976$	−2.18021	−	33.2636i	−0.0697868	−	1.06474i
$977$	3.78325	−	28.7366i	0.121037	−	0.919366i	−0.817920	−	0.575331i	$-0.804873\pi$
$977$	3.78325	−	28.7366i	0.121037	−	0.919366i	0.938957	−	0.344034i	$-0.111794\pi$
$978$	−0.197156	−	30.5069i	−0.00630436	−	0.975503i
$979$	19.5811	−	39.7065i	0.625814	−	1.26903i
$980$	0.623246	−	3.13327i	0.0199089	−	0.100089i
$981$	8.33290	+	9.25769i	0.266049	+	0.295575i
$982$	−5.02475	+	5.02475i	−0.160346	+	0.160346i
$983$	10.4806	−	9.19125i	0.334280	−	0.293155i	−0.475707	−	0.879604i	$-0.657808\pi$
$983$	10.4806	−	9.19125i	0.334280	−	0.293155i	0.809987	+	0.586449i	$0.199474\pi$
$984$	15.1059	+	3.94316i	0.481559	+	0.125703i
$985$	−11.7801	−	6.80123i	−0.375344	−	0.216705i
$986$	−24.1913	+	39.0476i	−0.770409	+	1.24353i
$987$	20.3675	−	2.81546i	0.648306	−	0.0896171i
$988$	0.394702	+	2.99806i	0.0125571	+	0.0953809i
$989$	34.2421	−	6.81117i	1.08883	−	0.216583i
$990$	8.31021	−	14.8332i	0.264116	−	0.471430i
$991$	−13.4573	−	8.99189i	−0.427485	−	0.285637i	0.323157	−	0.946345i	$-0.395256\pi$
$991$	−13.4573	−	8.99189i	−0.427485	−	0.285637i	−0.750642	+	0.660709i	$0.770256\pi$
$992$	−1.74070	−	5.12795i	−0.0552674	−	0.162813i
$993$	−34.2568	+	7.04456i	−1.08711	+	0.223552i
$994$	−91.7329	−	12.0769i	−2.90959	−	0.383055i
$995$	14.7275	+	1.93892i	0.466894	+	0.0614678i
$996$	4.17642	−	12.5696i	0.132335	−	0.398284i
$997$	2.04196	+	6.01542i	0.0646696	+	0.190510i	0.974462	−	0.224554i	$-0.0720925\pi$
$997$	2.04196	+	6.01542i	0.0646696	+	0.190510i	−0.909792	+	0.415064i	$0.863759\pi$
$998$	4.06076	+	2.71332i	0.128541	+	0.0858885i
$999$	43.5916	+	17.0739i	1.37918	+	0.540193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.113.4	yes	256
3.2	odd	2		459.2.y.a.368.13		256
9.2	odd	6	inner	153.2.s.a.11.4	✓	256
9.7	even	3		459.2.y.a.62.13		256
17.14	odd	16	inner	153.2.s.a.14.4	yes	256
51.14	even	16		459.2.y.a.422.13		256
153.65	even	48	inner	153.2.s.a.65.4	yes	256
153.133	odd	48		459.2.y.a.116.13		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.4	✓	256	9.2	odd	6	inner
153.2.s.a.14.4	yes	256	17.14	odd	16	inner
153.2.s.a.65.4	yes	256	153.65	even	48	inner
153.2.s.a.113.4	yes	256	1.1	even	1	trivial
459.2.y.a.62.13		256	9.7	even	3
459.2.y.a.116.13		256	153.133	odd	48
459.2.y.a.368.13		256	3.2	odd	2
459.2.y.a.422.13		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)

\(f(q)\)	\(=\)	\(q+(-1.68890 + 0.222348i) q^{2} +(1.30958 + 1.13358i) q^{3} +(0.871097 - 0.233410i) q^{4} +(-0.431798 - 0.875600i) q^{5} +(-2.46380 - 1.62332i) q^{6} +(2.92393 + 1.44192i) q^{7} +(1.72831 - 0.715890i) q^{8} +(0.429989 + 2.96903i) q^{9} +O(q^{10})\)	\(q+(-1.68890 + 0.222348i) q^{2} +(1.30958 + 1.13358i) q^{3} +(0.871097 - 0.233410i) q^{4} +(-0.431798 - 0.875600i) q^{5} +(-2.46380 - 1.62332i) q^{6} +(2.92393 + 1.44192i) q^{7} +(1.72831 - 0.715890i) q^{8} +(0.429989 + 2.96903i) q^{9} +(0.923953 + 1.38279i) q^{10} +(-3.22699 + 1.09542i) q^{11} +(1.40536 + 0.681791i) q^{12} +(0.485696 + 1.81264i) q^{13} +(-5.25883 - 1.78513i) q^{14} +(0.427090 - 1.63615i) q^{15} +(-4.32178 + 2.49518i) q^{16} +(3.35545 + 2.39603i) q^{17} +(-1.38637 - 4.91878i) q^{18} +(1.65080 + 0.683785i) q^{19} +(-0.580512 - 0.661947i) q^{20} +(2.19458 + 5.20282i) q^{21} +(5.20650 - 2.56756i) q^{22} +(-2.05951 + 2.34842i) q^{23} +(3.07488 + 1.02167i) q^{24} +(2.46358 - 3.21060i) q^{25} +(-1.22333 - 2.95338i) q^{26} +(-2.80253 + 4.37560i) q^{27} +(2.88358 + 0.573580i) q^{28} +(0.427734 - 6.52595i) q^{29} +(-0.357520 + 2.85825i) q^{30} +(0.365730 - 1.07741i) q^{31} +(3.77599 - 2.89742i) q^{32} +(-5.46774 - 2.22352i) q^{33} +(-6.19977 - 3.30059i) q^{34} -3.18281i q^{35} +(1.06756 + 2.48594i) q^{36} +(-1.75772 - 8.83664i) q^{37} +(-2.94008 - 0.787793i) q^{38} +(-1.41872 + 2.92437i) q^{39} +(-1.37312 - 1.20419i) q^{40} +(4.80798 - 0.315131i) q^{41} +(-4.86326 - 8.29909i) q^{42} +(-8.86751 - 6.80428i) q^{43} +(-2.55534 + 1.70742i) q^{44} +(2.41401 - 1.65852i) q^{45} +(2.95614 - 4.42418i) q^{46} +(0.942428 - 3.51719i) q^{47} +(-8.48820 - 1.63145i) q^{48} +(2.20889 + 2.87868i) q^{49} +(-3.44687 + 5.97016i) q^{50} +(1.67812 + 6.94146i) q^{51} +(0.846177 + 1.46562i) q^{52} +(0.730606 - 1.76384i) q^{53} +(3.76029 - 8.01309i) q^{54} +(2.35256 + 2.35256i) q^{55} +(6.08572 + 0.398879i) q^{56} +(1.38673 + 2.76679i) q^{57} +(0.728633 + 11.1168i) q^{58} +(-0.828213 + 6.29090i) q^{59} +(-0.00985512 - 1.52493i) q^{60} +(-2.95443 + 5.99099i) q^{61} +(-0.378123 + 1.90095i) q^{62} +(-3.02385 + 9.30123i) q^{63} +(1.32440 - 1.32440i) q^{64} +(1.37743 - 1.20797i) q^{65} +(9.72886 + 2.53957i) q^{66} +(4.41090 + 2.54663i) q^{67} +(3.48218 + 1.30398i) q^{68} +(-5.35922 + 0.740820i) q^{69} +(0.707692 + 5.37545i) q^{70} +(16.3403 - 3.25028i) q^{71} +(2.86865 + 4.82358i) q^{72} +(-13.5589 - 9.05977i) q^{73} +(4.93342 + 14.5334i) q^{74} +(6.86573 - 1.41186i) q^{75} +(1.59761 + 0.210330i) q^{76} +(-11.0150 - 1.45015i) q^{77} +(1.74585 - 5.25443i) q^{78} +(-0.357632 - 1.05355i) q^{79} +(4.05092 + 2.70674i) q^{80} +(-8.63022 + 2.55329i) q^{81} +(-8.05013 + 1.60127i) q^{82} +(-1.10682 - 8.40712i) q^{83} +(3.12608 + 4.01992i) q^{84} +(0.649091 - 3.97263i) q^{85} +(16.4893 + 9.52008i) q^{86} +(7.95785 - 8.06137i) q^{87} +(-4.79305 + 4.20339i) q^{88} +(-9.18621 + 9.18621i) q^{89} +(-3.70826 + 3.33782i) q^{90} +(-1.19355 + 6.00038i) q^{91} +(-1.24589 + 2.52641i) q^{92} +(1.70028 - 0.996363i) q^{93} +(-0.809628 + 6.14973i) q^{94} +(-0.114092 - 1.74070i) q^{95} +(8.22941 + 0.485994i) q^{96} +(13.2223 + 0.866637i) q^{97} +(-4.37066 - 4.37066i) q^{98} +(-4.63989 - 9.11000i) 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

L-functions

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