LMFDB - Embedded newform 315.2.bs.e.52.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(52,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3, 2]))

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

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

chi := DirichletCharacter("315.52");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bs (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			52.20
Character	$\chi$	$=$	315.52
Dual form			315.2.bs.e.103.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.108614 - 0.108614i) q^{2} +(1.61761 + 0.619140i) q^{3} -1.97641i q^{4} +(0.847505 - 2.06924i) q^{5} +(-0.108448 - 0.242943i) q^{6} +(0.0705295 + 2.64481i) q^{7} +(-0.431895 + 0.431895i) q^{8} +(2.23333 + 2.00306i) q^{9} +O(q^{10})$	\(q+(-0.108614 - 0.108614i) q^{2} +(1.61761 + 0.619140i) q^{3} -1.97641i q^{4} +(0.847505 - 2.06924i) q^{5} +(-0.108448 - 0.242943i) q^{6} +(0.0705295 + 2.64481i) q^{7} +(-0.431895 + 0.431895i) q^{8} +(2.23333 + 2.00306i) q^{9} +(-0.316800 + 0.132697i) q^{10} +(0.956327 + 1.65641i) q^{11} +(1.22367 - 3.19706i) q^{12} +(0.793782 - 2.96243i) q^{13} +(0.279604 - 0.294925i) q^{14} +(2.65208 - 2.82249i) q^{15} -3.85899 q^{16} +(-1.75988 - 6.56796i) q^{17} +(-0.0250111 - 0.460132i) q^{18} +(2.28209 + 3.95269i) q^{19} +(-4.08965 - 1.67501i) q^{20} +(-1.52342 + 4.32194i) q^{21} +(0.0760387 - 0.283780i) q^{22} +(-1.13167 - 4.22346i) q^{23} +(-0.966041 + 0.431234i) q^{24} +(-3.56347 - 3.50737i) q^{25} +(-0.407979 + 0.235547i) q^{26} +(2.37249 + 4.62291i) q^{27} +(5.22722 - 0.139395i) q^{28} +(1.50486 + 0.868834i) q^{29} +(-0.594617 + 0.0185093i) q^{30} +6.85954i q^{31} +(1.28293 + 1.28293i) q^{32} +(0.521417 + 3.27152i) q^{33} +(-0.522227 + 0.904523i) q^{34} +(5.53251 + 2.09555i) q^{35} +(3.95885 - 4.41397i) q^{36} +(-2.31270 + 8.63111i) q^{37} +(0.181452 - 0.677187i) q^{38} +(3.11819 - 4.30060i) q^{39} +(0.527659 + 1.25972i) q^{40} +(-3.09135 + 1.78479i) q^{41} +(0.634890 - 0.303960i) q^{42} +(0.252045 + 0.940643i) q^{43} +(3.27373 - 1.89009i) q^{44} +(6.03755 - 2.92369i) q^{45} +(-0.335812 + 0.581644i) q^{46} +(-7.36114 + 7.36114i) q^{47} +(-6.24235 - 2.38926i) q^{48} +(-6.99005 + 0.373074i) q^{49} +(0.00609292 + 0.767995i) q^{50} +(1.21969 - 11.7140i) q^{51} +(-5.85497 - 1.56883i) q^{52} +(-2.68833 - 10.0330i) q^{53} +(0.244428 - 0.759800i) q^{54} +(4.23799 - 0.575053i) q^{55} +(-1.17274 - 1.11182i) q^{56} +(1.24426 + 7.80685i) q^{57} +(-0.0690820 - 0.257818i) q^{58} +6.94689 q^{59} +(-5.57839 - 5.24159i) q^{60} +7.37156i q^{61} +(0.745044 - 0.745044i) q^{62} +(-5.14019 + 6.04801i) q^{63} +7.43929i q^{64} +(-5.45724 - 4.15320i) q^{65} +(0.298701 - 0.411968i) q^{66} +(1.16531 + 1.16531i) q^{67} +(-12.9810 + 3.47824i) q^{68} +(0.784308 - 7.53257i) q^{69} +(-0.373303 - 0.828517i) q^{70} -10.9017 q^{71} +(-1.82967 + 0.0994542i) q^{72} +(11.1248 - 2.98088i) q^{73} +(1.18865 - 0.686270i) q^{74} +(-3.59275 - 7.87986i) q^{75} +(7.81213 - 4.51033i) q^{76} +(-4.31343 + 2.64613i) q^{77} +(-0.805787 + 0.128427i) q^{78} +0.207278i q^{79} +(-3.27051 + 7.98516i) q^{80} +(0.975531 + 8.94697i) q^{81} +(0.529618 + 0.141911i) q^{82} +(-2.04964 + 0.549200i) q^{83} +(8.54191 + 3.01090i) q^{84} +(-15.0822 - 1.92477i) q^{85} +(0.0747917 - 0.129543i) q^{86} +(1.89636 + 2.33716i) q^{87} +(-1.12843 - 0.302361i) q^{88} +(1.64396 + 2.84742i) q^{89} +(-0.973319 - 0.338211i) q^{90} +(7.89106 + 1.89046i) q^{91} +(-8.34726 + 2.23664i) q^{92} +(-4.24702 + 11.0961i) q^{93} +1.59905 q^{94} +(10.1131 - 1.37225i) q^{95} +(1.28097 + 2.86960i) q^{96} +(-0.820966 - 3.06389i) q^{97} +(0.799741 + 0.718699i) q^{98} +(-1.18208 + 5.61488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 4 q^{2} - 18 q^{3} - 6 q^{5} + 24 q^{6} - 16 q^{8}+O(q^{10}) $ 160 * q + 4 * q^2 - 18 * q^3 - 6 * q^5 + 24 * q^6 - 16 * q^8	$ 160 q + 4 q^{2} - 18 q^{3} - 6 q^{5} + 24 q^{6} - 16 q^{8} - 24 q^{10} - 16 q^{11} - 30 q^{12} + 16 q^{15} - 152 q^{16} - 6 q^{17} + 58 q^{18} + 60 q^{20} - 36 q^{21} + 8 q^{22} + 8 q^{23} + 2 q^{25} - 36 q^{26} - 36 q^{27} + 22 q^{28} - 26 q^{30} + 12 q^{32} - 6 q^{33} - 36 q^{35} - 32 q^{36} - 4 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 28 q^{42} - 4 q^{43} - 54 q^{45} - 16 q^{46} - 18 q^{48} - 44 q^{50} + 80 q^{51} + 54 q^{52} + 8 q^{53} + 148 q^{56} - 4 q^{57} + 28 q^{58} + 104 q^{60} - 60 q^{63} - 124 q^{65} + 36 q^{66} - 24 q^{67} + 42 q^{68} - 34 q^{70} - 40 q^{71} + 70 q^{72} + 36 q^{73} - 60 q^{75} + 96 q^{76} + 58 q^{77} - 62 q^{78} + 36 q^{80} + 8 q^{81} - 66 q^{82} - 138 q^{83} - 20 q^{85} - 16 q^{86} + 102 q^{87} + 46 q^{88} + 18 q^{90} - 48 q^{91} - 26 q^{92} + 82 q^{93} + 188 q^{95} - 48 q^{96} + 48 q^{97} + 102 q^{98}+O(q^{100}) $ 160 * q + 4 * q^2 - 18 * q^3 - 6 * q^5 + 24 * q^6 - 16 * q^8 - 24 * q^10 - 16 * q^11 - 30 * q^12 + 16 * q^15 - 152 * q^16 - 6 * q^17 + 58 * q^18 + 60 * q^20 - 36 * q^21 + 8 * q^22 + 8 * q^23 + 2 * q^25 - 36 * q^26 - 36 * q^27 + 22 * q^28 - 26 * q^30 + 12 * q^32 - 6 * q^33 - 36 * q^35 - 32 * q^36 - 4 * q^37 - 18 * q^38 - 6 * q^40 - 12 * q^41 - 28 * q^42 - 4 * q^43 - 54 * q^45 - 16 * q^46 - 18 * q^48 - 44 * q^50 + 80 * q^51 + 54 * q^52 + 8 * q^53 + 148 * q^56 - 4 * q^57 + 28 * q^58 + 104 * q^60 - 60 * q^63 - 124 * q^65 + 36 * q^66 - 24 * q^67 + 42 * q^68 - 34 * q^70 - 40 * q^71 + 70 * q^72 + 36 * q^73 - 60 * q^75 + 96 * q^76 + 58 * q^77 - 62 * q^78 + 36 * q^80 + 8 * q^81 - 66 * q^82 - 138 * q^83 - 20 * q^85 - 16 * q^86 + 102 * q^87 + 46 * q^88 + 18 * q^90 - 48 * q^91 - 26 * q^92 + 82 * q^93 + 188 * q^95 - 48 * q^96 + 48 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.108614	−	0.108614i	−0.0768019	−	0.0768019i	0.667662	−	0.744464i	$-0.267295\pi$
$2$	−0.108614	−	0.108614i	−0.0768019	−	0.0768019i	−0.744464	+	0.667662i	$0.767295\pi$
$3$	1.61761	+	0.619140i	0.933928	+	0.357461i
$3$	1.61761	+	0.619140i	0.933928	+	0.357461i
$4$		−	1.97641i		−	0.988203i
$5$	0.847505	−	2.06924i	0.379016	−	0.925390i
$5$	0.847505	−	2.06924i	0.379016	−	0.925390i
$6$	−0.108448	−	0.242943i	−0.0442738	−	0.0991812i
$7$	0.0705295	+	2.64481i	0.0266576	+	0.999645i
$7$	0.0705295	+	2.64481i	0.0266576	+	0.999645i
$8$	−0.431895	+	0.431895i	−0.152698	+	0.152698i
$9$	2.23333	+	2.00306i	0.744444	+	0.667685i
$10$	−0.316800	+	0.132697i	−0.100181	+	0.0419626i
$11$	0.956327	+	1.65641i	0.288343	+	0.499426i	0.973414	−	0.229051i	$-0.0735622\pi$
$11$	0.956327	+	1.65641i	0.288343	+	0.499426i	−0.685071	+	0.728476i	$0.740229\pi$
$12$	1.22367	−	3.19706i	0.353244	−	0.922911i
$13$	0.793782	−	2.96243i	0.220155	−	0.821631i	−0.764132	−	0.645060i	$-0.776833\pi$
$13$	0.793782	−	2.96243i	0.220155	−	0.821631i	0.984288	−	0.176572i	$-0.0565008\pi$
$14$	0.279604	−	0.294925i	0.0747273	−	0.0788220i
$15$	2.65208	−	2.82249i	0.684764	−	0.728765i
$16$	−3.85899			−0.964748
$17$	−1.75988	−	6.56796i	−0.426834	−	1.59296i	−0.759886	−	0.650057i	$-0.774745\pi$
$17$	−1.75988	−	6.56796i	−0.426834	−	1.59296i	0.333052	−	0.942908i	$-0.391921\pi$
$18$	−0.0250111	−	0.460132i	−0.00589517	−	0.108454i
$19$	2.28209	+	3.95269i	0.523547	+	0.906810i	0.999624	+	0.0274067i	$0.00872492\pi$
$19$	2.28209	+	3.95269i	0.523547	+	0.906810i	−0.476077	+	0.879403i	$0.657942\pi$
$20$	−4.08965	−	1.67501i	−0.914473	−	0.374544i
$21$	−1.52342	+	4.32194i	−0.332437	+	0.943125i
$22$	0.0760387	−	0.283780i	0.0162115	−	0.0605022i
$23$	−1.13167	−	4.22346i	−0.235970	−	0.880652i	−0.977709	−	0.209963i	$-0.932666\pi$
$23$	−1.13167	−	4.22346i	−0.235970	−	0.880652i	0.741739	−	0.670688i	$-0.234001\pi$
$24$	−0.966041	+	0.431234i	−0.197192	+	0.0880253i
$25$	−3.56347	−	3.50737i	−0.712694	−	0.701475i
$26$	−0.407979	+	0.235547i	−0.0800112	+	0.0461945i
$27$	2.37249	+	4.62291i	0.456585	+	0.889680i
$28$	5.22722	−	0.139395i	0.987852	−	0.0263432i
$29$	1.50486	+	0.868834i	0.279446	+	0.161338i	0.633173	−	0.774011i	$-0.281752\pi$
$29$	1.50486	+	0.868834i	0.279446	+	0.161338i	−0.353726	+	0.935349i	$0.615086\pi$
$30$	−0.594617	+	0.0185093i	−0.108562	+	0.00337933i
$31$			6.85954i			1.23201i	0.787742	+	0.616005i	$0.211250\pi$
$31$			6.85954i			1.23201i	−0.787742	+	0.616005i	$0.788750\pi$
$32$	1.28293	+	1.28293i	0.226792	+	0.226792i
$33$	0.521417	+	3.27152i	0.0907670	+	0.569499i
$34$	−0.522227	+	0.904523i	−0.0895611	+	0.155124i
$35$	5.53251	+	2.09555i	0.935165	+	0.354212i
$36$	3.95885	−	4.41397i	0.659809	−	0.735661i
$37$	−2.31270	+	8.63111i	−0.380205	+	1.41895i	0.465383	+	0.885110i	$0.345917\pi$
$37$	−2.31270	+	8.63111i	−0.380205	+	1.41895i	−0.845588	+	0.533836i	$0.820750\pi$
$38$	0.181452	−	0.677187i	0.0294353	−	0.109854i
$39$	3.11819	−	4.30060i	0.499310	−	0.688648i
$40$	0.527659	+	1.25972i	0.0834302	+	0.199180i
$41$	−3.09135	+	1.78479i	−0.482787	+	0.278737i	−0.721577	−	0.692334i	$-0.756583\pi$
$41$	−3.09135	+	1.78479i	−0.482787	+	0.278737i	0.238790	+	0.971071i	$0.423249\pi$
$42$	0.634890	−	0.303960i	0.0979657	−	0.0469020i
$43$	0.252045	+	0.940643i	0.0384364	+	0.143447i	0.982478	−	0.186381i	$-0.0596759\pi$
$43$	0.252045	+	0.940643i	0.0384364	+	0.143447i	−0.944041	+	0.329828i	$0.893009\pi$
$44$	3.27373	−	1.89009i	0.493534	−	0.284942i
$45$	6.03755	−	2.92369i	0.900025	−	0.435837i
$46$	−0.335812	+	0.581644i	−0.0495128	+	0.0857587i
$47$	−7.36114	+	7.36114i	−1.07373	+	1.07373i	−0.0766768	+	0.997056i	$0.524431\pi$
$47$	−7.36114	+	7.36114i	−1.07373	+	1.07373i	−0.997056	+	0.0766768i	$0.975569\pi$
$48$	−6.24235	−	2.38926i	−0.901005	−	0.344860i
$49$	−6.99005	+	0.373074i	−0.998579	+	0.0532963i
$50$	0.00609292	+	0.767995i	0.000861668	+	0.108611i
$51$	1.21969	−	11.7140i	0.170791	−	1.64029i
$52$	−5.85497	−	1.56883i	−0.811938	−	0.217558i
$53$	−2.68833	−	10.0330i	−0.369270	−	1.37813i	−0.861539	−	0.507691i	$-0.830499\pi$
$53$	−2.68833	−	10.0330i	−0.369270	−	1.37813i	0.492269	−	0.870443i	$-0.336168\pi$
$54$	0.244428	−	0.759800i	0.0332625	−	0.103396i
$55$	4.23799	−	0.575053i	0.571450	−	0.0775401i
$56$	−1.17274	−	1.11182i	−0.156714	−	0.148573i
$57$	1.24426	+	7.80685i	0.164806	+	1.03404i
$58$	−0.0690820	−	0.257818i	−0.00907092	−	0.0338531i
$59$	6.94689			0.904408			0.452204	−	0.891915i	$-0.350638\pi$
$59$	6.94689			0.904408			0.452204	+	0.891915i	$0.350638\pi$
$60$	−5.57839	−	5.24159i	−0.720167	−	0.676686i
$61$			7.37156i			0.943832i	0.881644	+	0.471916i	$0.156437\pi$
$61$			7.37156i			0.943832i	−0.881644	+	0.471916i	$0.843563\pi$
$62$	0.745044	−	0.745044i	0.0946207	−	0.0946207i
$63$	−5.14019	+	6.04801i	−0.647603	+	0.761978i
$64$			7.43929i			0.929912i
$65$	−5.45724	−	4.15320i	−0.676887	−	0.515141i
$66$	0.298701	−	0.411968i	0.0367675	−	0.0507097i
$67$	1.16531	+	1.16531i	0.142365	+	0.142365i	0.774697	−	0.632332i	$-0.217902\pi$
$67$	1.16531	+	1.16531i	0.142365	+	0.142365i	−0.632332	+	0.774697i	$0.717902\pi$
$68$	−12.9810	+	3.47824i	−1.57417	+	0.421798i
$69$	0.784308	−	7.53257i	0.0944195	−	0.906815i
$70$	−0.373303	−	0.828517i	−0.0446183	−	0.0990267i
$71$	−10.9017			−1.29380			−0.646899	−	0.762576i	$-0.723934\pi$
$71$	−10.9017			−1.29380			−0.646899	+	0.762576i	$0.723934\pi$
$72$	−1.82967	+	0.0994542i	−0.215629	+	0.0117208i
$73$	11.1248	−	2.98088i	1.30206	−	0.348885i	0.459829	−	0.888007i	$-0.347911\pi$
$73$	11.1248	−	2.98088i	1.30206	−	0.348885i	0.842228	+	0.539122i	$0.181244\pi$
$74$	1.18865	−	0.686270i	0.138178	−	0.0797773i
$75$	−3.59275	−	7.87986i	−0.414855	−	0.909887i
$76$	7.81213	−	4.51033i	0.896112	−	0.517371i
$77$	−4.31343	+	2.64613i	−0.491561	+	0.301554i
$78$	−0.805787	+	0.128427i	−0.0912375	+	0.0145415i
$79$			0.207278i			0.0233205i	0.999932	+	0.0116603i	$0.00371166\pi$
$79$			0.207278i			0.0233205i	−0.999932	+	0.0116603i	$0.996288\pi$
$80$	−3.27051	+	7.98516i	−0.365655	+	0.892768i
$81$	0.975531	+	8.94697i	0.108392	+	0.994108i
$82$	0.529618	+	0.141911i	0.0584865	+	0.0156714i
$83$	−2.04964	+	0.549200i	−0.224978	+	0.0602826i	−0.369547	−	0.929212i	$-0.620487\pi$
$83$	−2.04964	+	0.549200i	−0.224978	+	0.0602826i	0.144569	+	0.989495i	$0.453820\pi$
$84$	8.54191	+	3.01090i	0.931999	+	0.328516i
$85$	−15.0822	−	1.92477i	−1.63589	−	0.208771i
$86$	0.0747917	−	0.129543i	0.00806499	−	0.0139690i
$87$	1.89636	+	2.33716i	0.203311	+	0.250570i
$88$	−1.12843	−	0.302361i	−0.120291	−	0.0322318i
$89$	1.64396	+	2.84742i	0.174259	+	0.301826i	0.939905	−	0.341437i	$-0.110914\pi$
$89$	1.64396	+	2.84742i	0.174259	+	0.301826i	−0.765645	+	0.643263i	$0.777580\pi$
$90$	−0.973319	−	0.338211i	−0.102597	−	0.0356505i
$91$	7.89106	+	1.89046i	0.827208	+	0.198174i
$92$	−8.34726	+	2.23664i	−0.870262	+	0.233186i
$93$	−4.24702	+	11.0961i	−0.440395	+	1.15061i
$94$	1.59905			0.164930
$95$	10.1131	−	1.37225i	1.03759	−	0.140790i
$96$	1.28097	+	2.86960i	0.130738	+	0.292877i
$97$	−0.820966	−	3.06389i	−0.0833565	−	0.311091i	0.911641	−	0.410987i	$-0.134816\pi$
$97$	−0.820966	−	3.06389i	−0.0833565	−	0.311091i	−0.994998	+	0.0998959i	$0.968149\pi$
$98$	0.799741	+	0.718699i	0.0807860	+	0.0725995i
$99$	−1.18208	+	5.61488i	−0.118804	+	0.564317i
$100$	−6.93200	+	7.04287i	−0.693200	+	0.704287i
$101$	10.6485	−	6.14793i	1.05957	−	0.611742i	0.134255	−	0.990947i	$-0.457136\pi$
$101$	10.6485	−	6.14793i	1.05957	−	0.611742i	0.925313	+	0.379205i	$0.123802\pi$
$102$	−1.40479	+	1.13983i	−0.139095	+	0.112860i
$103$	−6.78670	+	1.81849i	−0.668713	+	0.179181i	−0.577175	−	0.816620i	$-0.695845\pi$
$103$	−6.78670	+	1.81849i	−0.668713	+	0.179181i	−0.0915380	+	0.995802i	$0.529178\pi$
$104$	0.936629	+	1.62229i	0.0918441	+	0.159079i
$105$	7.65201	+	6.81518i	0.746760	+	0.665094i
$106$	−0.797733	+	1.38171i	−0.0774827	+	0.134204i
$107$	−0.484595	+	1.80853i	−0.0468475	+	0.174837i	−0.985386	−	0.170338i	$-0.945514\pi$
$107$	−0.484595	+	1.80853i	−0.0468475	+	0.174837i	0.938538	+	0.345176i	$0.112181\pi$
$108$	9.13675	−	4.68900i	0.879184	−	0.451199i
$109$	−6.53465	−	3.77278i	−0.625906	−	0.361367i	0.153259	−	0.988186i	$-0.451023\pi$
$109$	−6.53465	−	3.77278i	−0.625906	−	0.361367i	−0.779165	+	0.626819i	$0.784356\pi$
$110$	−0.522765	−	0.397847i	−0.0498437	−	0.0379332i
$111$	−9.08491	+	12.5299i	−0.862302	+	1.18928i
$112$	−0.272173	−	10.2063i	−0.0257179	−	0.964405i
$113$	2.07283	+	0.555414i	0.194996	+	0.0522489i	0.354995	−	0.934868i	$-0.384483\pi$
$113$	2.07283	+	0.555414i	0.194996	+	0.0522489i	−0.159999	+	0.987117i	$0.551149\pi$
$114$	0.712792	−	0.983081i	0.0667591	−	0.0920739i
$115$	−9.69842	−	1.23770i	−0.904383	−	0.115417i
$116$	1.71717	−	2.97422i	0.159435	−	0.276150i
$117$	7.70670	−	5.02610i	0.712485	−	0.464663i
$118$	−0.754532	−	0.754532i	−0.0694603	−	0.0694603i
$119$	17.2469	−	5.11779i	1.58102	−	0.469147i
$120$	0.0736006	+	2.36444i	0.00671879	+	0.215843i
$121$	3.67088	−	6.35815i	0.333716	−	0.578013i
$122$	0.800657	−	0.800657i	0.0724881	−	0.0724881i
$123$	−6.10563	+	0.973118i	−0.550526	+	0.0877431i
$124$	13.5572			1.21748
$125$	−10.2776	+	4.40114i	−0.919260	+	0.393650i
$126$	1.21520	−	0.0986025i	0.108259	−	0.00878421i
$127$	−13.4085	−	13.4085i	−1.18981	−	1.18981i	−0.977120	−	0.212691i	$-0.931777\pi$
$127$	−13.4085	−	13.4085i	−1.18981	−	1.18981i	−0.212691	−	0.977120i	$-0.568223\pi$
$128$	3.37388	−	3.37388i	0.298211	−	0.298211i
$129$	−0.174680	+	1.67765i	−0.0153797	+	0.147708i
$130$	0.141638	+	1.04383i	0.0124224	+	0.0915501i
$131$	8.94868	+	5.16652i	0.781850	+	0.451401i	0.837085	−	0.547072i	$-0.184258\pi$
$131$	8.94868	+	5.16652i	0.781850	+	0.451401i	−0.0552358	+	0.998473i	$0.517591\pi$
$132$	6.46586	−	1.03053i	0.562781	−	0.0896962i
$133$	−10.2932	+	6.31448i	−0.892531	+	0.547534i
$134$		−	0.253139i		−	0.0218679i
$135$	11.5766	−	0.991295i	0.996354	−	0.0853171i
$136$	3.59675	+	2.07659i	0.308419	+	0.178066i
$137$	−0.833390	+	3.11025i	−0.0712013	+	0.265727i	−0.992345	−	0.123495i	$-0.960590\pi$
$137$	−0.833390	+	3.11025i	−0.0712013	+	0.265727i	0.921144	+	0.389222i	$0.127256\pi$
$138$	−0.903332	+	0.732958i	−0.0768968	+	0.0623936i
$139$	2.18364	+	3.78218i	0.185214	+	0.320800i	0.943649	−	0.330949i	$-0.107369\pi$
$139$	2.18364	+	3.78218i	0.185214	+	0.320800i	−0.758435	+	0.651749i	$0.774035\pi$
$140$	4.14165	−	10.9345i	0.350034	−	0.924133i
$141$	−16.4650	+	7.34988i	−1.38661	+	0.618972i
$142$	1.18408	+	1.18408i	0.0993661	+	0.0993661i
$143$	5.66611	−	1.51823i	0.473824	−	0.126961i
$144$	−8.61840	−	7.72978i	−0.718200	−	0.644148i
$145$	3.07320	−	2.37758i	0.255216	−	0.197447i
$146$	−1.53208	−	0.884545i	−0.126796	−	0.0732054i
$147$	−11.5382	−	3.72433i	−0.951652	−	0.307178i
$148$	17.0586	+	4.57083i	1.40221	+	0.375720i
$149$	−8.13293	−	4.69555i	−0.666275	−	0.384674i	0.128389	−	0.991724i	$-0.459020\pi$
$149$	−8.13293	−	4.69555i	−0.666275	−	0.384674i	−0.794664	+	0.607050i	$0.792353\pi$
$150$	−0.465641	+	1.24609i	−0.0380194	+	0.101743i
$151$	−7.27604	−	12.6025i	−0.592116	−	1.02558i	−0.993947	−	0.109861i	$-0.964959\pi$
$151$	−7.27604	−	12.6025i	−0.592116	−	1.02558i	0.401831	−	0.915714i	$-0.368374\pi$
$152$	−2.69277	−	0.721525i	−0.218412	−	0.0585234i
$153$	9.22561	−	18.1936i	0.745846	−	1.47086i
$154$	0.755908	+	0.181093i	0.0609128	+	0.0145929i
$155$	14.1940	+	5.81349i	1.14009	+	0.466951i
$156$	−8.49974	−	6.16281i	−0.680524	−	0.493420i
$157$	15.2400	−	15.2400i	1.21628	−	1.21628i	0.247359	−	0.968924i	$-0.420437\pi$
$157$	15.2400	−	15.2400i	1.21628	−	1.21628i	0.968924	−	0.247359i	$-0.0795628\pi$
$158$	0.0225133	−	0.0225133i	0.00179106	−	0.00179106i
$159$	1.86315	−	17.8939i	0.147757	−	1.41908i
$160$	3.74198	−	1.56740i	0.295829	−	0.123914i
$161$	11.0904	−	3.29094i	0.874048	−	0.259362i
$162$	0.865813	−	1.07773i	0.0680247	−	0.0846742i
$163$	−9.27730	−	2.48584i	−0.726654	−	0.194706i	−0.123515	−	0.992343i	$-0.539417\pi$
$163$	−9.27730	−	2.48584i	−0.726654	−	0.194706i	−0.603139	+	0.797636i	$0.706083\pi$
$164$	3.52747	+	6.10975i	0.275449	+	0.477092i
$165$	7.21145	+	1.69370i	0.561411	+	0.131854i
$166$	0.282272	+	0.162970i	0.0219085	+	0.0126489i
$167$	3.89068	+	1.04250i	0.301070	+	0.0806714i	0.406191	−	0.913788i	$-0.366857\pi$
$167$	3.89068	+	1.04250i	0.301070	+	0.0806714i	−0.105122	+	0.994459i	$0.533523\pi$
$168$	−1.20867	−	2.52458i	−0.0932507	−	0.194776i
$169$	3.11241	+	1.79695i	0.239416	+	0.138227i
$170$	1.42908	+	1.84720i	0.109606	+	0.141674i
$171$	−2.82081	+	13.3988i	−0.215713	+	1.02463i
$172$	1.85909	−	0.498142i	0.141754	−	0.0379830i
$173$	−8.98375	−	8.98375i	−0.683022	−	0.683022i	0.277658	−	0.960680i	$-0.410442\pi$
$173$	−8.98375	−	8.98375i	−0.683022	−	0.683022i	−0.960680	+	0.277658i	$0.910442\pi$
$174$	0.0478775	−	0.459820i	0.00362958	−	0.0348589i
$175$	9.02501	−	9.67208i	0.682227	−	0.731141i
$176$	−3.69046	−	6.39206i	−0.278179	−	0.481820i
$177$	11.2374	+	4.30110i	0.844652	+	0.323290i
$178$	0.130713	−	0.487829i	0.00979737	−	0.0365643i
$179$	−8.52692	−	4.92302i	−0.637332	−	0.367964i	0.146254	−	0.989247i	$-0.453278\pi$
$179$	−8.52692	−	4.92302i	−0.637332	−	0.367964i	−0.783586	+	0.621283i	$0.786612\pi$
$180$	−5.77839	−	11.9327i	−0.430696	−	0.889408i
$181$			10.0475i			0.746822i	0.927666	+	0.373411i	$0.121812\pi$
$181$			10.0475i			0.746822i	−0.927666	+	0.373411i	$0.878188\pi$
$182$	−0.651751	−	1.06241i	−0.0483110	−	0.0787514i
$183$	−4.56403	+	11.9243i	−0.337383	+	0.881471i
$184$	2.31285	+	1.33533i	0.170506	+	0.0984415i
$185$	15.8998	+	12.1004i	1.16897	+	0.889641i
$186$	1.66648	−	0.743905i	0.122192	−	0.0545458i
$187$	9.19620	−	9.19620i	0.672493	−	0.672493i
$188$	14.5486	+	14.5486i	1.06107	+	1.06107i
$189$	−12.0594	+	6.60083i	−0.877192	+	0.480140i
$190$	−1.24748	−	0.949385i	−0.0905015	−	0.0688756i
$191$	10.2829			0.744042			0.372021	−	0.928224i	$-0.378665\pi$
$191$	10.2829			0.744042			0.372021	+	0.928224i	$0.378665\pi$
$192$	−4.60597	+	12.0339i	−0.332407	+	0.868471i
$193$	10.0039	−	10.0039i	0.720096	−	0.720096i	−0.248529	−	0.968625i	$-0.579947\pi$
$193$	10.0039	−	10.0039i	0.720096	−	0.720096i	0.968625	+	0.248529i	$0.0799470\pi$
$194$	−0.243613	+	0.421951i	−0.0174904	+	0.0302943i
$195$	−6.25628	−	10.0971i	−0.448021	−	0.723065i
$196$	0.737346	+	13.8152i	0.0526676	+	0.986798i
$197$	15.6301	+	15.6301i	1.11360	+	1.11360i	0.992660	+	0.120935i	$0.0385894\pi$
$197$	15.6301	+	15.6301i	1.11360	+	1.11360i	0.120935	+	0.992660i	$0.461411\pi$
$198$	0.738248	−	0.481466i	0.0524650	−	0.0342163i
$199$	11.2055	−	19.4086i	0.794340	−	1.37584i	−0.128917	−	0.991655i	$-0.541150\pi$
$199$	11.2055	−	19.4086i	0.794340	−	1.37584i	0.923257	−	0.384182i	$-0.125517\pi$
$200$	3.05386	−	0.0242279i	0.215941	−	0.00171317i
$201$	1.16353	+	2.60651i	0.0820690	+	0.183849i
$202$	−1.82434	−	0.488829i	−0.128360	−	0.0343939i
$203$	−2.19176	+	4.04136i	−0.153832	+	0.283648i
$204$	−23.1517	−	2.41060i	−1.62094	−	0.168776i
$205$	1.07322	+	7.90934i	0.0749569	+	0.552412i
$206$	0.934646	+	0.539618i	0.0651199	+	0.0375970i
$207$	5.93242	−	11.6992i	0.412332	−	0.813149i
$208$	−3.06320	+	11.4320i	−0.212395	+	0.792667i
$209$	−4.36485	+	7.56014i	−0.301923	+	0.522946i
$210$	−0.0908917	−	1.57134i	−0.00627213	−	0.108433i
$211$	−1.86129	−	3.22385i	−0.128137	−	0.221939i	0.794818	−	0.606848i	$-0.207566\pi$
$211$	−1.86129	−	3.22385i	−0.128137	−	0.221939i	−0.922955	+	0.384909i	$0.874233\pi$
$212$	−19.8292	+	5.31322i	−1.36188	+	0.364914i
$213$	−17.6348	−	6.74970i	−1.20831	−	0.462482i
$214$	0.249066	−	0.143799i	0.0170258	−	0.00982987i
$215$	2.16002	+	0.275660i	0.147312	+	0.0187999i
$216$	−3.02128	−	0.971946i	−0.205572	−	0.0661326i
$217$	−18.1422	+	0.483800i	−1.23157	+	0.0328425i
$218$	0.299978	+	1.11953i	0.0203171	+	0.0758245i
$219$	19.8411	+	2.06590i	1.34074	+	0.139601i
$220$	−1.13654	−	8.37598i	−0.0766254	−	0.564709i
$221$	−20.8541			−1.40280
$222$	2.34768	−	0.374174i	0.157566	−	0.0251129i
$223$	−1.64920	+	0.441902i	−0.110439	+	0.0295919i	−0.313615	−	0.949550i	$-0.601540\pi$
$223$	−1.64920	+	0.441902i	−0.110439	+	0.0295919i	0.203176	+	0.979142i	$0.434873\pi$
$224$	−3.30263	+	3.48360i	−0.220666	+	0.232757i
$225$	−0.932940	−	14.9710i	−0.0621960	−	0.998064i
$226$	−0.164813	−	0.285465i	−0.0109632	−	0.0189889i
$227$	2.37815	+	0.637222i	0.157843	+	0.0422939i	0.336875	−	0.941549i	$-0.390630\pi$
$227$	2.37815	+	0.637222i	0.157843	+	0.0422939i	−0.179032	+	0.983843i	$0.557297\pi$
$228$	15.4295	−	2.45916i	1.02184	−	0.162862i
$229$	−8.54548	+	14.8012i	−0.564701	+	0.978091i	0.432376	+	0.901693i	$0.357675\pi$
$229$	−8.54548	+	14.8012i	−0.564701	+	0.978091i	−0.997077	+	0.0763978i	$0.975658\pi$
$230$	0.918955	+	1.18782i	0.0605941	+	0.0783225i
$231$	−8.61578	+	1.60979i	−0.566877	+	0.105916i
$232$	−1.02519	+	0.274698i	−0.0673069	+	0.0180348i
$233$	−4.40714	−	1.18089i	−0.288721	−	0.0773626i	0.111552	−	0.993759i	$-0.464418\pi$
$233$	−4.40714	−	1.18089i	−0.288721	−	0.0773626i	−0.400273	+	0.916396i	$0.631085\pi$
$234$	−1.38296	−	0.291151i	−0.0904072	−	0.0190331i
$235$	8.99333	+	21.4705i	0.586660	+	1.40058i
$236$		−	13.7299i		−	0.893739i
$237$	−0.128334	+	0.335294i	−0.00833618	+	0.0217797i
$238$	−2.42913	−	1.31740i	−0.157457	−	0.0853941i
$239$	3.24647	−	1.87435i	0.209997	−	0.121242i	−0.391313	−	0.920258i	$-0.627979\pi$
$239$	3.24647	−	1.87435i	0.209997	−	0.121242i	0.601310	+	0.799016i	$0.294646\pi$
$240$	−10.2344	+	10.8920i	−0.660625	+	0.703074i
$241$	2.42873	−	1.40223i	0.156448	−	0.0903254i	−0.419732	−	0.907648i	$-0.637876\pi$
$241$	2.42873	−	1.40223i	0.156448	−	0.0903254i	0.576180	+	0.817323i	$0.304543\pi$
$242$	−1.08930	+	0.291876i	−0.0700226	+	0.0187625i
$243$	−3.96140	+	15.0767i	−0.254124	+	0.967172i
$244$	14.5692			0.932697
$245$	−5.15212	+	14.7802i	−0.329157	+	0.944275i
$246$	0.768853	+	0.557464i	0.0490203	+	0.0355426i
$247$	13.5211	−	3.62296i	0.860325	−	0.230523i
$248$	−2.96260	−	2.96260i	−0.188125	−	0.188125i
$249$	−3.65556	−	0.380625i	−0.231662	−	0.0241211i
$250$	1.59433	+	0.638272i	0.100834	+	0.0403679i
$251$		−	9.45065i		−	0.596520i	−0.954485	−	0.298260i	$-0.903594\pi$
$251$		−	9.45065i		−	0.596520i	0.954485	−	0.298260i	$-0.0964062\pi$
$252$	11.9533	+	10.1591i	0.752989	+	0.639963i
$253$	5.91351	−	5.91351i	0.371779	−	0.371779i
$254$			2.91271i			0.182759i
$255$	−23.2054	−	12.4515i	−1.45318	−	0.779744i
$256$	14.1457			0.884105
$257$	4.11101	+	15.3425i	0.256438	+	0.957039i	0.967285	+	0.253692i	$0.0816451\pi$
$257$	4.11101	+	15.3425i	0.256438	+	0.957039i	−0.710847	+	0.703346i	$0.751688\pi$
$258$	0.201189	−	0.163244i	0.0125255	−	0.0101631i
$259$	−22.9908	−	5.50790i	−1.42858	−	0.342244i
$260$	−8.20841	+	10.7857i	−0.509064	+	0.668902i
$261$	1.62054	+	4.95472i	0.100309	+	0.306690i
$262$	−0.410796	−	1.53311i	−0.0253791	−	0.0947160i
$263$	−10.7118	−	2.87022i	−0.660518	−	0.176985i	−0.0870383	−	0.996205i	$-0.527740\pi$
$263$	−10.7118	−	2.87022i	−0.660518	−	0.176985i	−0.573480	+	0.819220i	$0.694407\pi$
$264$	−1.63815	−	1.18776i	−0.100821	−	0.0731013i
$265$	−23.0389	−	2.94021i	−1.41527	−	0.180616i
$266$	1.80383	+	0.432144i	0.110600	+	0.0264964i
$267$	0.896334	+	5.62386i	0.0548547	+	0.344175i
$268$	2.30313	−	2.30313i	0.140686	−	0.140686i
$269$	−8.03142	+	13.9108i	−0.489684	+	0.848158i	−0.999930	−	0.0118710i	$-0.996221\pi$
$269$	−8.03142	+	13.9108i	−0.489684	+	0.848158i	0.510245	+	0.860029i	$0.329555\pi$
$270$	−1.36505	−	1.14971i	−0.0830744	−	0.0699694i
$271$	17.4798	−	10.0920i	1.06182	−	0.613044i	0.135887	−	0.990724i	$-0.456612\pi$
$271$	17.4798	−	10.0920i	1.06182	−	0.613044i	0.925936	+	0.377681i	$0.123278\pi$
$272$	6.79136	+	25.3457i	0.411787	+	1.53681i
$273$	11.5942	+	7.94371i	0.701713	+	0.480775i
$274$	0.428336	−	0.247300i	0.0258767	−	0.0149399i
$275$	2.40180	−	9.25676i	0.144834	−	0.558203i
$276$	−14.8874	−	1.55011i	−0.896117	−	0.0933057i
$277$	1.82359	−	6.80574i	0.109569	−	0.408917i	−0.889254	−	0.457413i	$-0.848776\pi$
$277$	1.82359	−	6.80574i	0.109569	−	0.408917i	0.998823	+	0.0484957i	$0.0154427\pi$
$278$	0.173624	−	0.647974i	0.0104133	−	0.0388629i
$279$	−13.7400	+	15.3196i	−0.822595	+	0.917162i
$280$	−3.29452	+	1.48441i	−0.196885	+	0.0887102i
$281$	11.3255	−	19.6163i	0.675622	−	1.17021i	−0.300665	−	0.953730i	$-0.597209\pi$
$281$	11.3255	−	19.6163i	0.675622	−	1.17021i	0.976287	−	0.216482i	$-0.0694581\pi$
$282$	2.58664	+	0.990037i	0.154032	+	0.0589558i
$283$	−4.34742	−	4.34742i	−0.258427	−	0.258427i	0.565987	−	0.824414i	$-0.308495\pi$
$283$	−4.34742	−	4.34742i	−0.258427	−	0.258427i	−0.824414	+	0.565987i	$0.808495\pi$
$284$			21.5462i			1.27853i
$285$	17.2087	+	4.04168i	1.01936	+	0.239408i
$286$	−0.780322	−	0.450519i	−0.0461414	−	0.0266398i
$287$	−4.93846	−	8.05014i	−0.291508	−	0.475185i
$288$	0.295426	+	5.43499i	0.0174081	+	0.320260i
$289$	−25.3185	+	14.6177i	−1.48932	+	0.859862i
$290$	−0.592033	−	0.0755547i	−0.0347654	−	0.00443673i
$291$	0.568972	−	5.46447i	0.0333537	−	0.320333i
$292$	−5.89142	−	21.9871i	−0.344769	−	1.28670i
$293$	7.33056	−	27.3580i	0.428256	−	1.59827i	−0.328452	−	0.944521i	$-0.606527\pi$
$293$	7.33056	−	27.3580i	0.428256	−	1.59827i	0.756708	−	0.653753i	$-0.226806\pi$
$294$	0.848695	+	1.65773i	0.0494969	+	0.0966806i
$295$	5.88752	−	14.3747i	0.342785	−	0.836930i
$296$	−2.72889	−	4.72657i	−0.158613	−	0.274726i
$297$	−5.38855	+	8.35082i	−0.312675	+	0.484564i
$298$	0.373349	+	1.39336i	0.0216275	+	0.0807149i
$299$	−13.4100			−0.775521
$300$	−15.5738	+	7.10074i	−0.899153	+	0.409961i
$301$	−2.47005	+	0.732953i	−0.142371	+	0.0422467i
$302$	−0.578527	+	2.15909i	−0.0332905	+	0.124242i
$303$	21.0316	−	3.35203i	1.20823	−	0.192569i
$304$	−8.80656	−	15.2534i	−0.505091	−	0.874843i
$305$	15.2535	+	6.24743i	0.873413	+	0.357727i
$306$	−2.97812	+	0.974050i	−0.170248	+	0.0556827i
$307$	22.9955	−	22.9955i	1.31242	−	1.31242i	0.392800	−	0.919624i	$-0.371506\pi$
$307$	22.9955	−	22.9955i	1.31242	−	1.31242i	0.919624	−	0.392800i	$-0.128494\pi$
$308$	5.22983	+	8.52510i	0.297997	+	0.485762i
$309$	−12.1041	−	1.26031i	−0.688580	−	0.0716964i
$310$	−0.910244	−	2.17310i	−0.0516984	−	0.123424i
$311$			7.94940i			0.450769i	0.974270	+	0.225385i	$0.0723639\pi$
$311$			7.94940i			0.450769i	−0.974270	+	0.225385i	$0.927636\pi$
$312$	0.510677	+	3.20414i	0.0289114	+	0.181399i
$313$	11.4256	+	11.4256i	0.645815	+	0.645815i	0.951979	−	0.306164i	$-0.0990455\pi$
$313$	11.4256	+	11.4256i	0.645815	+	0.645815i	−0.306164	+	0.951979i	$0.599045\pi$
$314$	−3.31056			−0.186826
$315$	8.15842	+	15.7620i	0.459675	+	0.888087i
$316$	0.409665			0.0230454
$317$	−24.6167	−	24.6167i	−1.38261	−	1.38261i	−0.839952	−	0.542660i	$-0.817417\pi$
$317$	−24.6167	−	24.6167i	−1.38261	−	1.38261i	−0.542660	−	0.839952i	$-0.682583\pi$
$318$	−2.14590	+	1.74117i	−0.120336	+	0.0976399i
$319$			3.32356i			0.186083i
$320$	15.3937	+	6.30484i	0.860531	+	0.352451i
$321$	−1.90362	+	2.62547i	−0.106250	+	0.146539i
$322$	−1.56202	−	0.847137i	−0.0870481	−	0.0472091i
$323$	21.9449	−	21.9449i	1.22105	−	1.22105i
$324$	17.6829	−	1.92804i	0.982381	−	0.107114i
$325$	−13.2190	+	7.77246i	−0.733257	+	0.431138i
$326$	0.737649	+	1.27765i	0.0408546	+	0.0707622i
$327$	−8.23464	−	10.1488i	−0.455377	−	0.561228i
$328$	0.564295	−	2.10598i	0.0311580	−	0.116283i
$329$	−19.9880	−	18.9497i	−1.10197	−	1.04473i
$330$	−0.599307	−	0.967227i	−0.0329908	−	0.0532441i
$331$	−16.3506			−0.898711			−0.449356	−	0.893353i	$-0.648346\pi$
$331$	−16.3506			−0.898711			−0.449356	+	0.893353i	$0.648346\pi$
$332$	1.08544	+	4.05093i	0.0595714	+	0.222324i
$333$	−22.4536	+	14.6437i	−1.23045	+	0.802467i
$334$	−0.309352	−	0.535814i	−0.0169270	−	0.0293184i
$335$	3.39891	−	1.42370i	0.185702	−	0.0777849i
$336$	5.87886	−	16.6783i	0.320718	−	0.909878i
$337$	−4.87086	+	18.1783i	−0.265333	+	0.990235i	0.696714	+	0.717349i	$0.254645\pi$
$337$	−4.87086	+	18.1783i	−0.265333	+	0.990235i	−0.962046	+	0.272886i	$0.912022\pi$
$338$	−0.142878	−	0.533226i	−0.00777152	−	0.0290037i
$339$	3.00916	+	2.18182i	0.163435	+	0.118500i
$340$	−3.80413	+	29.8085i	−0.206308	+	1.61659i
$341$	−11.3622	+	6.55996i	−0.615297	+	0.355242i
$342$	1.76168	−	1.14892i	0.0952610	−	0.0621267i
$343$	−1.47972	−	18.4611i	−0.0798972	−	0.996803i
$344$	−0.515115	−	0.297402i	−0.0277732	−	0.0160348i
$345$	−14.9220	−	8.00681i	−0.803371	−	0.431072i
$346$			1.95153i			0.104915i
$347$	−8.47547	−	8.47547i	−0.454987	−	0.454987i	0.442019	−	0.897006i	$-0.354262\pi$
$347$	−8.47547	−	8.47547i	−0.454987	−	0.454987i	−0.897006	+	0.442019i	$0.854262\pi$
$348$	4.61917	−	3.74797i	0.247614	−	0.200912i
$349$	−12.3834	+	21.4487i	−0.662868	+	1.14812i	0.316991	+	0.948429i	$0.397328\pi$
$349$	−12.3834	+	21.4487i	−0.662868	+	1.14812i	−0.979859	+	0.199692i	$0.936006\pi$
$350$	−2.03077	+	0.0702809i	−0.108549	+	0.00375667i
$351$	15.5783	−	3.35875i	0.831508	−	0.179277i
$352$	−0.898154	+	3.35196i	−0.0478718	+	0.178660i
$353$	−7.57335	+	28.2641i	−0.403089	+	1.50435i	0.404464	+	0.914554i	$0.367458\pi$
$353$	−7.57335	+	28.2641i	−0.403089	+	1.50435i	−0.807553	+	0.589795i	$0.799209\pi$
$354$	−0.753378	−	1.68770i	−0.0400416	−	0.0897002i
$355$	−9.23927	+	22.5582i	−0.490369	+	1.19727i
$356$	5.62766	−	3.24913i	0.298266	−	0.172204i
$357$	31.0674	+	2.39966i	1.64426	+	0.127004i
$358$	0.391435	+	1.46086i	0.0206880	+	0.0772087i
$359$	16.3870	−	9.46105i	0.864874	−	0.499335i	−0.000767748	−	1.00000i	$-0.500244\pi$
$359$	16.3870	−	9.46105i	0.864874	−	0.499335i	0.865641	+	0.500665i	$0.166911\pi$
$360$	−1.34486	+	3.87031i	−0.0708805	+	0.203983i
$361$	−0.915859	+	1.58632i	−0.0482031	+	0.0834903i
$362$	1.09130	−	1.09130i	0.0573574	−	0.0573574i
$363$	9.87464	−	8.01222i	0.518284	−	0.420532i
$364$	3.73632	−	15.5959i	0.195837	−	0.817449i
$365$	3.26017	−	25.5461i	0.170645	−	1.33714i
$366$	1.79087	−	0.799433i	0.0936103	−	0.0417870i
$367$	5.07991	+	1.36116i	0.265169	+	0.0710518i	0.388954	−	0.921257i	$-0.372837\pi$
$367$	5.07991	+	1.36116i	0.265169	+	0.0710518i	−0.123785	+	0.992309i	$0.539503\pi$
$368$	4.36711	+	16.2983i	0.227651	+	0.849607i
$369$	−10.4790	−	2.20612i	−0.545517	−	0.114846i
$370$	−0.412664	−	3.04122i	−0.0214534	−	0.158106i
$371$	26.3457	−	7.81773i	1.36780	−	0.405877i
$372$	21.9303	+	8.39383i	1.13703	+	0.435200i
$373$	0.969769	+	3.61923i	0.0502128	+	0.187397i	0.986477	−	0.163900i	$-0.0524075\pi$
$373$	0.969769	+	3.61923i	0.0502128	+	0.187397i	−0.936264	+	0.351297i	$0.885741\pi$
$374$	−1.99768			−0.103297
$375$	−19.3502	+	0.756036i	−0.999238	+	0.0390415i
$376$		−	6.35848i		−	0.327913i
$377$	3.76840	−	3.76840i	0.194082	−	0.194082i
$378$	2.02677	+	0.592878i	0.104246	+	0.0304944i
$379$			0.408667i			0.0209918i	0.999945	+	0.0104959i	$0.00334101\pi$
$379$			0.408667i			0.0209918i	−0.999945	+	0.0104959i	$0.996659\pi$
$380$	−2.71213	−	19.9877i	−0.139129	−	1.02535i
$381$	−13.3880	−	29.9914i	−0.685887	−	1.53651i
$382$	−1.11687	−	1.11687i	−0.0571439	−	0.0571439i
$383$	−19.8430	+	5.31692i	−1.01393	+	0.271682i	−0.727271	−	0.686351i	$-0.759211\pi$
$383$	−19.8430	+	5.31692i	−1.01393	+	0.271682i	−0.286659	+	0.958033i	$0.592545\pi$
$384$	7.54652	−	3.36872i	0.385107	−	0.171909i
$385$	1.81981	+	11.1681i	0.0927461	+	0.569180i
$386$	−2.17313			−0.110609
$387$	−1.32126	+	2.60563i	−0.0671635	+	0.132451i
$388$	−6.05548	+	1.62256i	−0.307421	+	0.0823731i
$389$	8.23201	−	4.75275i	0.417379	−	0.240974i	−0.276576	−	0.960992i	$-0.589200\pi$
$389$	8.23201	−	4.75275i	0.417379	−	0.240974i	0.693956	+	0.720018i	$0.255866\pi$
$390$	−0.417164	+	1.77621i	−0.0211239	+	0.0899417i
$391$	−25.7479	+	14.8656i	−1.30213	+	0.751783i
$392$	2.85784	−	3.18009i	0.144343	−	0.160619i
$393$	11.2767	+	13.8979i	0.568833	+	0.701057i
$394$		−	3.39530i		−	0.171053i
$395$	0.428906	+	0.175669i	0.0215806	+	0.00883885i
$396$	11.0973	+	2.33627i	0.557660	+	0.117402i
$397$	−3.08129	−	0.825628i	−0.154645	−	0.0414371i	0.180666	−	0.983545i	$-0.442175\pi$
$397$	−3.08129	−	0.825628i	−0.154645	−	0.0414371i	−0.335311	+	0.942107i	$0.608841\pi$
$398$	−3.32513	+	0.890967i	−0.166674	+	0.0446601i
$399$	−20.5599	+	3.84145i	−1.02928	+	0.192313i
$400$	13.7514	+	13.5349i	0.687570	+	0.676746i
$401$	−6.74544	+	11.6834i	−0.336851	+	0.583444i	−0.983839	−	0.179057i	$-0.942695\pi$
$401$	−6.74544	+	11.6834i	−0.336851	+	0.583444i	0.646987	+	0.762501i	$0.276029\pi$
$402$	0.156729	−	0.409481i	0.00781691	−	0.0204230i
$403$	20.3209	+	5.44498i	1.01226	+	0.271234i
$404$	−12.1508	−	21.0458i	−0.604525	−	1.04707i
$405$	19.3402	+	5.56400i	0.961020	+	0.276477i
$406$	0.677007	−	0.200893i	0.0335993	−	0.00997014i
$407$	−16.5083	+	4.42339i	−0.818287	+	0.219259i
$408$	4.53245	+	5.58600i	0.224390	+	0.276548i
$409$	−6.98337			−0.345305			−0.172653	−	0.984983i	$-0.555234\pi$
$409$	−6.98337			−0.345305			−0.172653	+	0.984983i	$0.555234\pi$
$410$	0.742501	−	0.975635i	0.0366695	−	0.0481832i
$411$	−3.27379	+	4.51520i	−0.161484	+	0.222718i
$412$	3.59407	+	13.4133i	0.177067	+	0.660824i
$413$	0.489961	+	18.3732i	0.0241094	+	0.904086i
$414$	−1.91504	+	0.626352i	−0.0941193	+	0.0307835i
$415$	−0.600658	+	4.70665i	−0.0294851	+	0.231040i
$416$	4.81897	−	2.78223i	0.236269	−	0.136410i
$417$	1.19058	+	7.47008i	0.0583031	+	0.365811i
$418$	1.29522	−	0.347054i	0.0633515	−	0.0169750i
$419$	14.9549	+	25.9027i	0.730596	+	1.26543i	0.956629	+	0.291310i	$0.0940911\pi$
$419$	14.9549	+	25.9027i	0.730596	+	1.26543i	−0.226032	+	0.974120i	$0.572576\pi$
$420$	13.4696	−	15.1235i	0.657248	−	0.737950i
$421$	15.8660	−	27.4807i	0.773260	−	1.33932i	−0.162508	−	0.986707i	$-0.551958\pi$
$421$	15.8660	−	27.4807i	0.773260	−	1.33932i	0.935767	−	0.352618i	$-0.114708\pi$
$422$	−0.147994	+	0.552320i	−0.00720421	+	0.0268865i
$423$	−31.1846	+	1.69508i	−1.51625	+	0.0824177i
$424$	5.49426	+	3.17211i	0.266825	+	0.154051i
$425$	−16.7650	+	29.5773i	−0.813223	+	1.43471i
$426$	1.18227	+	2.64850i	0.0572813	+	0.128320i
$427$	−19.4964	+	0.519912i	−0.943496	+	0.0251603i
$428$	3.57439	+	0.957756i	0.172775	+	0.0462949i
$429$	10.1056	+	1.05221i	0.487901	+	0.0508013i
$430$	−0.204669	−	0.264550i	−0.00987000	−	0.0127577i
$431$	−8.81035	+	15.2600i	−0.424380	+	0.735047i	−0.996362	−	0.0852186i	$-0.972841\pi$
$431$	−8.81035	+	15.2600i	−0.424380	+	0.735047i	0.571983	+	0.820266i	$0.306174\pi$
$432$	−9.15541	−	17.8398i	−0.440490	−	0.858317i
$433$	7.06087	+	7.06087i	0.339324	+	0.339324i	0.856113	−	0.516789i	$-0.172873\pi$
$433$	7.06087	+	7.06087i	0.339324	+	0.339324i	−0.516789	+	0.856113i	$0.672873\pi$
$434$	2.02305	+	1.91795i	0.0971095	+	0.0920647i
$435$	6.44330	−	1.94325i	0.308933	−	0.0931719i
$436$	−7.45655	+	12.9151i	−0.357104	+	0.618522i
$437$	14.1115	−	14.1115i	0.675042	−	0.675042i
$438$	−1.93065	−	2.37942i	−0.0922499	−	0.113693i
$439$	22.4377			1.07089			0.535446	−	0.844570i	$-0.320144\pi$
$439$	22.4377			1.07089			0.535446	+	0.844570i	$0.320144\pi$
$440$	−1.58200	+	2.07873i	−0.0754190	+	0.0990994i
$441$	−16.3584	−	13.1683i	−0.778971	−	0.627060i
$442$	2.26506	+	2.26506i	0.107738	+	0.107738i
$443$	6.78540	−	6.78540i	0.322384	−	0.322384i	−0.527297	−	0.849681i	$-0.676795\pi$
$443$	6.78540	−	6.78540i	0.322384	−	0.322384i	0.849681	+	0.527297i	$0.176795\pi$
$444$	24.7642	+	17.9555i	1.17525	+	0.852129i
$445$	7.28525	−	0.988536i	0.345354	−	0.0468611i
$446$	0.227124	+	0.131130i	0.0107546	+	0.00620918i
$447$	−10.2487	−	12.6310i	−0.484747	−	0.597425i
$448$	−19.6755	+	0.524690i	−0.929581	+	0.0247893i
$449$		−	23.7455i		−	1.12062i	−0.828284	−	0.560309i	$-0.810683\pi$
$449$		−	23.7455i		−	1.12062i	0.828284	−	0.560309i	$-0.189317\pi$
$450$	−1.52473	+	1.72739i	−0.0718765	+	0.0814300i
$451$	−5.91267	−	3.41368i	−0.278417	−	0.160744i
$452$	1.09772	−	4.09676i	0.0516325	−	0.192695i
$453$	−3.96711	−	24.8908i	−0.186391	−	1.16947i
$454$	−0.189089	−	0.327512i	−0.00887440	−	0.0153709i
$455$	10.5995	−	14.7263i	0.496914	−	0.690379i
$456$	−3.90913	−	2.83435i	−0.183062	−	0.132731i
$457$	4.50909	+	4.50909i	0.210926	+	0.210926i	0.804661	−	0.593735i	$-0.202347\pi$
$457$	4.50909	+	4.50909i	0.210926	+	0.210926i	−0.593735	+	0.804661i	$0.702347\pi$
$458$	2.53578	−	0.679461i	0.118489	−	0.0317491i
$459$	26.1878	−	23.7182i	1.22234	−	1.10707i
$460$	−2.44621	+	19.1680i	−0.114055	+	0.893714i
$461$	−20.2839	−	11.7109i	−0.944717	−	0.545432i	−0.0532809	−	0.998580i	$-0.516968\pi$
$461$	−20.2839	−	11.7109i	−0.944717	−	0.545432i	−0.891436	+	0.453147i	$0.850301\pi$
$462$	1.11064	+	0.760952i	0.0516718	+	0.0354027i
$463$	24.2379	+	6.49451i	1.12643	+	0.301826i	0.773482	−	0.633818i	$-0.218513\pi$
$463$	24.2379	+	6.49451i	1.12643	+	0.301826i	0.352946	+	0.935644i	$0.385180\pi$
$464$	−5.80726	−	3.35282i	−0.269595	−	0.155651i
$465$	19.3610	+	18.1921i	0.897845	+	0.843636i
$466$	0.350417	+	0.606940i	0.0162327	+	0.0281159i
$467$	8.76353	+	2.34818i	0.405528	+	0.108661i	0.455816	−	0.890074i	$-0.349347\pi$
$467$	8.76353	+	2.34818i	0.405528	+	0.108661i	−0.0502885	+	0.998735i	$0.516014\pi$
$468$	−9.93362	−	15.2316i	−0.459182	−	0.704079i
$469$	−2.99984	+	3.16422i	−0.138520	+	0.146110i
$470$	1.35520	−	3.30881i	0.0625109	−	0.152624i
$471$	34.0881	−	15.2167i	1.57069	−	0.701147i
$472$	−3.00032	+	3.00032i	−0.138101	+	0.138101i
$473$	−1.31705	+	1.31705i	−0.0605581	+	0.0605581i
$474$	0.0503567	−	0.0224789i	0.00231296	−	0.00103249i
$475$	5.73142	−	22.0895i	0.262976	−	1.01353i
$476$	−10.1148	−	34.0869i	−0.463612	−	1.56237i
$477$	14.0927	−	27.7918i	0.645260	−	1.27250i
$478$	−0.556195	−	0.149032i	−0.0254397	−	0.00681656i
$479$	6.72516	+	11.6483i	0.307280	+	0.532225i	0.977766	−	0.209697i	$-0.0672477\pi$
$479$	6.72516	+	11.6483i	0.307280	+	0.532225i	−0.670486	+	0.741922i	$0.733914\pi$
$480$	7.02350	−	0.218629i	0.320578	−	0.00997898i
$481$	23.7333	+	13.7024i	1.08215	+	0.624777i
$482$	−0.416097	−	0.111493i	−0.0189527	−	0.00507836i
$483$	19.9775	+	1.54308i	0.909010	+	0.0702124i
$484$	−12.5663	−	7.25514i	−0.571194	−	0.329779i
$485$	−7.03568	−	0.897887i	−0.319474	−	0.0407710i
$486$	2.06781	−	1.20728i	0.0937979	−	0.0547634i
$487$	−3.57834	+	0.958813i	−0.162150	+	0.0434480i	−0.338981	−	0.940793i	$-0.610082\pi$
$487$	−3.57834	+	0.958813i	−0.162150	+	0.0434480i	0.176831	+	0.984241i	$0.443415\pi$
$488$	−3.18374	−	3.18374i	−0.144121	−	0.144121i
$489$	−13.4680	−	9.76508i	−0.609043	−	0.441592i
$490$	2.16494	−	1.04575i	0.0978021	−	0.0472423i
$491$	16.9041	+	29.2787i	0.762871	+	1.32133i	0.941365	+	0.337390i	$0.109544\pi$
$491$	16.9041	+	29.2787i	0.762871	+	1.32133i	−0.178494	+	0.983941i	$0.557122\pi$
$492$	1.92328	+	12.0672i	0.0867080	+	0.544031i
$493$	3.05809	−	11.4129i	0.137729	−	0.514013i
$494$	−1.86209	−	1.07508i	−0.0837793	−	0.0483700i
$495$	10.6167	+	7.20465i	0.477185	+	0.323825i
$496$		−	26.4709i		−	1.18858i
$497$	−0.768893	−	28.8330i	−0.0344896	−	1.29334i
$498$	0.355705	+	0.438387i	0.0159395	+	0.0196446i
$499$	−0.814433	−	0.470213i	−0.0364590	−	0.0210496i	0.481660	−	0.876358i	$-0.340034\pi$
$499$	−0.814433	−	0.470213i	−0.0364590	−	0.0210496i	−0.518119	+	0.855309i	$0.673367\pi$
$500$	8.69845	+	20.3128i	0.389006	+	0.908416i
$501$	5.64814	+	4.09524i	0.252341	+	0.182962i
$502$	−1.02648	+	1.02648i	−0.0458139	+	0.0458139i
$503$	−24.7219	−	24.7219i	−1.10230	−	1.10230i	−0.994133	−	0.108163i	$-0.965503\pi$
$503$	−24.7219	−	24.7219i	−1.10230	−	1.10230i	−0.108163	−	0.994133i	$-0.534497\pi$
$504$	−0.392083	−	4.83212i	−0.0174648	−	0.215240i
$505$	−3.69684	−	27.2447i	−0.164507	−	1.21237i
$506$	−1.28458			−0.0571068
$507$	3.92210	+	4.83378i	0.174187	+	0.214676i
$508$	−26.5006	+	26.5006i	−1.17577	+	1.17577i
$509$	6.77894	−	11.7415i	0.300471	−	0.520431i	−0.675772	−	0.737111i	$-0.736189\pi$
$509$	6.77894	−	11.7415i	0.300471	−	0.520431i	0.976243	+	0.216680i	$0.0695228\pi$
$510$	1.16802	+	3.87285i	0.0517210	+	0.171493i
$511$	8.66848	+	29.2127i	0.383471	+	1.29229i
$512$	−8.28418	−	8.28418i	−0.366112	−	0.366112i
$513$	−12.8587	+	19.9276i	−0.567727	+	0.879825i
$514$	1.21990	−	2.11293i	0.0538075	−	0.0931973i
$515$	−1.98887	+	15.5844i	−0.0876403	+	0.686733i
$516$	3.31571	+	0.345239i	0.145966	+	0.0151983i
$517$	−19.2327	−	5.15339i	−0.845853	−	0.226646i
$518$	1.89889	+	3.09536i	0.0834324	+	0.136002i
$519$	−8.97001	−	20.0944i	−0.393740	−	0.882047i
$520$	4.15070	−	0.563208i	0.182020	−	0.0246983i
$521$	−37.4230	−	21.6062i	−1.63953	−	0.946585i	−0.980994	−	0.194038i	$-0.937841\pi$
$521$	−37.4230	−	21.6062i	−1.63953	−	0.946585i	−0.658539	−	0.752546i	$-0.728825\pi$
$522$	0.362140	−	0.714167i	0.0158505	−	0.0312583i
$523$	1.21320	−	4.52774i	0.0530497	−	0.197984i	−0.934315	−	0.356448i	$-0.883988\pi$
$523$	1.21320	−	4.52774i	0.0530497	−	0.197984i	0.987365	+	0.158464i	$0.0506542\pi$
$524$	10.2111	−	17.6862i	0.446076	−	0.772626i
$525$	20.5873	−	10.0579i	0.898505	−	0.438963i
$526$	0.851708	+	1.47520i	0.0371363	+	0.0643219i
$527$	45.0532	−	12.0720i	1.96255	−	0.525863i
$528$	−2.01214	−	12.6248i	−0.0875673	−	0.549423i
$529$	3.36168	−	1.94087i	0.146160	−	0.0843856i
$530$	2.18301	+	2.82171i	0.0948239	+	0.122567i
$531$	15.5147	+	13.9150i	0.673281	+	0.603860i
$532$	12.4800	+	20.3435i	0.541075	+	0.882002i
$533$	2.83347	+	10.5746i	0.122731	+	0.458038i
$534$	0.513478	−	0.708187i	0.0222203	−	0.0306462i
$535$	3.33158	+	2.53548i	0.144037	+	0.109618i
$536$	−1.00658			−0.0434778
$537$	−10.7452	−	13.2429i	−0.463690	−	0.571473i
$538$	2.38324	−	0.638588i	0.102749	−	0.0275315i
$539$	−7.30274	−	11.2216i	−0.314551	−	0.483348i
$540$	−1.95920	−	22.8800i	−0.0843106	−	0.984600i
$541$	10.2759	+	17.7983i	0.441794	+	0.765209i	0.997823	−	0.0659536i	$-0.0210089\pi$
$541$	10.2759	+	17.7983i	0.441794	+	0.765209i	−0.556029	+	0.831163i	$0.687676\pi$
$542$	−2.99469	−	0.802425i	−0.128633	−	0.0344671i
$543$	−6.22079	+	16.2529i	−0.266960	+	0.697479i
$544$	6.16844	−	10.6840i	0.264470	−	0.458075i
$545$	−13.3449	+	10.3243i	−0.571634	+	0.442243i
$546$	−0.396496	−	2.12210i	−0.0169685	−	0.0908174i
$547$	−2.15926	+	0.578572i	−0.0923233	+	0.0247380i	−0.304685	−	0.952453i	$-0.598551\pi$
$547$	−2.15926	+	0.578572i	−0.0923233	+	0.0247380i	0.212362	+	0.977191i	$0.431885\pi$
$548$	6.14713	+	1.64712i	0.262592	+	0.0703614i
$549$	−14.7657	+	16.4631i	−0.630183	+	0.702629i
$550$	−1.26629	+	0.744547i	−0.0539946	+	0.0317476i
$551$			7.93102i			0.337873i
$552$	2.91454	+	3.59202i	0.124051	+	0.152886i
$553$	−0.548210	+	0.0146192i	−0.0233123	+	0.000621671i
$554$	−0.937270	+	0.541133i	−0.0398208	+	0.0229905i
$555$	18.2278	+	29.4180i	0.773727	+	1.24872i
$556$	7.47512	−	4.31576i	0.317016	−	0.183029i
$557$	−24.6777	+	6.61238i	−1.04563	+	0.280175i	−0.740444	−	0.672118i	$-0.765385\pi$
$557$	−24.6777	+	6.61238i	−1.04563	+	0.280175i	−0.305185	+	0.952293i	$0.598718\pi$
$558$	3.15630	−	0.171564i	0.133617	−	0.00726290i
$559$	2.98666			0.126322
$560$	−21.3499	−	8.08670i	−0.902199	−	0.341726i
$561$	20.5696	−	9.18213i	0.868450	−	0.387670i
$562$	−3.36072	+	0.900503i	−0.141764	+	0.0379854i
$563$	−19.3730	−	19.3730i	−0.816473	−	0.816473i	0.169122	−	0.985595i	$-0.445907\pi$
$563$	−19.3730	−	19.3730i	−0.816473	−	0.816473i	−0.985595	+	0.169122i	$0.945907\pi$
$564$	14.5264	+	32.5416i	0.611670	+	1.37025i
$565$	2.90602	−	3.81846i	0.122257	−	0.160644i
$566$			0.944384i			0.0396954i
$567$	−23.5943	+	3.21112i	−0.990865	+	0.134854i
$568$	4.70840	−	4.70840i	0.197560	−	0.197560i
$569$			6.74145i			0.282616i	0.989966	+	0.141308i	$0.0451308\pi$
$569$			6.74145i			0.282616i	−0.989966	+	0.141308i	$0.954869\pi$
$570$	−1.43013	−	2.30810i	−0.0599016	−	0.0966757i
$571$	−6.32944			−0.264879			−0.132439	−	0.991191i	$-0.542281\pi$
$571$	−6.32944			−0.264879			−0.132439	+	0.991191i	$0.542281\pi$
$572$	−3.00064	−	11.1985i	−0.125463	−	0.468234i
$573$	16.6337	+	6.36654i	0.694882	+	0.265966i
$574$	−0.337973	+	1.41075i	−0.0141067	+	0.0588835i
$575$	−10.7806	+	19.0194i	−0.449581	+	0.793162i
$576$	−14.9013	+	16.6144i	−0.620889	+	0.692267i
$577$	5.34263	+	19.9390i	0.222417	+	0.830071i	0.983423	+	0.181326i	$0.0580390\pi$
$577$	5.34263	+	19.9390i	0.222417	+	0.830071i	−0.761006	+	0.648745i	$0.775294\pi$
$578$	4.33764	+	1.16227i	0.180422	+	0.0483440i
$579$	22.3762	−	9.98859i	0.929924	−	0.415112i
$580$	−4.69906	−	6.07389i	−0.195118	−	0.252205i
$581$	−1.59709	−	5.38219i	−0.0662585	−	0.223291i
$582$	−0.655318	+	0.531721i	−0.0271638	+	0.0220406i
$583$	14.0478	−	14.0478i	0.581799	−	0.581799i
$584$	−3.51731	+	6.09216i	−0.145547	+	0.252095i
$585$	−3.86873	−	20.2066i	−0.159952	−	0.835441i
$586$	−3.76768	+	2.17527i	−0.155641	+	0.0898596i
$587$	−0.0383028	−	0.142948i	−0.00158092	−	0.00590009i	0.965131	−	0.261768i	$-0.0843055\pi$
$587$	−0.0383028	−	0.142948i	−0.00158092	−	0.00590009i	−0.966712	+	0.255868i	$0.917639\pi$
$588$	−7.36079	+	22.8041i	−0.303554	+	0.940425i
$589$	−27.1137	+	15.6541i	−1.11720	+	0.645015i
$590$	−2.20077	+	0.921835i	−0.0906044	+	0.0379513i
$591$	15.6062	+	34.9606i	0.641952	+	1.43809i
$592$	8.92469	−	33.3074i	0.366802	−	1.36892i
$593$	4.55654	−	17.0052i	0.187115	−	0.698322i	−0.807053	−	0.590479i	$-0.798939\pi$
$593$	4.55654	−	17.0052i	0.187115	−	0.698322i	0.994168	−	0.107843i	$-0.0343944\pi$
$594$	1.49229	−	0.321745i	0.0612295	−	0.0132014i
$595$	4.02692	−	40.0252i	0.165088	−	1.64087i
$596$	−9.28031	+	16.0740i	−0.380136	+	0.658415i
$597$	30.1428	−	24.4577i	1.23366	−	1.00099i
$598$	1.45652	+	1.45652i	0.0595615	+	0.0595615i
$599$			12.9613i			0.529586i	0.964305	+	0.264793i	$0.0853037\pi$
$599$			12.9613i			0.529586i	−0.964305	+	0.264793i	$0.914696\pi$
$600$	4.95496	+	1.85158i	0.202285	+	0.0755903i
$601$	30.0240	+	17.3344i	1.22470	+	0.707084i	0.965917	−	0.258851i	$-0.0833438\pi$
$601$	30.0240	+	17.3344i	1.22470	+	0.707084i	0.258787	+	0.965934i	$0.416677\pi$
$602$	0.347892	+	0.188673i	0.0141790	+	0.00768975i
$603$	0.268341	+	4.93671i	0.0109277	+	0.201038i
$604$	−24.9076	+	14.3804i	−1.01348	+	0.585131i
$605$	−10.0454	−	12.9845i	−0.408404	−	0.527894i
$606$	−2.64841	−	1.92026i	−0.107584	−	0.0780051i
$607$	5.22984	+	19.5180i	0.212273	+	0.792212i	0.987109	+	0.160050i	$0.0511656\pi$
$607$	5.22984	+	19.5180i	0.212273	+	0.792212i	−0.774836	+	0.632162i	$0.782168\pi$
$608$	−2.14327	+	7.99880i	−0.0869211	+	0.324394i
$609$	−6.04759	+	5.18034i	−0.245061	+	0.209918i
$610$	−0.978187	−	2.33531i	−0.0396056	−	0.0945539i
$611$	15.9638	+	27.6500i	0.645824	+	1.11860i
$612$	−35.9579	−	18.2335i	−1.45351	−	0.737047i
$613$	4.34093	+	16.2006i	0.175329	+	0.654335i	0.996495	+	0.0836471i	$0.0266568\pi$
$613$	4.34093	+	16.2006i	0.175329	+	0.654335i	−0.821167	+	0.570688i	$0.806676\pi$
$614$	−4.99529			−0.201593
$615$	−3.16094	+	13.4587i	−0.127461	+	0.542707i
$616$	0.720100	−	3.00580i	0.0290137	−	0.121107i
$617$	−4.80824	+	17.9446i	−0.193572	+	0.722422i	0.799059	+	0.601252i	$0.205331\pi$
$617$	−4.80824	+	17.9446i	−0.193572	+	0.722422i	−0.992632	+	0.121170i	$0.961335\pi$
$618$	1.17779	+	1.45157i	0.0473779	+	0.0583907i
$619$	−3.85046	−	6.66920i	−0.154763	−	0.268058i	0.778210	−	0.628005i	$-0.216128\pi$
$619$	−3.85046	−	6.66920i	−0.154763	−	0.268058i	−0.932973	+	0.359947i	$0.882795\pi$
$620$	11.4898	−	28.0531i	0.461442	−	1.12664i
$621$	16.8398	−	15.2517i	0.675757	−	0.612030i
$622$	0.863419	−	0.863419i	0.0346200	−	0.0346200i
$623$	−7.41495	+	4.54879i	−0.297074	+	0.182243i
$624$	−12.0331	+	16.5960i	−0.481709	+	0.664371i
$625$	0.396652	+	24.9969i	0.0158661	+	0.999874i
$626$		−	2.48198i		−	0.0991997i
$627$	−11.7414	+	9.52691i	−0.468907	+	0.380468i
$628$	−30.1204	−	30.1204i	−1.20193	−	1.20193i
$629$	60.7589			2.42262
$630$	0.825855	−	2.59810i	0.0329029	−	0.103511i
$631$	−49.3225			−1.96350			−0.981749	−	0.190182i	$-0.939092\pi$
$631$	−49.3225			−1.96350			−0.981749	+	0.190182i	$0.939092\pi$
$632$	−0.0895221	−	0.0895221i	−0.00356100	−	0.00356100i
$633$	−1.01483	−	6.36734i	−0.0403358	−	0.253079i
$634$			5.34746i			0.212375i
$635$	−39.1091	+	16.3816i	−1.55200	+	0.650082i
$636$	−35.3656	−	3.68234i	−1.40234	−	0.146014i
$637$	−4.44337	+	21.0037i	−0.176053	+	0.832197i
$638$	0.360986	−	0.360986i	0.0142916	−	0.0142916i
$639$	−24.3472	−	21.8368i	−0.963159	−	0.863849i
$640$	−4.12197	−	9.84072i	−0.162935	−	0.388989i
$641$	3.05161	+	5.28554i	0.120531	+	0.208766i	0.919977	−	0.391972i	$-0.128207\pi$
$641$	3.05161	+	5.28554i	0.120531	+	0.208766i	−0.799446	+	0.600738i	$0.794874\pi$
$642$	0.491924	−	0.0784031i	0.0194147	−	0.00309432i
$643$	1.99046	−	7.42851i	0.0784962	−	0.292952i	−0.915507	−	0.402302i	$-0.868210\pi$
$643$	1.99046	−	7.42851i	0.0784962	−	0.292952i	0.994003	+	0.109350i	$0.0348769\pi$
$644$	−6.50423	−	21.9192i	−0.256302	−	0.863737i
$645$	3.32340	+	1.78327i	0.130859	+	0.0702161i
$646$	−4.76707			−0.187558
$647$	0.694835	+	2.59316i	0.0273168	+	0.101948i	0.978238	−	0.207485i	$-0.0665277\pi$
$647$	0.694835	+	2.59316i	0.0273168	+	0.101948i	−0.950922	+	0.309432i	$0.899861\pi$
$648$	−4.28548	−	3.44282i	−0.168349	−	0.135247i
$649$	6.64350	+	11.5069i	0.260780	+	0.451684i
$650$	2.27997	+	0.591571i	0.0894278	+	0.0232033i
$651$	−29.6465	−	10.4500i	−1.16194	−	0.409566i
$652$	−4.91304	+	18.3357i	−0.192409	+	0.718081i
$653$	−5.04068	−	18.8121i	−0.197257	−	0.736174i	−0.991671	−	0.128797i	$-0.958888\pi$
$653$	−5.04068	−	18.8121i	−0.197257	−	0.736174i	0.794414	−	0.607377i	$-0.207778\pi$
$654$	−0.207901	+	1.99670i	−0.00812956	+	0.0780772i
$655$	18.2748	−	14.1383i	0.714055	−	0.552428i
$656$	11.9295	−	6.88749i	0.465768	−	0.268911i
$657$	30.8162	+	15.6263i	1.20225	+	0.609639i
$658$	0.112780	+	4.22919i	0.00439663	+	0.164871i
$659$	14.1083	+	8.14544i	0.549582	+	0.317301i	0.748953	−	0.662623i	$-0.230557\pi$
$659$	14.1083	+	8.14544i	0.549582	+	0.317301i	−0.199371	+	0.979924i	$0.563890\pi$
$660$	3.34743	−	14.2528i	0.130299	−	0.554788i
$661$			24.8305i			0.965796i	0.875677	+	0.482898i	$0.160416\pi$
$661$			24.8305i			0.965796i	−0.875677	+	0.482898i	$0.839584\pi$
$662$	1.77591	+	1.77591i	0.0690228	+	0.0690228i
$663$	−33.7338	−	12.9116i	−1.31011	−	0.501446i
$664$	0.648034	−	1.12243i	0.0251486	−	0.0435586i
$665$	4.34262	+	26.6505i	0.168400	+	1.03346i
$666$	4.02930	+	0.848274i	0.156132	+	0.0328700i
$667$	1.96647	−	7.33896i	0.0761420	−	0.284166i
$668$	2.06041	−	7.68956i	0.0797197	−	0.297518i
$669$	−2.94136	−	0.306261i	−0.113720	−	0.0118407i
$670$	−0.523804	−	0.214537i	−0.0202363	−	0.00828827i
$671$	−12.2103	+	7.04962i	−0.471374	+	0.272148i
$672$	−7.49920	+	3.59031i	−0.289288	+	0.138499i
$673$	3.07801	+	11.4873i	0.118649	+	0.442803i	0.999534	−	0.0305270i	$-0.00971856\pi$
$673$	3.07801	+	11.4873i	0.118649	+	0.442803i	−0.880885	+	0.473330i	$0.843052\pi$
$674$	2.50347	−	1.44538i	0.0964300	−	0.0556739i
$675$	7.75999	−	24.7948i	0.298682	−	0.954353i
$676$	3.55150	−	6.15138i	0.136596	−	0.236591i
$677$	−6.98600	+	6.98600i	−0.268494	+	0.268494i	−0.828493	−	0.559999i	$-0.810801\pi$
$677$	−6.98600	+	6.98600i	−0.268494	+	0.268494i	0.559999	+	0.828493i	$0.310801\pi$
$678$	−0.0898609	−	0.563814i	−0.00345109	−	0.0216532i
$679$	8.04550	−	2.38739i	0.308758	−	0.0916198i
$680$	7.34521	−	5.68261i	0.281676	−	0.217918i
$681$	3.45239	+	2.50318i	0.132296	+	0.0959222i
$682$	1.94660	+	0.521591i	0.0745393	+	0.0199727i
$683$	4.39292	+	16.3946i	0.168091	+	0.627323i	0.997626	+	0.0688682i	$0.0219388\pi$
$683$	4.39292	+	16.3946i	0.168091	+	0.627323i	−0.829535	+	0.558454i	$0.811395\pi$
$684$	26.4815	+	5.57507i	1.01255	+	0.213168i
$685$	5.72955	+	4.36044i	0.218915	+	0.166604i
$686$	−1.84442	+	2.16585i	−0.0704201	+	0.0826927i
$687$	−22.9873	+	18.6517i	−0.877020	+	0.711608i
$688$	−0.972638	−	3.62993i	−0.0370815	−	0.138390i
$689$	−31.8559			−1.21361
$690$	0.751085	+	2.49039i	0.0285933	+	0.0948077i
$691$			2.92419i			0.111241i	0.998452	+	0.0556206i	$0.0177137\pi$
$691$			2.92419i			0.111241i	−0.998452	+	0.0556206i	$0.982286\pi$
$692$	−17.7555	+	17.7555i	−0.674964	+	0.674964i
$693$	−14.9337	−	2.73037i	−0.567283	−	0.103718i
$694$			1.84111i			0.0698877i
$695$	9.67687	−	1.31305i	0.367064	−	0.0498070i
$696$	−1.82843	−	0.190380i	−0.0693065	−	0.00721634i
$697$	17.1628	+	17.1628i	0.650088	+	0.650088i
$698$	3.67465	−	0.984619i	0.139087	−	0.0372684i
$699$	−6.39790	−	4.63885i	−0.241991	−	0.175458i
$700$	−19.1160	−	17.8371i	−0.722515	−	0.674179i
$701$	−13.5199			−0.510640			−0.255320	−	0.966857i	$-0.582181\pi$
$701$	−13.5199			−0.510640			−0.255320	+	0.966857i	$0.582181\pi$
$702$	−2.05684	−	1.32722i	−0.0776303	−	0.0500926i
$703$	−39.3939	+	10.5556i	−1.48577	+	0.398111i
$704$	−12.3225	+	7.11440i	−0.464422	+	0.268134i
$705$	1.25444	+	40.2991i	0.0472448	+	1.51775i
$706$	3.89247	−	2.24732i	0.146495	−	0.0845789i
$707$	17.0112	+	27.7297i	0.639770	+	1.04288i
$708$	8.50072	−	22.2096i	0.319477	−	0.834688i
$709$			21.7405i			0.816483i	0.912874	+	0.408242i	$0.133858\pi$
$709$			21.7405i			0.816483i	−0.912874	+	0.408242i	$0.866142\pi$
$710$	3.45367	−	1.44663i	0.129614	−	0.0542911i
$711$	−0.415189	+	0.462919i	−0.0155708	+	0.0173608i
$712$	−1.93980	−	0.519769i	−0.0726972	−	0.0194792i
$713$	28.9710	−	7.76275i	1.08497	−	0.290717i
$714$	−3.11373	−	3.63500i	−0.116528	−	0.136037i
$715$	1.66048	−	13.0112i	0.0620985	−	0.486592i
$716$	−9.72989	+	16.8527i	−0.363623	+	0.629813i
$717$	6.41201	−	1.02195i	0.239461	−	0.0381654i
$718$	−2.80747	−	0.752259i	−0.104774	−	0.0280741i
$719$	4.33560	+	7.50947i	0.161690	+	0.280056i	0.935475	−	0.353393i	$-0.114972\pi$
$719$	4.33560	+	7.50947i	0.161690	+	0.280056i	−0.773785	+	0.633449i	$0.781639\pi$
$720$	−23.2989	+	11.2825i	−0.868298	+	0.420473i
$721$	−5.28822	−	17.8213i	−0.196944	−	0.663699i
$722$	0.271772	−	0.0728211i	0.0101143	−	0.00271012i
$723$	4.79692	−	0.764534i	0.178399	−	0.0284333i
$724$	19.8579			0.738012
$725$	−2.31522	−	8.37419i	−0.0859849	−	0.311010i
$726$	−1.94277	−	0.202285i	−0.0721029	−	0.00750751i
$727$	10.4918	+	39.1559i	0.389119	+	1.45221i	0.831571	+	0.555418i	$0.187442\pi$
$727$	10.4918	+	39.1559i	0.389119	+	1.45221i	−0.442453	+	0.896792i	$0.645891\pi$
$728$	−4.22459	+	2.59163i	−0.156574	+	0.0960521i
$729$	−15.7426	+	21.9356i	−0.583060	+	0.812429i
$730$	−3.12877	+	2.42057i	−0.115801	+	0.0895894i
$731$	5.73454	−	3.31084i	0.212100	−	0.122456i
$732$	23.5673	+	9.02038i	0.871072	+	0.333403i
$733$	4.92715	−	1.32023i	0.181989	−	0.0487637i	−0.166674	−	0.986012i	$-0.553303\pi$
$733$	4.92715	−	1.32023i	0.181989	−	0.0487637i	0.348662	+	0.937248i	$0.386636\pi$
$734$	−0.403909	−	0.699592i	−0.0149086	−	0.0258224i
$735$	−17.4852	+	20.7188i	−0.644950	+	0.764224i
$736$	3.96655	−	6.87026i	0.146209	−	0.253241i
$737$	−0.815811	+	3.04465i	−0.0300508	+	0.112151i
$738$	0.898557	+	1.37779i	0.0330763	+	0.0507171i
$739$	−40.5652	−	23.4203i	−1.49222	−	0.861531i	−0.492255	−	0.870451i	$-0.663827\pi$
$739$	−40.5652	−	23.4203i	−1.49222	−	0.861531i	−0.999960	+	0.00892023i	$0.997161\pi$
$740$	23.9154	−	31.4244i	0.879146	−	1.15518i
$741$	24.1150	+	2.51090i	0.885885	+	0.0922402i
$742$	−3.71064	−	2.01240i	−0.136222	−	0.0738776i
$743$	−18.2177	−	4.88143i	−0.668344	−	0.179082i	−0.0913354	−	0.995820i	$-0.529114\pi$
$743$	−18.2177	−	4.88143i	−0.668344	−	0.179082i	−0.577009	+	0.816738i	$0.695780\pi$
$744$	−2.95807	−	6.62660i	−0.108448	−	0.242943i
$745$	−16.6089	+	12.8494i	−0.608503	+	0.470767i
$746$	0.287769	−	0.498431i	0.0105360	−	0.0182489i
$747$	−5.67761	−	2.87901i	−0.207733	−	0.105337i
$748$	−18.1754	−	18.1754i	−0.664559	−	0.664559i
$749$	−4.81740	−	1.15411i	−0.176024	−	0.0421701i
$750$	2.18382	+	2.01959i	0.0797418	+	0.0737449i
$751$	6.22791	−	10.7870i	0.227259	−	0.393625i	−0.729735	−	0.683730i	$-0.760357\pi$
$751$	6.22791	−	10.7870i	0.227259	−	0.393625i	0.956995	+	0.290105i	$0.0936901\pi$
$752$	28.4066	−	28.4066i	1.03588	−	1.03588i
$753$	5.85128	−	15.2875i	0.213232	−	0.557107i
$754$	−0.818604			−0.0298118
$755$	−32.2440	+	4.37519i	−1.17348	+	0.159229i
$756$	13.0459	+	23.8343i	0.474476	+	0.866844i
$757$	−34.0156	−	34.0156i	−1.23632	−	1.23632i	−0.961495	−	0.274821i	$-0.911381\pi$
$757$	−34.0156	−	34.0156i	−1.23632	−	1.23632i	−0.274821	−	0.961495i	$-0.588619\pi$
$758$	0.0443871	−	0.0443871i	0.00161221	−	0.00161221i
$759$	13.2271	−	5.90447i	0.480112	−	0.214319i
$760$	−3.77514	+	4.96048i	−0.136939	+	0.179935i
$761$	20.1480	+	11.6324i	0.730363	+	0.421675i	0.818555	−	0.574428i	$-0.194776\pi$
$761$	20.1480	+	11.6324i	0.730363	+	0.421675i	−0.0881918	+	0.996104i	$0.528109\pi$
$762$	−1.80337	+	4.71163i	−0.0653293	+	0.170684i
$763$	9.51741	−	17.5490i	0.344553	−	0.635317i
$764$		−	20.3231i		−	0.735264i
$765$	−29.8280	−	34.5091i	−1.07844	−	1.24768i
$766$	2.73273	+	1.57774i	0.0987375	+	0.0570061i
$767$	5.51431	−	20.5797i	0.199110	−	0.743090i
$768$	22.8822	+	8.75816i	0.825691	+	0.316033i
$769$	9.48022	+	16.4202i	0.341866	+	0.592129i	0.984779	−	0.173810i	$-0.0556079\pi$
$769$	9.48022	+	16.4202i	0.341866	+	0.592129i	−0.642914	+	0.765939i	$0.722275\pi$
$770$	1.01536	−	1.41068i	0.0365911	−	0.0508372i
$771$	−2.84914	+	27.3635i	−0.102609	+	0.985472i
$772$	−19.7717	−	19.7717i	−0.711601	−	0.711601i
$773$	27.3055	−	7.31649i	0.982111	−	0.263156i	0.268178	−	0.963370i	$-0.413579\pi$
$773$	27.3055	−	7.31649i	0.982111	−	0.263156i	0.713933	+	0.700214i	$0.246912\pi$
$774$	0.426516	−	0.139500i	0.0153308	−	0.00501424i
$775$	24.0590	−	24.4438i	0.864224	−	0.878046i
$776$	1.67785	+	0.968706i	0.0602312	+	0.0347745i
$777$	−33.7800	−	23.1442i	−1.21185	−	0.830292i
$778$	−1.41033	−	0.377897i	−0.0505628	−	0.0135483i
$779$	−14.1095	−	8.14610i	−0.505524	−	0.291864i
$780$	−19.9559	+	12.3649i	−0.714535	+	0.442736i
$781$	−10.4256	−	18.0577i	−0.373058	−	0.646155i
$782$	4.41120	+	1.18198i	0.157744	+	0.0422675i
$783$	−0.446270	+	9.01815i	−0.0159484	+	0.322282i
$784$	26.9746	−	1.43969i	0.963377	−	0.0514175i
$785$	−18.6192	−	44.4511i	−0.664546	−	1.58653i
$786$	0.284703	−	2.73432i	0.0101550	−	0.0975300i
$787$	−17.9505	+	17.9505i	−0.639865	+	0.639865i	−0.950522	−	0.310657i	$-0.899451\pi$
$787$	−17.9505	+	17.9505i	−0.639865	+	0.639865i	0.310657	+	0.950522i	$0.399451\pi$
$788$	30.8913	−	30.8913i	1.10046	−	1.10046i
$789$	−15.5505	−	11.2750i	−0.553611	−	0.401401i
$790$	−0.0275052	−	0.0656655i	−0.000978591	−	0.00233627i
$791$	−1.32277	+	5.52142i	−0.0470322	+	0.196319i
$792$	−1.91450	−	2.93557i	−0.0680289	−	0.104311i
$793$	21.8378	+	5.85141i	0.775482	+	0.207790i
$794$	0.244997	+	0.424347i	0.00869461	+	0.0150595i
$795$	−35.4476	−	19.0205i	−1.25720	−	0.674586i
$796$	−38.3592	−	22.1467i	−1.35961	−	0.784969i
$797$	−17.9099	−	4.79893i	−0.634400	−	0.169987i	−0.0727342	−	0.997351i	$-0.523172\pi$
$797$	−17.9099	−	4.79893i	−0.634400	−	0.169987i	−0.561665	+	0.827364i	$0.689839\pi$
$798$	2.65034	+	1.81586i	0.0938209	+	0.0642809i
$799$	61.3024	+	35.3930i	2.16872	+	1.25211i
$800$	−0.0719683	−	9.07141i	−0.00254446	−	0.320723i
$801$	−2.03204	+	9.65218i	−0.0717987	+	0.341043i
$802$	2.00164	−	0.536338i	0.0706804	−	0.0189388i
$803$	15.5765	+	15.5765i	0.549682	+	0.549682i
$804$	5.15153	−	2.29961i	0.181680	−	0.0811009i
$805$	2.58947	−	25.7378i	0.0912668	−	0.907138i
$806$	−1.61574	−	2.79855i	−0.0569121	−	0.0985746i
$807$	−21.6045	+	17.5297i	−0.760513	+	0.617076i
$808$	−1.94378	+	7.25430i	−0.0683821	+	0.255205i
$809$	45.8770	+	26.4871i	1.61295	+	0.931236i	0.988682	+	0.150024i	$0.0479351\pi$
$809$	45.8770	+	26.4871i	1.61295	+	0.931236i	0.624266	+	0.781212i	$0.285398\pi$
$810$	−1.49629	−	2.70495i	−0.0525742	−	0.0950422i
$811$		−	27.5702i		−	0.968122i	−0.875034	−	0.484061i	$-0.839161\pi$
$811$		−	27.5702i		−	0.968122i	0.875034	−	0.484061i	$-0.160839\pi$
$812$	7.98737	+	4.33182i	0.280302	+	0.152017i
$813$	34.5239	−	5.50243i	1.21081	−	0.192979i
$814$	2.27348	+	1.31260i	0.0796856	+	0.0460065i
$815$	−13.0063	+	17.0901i	−0.455593	+	0.598642i
$816$	−4.70677	+	45.2043i	−0.164770	+	1.58247i
$817$	−3.14289	+	3.14289i	−0.109956	+	0.109956i
$818$	0.758494	+	0.758494i	0.0265201	+	0.0265201i
$819$	13.8366	+	20.0283i	0.483492	+	0.699844i
$820$	15.6321	−	2.12112i	0.545895	−	0.0740726i
$821$	6.79021			0.236980			0.118490	−	0.992955i	$-0.462195\pi$
$821$	6.79021			0.236980			0.118490	+	0.992955i	$0.462195\pi$
$822$	0.845995	−	0.134835i	0.0295075	−	0.00470291i
$823$	−7.86640	+	7.86640i	−0.274206	+	0.274206i	−0.830791	−	0.556585i	$-0.812111\pi$
$823$	−7.86640	+	7.86640i	−0.274206	+	0.274206i	0.556585	+	0.830791i	$0.312111\pi$
$824$	2.14574	−	3.71653i	0.0747505	−	0.129472i
$825$	9.61640	−	13.4868i	0.334800	−	0.469549i
$826$	1.94238	−	2.04881i	0.0675839	−	0.0712872i
$827$	33.2613	+	33.2613i	1.15661	+	1.15661i	0.985200	+	0.171409i	$0.0548319\pi$
$827$	33.2613	+	33.2613i	1.15661	+	1.15661i	0.171409	+	0.985200i	$0.445168\pi$
$828$	−23.1223	−	11.7249i	−0.803556	−	0.407468i
$829$	11.8491	−	20.5233i	0.411537	−	0.712803i	−0.583521	−	0.812098i	$-0.698325\pi$
$829$	11.8491	−	20.5233i	0.411537	−	0.712803i	0.995058	+	0.0992951i	$0.0316588\pi$
$830$	0.576449	−	0.445969i	0.0200088	−	0.0154798i
$831$	7.16358	−	9.87999i	0.248502	−	0.342733i
$832$	22.0384	+	5.90518i	0.764045	+	0.204725i
$833$	14.7520	+	45.2538i	0.511126	+	1.56795i
$834$	0.682043	−	0.940672i	0.0236172	−	0.0325728i
$835$	5.45455	−	7.16720i	0.188763	−	0.248031i
$836$	14.9419	+	8.62671i	0.516776	+	0.298361i
$837$	−31.7110	+	16.2742i	−1.09609	+	0.562518i
$838$	1.18908	−	4.43772i	0.0410763	−	0.153299i
$839$	−28.2248	+	48.8867i	−0.974428	+	1.68776i	−0.292616	+	0.956230i	$0.594526\pi$
$839$	−28.2248	+	48.8867i	−0.974428	+	1.68776i	−0.681811	+	0.731528i	$0.738808\pi$
$840$	−6.24830	+	0.361422i	−0.215587	+	0.0124703i
$841$	−12.9903	−	22.4998i	−0.447940	−	0.775855i
$842$	−4.70806	+	1.26152i	−0.162251	+	0.0434749i
$843$	30.4655	−	24.7195i	1.04929	−	0.851385i
$844$	−6.37164	+	3.67867i	−0.219321	+	0.126625i
$845$	6.35609	−	4.91738i	0.218656	−	0.169163i
$846$	3.57121	+	3.20299i	0.122781	+	0.110121i
$847$	17.0750	+	9.26034i	0.586704	+	0.318189i
$848$	10.3742	+	38.7171i	0.356252	+	1.32955i
$849$	−4.34077	−	9.72410i	−0.148975	−	0.333730i
$850$	5.03344	−	1.39160i	0.172646	−	0.0477314i
$851$	39.0703			1.33931
$852$	−13.3401	+	34.8534i	−0.457026	+	1.19406i
$853$	34.8445	−	9.33655i	1.19305	−	0.319677i	0.392961	−	0.919555i	$-0.371451\pi$
$853$	34.8445	−	9.33655i	1.19305	−	0.319677i	0.800092	+	0.599878i	$0.204784\pi$
$854$	2.17406	+	2.06112i	0.0743947	+	0.0705300i
$855$	25.3347	+	17.1925i	0.866428	+	0.587971i
$856$	−0.571802	−	0.990389i	−0.0195438	−	0.0338508i
$857$	35.3051	+	9.45996i	1.20600	+	0.323146i	0.805191	−	0.593016i	$-0.202063\pi$
$857$	35.3051	+	9.45996i	1.20600	+	0.323146i	0.400807	+	0.916162i	$0.368730\pi$
$858$	−0.983323	−	1.21189i	−0.0335701	−	0.0413734i
$859$	15.4260	−	26.7186i	0.526329	−	0.911629i	−0.473200	−	0.880955i	$-0.656901\pi$
$859$	15.4260	−	26.7186i	0.526329	−	0.911629i	0.999529	−	0.0306738i	$-0.00976530\pi$
$860$	0.544816	−	4.26908i	0.0185781	−	0.145574i
$861$	−3.00434	−	16.0796i	−0.102388	−	0.547991i
$862$	2.61438	−	0.700522i	0.0890462	−	0.0238599i
$863$	−34.2573	−	9.17921i	−1.16613	−	0.312464i	−0.376719	−	0.926327i	$-0.622948\pi$
$863$	−34.2573	−	9.17921i	−1.16613	−	0.312464i	−0.789412	+	0.613863i	$0.789615\pi$
$864$	−2.88714	+	8.97461i	−0.0982225	+	0.305323i
$865$	−26.2033	+	10.9757i	−0.890938	+	0.373186i
$866$		−	1.53382i		−	0.0521214i
$867$	−50.0059	+	7.96996i	−1.69829	+	0.270674i
$868$	0.956185	+	35.8563i	0.0324550	+	1.21704i
$869$	−0.343336	+	0.198225i	−0.0116469	+	0.00672433i
$870$	−0.910900	−	0.488770i	−0.0308824	−	0.0165708i
$871$	4.37716	−	2.52716i	0.148314	−	0.0856294i
$872$	4.45172	−	1.19284i	0.150754	−	0.0403945i
$873$	4.30365	−	8.48711i	0.145656	−	0.287245i
$874$	−3.06541			−0.103689
$875$	−12.3651	−	26.8720i	−0.418016	−	0.908440i
$876$	4.08306	−	39.2142i	0.137954	−	1.32492i
$877$	22.6737	−	6.07539i	0.765636	−	0.205152i	0.145193	−	0.989403i	$-0.453620\pi$
$877$	22.6737	−	6.07539i	0.765636	−	0.205152i	0.620443	+	0.784252i	$0.286953\pi$
$878$	−2.43705	−	2.43705i	−0.0822465	−	0.0822465i
$879$	28.7965	−	39.7160i	0.971280	−	1.33959i
$880$	−16.3544	+	2.21912i	−0.551305	+	0.0748067i
$881$			11.0829i			0.373393i	0.982418	+	0.186697i	$0.0597781\pi$
$881$			11.0829i			0.373393i	−0.982418	+	0.186697i	$0.940222\pi$
$882$	0.346492	+	3.20702i	0.0116670	+	0.107986i
$883$	−10.2116	+	10.2116i	−0.343649	+	0.343649i	−0.857737	−	0.514088i	$-0.828130\pi$
$883$	−10.2116	+	10.2116i	−0.343649	+	0.343649i	0.514088	+	0.857737i	$0.328130\pi$
$884$			41.2162i			1.38625i
$885$	18.4237	−	19.6075i	0.619306	−	0.659101i
$886$	−1.47398			−0.0495194
$887$	−12.1905	−	45.4957i	−0.409318	−	1.52760i	−0.795950	−	0.605363i	$-0.793028\pi$
$887$	−12.1905	−	45.4957i	−0.409318	−	1.52760i	0.386631	−	0.922234i	$-0.373639\pi$
$888$	−1.48787	−	9.33532i	−0.0499296	−	0.313273i
$889$	34.5172	−	36.4086i	1.15767	−	1.22110i
$890$	−0.898652	−	0.683914i	−0.0301229	−	0.0229248i
$891$	−13.8869	+	10.1721i	−0.465229	+	0.340778i
$892$	0.873378	+	3.25949i	0.0292429	+	0.109136i
$893$	−45.8951	−	12.2976i	−1.53582	−	0.411522i
$894$	−0.258750	+	2.48506i	−0.00865390	+	0.0831129i
$895$	−17.4135	+	13.4719i	−0.582069	+	0.450317i
$896$	9.16122	+	8.68531i	0.306055	+	0.290156i
$897$	−21.6922	−	8.30268i	−0.724281	−	0.277218i
$898$	−2.57910	+	2.57910i	−0.0860656	+	0.0860656i
$899$	−5.95980	+	10.3227i	−0.198770	+	0.344281i
$900$	−29.5887	+	1.84387i	−0.986290	+	0.0614623i
$901$	−61.1650	+	35.3136i	−2.03770	+	1.17647i
$902$	0.271426	+	1.01298i	0.00903750	+	0.0337284i
$903$	−4.44938	−	0.343672i	−0.148066	−	0.0114367i
$904$	−1.13513	+	0.655365i	−0.0377537	+	0.0217971i
$905$	20.7906	+	8.51528i	0.691102	+	0.283057i
$906$	−2.27261	+	3.13438i	−0.0755025	+	0.104133i
$907$	−3.29750	+	12.3064i	−0.109492	+	0.408629i	−0.998816	−	0.0486485i	$-0.984509\pi$
$907$	−3.29750	+	12.3064i	−0.109492	+	0.408629i	0.889324	+	0.457277i	$0.151175\pi$
$908$	1.25941	−	4.70018i	0.0417950	−	0.155981i
$909$	36.0963	+	7.59924i	1.19724	+	0.252051i
$910$	−2.75075	+	0.448225i	−0.0911864	+	0.0148585i
$911$	−6.52406	+	11.3000i	−0.216152	+	0.374386i	−0.953628	−	0.300987i	$-0.902684\pi$
$911$	−6.52406	+	11.3000i	−0.216152	+	0.374386i	0.737477	+	0.675373i	$0.236017\pi$
$912$	−4.80159	−	30.1266i	−0.158996	−	0.997591i
$913$	−2.86983	−	2.86983i	−0.0949775	−	0.0949775i
$914$		−	0.979503i		−	0.0323991i
$915$	20.8062	+	19.5500i	0.687831	+	0.646302i
$916$	29.2532	+	16.8893i	0.966552	+	0.558039i
$917$	−13.0333	+	24.0320i	−0.430398	+	0.793605i
$918$	−5.42051	−	0.268238i	−0.178903	−	0.00885317i
$919$	40.5123	−	23.3898i	1.33638	−	0.771558i	0.350109	−	0.936709i	$-0.386145\pi$
$919$	40.5123	−	23.3898i	1.33638	−	0.771558i	0.986268	+	0.165151i	$0.0528113\pi$
$920$	4.72326	−	3.65414i	0.155721	−	0.120473i
$921$	51.4353	−	22.9604i	1.69485	−	0.756569i
$922$	0.931150	+	3.47510i	0.0306658	+	0.114446i
$923$	−8.65359	+	32.2956i	−0.284836	+	1.06302i
$924$	3.18159	+	17.0283i	0.104667	+	0.560190i
$925$	38.5138	−	22.6452i	1.26632	−	0.744570i
$926$	−1.92718	−	3.33798i	−0.0633311	−	0.109693i
$927$	−18.7995	−	9.53284i	−0.617456	−	0.313100i
$928$	0.815983	+	3.04529i	0.0267860	+	0.0999666i
$929$	47.0221			1.54274			0.771372	−	0.636384i	$-0.219571\pi$
$929$	47.0221			1.54274			0.771372	+	0.636384i	$0.219571\pi$
$930$	−0.126966	−	4.07880i	−0.00416336	−	0.133749i
$931$	−17.4266	−	26.7781i	−0.571133	−	0.877618i
$932$	−2.33392	+	8.71029i	−0.0764499	+	0.285315i
$933$	−4.92180	+	12.8590i	−0.161132	+	0.420986i
$934$	−0.696799	−	1.20689i	−0.0228000	−	0.0394907i
$935$	−11.2353	−	26.8229i	−0.367433	−	0.877203i
$936$	−1.15773	+	5.49923i	−0.0378417	+	0.179748i
$937$	7.06730	−	7.06730i	0.230879	−	0.230879i	−0.582181	−	0.813059i	$-0.697800\pi$
$937$	7.06730	−	7.06730i	0.230879	−	0.230879i	0.813059	+	0.582181i	$0.197800\pi$
$938$	0.669505	−	0.0178538i	0.0218601	−	0.000582946i
$939$	11.4082	+	25.5563i	0.372291	+	0.833999i
$940$	42.4345	−	17.7745i	1.38406	−	0.579739i
$941$		−	21.3888i		−	0.697254i	−0.937262	−	0.348627i	$-0.886648\pi$
$941$		−	21.3888i		−	0.697254i	0.937262	−	0.348627i	$-0.113352\pi$
$942$	−5.35520	−	2.04970i	−0.174482	−	0.0667829i
$943$	11.0364	+	11.0364i	0.359394	+	0.359394i
$944$	−26.8080			−0.872526
$945$	3.43828	+	30.5480i	0.111847	+	0.993725i
$946$	0.286101			0.00930195
$947$	12.6421	+	12.6421i	0.410813	+	0.410813i	0.882022	−	0.471209i	$-0.156182\pi$
$947$	12.6421	+	12.6421i	0.410813	+	0.410813i	−0.471209	+	0.882022i	$0.656182\pi$
$948$	0.662678	+	0.253640i	0.0215228	+	0.00823784i
$949$		−	35.3226i		−	1.14662i
$950$	−3.02175	+	1.77672i	−0.0980384	+	0.0576443i
$951$	−24.5791	−	55.0615i	−0.797031	−	1.78549i
$952$	−5.23850	+	9.65919i	−0.169781	+	0.313056i
$953$	1.91555	−	1.91555i	0.0620508	−	0.0620508i	−0.675400	−	0.737451i	$-0.736029\pi$
$953$	1.91555	−	1.91555i	0.0620508	−	0.0620508i	0.737451	+	0.675400i	$0.236029\pi$
$954$	−4.54926	+	1.48792i	−0.147288	+	0.0481732i
$955$	8.71478	−	21.2777i	0.282004	−	0.688529i
$956$	−3.70448	−	6.41634i	−0.119811	−	0.207519i
$957$	−2.05775	+	5.37622i	−0.0665176	+	0.173789i
$958$	0.534726	−	1.99562i	0.0172762	−	0.0644757i
$959$	−8.28481	−	1.98480i	−0.267531	−	0.0640924i
$960$	20.9974	+	19.7296i	0.677687	+	0.636770i
$961$	−16.0533			−0.517848
$962$	−1.08950	−	4.06606i	−0.0351268	−	0.131095i
$963$	−4.70485	+	3.06838i	−0.151612	+	0.0988772i
$964$	−2.77137	−	4.80016i	−0.0892598	−	0.154603i
$965$	−12.2221	−	29.1788i	−0.393442	−	0.939297i
$966$	−2.00225	−	2.33745i	−0.0644213	−	0.0752062i
$967$	−7.29612	+	27.2295i	−0.234627	+	0.875641i	0.743689	+	0.668526i	$0.233074\pi$
$967$	−7.29612	+	27.2295i	−0.234627	+	0.875641i	−0.978316	+	0.207116i	$0.933592\pi$
$968$	1.16062	+	4.33148i	0.0373036	+	0.139219i
$969$	49.0854	−	21.9114i	1.57685	−	0.703895i
$970$	0.666652	+	0.861699i	0.0214049	+	0.0276675i
$971$	−45.8495	+	26.4712i	−1.47138	+	0.849503i	−0.999483	−	0.0321499i	$-0.989765\pi$
$971$	−45.8495	+	26.4712i	−1.47138	+	0.849503i	−0.471899	+	0.881653i	$0.656431\pi$
$972$	29.7977	+	7.82934i	0.955762	+	0.251126i
$973$	−9.84914	+	6.04208i	−0.315749	+	0.193700i
$974$	0.492800	+	0.284518i	0.0157903	+	0.00911655i
$975$	−26.1954	+	4.38841i	−0.838925	+	0.140542i
$976$		−	28.4468i		−	0.910560i
$977$	−16.3059	−	16.3059i	−0.521672	−	0.521672i	0.396404	−	0.918076i	$-0.370258\pi$
$977$	−16.3059	−	16.3059i	−0.521672	−	0.521672i	−0.918076	+	0.396404i	$0.870258\pi$
$978$	0.402187	+	2.52344i	0.0128605	+	0.0806908i
$979$	−3.14433	+	5.44613i	−0.100493	+	0.174059i
$980$	29.2118	+	10.1827i	0.933135	+	0.325274i
$981$	−7.03694	−	21.5151i	−0.224672	−	0.686925i
$982$	1.34406	−	5.01612i	0.0428908	−	0.160071i
$983$	−12.4675	+	46.5295i	−0.397653	+	1.48406i	0.419561	+	0.907727i	$0.362184\pi$
$983$	−12.4675	+	46.5295i	−0.397653	+	1.48406i	−0.817214	+	0.576334i	$0.804483\pi$
$984$	2.21670	−	3.05727i	0.0706660	−	0.0974623i
$985$	45.5888	−	19.0957i	1.45258	−	0.608440i
$986$	−1.57176	+	0.907456i	−0.0500551	+	0.0288993i
$987$	−20.6003	−	43.0285i	−0.655716	−	1.36961i
$988$	−7.16044	−	26.7231i	−0.227804	−	0.850176i
$989$	3.68753	−	2.12900i	0.117257	−	0.0676982i
$990$	−0.370597	−	1.93565i	−0.0117783	−	0.0615191i
$991$	24.5945	−	42.5990i	0.781271	−	1.35320i	−0.149931	−	0.988696i	$-0.547905\pi$
$991$	24.5945	−	42.5990i	0.781271	−	1.35320i	0.931202	−	0.364504i	$-0.118762\pi$
$992$	−8.80032	+	8.80032i	−0.279410	+	0.279410i
$993$	−26.4489	−	10.1233i	−0.839332	−	0.321254i
$994$	−3.04817	+	3.21519i	−0.0966819	+	0.101980i
$995$	−30.6642	−	39.6358i	−0.972119	−	1.25654i
$996$	−0.752269	+	7.22487i	−0.0238365	+	0.228929i
$997$	20.0133	+	5.36254i	0.633827	+	0.169833i	0.561406	−	0.827541i	$-0.310261\pi$
$997$	20.0133	+	5.36254i	0.633827	+	0.169833i	0.0724212	+	0.997374i	$0.476927\pi$
$998$	0.0373872	+	0.139531i	0.00118347	+	0.00441678i
$999$	−45.3877	+	9.78579i	−1.43600	+	0.309609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bs.e.52.20	✓	160
3.2	odd	2		945.2.bv.e.262.21		160
5.3	odd	4	inner	315.2.bs.e.178.20	yes	160
7.5	odd	6		315.2.cg.e.187.20	yes	160
9.4	even	3		315.2.cg.e.157.21	yes	160
9.5	odd	6		945.2.cj.e.577.20		160
15.8	even	4		945.2.bv.e.73.21		160
21.5	even	6		945.2.cj.e.397.21		160
35.33	even	12		315.2.cg.e.313.21	yes	160
45.13	odd	12		315.2.cg.e.283.20	yes	160
45.23	even	12		945.2.cj.e.388.21		160
63.5	even	6		945.2.bv.e.712.21		160
63.40	odd	6	inner	315.2.bs.e.292.20	yes	160
105.68	odd	12		945.2.cj.e.208.20		160
315.68	odd	12		945.2.bv.e.523.21		160
315.103	even	12	inner	315.2.bs.e.103.20	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.20	✓	160	1.1	even	1	trivial
315.2.bs.e.103.20	yes	160	315.103	even	12	inner
315.2.bs.e.178.20	yes	160	5.3	odd	4	inner
315.2.bs.e.292.20	yes	160	63.40	odd	6	inner
315.2.cg.e.157.21	yes	160	9.4	even	3
315.2.cg.e.187.20	yes	160	7.5	odd	6
315.2.cg.e.283.20	yes	160	45.13	odd	12
315.2.cg.e.313.21	yes	160	35.33	even	12
945.2.bv.e.73.21		160	15.8	even	4
945.2.bv.e.262.21		160	3.2	odd	2
945.2.bv.e.523.21		160	315.68	odd	12
945.2.bv.e.712.21		160	63.5	even	6
945.2.cj.e.208.20		160	105.68	odd	12
945.2.cj.e.388.21		160	45.23	even	12
945.2.cj.e.397.21		160	21.5	even	6
945.2.cj.e.577.20		160	9.5	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.108614 - 0.108614i) q^{2} +(1.61761 + 0.619140i) q^{3} -1.97641i q^{4} +(0.847505 - 2.06924i) q^{5} +(-0.108448 - 0.242943i) q^{6} +(0.0705295 + 2.64481i) q^{7} +(-0.431895 + 0.431895i) q^{8} +(2.23333 + 2.00306i) q^{9} +O(q^{10})\)	\(q+(-0.108614 - 0.108614i) q^{2} +(1.61761 + 0.619140i) q^{3} -1.97641i q^{4} +(0.847505 - 2.06924i) q^{5} +(-0.108448 - 0.242943i) q^{6} +(0.0705295 + 2.64481i) q^{7} +(-0.431895 + 0.431895i) q^{8} +(2.23333 + 2.00306i) q^{9} +(-0.316800 + 0.132697i) q^{10} +(0.956327 + 1.65641i) q^{11} +(1.22367 - 3.19706i) q^{12} +(0.793782 - 2.96243i) q^{13} +(0.279604 - 0.294925i) q^{14} +(2.65208 - 2.82249i) q^{15} -3.85899 q^{16} +(-1.75988 - 6.56796i) q^{17} +(-0.0250111 - 0.460132i) q^{18} +(2.28209 + 3.95269i) q^{19} +(-4.08965 - 1.67501i) q^{20} +(-1.52342 + 4.32194i) q^{21} +(0.0760387 - 0.283780i) q^{22} +(-1.13167 - 4.22346i) q^{23} +(-0.966041 + 0.431234i) q^{24} +(-3.56347 - 3.50737i) q^{25} +(-0.407979 + 0.235547i) q^{26} +(2.37249 + 4.62291i) q^{27} +(5.22722 - 0.139395i) q^{28} +(1.50486 + 0.868834i) q^{29} +(-0.594617 + 0.0185093i) q^{30} +6.85954i q^{31} +(1.28293 + 1.28293i) q^{32} +(0.521417 + 3.27152i) q^{33} +(-0.522227 + 0.904523i) q^{34} +(5.53251 + 2.09555i) q^{35} +(3.95885 - 4.41397i) q^{36} +(-2.31270 + 8.63111i) q^{37} +(0.181452 - 0.677187i) q^{38} +(3.11819 - 4.30060i) q^{39} +(0.527659 + 1.25972i) q^{40} +(-3.09135 + 1.78479i) q^{41} +(0.634890 - 0.303960i) q^{42} +(0.252045 + 0.940643i) q^{43} +(3.27373 - 1.89009i) q^{44} +(6.03755 - 2.92369i) q^{45} +(-0.335812 + 0.581644i) q^{46} +(-7.36114 + 7.36114i) q^{47} +(-6.24235 - 2.38926i) q^{48} +(-6.99005 + 0.373074i) q^{49} +(0.00609292 + 0.767995i) q^{50} +(1.21969 - 11.7140i) q^{51} +(-5.85497 - 1.56883i) q^{52} +(-2.68833 - 10.0330i) q^{53} +(0.244428 - 0.759800i) q^{54} +(4.23799 - 0.575053i) q^{55} +(-1.17274 - 1.11182i) q^{56} +(1.24426 + 7.80685i) q^{57} +(-0.0690820 - 0.257818i) q^{58} +6.94689 q^{59} +(-5.57839 - 5.24159i) q^{60} +7.37156i q^{61} +(0.745044 - 0.745044i) q^{62} +(-5.14019 + 6.04801i) q^{63} +7.43929i q^{64} +(-5.45724 - 4.15320i) q^{65} +(0.298701 - 0.411968i) q^{66} +(1.16531 + 1.16531i) q^{67} +(-12.9810 + 3.47824i) q^{68} +(0.784308 - 7.53257i) q^{69} +(-0.373303 - 0.828517i) q^{70} -10.9017 q^{71} +(-1.82967 + 0.0994542i) q^{72} +(11.1248 - 2.98088i) q^{73} +(1.18865 - 0.686270i) q^{74} +(-3.59275 - 7.87986i) q^{75} +(7.81213 - 4.51033i) q^{76} +(-4.31343 + 2.64613i) q^{77} +(-0.805787 + 0.128427i) q^{78} +0.207278i q^{79} +(-3.27051 + 7.98516i) q^{80} +(0.975531 + 8.94697i) q^{81} +(0.529618 + 0.141911i) q^{82} +(-2.04964 + 0.549200i) q^{83} +(8.54191 + 3.01090i) q^{84} +(-15.0822 - 1.92477i) q^{85} +(0.0747917 - 0.129543i) q^{86} +(1.89636 + 2.33716i) q^{87} +(-1.12843 - 0.302361i) q^{88} +(1.64396 + 2.84742i) q^{89} +(-0.973319 - 0.338211i) q^{90} +(7.89106 + 1.89046i) q^{91} +(-8.34726 + 2.23664i) q^{92} +(-4.24702 + 11.0961i) q^{93} +1.59905 q^{94} +(10.1131 - 1.37225i) q^{95} +(1.28097 + 2.86960i) q^{96} +(-0.820966 - 3.06389i) q^{97} +(0.799741 + 0.718699i) q^{98} +(-1.18208 + 5.61488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 4 q^{2} - 18 q^{3} - 6 q^{5} + 24 q^{6} - 16 q^{8}+O(q^{10}) \) 160 * q + 4 * q^2 - 18 * q^3 - 6 * q^5 + 24 * q^6 - 16 * q^8	\( 160 q + 4 q^{2} - 18 q^{3} - 6 q^{5} + 24 q^{6} - 16 q^{8} - 24 q^{10} - 16 q^{11} - 30 q^{12} + 16 q^{15} - 152 q^{16} - 6 q^{17} + 58 q^{18} + 60 q^{20} - 36 q^{21} + 8 q^{22} + 8 q^{23} + 2 q^{25} - 36 q^{26} - 36 q^{27} + 22 q^{28} - 26 q^{30} + 12 q^{32} - 6 q^{33} - 36 q^{35} - 32 q^{36} - 4 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 28 q^{42} - 4 q^{43} - 54 q^{45} - 16 q^{46} - 18 q^{48} - 44 q^{50} + 80 q^{51} + 54 q^{52} + 8 q^{53} + 148 q^{56} - 4 q^{57} + 28 q^{58} + 104 q^{60} - 60 q^{63} - 124 q^{65} + 36 q^{66} - 24 q^{67} + 42 q^{68} - 34 q^{70} - 40 q^{71} + 70 q^{72} + 36 q^{73} - 60 q^{75} + 96 q^{76} + 58 q^{77} - 62 q^{78} + 36 q^{80} + 8 q^{81} - 66 q^{82} - 138 q^{83} - 20 q^{85} - 16 q^{86} + 102 q^{87} + 46 q^{88} + 18 q^{90} - 48 q^{91} - 26 q^{92} + 82 q^{93} + 188 q^{95} - 48 q^{96} + 48 q^{97} + 102 q^{98}+O(q^{100}) \) 160 * q + 4 * q^2 - 18 * q^3 - 6 * q^5 + 24 * q^6 - 16 * q^8 - 24 * q^10 - 16 * q^11 - 30 * q^12 + 16 * q^15 - 152 * q^16 - 6 * q^17 + 58 * q^18 + 60 * q^20 - 36 * q^21 + 8 * q^22 + 8 * q^23 + 2 * q^25 - 36 * q^26 - 36 * q^27 + 22 * q^28 - 26 * q^30 + 12 * q^32 - 6 * q^33 - 36 * q^35 - 32 * q^36 - 4 * q^37 - 18 * q^38 - 6 * q^40 - 12 * q^41 - 28 * q^42 - 4 * q^43 - 54 * q^45 - 16 * q^46 - 18 * q^48 - 44 * q^50 + 80 * q^51 + 54 * q^52 + 8 * q^53 + 148 * q^56 - 4 * q^57 + 28 * q^58 + 104 * q^60 - 60 * q^63 - 124 * q^65 + 36 * q^66 - 24 * q^67 + 42 * q^68 - 34 * q^70 - 40 * q^71 + 70 * q^72 + 36 * q^73 - 60 * q^75 + 96 * q^76 + 58 * q^77 - 62 * q^78 + 36 * q^80 + 8 * q^81 - 66 * q^82 - 138 * q^83 - 20 * q^85 - 16 * q^86 + 102 * q^87 + 46 * q^88 + 18 * q^90 - 48 * q^91 - 26 * q^92 + 82 * q^93 + 188 * q^95 - 48 * q^96 + 48 * q^97 + 102 * q^98

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