LMFDB - Embedded newform 260.2.j.a.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(31,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("260.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.j (of order $4$, degree $2$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	260.31
Dual form			260.2.j.a.151.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08931 - 0.901894i) q^{2} +0.947478i q^{3} +(0.373176 + 1.96488i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.854524 - 1.03209i) q^{6} +(-2.28468 + 2.28468i) q^{7} +(1.36561 - 2.47692i) q^{8} +2.10229 q^{9} +O(q^{10})$	\(q+(-1.08931 - 0.901894i) q^{2} +0.947478i q^{3} +(0.373176 + 1.96488i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.854524 - 1.03209i) q^{6} +(-2.28468 + 2.28468i) q^{7} +(1.36561 - 2.47692i) q^{8} +2.10229 q^{9} +(-1.40799 + 0.132521i) q^{10} +(-0.580083 + 0.580083i) q^{11} +(-1.86168 + 0.353575i) q^{12} +(-1.28456 + 3.36896i) q^{13} +(4.54926 - 0.428178i) q^{14} +(0.669968 + 0.669968i) q^{15} +(-3.72148 + 1.46649i) q^{16} +4.81491i q^{17} +(-2.29003 - 1.89604i) q^{18} +(1.96537 + 1.96537i) q^{19} +(1.65325 + 1.12550i) q^{20} +(-2.16468 - 2.16468i) q^{21} +(1.15506 - 0.108715i) q^{22} +3.19730 q^{23} +(2.34682 + 1.29388i) q^{24} -1.00000i q^{25} +(4.43772 - 2.51130i) q^{26} +4.83430i q^{27} +(-5.34170 - 3.63653i) q^{28} +3.73707 q^{29} +(-0.125560 - 1.33404i) q^{30} +(0.835217 + 0.835217i) q^{31} +(5.37645 + 1.75893i) q^{32} +(-0.549616 - 0.549616i) q^{33} +(4.34254 - 5.24491i) q^{34} +3.23103i q^{35} +(0.784522 + 4.13073i) q^{36} +(-5.67234 - 5.67234i) q^{37} +(-0.368335 - 3.91345i) q^{38} +(-3.19202 - 1.21709i) q^{39} +(-0.785814 - 2.71707i) q^{40} +(0.160789 - 0.160789i) q^{41} +(0.405689 + 4.31032i) q^{42} +6.05218 q^{43} +(-1.35627 - 0.923320i) q^{44} +(1.48654 - 1.48654i) q^{45} +(-3.48284 - 2.88363i) q^{46} +(1.78661 - 1.78661i) q^{47} +(-1.38946 - 3.52602i) q^{48} -3.43953i q^{49} +(-0.901894 + 1.08931i) q^{50} -4.56202 q^{51} +(-7.09896 - 1.26678i) q^{52} -8.61749 q^{53} +(4.36003 - 5.26603i) q^{54} +0.820362i q^{55} +(2.53899 + 8.77894i) q^{56} +(-1.86215 + 1.86215i) q^{57} +(-4.07082 - 3.37044i) q^{58} +(5.40370 - 5.40370i) q^{59} +(-1.06639 + 1.56642i) q^{60} -1.47327 q^{61} +(-0.156530 - 1.66308i) q^{62} +(-4.80305 + 4.80305i) q^{63} +(-4.27023 - 6.76499i) q^{64} +(1.47390 + 3.29054i) q^{65} +(0.103005 + 1.09440i) q^{66} +(-11.0184 - 11.0184i) q^{67} +(-9.46070 + 1.79681i) q^{68} +3.02937i q^{69} +(2.91404 - 3.51958i) q^{70} +(-8.71653 - 8.71653i) q^{71} +(2.87090 - 5.20719i) q^{72} +(-6.49138 - 6.49138i) q^{73} +(1.06307 + 11.2948i) q^{74} +0.947478 q^{75} +(-3.12829 + 4.59514i) q^{76} -2.65061i q^{77} +(2.37940 + 4.20464i) q^{78} +6.22808i q^{79} +(-1.59452 + 3.66845i) q^{80} +1.72647 q^{81} +(-0.320162 + 0.0301338i) q^{82} +(10.9734 + 10.9734i) q^{83} +(3.44553 - 5.06114i) q^{84} +(3.40465 + 3.40465i) q^{85} +(-6.59268 - 5.45842i) q^{86} +3.54079i q^{87} +(0.644652 + 2.22898i) q^{88} +(8.29440 + 8.29440i) q^{89} +(-2.96000 + 0.278596i) q^{90} +(-4.76220 - 10.6318i) q^{91} +(1.19315 + 6.28230i) q^{92} +(-0.791350 + 0.791350i) q^{93} +(-3.55750 + 0.334833i) q^{94} +2.77946 q^{95} +(-1.66654 + 5.09406i) q^{96} +(9.44730 - 9.44730i) q^{97} +(-3.10209 + 3.74671i) q^{98} +(-1.21950 + 1.21950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.08931	−	0.901894i	−0.770256	−	0.637735i
$2$	−1.08931	−	0.901894i	−0.770256	−	0.637735i
$3$			0.947478i			0.547026i	0.961868	+	0.273513i	$0.0881857\pi$
$3$			0.947478i			0.547026i	−0.961868	+	0.273513i	$0.911814\pi$
$4$	0.373176	+	1.96488i	0.186588	+	0.982438i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	0.854524	−	1.03209i	0.348858	−	0.421350i
$7$	−2.28468	+	2.28468i	−0.863528	+	0.863528i	−0.991746	−	0.128218i	$-0.959074\pi$
$7$	−2.28468	+	2.28468i	−0.863528	+	0.863528i	0.128218	+	0.991746i	$0.459074\pi$
$8$	1.36561	−	2.47692i	0.482815	−	0.875722i
$9$	2.10229			0.700762
$10$	−1.40799	+	0.132521i	−0.445246	+	0.0419067i
$11$	−0.580083	+	0.580083i	−0.174902	+	0.174902i	−0.789129	−	0.614227i	$-0.789468\pi$
$11$	−0.580083	+	0.580083i	−0.174902	+	0.174902i	0.614227	+	0.789129i	$0.289468\pi$
$12$	−1.86168	+	0.353575i	−0.537420	+	0.102068i
$13$	−1.28456	+	3.36896i	−0.356272	+	0.934382i
$13$	−1.28456	+	3.36896i	−0.356272	+	0.934382i
$14$	4.54926	−	0.428178i	1.21584	−	0.114435i
$15$	0.669968	+	0.669968i	0.172985	+	0.172985i
$16$	−3.72148	+	1.46649i	−0.930370	+	0.366622i
$17$			4.81491i			1.16779i	0.811830	+	0.583893i	$0.198471\pi$
$17$			4.81491i			1.16779i	−0.811830	+	0.583893i	$0.801529\pi$
$18$	−2.29003	−	1.89604i	−0.539766	−	0.446901i
$19$	1.96537	+	1.96537i	0.450887	+	0.450887i	0.895649	−	0.444762i	$-0.146712\pi$
$19$	1.96537	+	1.96537i	0.450887	+	0.450887i	−0.444762	+	0.895649i	$0.646712\pi$
$20$	1.65325	+	1.12550i	0.369678	+	0.251670i
$21$	−2.16468	−	2.16468i	−0.472373	−	0.472373i
$22$	1.15506	−	0.108715i	0.246260	−	0.0231781i
$23$	3.19730			0.666684			0.333342	−	0.942806i	$-0.391824\pi$
$23$	3.19730			0.666684			0.333342	+	0.942806i	$0.391824\pi$
$24$	2.34682	+	1.29388i	0.479043	+	0.264113i
$25$		−	1.00000i		−	0.200000i
$26$	4.43772	−	2.51130i	0.870309	−	0.492506i
$27$			4.83430i			0.930362i
$28$	−5.34170	−	3.63653i	−1.00949	−	0.687239i
$29$	3.73707			0.693957			0.346978	−	0.937873i	$-0.387208\pi$
$29$	3.73707			0.693957			0.346978	+	0.937873i	$0.387208\pi$
$30$	−0.125560	−	1.33404i	−0.0229241	−	0.243561i
$31$	0.835217	+	0.835217i	0.150009	+	0.150009i	0.778122	−	0.628113i	$-0.216172\pi$
$31$	0.835217	+	0.835217i	0.150009	+	0.150009i	−0.628113	+	0.778122i	$0.716172\pi$
$32$	5.37645	+	1.75893i	0.950431	+	0.310937i
$33$	−0.549616	−	0.549616i	−0.0956759	−	0.0956759i
$34$	4.34254	−	5.24491i	0.744739	−	0.899495i
$35$			3.23103i			0.546143i
$36$	0.784522	+	4.13073i	0.130754	+	0.688455i
$37$	−5.67234	−	5.67234i	−0.932527	−	0.932527i	0.0653364	−	0.997863i	$-0.479188\pi$
$37$	−5.67234	−	5.67234i	−0.932527	−	0.932527i	−0.997863	+	0.0653364i	$0.979188\pi$
$38$	−0.368335	−	3.91345i	−0.0597519	−	0.634845i
$39$	−3.19202	−	1.21709i	−0.511132	−	0.194890i
$40$	−0.785814	−	2.71707i	−0.124248	−	0.429607i
$41$	0.160789	−	0.160789i	0.0251110	−	0.0251110i	−0.694440	−	0.719551i	$-0.744348\pi$
$41$	0.160789	−	0.160789i	0.0251110	−	0.0251110i	0.719551	+	0.694440i	$0.244348\pi$
$42$	0.405689	+	4.31032i	0.0625991	+	0.665097i
$43$	6.05218			0.922949			0.461474	−	0.887154i	$-0.347321\pi$
$43$	6.05218			0.922949			0.461474	+	0.887154i	$0.347321\pi$
$44$	−1.35627	−	0.923320i	−0.204465	−	0.139196i
$45$	1.48654	−	1.48654i	0.221600	−	0.221600i
$46$	−3.48284	−	2.88363i	−0.513517	−	0.425168i
$47$	1.78661	−	1.78661i	0.260604	−	0.260604i	−0.564695	−	0.825299i	$-0.691006\pi$
$47$	1.78661	−	1.78661i	0.260604	−	0.260604i	0.825299	+	0.564695i	$0.191006\pi$
$48$	−1.38946	−	3.52602i	−0.200552	−	0.508937i
$49$		−	3.43953i		−	0.491362i
$50$	−0.901894	+	1.08931i	−0.127547	+	0.154051i
$51$	−4.56202			−0.638810
$52$	−7.09896	−	1.26678i	−0.984449	−	0.175671i
$53$	−8.61749			−1.18370			−0.591851	−	0.806047i	$-0.701603\pi$
$53$	−8.61749			−1.18370			−0.591851	+	0.806047i	$0.701603\pi$
$54$	4.36003	−	5.26603i	0.593324	−	0.716617i
$55$			0.820362i			0.110618i
$56$	2.53899	+	8.77894i	0.339286	+	1.17314i
$57$	−1.86215	+	1.86215i	−0.246647	+	0.246647i
$58$	−4.07082	−	3.37044i	−0.534524	−	0.442561i
$59$	5.40370	−	5.40370i	0.703502	−	0.703502i	−0.261659	−	0.965161i	$-0.584269\pi$
$59$	5.40370	−	5.40370i	0.703502	−	0.703502i	0.965161	+	0.261659i	$0.0842694\pi$
$60$	−1.06639	+	1.56642i	−0.137670	+	0.202224i
$61$	−1.47327			−0.188633			−0.0943163	−	0.995542i	$-0.530067\pi$
$61$	−1.47327			−0.188633			−0.0943163	+	0.995542i	$0.530067\pi$
$62$	−0.156530	−	1.66308i	−0.0198793	−	0.211212i
$63$	−4.80305	+	4.80305i	−0.605128	+	0.605128i
$64$	−4.27023	−	6.76499i	−0.533779	−	0.845624i
$65$	1.47390	+	3.29054i	0.182814	+	0.408141i
$66$	0.103005	+	1.09440i	0.0126790	+	0.134711i
$67$	−11.0184	−	11.0184i	−1.34611	−	1.34611i	−0.889842	−	0.456269i	$-0.849185\pi$
$67$	−11.0184	−	11.0184i	−1.34611	−	1.34611i	−0.456269	−	0.889842i	$-0.650815\pi$
$68$	−9.46070	+	1.79681i	−1.14728	+	0.217895i
$69$			3.02937i			0.364694i
$70$	2.91404	−	3.51958i	0.348295	−	0.420670i
$71$	−8.71653	−	8.71653i	−1.03446	−	1.03446i	−0.999385	−	0.0350766i	$-0.988832\pi$
$71$	−8.71653	−	8.71653i	−1.03446	−	1.03446i	−0.0350766	−	0.999385i	$-0.511168\pi$
$72$	2.87090	−	5.20719i	0.338339	−	0.613673i
$73$	−6.49138	−	6.49138i	−0.759759	−	0.759759i	0.216520	−	0.976278i	$-0.430529\pi$
$73$	−6.49138	−	6.49138i	−0.759759	−	0.759759i	−0.976278	+	0.216520i	$0.930529\pi$
$74$	1.06307	+	11.2948i	0.123579	+	1.31299i
$75$	0.947478			0.109405
$76$	−3.12829	+	4.59514i	−0.358839	+	0.527099i
$77$		−	2.65061i		−	0.302065i
$78$	2.37940	+	4.20464i	0.269414	+	0.476082i
$79$			6.22808i			0.700713i	0.936616	+	0.350357i	$0.113940\pi$
$79$			6.22808i			0.700713i	−0.936616	+	0.350357i	$0.886060\pi$
$80$	−1.59452	+	3.66845i	−0.178273	+	0.410145i
$81$	1.72647			0.191829
$82$	−0.320162	+	0.0301338i	−0.0353560	+	0.00332772i
$83$	10.9734	+	10.9734i	1.20449	+	1.20449i	0.972786	+	0.231705i	$0.0744304\pi$
$83$	10.9734	+	10.9734i	1.20449	+	1.20449i	0.231705	+	0.972786i	$0.425570\pi$
$84$	3.44553	−	5.06114i	0.375938	−	0.552216i
$85$	3.40465	+	3.40465i	0.369287	+	0.369287i
$86$	−6.59268	−	5.45842i	−0.710907	−	0.588597i
$87$			3.54079i			0.379613i
$88$	0.644652	+	2.22898i	0.0687201	+	0.237611i
$89$	8.29440	+	8.29440i	0.879204	+	0.879204i	0.993452	−	0.114248i	$-0.0364458\pi$
$89$	8.29440	+	8.29440i	0.879204	+	0.879204i	−0.114248	+	0.993452i	$0.536446\pi$
$90$	−2.96000	+	0.278596i	−0.312011	+	0.0293666i
$91$	−4.76220	−	10.6318i	−0.499214	−	1.11452i
$92$	1.19315	+	6.28230i	0.124395	+	0.654976i
$93$	−0.791350	+	0.791350i	−0.0820592	+	0.0820592i
$94$	−3.55750	+	0.334833i	−0.366928	+	0.0345354i
$95$	2.77946			0.285166
$96$	−1.66654	+	5.09406i	−0.170091	+	0.519911i
$97$	9.44730	−	9.44730i	0.959228	−	0.959228i	−0.0399725	−	0.999201i	$-0.512727\pi$
$97$	9.44730	−	9.44730i	0.959228	−	0.959228i	0.999201	+	0.0399725i	$0.0127270\pi$
$98$	−3.10209	+	3.74671i	−0.313359	+	0.378474i
$99$	−1.21950	+	1.21950i	−0.122565	+	0.122565i
$100$	1.96488	−	0.373176i	0.196488	−	0.0373176i
$101$		−	8.88716i		−	0.884306i	−0.896940	−	0.442153i	$-0.854215\pi$
$101$		−	8.88716i		−	0.884306i	0.896940	−	0.442153i	$-0.145785\pi$
$102$	4.96943	+	4.11446i	0.492047	+	0.407392i
$103$	9.32607			0.918925			0.459462	−	0.888197i	$-0.348042\pi$
$103$	9.32607			0.918925			0.459462	+	0.888197i	$0.348042\pi$
$104$	6.59044	+	7.78242i	0.646246	+	0.763129i
$105$	−3.06133			−0.298755
$106$	9.38708	+	7.77206i	0.911754	+	0.754889i
$107$		−	18.7360i		−	1.81128i	−0.424047	−	0.905640i	$-0.639391\pi$
$107$		−	18.7360i		−	1.81128i	0.424047	−	0.905640i	$-0.360609\pi$
$108$	−9.49881	+	1.80404i	−0.914023	+	0.173594i
$109$	4.83351	−	4.83351i	0.462967	−	0.462967i	−0.436660	−	0.899627i	$-0.643839\pi$
$109$	4.83351	−	4.83351i	0.462967	−	0.462967i	0.899627	+	0.436660i	$0.143839\pi$
$110$	0.739879	−	0.893625i	0.0705447	−	0.0852038i
$111$	5.37441	−	5.37441i	0.510117	−	0.510117i
$112$	5.15194	−	11.8529i	0.486812	−	1.11999i
$113$	12.8780			1.21146			0.605728	−	0.795672i	$-0.292882\pi$
$113$	12.8780			1.21146			0.605728	+	0.795672i	$0.292882\pi$
$114$	3.70791	−	0.348989i	0.347277	−	0.0326859i
$115$	2.26083	−	2.26083i	0.210824	−	0.210824i
$116$	1.39458	+	7.34289i	0.129484	+	0.681770i
$117$	−2.70051	+	7.08252i	−0.249662	+	0.654780i
$118$	−10.7598	+	1.01272i	−0.990524	+	0.0932285i
$119$	−11.0005	−	11.0005i	−1.00842	−	1.00842i
$120$	2.57437	−	0.744541i	0.235007	−	0.0679670i
$121$			10.3270i			0.938819i
$122$	1.60484	+	1.32873i	0.145295	+	0.120298i
$123$	0.152344	+	0.152344i	0.0137364	+	0.0137364i
$124$	−1.32942	+	1.95278i	−0.119385	+	0.175365i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	9.56384	−	0.900152i	0.852014	−	0.0801919i
$127$	9.47995			0.841210			0.420605	−	0.907244i	$-0.361818\pi$
$127$	9.47995			0.841210			0.420605	+	0.907244i	$0.361818\pi$
$128$	−1.44971	+	11.2204i	−0.128138	+	0.991756i
$129$			5.73431i			0.504877i
$130$	1.36219	−	4.91370i	0.119472	−	0.430960i
$131$		−	18.7995i		−	1.64252i	−0.570553	−	0.821261i	$-0.693271\pi$
$131$		−	18.7995i		−	1.64252i	0.570553	−	0.821261i	$-0.306729\pi$
$132$	0.874825	−	1.28503i	0.0761437	−	0.111848i
$133$	−8.98050			−0.778708
$134$	2.06498	+	21.9398i	0.178387	+	1.89531i
$135$	3.41837	+	3.41837i	0.294206	+	0.294206i
$136$	11.9261	+	6.57528i	1.02266	+	0.563825i
$137$	13.1384	+	13.1384i	1.12249	+	1.12249i	0.991366	+	0.131123i	$0.0418582\pi$
$137$	13.1384	+	13.1384i	1.12249	+	1.12249i	0.131123	+	0.991366i	$0.458142\pi$
$138$	2.73217	−	3.29991i	0.232578	−	0.280907i
$139$			13.9388i			1.18227i	0.806571	+	0.591137i	$0.201321\pi$
$139$			13.9388i			1.18227i	−0.806571	+	0.591137i	$0.798679\pi$
$140$	−6.34857	+	1.20574i	−0.536552	+	0.101904i
$141$	1.69277	+	1.69277i	0.142557	+	0.142557i
$142$	1.63358	+	17.3563i	0.137087	+	1.45651i
$143$	−1.20913	−	2.69943i	−0.101112	−	0.225738i
$144$	−7.82362	+	3.08298i	−0.651968	+	0.256915i
$145$	2.64251	−	2.64251i	0.219448	−	0.219448i
$146$	1.21657	+	12.9256i	0.100684	+	1.06973i
$147$	3.25888			0.268788
$148$	9.02867	−	13.2622i	0.742152	−	1.09015i
$149$	2.81594	−	2.81594i	0.230691	−	0.230691i	−0.582290	−	0.812981i	$-0.697843\pi$
$149$	2.81594	−	2.81594i	0.230691	−	0.230691i	0.812981	+	0.582290i	$0.197843\pi$
$150$	−1.03209	−	0.854524i	−0.0842701	−	0.0697716i
$151$	−16.5883	+	16.5883i	−1.34994	+	1.34994i	−0.464212	+	0.885724i	$0.653662\pi$
$151$	−16.5883	+	16.5883i	−1.34994	+	1.34994i	−0.885724	+	0.464212i	$0.846338\pi$
$152$	7.55199	−	2.18414i	0.612548	−	0.177157i
$153$			10.1223i			0.818341i
$154$	−2.39057	+	2.88733i	−0.192638	+	0.232667i
$155$	1.18118			0.0948743
$156$	1.20025	−	6.72611i	0.0960967	−	0.538520i
$157$	−16.7512			−1.33689			−0.668447	−	0.743759i	$-0.733041\pi$
$157$	−16.7512			−1.33689			−0.668447	+	0.743759i	$0.733041\pi$
$158$	5.61706	−	6.78428i	0.446869	−	0.539728i
$159$		−	8.16488i		−	0.647517i
$160$	5.04547	−	2.55797i	0.398879	−	0.202226i
$161$	−7.30482	+	7.30482i	−0.575700	+	0.575700i
$162$	−1.88065	−	1.55709i	−0.147758	−	0.122336i
$163$	−0.734690	+	0.734690i	−0.0575454	+	0.0575454i	−0.735294	−	0.677748i	$-0.762956\pi$
$163$	−0.734690	+	0.734690i	−0.0575454	+	0.0575454i	0.677748	+	0.735294i	$0.262956\pi$
$164$	0.375932	+	0.255927i	0.0293554	+	0.0199846i
$165$	−0.777275			−0.0605107
$166$	−2.05656	−	21.8503i	−0.159620	−	1.69591i
$167$	−3.49386	+	3.49386i	−0.270363	+	0.270363i	−0.829246	−	0.558883i	$-0.811230\pi$
$167$	−3.49386	+	3.49386i	−0.270363	+	0.270363i	0.558883	+	0.829246i	$0.311230\pi$
$168$	−8.31785	+	2.40563i	−0.641736	+	0.185599i
$169$	−9.69983	−	8.65525i	−0.746140	−	0.665789i
$170$	−0.638074	−	6.77935i	−0.0489381	−	0.519952i
$171$	4.13178	+	4.13178i	0.315965	+	0.315965i
$172$	2.25853	+	11.8918i	0.172211	+	0.906740i
$173$		−	6.24409i		−	0.474729i	−0.971421	−	0.237365i	$-0.923716\pi$
$173$		−	6.24409i		−	0.474729i	0.971421	−	0.237365i	$-0.0762836\pi$
$174$	3.19342	−	3.85701i	0.242092	−	0.292399i
$175$	2.28468	+	2.28468i	0.172706	+	0.172706i
$176$	1.30808	−	3.00945i	0.0986005	−	0.226846i
$177$	5.11989	+	5.11989i	0.384834	+	0.384834i
$178$	−1.55447	−	16.5158i	−0.116513	−	1.23791i
$179$	−14.2058			−1.06179			−0.530896	−	0.847437i	$-0.678144\pi$
$179$	−14.2058			−1.06179			−0.530896	+	0.847437i	$0.678144\pi$
$180$	3.47561	+	2.36613i	0.259057	+	0.176361i
$181$		−	0.0242100i		−	0.00179951i	−1.00000		0.000899756i	$-0.999714\pi$
$181$		−	0.0242100i		−	0.00179951i	1.00000		0.000899756i	$-0.000286401\pi$
$182$	−4.40127	+	15.8763i	−0.326244	+	1.17683i
$183$		−	1.39589i		−	0.103187i
$184$	4.36626	−	7.91945i	0.321885	−	0.583830i
$185$	−8.02190			−0.589782
$186$	1.57574	−	0.148309i	0.115539	−	0.0108745i
$187$	−2.79305	−	2.79305i	−0.204248	−	0.204248i
$188$	4.17719	+	2.84375i	0.304653	+	0.207402i
$189$	−11.0448	−	11.0448i	−0.803394	−	0.803394i
$190$	−3.02768	−	2.50677i	−0.219651	−	0.181861i
$191$		−	2.96256i		−	0.214363i	−0.994239	−	0.107182i	$-0.965817\pi$
$191$		−	2.96256i		−	0.214363i	0.994239	−	0.107182i	$-0.0341827\pi$
$192$	6.40968	−	4.04595i	0.462579	−	0.291991i
$193$	12.7676	+	12.7676i	0.919030	+	0.919030i	0.996959	−	0.0779292i	$-0.0248308\pi$
$193$	12.7676	+	12.7676i	0.919030	+	0.919030i	−0.0779292	+	0.996959i	$0.524831\pi$
$194$	−18.8115	+	1.77054i	−1.35058	+	0.127117i
$195$	−3.11771	+	1.39648i	−0.223264	+	0.100004i
$196$	6.75826	−	1.28355i	0.482733	−	0.0916821i
$197$	16.3620	−	16.3620i	1.16574	−	1.16574i	0.182546	−	0.983197i	$-0.441566\pi$
$197$	16.3620	−	16.3620i	1.16574	−	1.16574i	0.983197	−	0.182546i	$-0.0584338\pi$
$198$	2.42827	−	0.228550i	0.172570	−	0.0162423i
$199$	−1.83103			−0.129798			−0.0648992	−	0.997892i	$-0.520673\pi$
$199$	−1.83103			−0.129798			−0.0648992	+	0.997892i	$0.520673\pi$
$200$	−2.47692	−	1.36561i	−0.175144	−	0.0965630i
$201$	10.4397	−	10.4397i	0.736358	−	0.736358i
$202$	−8.01528	+	9.68084i	−0.563953	+	0.681142i
$203$	−8.53802	+	8.53802i	−0.599251	+	0.599251i
$204$	−1.70243	−	8.96380i	−0.119194	−	0.627592i
$205$		−	0.227389i		−	0.0158816i
$206$	−10.1589	−	8.41112i	−0.707807	−	0.586031i
$207$	6.72164			0.467187
$208$	−0.160089	−	14.4213i	−0.0111001	−	0.999938i
$209$	−2.28016			−0.157722
$210$	3.33472	+	2.76099i	0.230118	+	0.190526i
$211$			9.10765i			0.626996i	0.949589	+	0.313498i	$0.101501\pi$
$211$			9.10765i			0.626996i	−0.949589	+	0.313498i	$0.898499\pi$
$212$	−3.21584	−	16.9323i	−0.220864	−	1.16292i
$213$	8.25871	−	8.25871i	0.565878	−	0.565878i
$214$	−16.8979	+	20.4093i	−1.15512	+	1.39515i
$215$	4.27954	−	4.27954i	0.291862	−	0.291862i
$216$	11.9742	+	6.60176i	0.814739	+	0.449193i
$217$	−3.81641			−0.259075
$218$	−9.62449	+	0.905860i	−0.651853	+	0.0613526i
$219$	6.15044	−	6.15044i	0.415608	−	0.415608i
$220$	−1.61191	+	0.306139i	−0.108675	+	0.0206399i
$221$	−16.2213	−	6.18503i	−1.09116	−	0.416050i
$222$	−10.7015	+	1.00723i	−0.718240	+	0.0676010i
$223$	11.8411	+	11.8411i	0.792936	+	0.792936i	0.981970	−	0.189034i	$-0.0605358\pi$
$223$	11.8411	+	11.8411i	0.792936	+	0.792936i	−0.189034	+	0.981970i	$0.560536\pi$
$224$	−16.3020	+	8.26488i	−1.08923	+	0.552221i
$225$		−	2.10229i		−	0.140152i
$226$	−14.0280	−	11.6145i	−0.933131	−	0.772588i
$227$	0.884402	+	0.884402i	0.0586999	+	0.0586999i	0.735847	−	0.677147i	$-0.236784\pi$
$227$	0.884402	+	0.884402i	0.0586999	+	0.0586999i	−0.677147	+	0.735847i	$0.736784\pi$
$228$	−4.35380	−	2.96398i	−0.288337	−	0.196294i
$229$	−10.4538	−	10.4538i	−0.690805	−	0.690805i	0.271604	−	0.962409i	$-0.412446\pi$
$229$	−10.4538	−	10.4538i	−0.690805	−	0.690805i	−0.962409	+	0.271604i	$0.912446\pi$
$230$	−4.50177	+	0.423708i	−0.296838	+	0.0279385i
$231$	2.51139			0.165238
$232$	5.10337	−	9.25642i	0.335053	−	0.607714i
$233$			9.45057i			0.619128i	0.950879	+	0.309564i	$0.100183\pi$
$233$			9.45057i			0.619128i	−0.950879	+	0.309564i	$0.899817\pi$
$234$	9.32936	−	5.27947i	0.609880	−	0.345130i
$235$		−	2.52665i		−	0.164820i
$236$	12.6341	+	8.60108i	0.822412	+	0.559882i
$237$	−5.90096			−0.383309
$238$	2.06164	+	21.9043i	0.133636	+	1.41984i
$239$	6.53787	+	6.53787i	0.422899	+	0.422899i	0.886201	−	0.463301i	$-0.153335\pi$
$239$	6.53787	+	6.53787i	0.422899	+	0.422899i	−0.463301	+	0.886201i	$0.653335\pi$
$240$	−3.47577	−	1.51077i	−0.224360	−	0.0975199i
$241$	6.86589	+	6.86589i	0.442271	+	0.442271i	0.892775	−	0.450504i	$-0.148756\pi$
$241$	6.86589	+	6.86589i	0.442271	+	0.442271i	−0.450504	+	0.892775i	$0.648756\pi$
$242$	9.31386	−	11.2493i	0.598718	−	0.723131i
$243$			16.1387i			1.03530i
$244$	−0.549787	−	2.89479i	−0.0351965	−	0.185320i
$245$	−2.43212	−	2.43212i	−0.155382	−	0.155382i
$246$	−0.0285511	−	0.303347i	−0.00182035	−	0.0193407i
$247$	−9.14590	+	4.09664i	−0.581940	+	0.260663i
$248$	3.20934	−	0.928185i	0.203793	−	0.0589398i
$249$	−10.3971	+	10.3971i	−0.658889	+	0.658889i
$250$	0.132521	+	1.40799i	0.00838134	+	0.0890492i
$251$	−13.8306			−0.872979			−0.436489	−	0.899709i	$-0.643778\pi$
$251$	−13.8306			−0.872979			−0.436489	+	0.899709i	$0.643778\pi$
$252$	−11.2298	−	7.64502i	−0.707410	−	0.481591i
$253$	−1.85470	+	1.85470i	−0.116604	+	0.116604i
$254$	−10.3266	−	8.54991i	−0.647946	−	0.536469i
$255$	−3.22583	+	3.22583i	−0.202010	+	0.202010i
$256$	11.6988	−	10.9150i	0.731177	−	0.682188i
$257$		−	12.5495i		−	0.782816i	−0.920217	−	0.391408i	$-0.871988\pi$
$257$		−	12.5495i		−	0.782816i	0.920217	−	0.391408i	$-0.128012\pi$
$258$	5.17173	−	6.24641i	0.321978	−	0.388885i
$259$	25.9190			1.61053
$260$	−5.91547	+	4.12397i	−0.366862	+	0.255758i
$261$	7.85640			0.486299
$262$	−16.9552	+	20.4784i	−1.04749	+	1.26516i
$263$		−	17.9758i		−	1.10843i	−0.832372	−	0.554217i	$-0.813018\pi$
$263$		−	17.9758i		−	1.10843i	0.832372	−	0.554217i	$-0.186982\pi$
$264$	−2.11191	+	0.610793i	−0.129979	+	0.0375917i
$265$	−6.09348	+	6.09348i	−0.374320	+	0.374320i
$266$	9.78251	+	8.09946i	0.599804	+	0.496610i
$267$	−7.85876	+	7.85876i	−0.480948	+	0.480948i
$268$	17.5380	−	25.7616i	1.07130	−	1.57364i
$269$	0.701465			0.0427691			0.0213845	−	0.999771i	$-0.493193\pi$
$269$	0.701465			0.0427691			0.0213845	+	0.999771i	$0.493193\pi$
$270$	−0.640644	−	6.80665i	−0.0389884	−	0.414240i
$271$	−4.24212	+	4.24212i	−0.257691	+	0.257691i	−0.824114	−	0.566424i	$-0.808327\pi$
$271$	−4.24212	+	4.24212i	−0.257691	+	0.257691i	0.566424	+	0.824114i	$0.308327\pi$
$272$	−7.06100	−	17.9186i	−0.428136	−	1.08647i
$273$	10.0734	−	4.51208i	0.609670	−	0.273084i
$274$	−2.46230	−	26.1612i	−0.148753	−	1.58045i
$275$	0.580083	+	0.580083i	0.0349803	+	0.0349803i
$276$	−5.95234	+	1.13049i	−0.358289	+	0.0680474i
$277$			3.76068i			0.225957i	0.993597	+	0.112979i	$0.0360392\pi$
$277$			3.76068i			0.225957i	−0.993597	+	0.112979i	$0.963961\pi$
$278$	12.5713	−	15.1836i	0.753977	−	0.910653i
$279$	1.75587	+	1.75587i	0.105121	+	0.105121i
$280$	8.00298	+	4.41231i	0.478270	+	0.263686i
$281$	3.45456	+	3.45456i	0.206082	+	0.206082i	0.802600	−	0.596518i	$-0.203450\pi$
$281$	3.45456	+	3.45456i	0.206082	+	0.206082i	−0.596518	+	0.802600i	$0.703450\pi$
$282$	−0.317247	−	3.37065i	−0.0188918	−	0.200719i
$283$	18.9157			1.12442			0.562210	−	0.826994i	$-0.309951\pi$
$283$	18.9157			1.12442			0.562210	+	0.826994i	$0.309951\pi$
$284$	13.8741	−	20.3797i	0.823277	−	1.20931i
$285$			2.63347i			0.155994i
$286$	−1.11749	+	4.03101i	−0.0660784	+	0.238359i
$287$			0.734701i			0.0433680i
$288$	11.3028	+	3.69776i	0.666026	+	0.217893i
$289$	−6.18335			−0.363726
$290$	−5.26176	+	0.495239i	−0.308981	+	0.0290814i
$291$	8.95111	+	8.95111i	0.524723	+	0.524723i
$292$	10.3323	−	15.1772i	0.604654	−	0.888178i
$293$	−12.8751	−	12.8751i	−0.752173	−	0.752173i	0.222712	−	0.974884i	$-0.428509\pi$
$293$	−12.8751	−	12.8751i	−0.752173	−	0.752173i	−0.974884	+	0.222712i	$0.928509\pi$
$294$	−3.54992	−	2.93916i	−0.207035	−	0.171416i
$295$		−	7.64199i		−	0.444934i
$296$	−21.7961	+	6.30372i	−1.26687	+	0.366396i
$297$	−2.80430	−	2.80430i	−0.162722	−	0.162722i
$298$	−5.60711	+	0.527743i	−0.324811	+	0.0305713i
$299$	−4.10712	+	10.7716i	−0.237521	+	0.622937i
$300$	0.353575	+	1.86168i	0.0204137	+	0.107484i
$301$	−13.8273	+	13.8273i	−0.796992	+	0.796992i
$302$	33.0306	−	3.10885i	1.90070	−	0.178894i
$303$	8.42039			0.483739
$304$	−10.1963	−	4.43190i	−0.584797	−	0.254187i
$305$	−1.04176	+	1.04176i	−0.0596509	+	0.0596509i
$306$	9.12925	−	11.0263i	0.521885	−	0.630332i
$307$	−14.1449	+	14.1449i	−0.807289	+	0.807289i	−0.984223	−	0.176933i	$-0.943382\pi$
$307$	−14.1449	+	14.1449i	−0.807289	+	0.807289i	0.176933	+	0.984223i	$0.443382\pi$
$308$	5.20812	−	0.989143i	0.296760	−	0.0563617i
$309$			8.83624i			0.502676i
$310$	−1.28666	−	1.06530i	−0.0730775	−	0.0605047i
$311$	24.1829			1.37129			0.685644	−	0.727937i	$-0.259521\pi$
$311$	24.1829			1.37129			0.685644	+	0.727937i	$0.259521\pi$
$312$	−7.37367	+	6.24429i	−0.417452	+	0.353514i
$313$	22.5940			1.27709			0.638545	−	0.769584i	$-0.279536\pi$
$313$	22.5940			1.27709			0.638545	+	0.769584i	$0.279536\pi$
$314$	18.2472	+	15.1078i	1.02975	+	0.852585i
$315$			6.79254i			0.382716i
$316$	−12.2374	+	2.32417i	−0.688407	+	0.130744i
$317$	−10.7699	+	10.7699i	−0.604896	+	0.604896i	−0.941608	−	0.336712i	$-0.890685\pi$
$317$	−10.7699	+	10.7699i	−0.604896	+	0.604896i	0.336712	+	0.941608i	$0.390685\pi$
$318$	−7.36385	+	8.89405i	−0.412944	+	0.498754i
$319$	−2.16781	+	2.16781i	−0.121374	+	0.121374i
$320$	−7.80308	−	1.76406i	−0.436206	−	0.0986140i
$321$	17.7520			0.990818
$322$	14.5453	−	1.36901i	0.810581	−	0.0762921i
$323$	−9.46309	+	9.46309i	−0.526541	+	0.526541i
$324$	0.644275	+	3.39229i	0.0357930	+	0.188461i
$325$	3.36896	+	1.28456i	0.186876	+	0.0712544i
$326$	1.46291	−	0.137690i	0.0810234	−	0.00762595i
$327$	4.57965	+	4.57965i	0.253255	+	0.253255i
$328$	−0.178686	−	0.617834i	−0.00986627	−	0.0341142i
$329$			8.16367i			0.450078i
$330$	0.846690	+	0.701019i	0.0466087	+	0.0385898i
$331$	4.37758	+	4.37758i	0.240614	+	0.240614i	0.817104	−	0.576490i	$-0.195578\pi$
$331$	4.37758	+	4.37758i	0.240614	+	0.240614i	−0.576490	+	0.817104i	$0.695578\pi$
$332$	−17.4664	+	25.6565i	−0.958595	+	1.40808i
$333$	−11.9249	−	11.9249i	−0.653479	−	0.653479i
$334$	6.95698	−	0.654793i	0.380669	−	0.0358287i
$335$	−15.5824			−0.851355
$336$	11.2303	+	4.88135i	0.612664	+	0.266299i
$337$		−	20.7201i		−	1.12870i	−0.825537	−	0.564349i	$-0.809127\pi$
$337$		−	20.7201i		−	1.12870i	0.825537	−	0.564349i	$-0.190873\pi$
$338$	2.75996	+	18.1764i	0.150122	+	0.988667i
$339$			12.2016i			0.662699i
$340$	−5.41919	+	7.96026i	−0.293897	+	0.431706i
$341$	−0.968992			−0.0524738
$342$	−0.774346	−	8.22719i	−0.0418718	−	0.444876i
$343$	−8.13453	−	8.13453i	−0.439223	−	0.439223i
$344$	8.26490	−	14.9907i	0.445614	−	0.808247i
$345$	2.14209	+	2.14209i	0.115326	+	0.115326i
$346$	−5.63150	+	6.80172i	−0.302751	+	0.365663i
$347$			18.6749i			1.00252i	0.865296	+	0.501261i	$0.167130\pi$
$347$			18.6749i			1.00252i	−0.865296	+	0.501261i	$0.832870\pi$
$348$	−6.95722	+	1.32134i	−0.372946	+	0.0708311i
$349$	8.35663	+	8.35663i	0.447320	+	0.447320i	0.894463	−	0.447143i	$-0.147558\pi$
$349$	8.35663	+	8.35663i	0.447320	+	0.447320i	−0.447143	+	0.894463i	$0.647558\pi$
$350$	−0.428178	−	4.54926i	−0.0228871	−	0.243168i
$351$	−16.2866	−	6.20994i	−0.869314	−	0.331462i
$352$	−4.13911	+	2.09846i	−0.220615	+	0.111849i
$353$	12.2214	−	12.2214i	0.650480	−	0.650480i	−0.302629	−	0.953109i	$-0.597864\pi$
$353$	12.2214	−	12.2214i	0.650480	−	0.650480i	0.953109	+	0.302629i	$0.0978642\pi$
$354$	−0.959530	−	10.1947i	−0.0509984	−	0.541843i
$355$	−12.3270			−0.654251
$356$	−13.2022	+	19.3927i	−0.699715	+	1.02781i
$357$	10.4228	−	10.4228i	0.551631	−	0.551631i
$358$	15.4745	+	12.8121i	0.817851	+	0.677142i
$359$	4.21307	−	4.21307i	0.222357	−	0.222357i	−0.587133	−	0.809490i	$-0.699743\pi$
$359$	4.21307	−	4.21307i	0.222357	−	0.222357i	0.809490	+	0.587133i	$0.199743\pi$
$360$	−1.65201	−	5.71207i	−0.0870684	−	0.301052i
$361$		−	11.2746i		−	0.593401i
$362$	−0.0218348	+	0.0263721i	−0.00114761	+	0.00138608i
$363$	−9.78461			−0.513559
$364$	19.1131	−	13.3247i	1.00180	−	0.698403i
$365$	−9.18020			−0.480514
$366$	−1.25894	+	1.52055i	−0.0658060	+	0.0794804i
$367$		−	6.91838i		−	0.361136i	−0.983562	−	0.180568i	$-0.942206\pi$
$367$		−	6.91838i		−	0.361136i	0.983562	−	0.180568i	$-0.0577937\pi$
$368$	−11.8987	+	4.68880i	−0.620262	+	0.244421i
$369$	0.338024	−	0.338024i	0.0175968	−	0.0175968i
$370$	8.73830	+	7.23490i	0.454283	+	0.376125i
$371$	19.6882	−	19.6882i	1.02216	−	1.02216i
$372$	−1.85022	−	1.25959i	−0.0959293	−	0.0653068i
$373$	−0.727402			−0.0376635			−0.0188317	−	0.999823i	$-0.505995\pi$
$373$	−0.727402			−0.0376635			−0.0188317	+	0.999823i	$0.505995\pi$
$374$	0.523452	+	5.56152i	0.0270671	+	0.287579i
$375$	0.669968	−	0.669968i	0.0345970	−	0.0345970i
$376$	−1.98548	−	6.86509i	−0.102393	−	0.354040i
$377$	−4.80048	+	12.5901i	−0.247237	+	0.648421i
$378$	2.06994	+	21.9925i	0.106466	+	1.13117i
$379$	−21.8179	−	21.8179i	−1.12071	−	1.12071i	−0.991635	−	0.129075i	$-0.958799\pi$
$379$	−21.8179	−	21.8179i	−1.12071	−	1.12071i	−0.129075	−	0.991635i	$-0.541201\pi$
$380$	1.03723	+	5.46129i	0.0532085	+	0.280158i
$381$			8.98204i			0.460164i
$382$	−2.67192	+	3.22714i	−0.136707	+	0.165115i
$383$	−26.7948	−	26.7948i	−1.36915	−	1.36915i	−0.861652	−	0.507500i	$-0.830570\pi$
$383$	−26.7948	−	26.7948i	−1.36915	−	1.36915i	−0.507500	−	0.861652i	$-0.669430\pi$
$384$	−10.6311	−	1.37357i	−0.542517	−	0.0700948i
$385$	−1.87427	−	1.87427i	−0.0955214	−	0.0955214i
$386$	−2.39280	−	25.4228i	−0.121790	−	1.29399i
$387$	12.7234			0.646768
$388$	22.0883	+	15.0373i	1.12136	+	0.763402i
$389$			14.1722i			0.718560i	0.933230	+	0.359280i	$0.116978\pi$
$389$			14.1722i			0.718560i	−0.933230	+	0.359280i	$0.883022\pi$
$390$	4.65562	+	1.29064i	0.235747	+	0.0653542i
$391$			15.3947i			0.778545i
$392$	−8.51944	−	4.69705i	−0.430297	−	0.237237i
$393$	17.8121			0.898503
$394$	−32.5800	+	3.06644i	−1.64136	+	0.154485i
$395$	4.40391	+	4.40391i	0.221585	+	0.221585i
$396$	−2.85126	−	1.94108i	−0.143281	−	0.0975430i
$397$	17.6729	+	17.6729i	0.886978	+	0.886978i	0.994232	−	0.107254i	$-0.0342057\pi$
$397$	17.6729	+	17.6729i	0.886978	+	0.886978i	−0.107254	+	0.994232i	$0.534206\pi$
$398$	1.99455	+	1.65140i	0.0999780	+	0.0827770i
$399$		−	8.50882i		−	0.425974i
$400$	1.46649	+	3.72148i	0.0733244	+	0.186074i
$401$	−3.08423	−	3.08423i	−0.154019	−	0.154019i	0.625891	−	0.779910i	$-0.284735\pi$
$401$	−3.08423	−	3.08423i	−0.154019	−	0.154019i	−0.779910	+	0.625891i	$0.784735\pi$
$402$	−20.7875	+	1.95653i	−1.03679	+	0.0975826i
$403$	−3.88670	+	1.74093i	−0.193610	+	0.0867220i
$404$	17.4622	−	3.31647i	0.868776	−	0.165001i
$405$	1.22080	−	1.22080i	0.0606618	−	0.0606618i
$406$	17.0009	−	1.60013i	0.843741	−	0.0794131i
$407$	6.58086			0.326201
$408$	−6.22993	+	11.2997i	−0.308427	+	0.559420i
$409$	−24.2722	+	24.2722i	−1.20018	+	1.20018i	−0.226069	+	0.974111i	$0.572588\pi$
$409$	−24.2722	+	24.2722i	−1.20018	+	1.20018i	−0.974111	+	0.226069i	$0.927412\pi$
$410$	−0.205081	+	0.247697i	−0.0101282	+	0.0122329i
$411$	−12.4483	+	12.4483i	−0.614031	+	0.614031i
$412$	3.48026	+	18.3246i	0.171460	+	0.902787i
$413$			24.6915i			1.21499i
$414$	−7.32193	−	6.06221i	−0.359853	−	0.297941i
$415$	15.5188			0.761787
$416$	−12.8321	+	15.8536i	−0.629146	+	0.777287i
$417$	−13.2067			−0.646735
$418$	2.48379	+	2.05646i	0.121486	+	0.100585i
$419$		−	38.0204i		−	1.85742i	−0.370807	−	0.928710i	$-0.620919\pi$
$419$		−	38.0204i		−	1.85742i	0.370807	−	0.928710i	$-0.379081\pi$
$420$	−1.14241	−	6.01513i	−0.0557440	−	0.293508i
$421$	26.0315	−	26.0315i	1.26870	−	1.26870i	0.321937	−	0.946761i	$-0.395666\pi$
$421$	26.0315	−	26.0315i	1.26870	−	1.26870i	0.946761	−	0.321937i	$-0.104334\pi$
$422$	8.21413	−	9.92102i	0.399858	−	0.482948i
$423$	3.75597	−	3.75597i	0.182621	−	0.182621i
$424$	−11.7681	+	21.3448i	−0.571510	+	1.03659i
$425$	4.81491			0.233557
$426$	−16.4447	+	1.54779i	−0.796751	+	0.0749904i
$427$	3.36595	−	3.36595i	0.162890	−	0.162890i
$428$	36.8140	−	6.99183i	1.77947	−	0.337963i
$429$	2.55765	−	1.14562i	0.123484	−	0.0553112i
$430$	−8.52141	+	0.802038i	−0.410939	+	0.0386777i
$431$	14.1746	+	14.1746i	0.682768	+	0.682768i	0.960623	−	0.277855i	$-0.0896235\pi$
$431$	14.1746	+	14.1746i	0.682768	+	0.682768i	−0.277855	+	0.960623i	$0.589623\pi$
$432$	−7.08944	−	17.9908i	−0.341091	−	0.865581i
$433$			2.87920i			0.138366i	0.997604	+	0.0691828i	$0.0220392\pi$
$433$			2.87920i			0.138366i	−0.997604	+	0.0691828i	$0.977961\pi$
$434$	4.15724	+	3.44200i	0.199554	+	0.165221i
$435$	2.50372	+	2.50372i	0.120044	+	0.120044i
$436$	11.3010	+	7.69351i	0.541220	+	0.368452i
$437$	6.28389	+	6.28389i	0.300599	+	0.300599i
$438$	−12.2468	+	1.15267i	−0.585172	+	0.0550766i
$439$	24.1718			1.15366			0.576828	−	0.816866i	$-0.304290\pi$
$439$	24.1718			1.15366			0.576828	+	0.816866i	$0.304290\pi$
$440$	2.03197	+	1.12029i	0.0968703	+	0.0534078i
$441$		−	7.23088i		−	0.344328i
$442$	12.0917	+	21.3672i	0.575142	+	1.01634i
$443$		−	21.9087i		−	1.04091i	−0.853888	−	0.520457i	$-0.825761\pi$
$443$		−	21.9087i		−	1.04091i	0.853888	−	0.520457i	$-0.174239\pi$
$444$	12.5657	+	8.55446i	0.596340	+	0.405977i
$445$	11.7301			0.556058
$446$	−2.21916	−	23.5779i	−0.105080	−	1.11645i
$447$	2.66804	+	2.66804i	0.126194	+	0.126194i
$448$	25.2120	+	5.69973i	1.19115	+	0.269287i
$449$	−29.1436	−	29.1436i	−1.37537	−	1.37537i	−0.852273	−	0.523098i	$-0.824776\pi$
$449$	−29.1436	−	29.1436i	−1.37537	−	1.37537i	−0.523098	−	0.852273i	$-0.675224\pi$
$450$	−1.89604	+	2.29003i	−0.0893801	+	0.107953i
$451$			0.186542i			0.00878390i
$452$	4.80574	+	25.3036i	0.226043	+	1.19018i
$453$	−15.7170	−	15.7170i	−0.738451	−	0.738451i
$454$	−0.165748	−	1.76102i	−0.00777894	−	0.0826489i
$455$	−10.8852	−	4.15044i	−0.510307	−	0.194576i
$456$	2.06942	+	7.15534i	0.0969095	+	0.335080i
$457$	−28.1071	+	28.1071i	−1.31479	+	1.31479i	−0.396957	+	0.917837i	$0.629934\pi$
$457$	−28.1071	+	28.1071i	−1.31479	+	1.31479i	−0.917837	+	0.396957i	$0.870066\pi$
$458$	1.95917	+	20.8156i	0.0915459	+	0.972647i
$459$	−23.2767			−1.08646
$460$	5.28595	+	3.59857i	0.246459	+	0.167784i
$461$	−17.0485	+	17.0485i	−0.794028	+	0.794028i	−0.982146	−	0.188118i	$-0.939761\pi$
$461$	−17.0485	+	17.0485i	−0.794028	+	0.794028i	0.188118	+	0.982146i	$0.439761\pi$
$462$	−2.73568	−	2.26501i	−0.127275	−	0.105378i
$463$	−18.1565	+	18.1565i	−0.843803	+	0.843803i	−0.989351	−	0.145549i	$-0.953505\pi$
$463$	−18.1565	+	18.1565i	−0.843803	+	0.843803i	0.145549	+	0.989351i	$0.453505\pi$
$464$	−13.9074	+	5.48037i	−0.645637	+	0.254420i
$465$			1.11914i			0.0518988i
$466$	8.52341	−	10.2946i	0.394839	−	0.476887i
$467$	19.1226			0.884891			0.442445	−	0.896795i	$-0.354111\pi$
$467$	19.1226			0.884891			0.442445	+	0.896795i	$0.354111\pi$
$468$	−14.9240	−	2.66314i	−0.689864	−	0.123104i
$469$	50.3470			2.32481
$470$	−2.27877	+	2.75229i	−0.105112	+	0.126954i
$471$		−	15.8714i		−	0.731317i
$472$	−6.00518	−	20.7639i	−0.276411	−	0.955734i
$473$	−3.51077	+	3.51077i	−0.161425	+	0.161425i
$474$	6.42795	+	5.32204i	0.295246	+	0.244449i
$475$	1.96537	−	1.96537i	0.0901775	−	0.0901775i
$476$	17.5096	−	25.7198i	0.802549	−	1.17887i
$477$	−18.1164			−0.829494
$478$	−1.22528	−	13.0182i	−0.0560429	−	0.595439i
$479$	0.856620	−	0.856620i	0.0391400	−	0.0391400i	−0.687266	−	0.726406i	$-0.741189\pi$
$479$	0.856620	−	0.856620i	0.0391400	−	0.0391400i	0.726406	+	0.687266i	$0.241189\pi$
$480$	2.42362	+	4.78047i	0.110623	+	0.218198i
$481$	26.3963	−	11.8235i	1.20357	−	0.539103i
$482$	−1.28675	−	13.6714i	−0.0586100	−	0.622713i
$483$	−6.92115	−	6.92115i	−0.314923	−	0.314923i
$484$	−20.2913	+	3.85379i	−0.922332	+	0.175172i
$485$		−	13.3605i		−	0.606669i
$486$	14.5554	−	17.5800i	0.660246	−	0.797444i
$487$	−20.9162	−	20.9162i	−0.947805	−	0.947805i	0.0508993	−	0.998704i	$-0.483791\pi$
$487$	−20.9162	−	20.9162i	−0.947805	−	0.947805i	−0.998704	+	0.0508993i	$0.983791\pi$
$488$	−2.01191	+	3.64916i	−0.0910747	+	0.165190i
$489$	−0.696102	−	0.696102i	−0.0314788	−	0.0314788i
$490$	0.455809	+	4.84283i	0.0205914	+	0.218777i
$491$	−10.9829			−0.495651			−0.247826	−	0.968805i	$-0.579716\pi$
$491$	−10.9829			−0.495651			−0.247826	+	0.968805i	$0.579716\pi$
$492$	−0.242485	+	0.356187i	−0.0109321	+	0.0160582i
$493$			17.9937i			0.810394i
$494$	13.6574	+	3.78614i	0.614476	+	0.170347i
$495$			1.72464i			0.0775166i
$496$	−4.33308	−	1.88341i	−0.194561	−	0.0845676i
$497$	39.8290			1.78657
$498$	20.7027	−	1.94854i	0.927709	−	0.0873163i
$499$	15.6900	+	15.6900i	0.702380	+	0.702380i	0.964921	−	0.262541i	$-0.0845605\pi$
$499$	15.6900	+	15.6900i	0.702380	+	0.702380i	−0.262541	+	0.964921i	$0.584560\pi$
$500$	1.12550	−	1.65325i	0.0503340	−	0.0739357i
$501$	−3.31036	−	3.31036i	−0.147896	−	0.147896i
$502$	15.0657	+	12.4737i	0.672417	+	0.556729i
$503$		−	6.62913i		−	0.295578i	−0.989019	−	0.147789i	$-0.952784\pi$
$503$		−	6.62913i		−	0.295578i	0.989019	−	0.147789i	$-0.0472157\pi$
$504$	5.33768	+	18.4558i	0.237759	+	0.822089i
$505$	−6.28417	−	6.28417i	−0.279642	−	0.279642i
$506$	3.69308	−	0.347594i	0.164178	−	0.0154524i
$507$	8.20066	−	9.19037i	0.364204	−	0.408159i
$508$	3.53769	+	18.6269i	0.156959	+	0.826436i
$509$	27.1018	−	27.1018i	1.20127	−	1.20127i	0.227487	−	0.973781i	$-0.426949\pi$
$509$	27.1018	−	27.1018i	1.20127	−	1.20127i	0.973781	−	0.227487i	$-0.0730509\pi$
$510$	6.42328	−	0.604561i	0.284428	−	0.0267704i
$511$	29.6615			1.31215
$512$	−22.5878	+	1.33869i	−0.998248	+	0.0591621i
$513$	−9.50121	+	9.50121i	−0.419489	+	0.419489i
$514$	−11.3183	+	13.6702i	−0.499229	+	0.602968i
$515$	6.59453	−	6.59453i	0.290590	−	0.290590i
$516$	−11.2672	+	2.13990i	−0.496011	+	0.0942039i
$517$			2.07277i			0.0911602i
$518$	−28.2337	−	23.3762i	−1.24052	−	1.02709i
$519$	5.91613			0.259689
$520$	10.1631	+	0.842859i	0.445684	+	0.0369618i
$521$	−3.59679			−0.157578			−0.0787891	−	0.996891i	$-0.525105\pi$
$521$	−3.59679			−0.157578			−0.0787891	+	0.996891i	$0.525105\pi$
$522$	−8.55802	−	7.08563i	−0.374574	−	0.310130i
$523$		−	28.7218i		−	1.25592i	−0.778247	−	0.627959i	$-0.783891\pi$
$523$		−	28.7218i		−	1.25592i	0.778247	−	0.627959i	$-0.216109\pi$
$524$	36.9387	−	7.01552i	1.61368	−	0.306474i
$525$	−2.16468	+	2.16468i	−0.0944746	+	0.0944746i
$526$	−16.2122	+	19.5811i	−0.706887	+	0.853778i
$527$	−4.02150	+	4.02150i	−0.175179	+	0.175179i
$528$	2.85139	+	1.23938i	0.124091	+	0.0539371i
$529$	−12.7773			−0.555533
$530$	12.1333	−	1.14199i	0.527039	−	0.0496051i
$531$	11.3601	−	11.3601i	0.492987	−	0.492987i
$532$	−3.35130	−	17.6456i	−0.145297	−	0.765033i
$533$	0.335149	+	0.748233i	0.0145169	+	0.0324096i
$534$	15.6484	−	1.47283i	0.677171	−	0.0637355i
$535$	−13.2484	−	13.2484i	−0.572777	−	0.572777i
$536$	−42.3384	+	12.2448i	−1.82874	+	0.528897i
$537$		−	13.4597i		−	0.580828i
$538$	−0.764110	−	0.632647i	−0.0329431	−	0.0272753i
$539$	1.99522	+	1.99522i	0.0859401	+	0.0859401i
$540$	−5.44102	+	7.99232i	−0.234144	+	0.343935i
$541$	−4.12032	−	4.12032i	−0.177147	−	0.177147i	0.612964	−	0.790111i	$-0.289977\pi$
$541$	−4.12032	−	4.12032i	−0.177147	−	0.177147i	−0.790111	+	0.612964i	$0.789977\pi$
$542$	8.44692	−	0.795027i	0.362826	−	0.0341493i
$543$	0.0229384			0.000984381
$544$	−8.46907	+	25.8871i	−0.363108	+	1.10990i
$545$		−	6.83562i		−	0.292806i
$546$	−15.0424	−	4.17010i	−0.643757	−	0.178464i
$547$		−	23.3477i		−	0.998276i	−0.866523	−	0.499138i	$-0.833650\pi$
$547$		−	23.3477i		−	0.998276i	0.866523	−	0.499138i	$-0.166350\pi$
$548$	−20.9124	+	30.7182i	−0.893333	+	1.31222i
$549$	−3.09723			−0.132187
$550$	−0.108715	−	1.15506i	−0.00463562	−	0.0492520i
$551$	7.34474	+	7.34474i	0.312897	+	0.312897i
$552$	7.50350	+	4.13693i	0.319370	+	0.176080i
$553$	−14.2292	−	14.2292i	−0.605086	−	0.605086i
$554$	3.39174	−	4.09653i	0.144101	−	0.174045i
$555$		−	7.60057i		−	0.322626i
$556$	−27.3880	+	5.20162i	−1.16151	+	0.220598i
$557$	−10.9355	−	10.9355i	−0.463352	−	0.463352i	0.436401	−	0.899752i	$-0.356253\pi$
$557$	−10.9355	−	10.9355i	−0.463352	−	0.463352i	−0.899752	+	0.436401i	$0.856253\pi$
$558$	−0.329071	−	3.49628i	−0.0139307	−	0.148009i
$559$	−7.77437	+	20.3896i	−0.328821	+	0.862387i
$560$	−4.73826	−	12.0242i	−0.200228	−	0.508115i
$561$	2.64635	−	2.64635i	0.111729	−	0.111729i
$562$	−0.647427	−	6.87871i	−0.0273101	−	0.290161i
$563$	−1.45090			−0.0611483			−0.0305741	−	0.999533i	$-0.509734\pi$
$563$	−1.45090			−0.0611483			−0.0305741	+	0.999533i	$0.509734\pi$
$564$	−2.69439	+	3.95779i	−0.113454	+	0.166653i
$565$	9.10609	−	9.10609i	0.383096	−	0.383096i
$566$	−20.6050	−	17.0599i	−0.866092	−	0.717083i
$567$	−3.94442	+	3.94442i	−0.165650	+	0.165650i
$568$	−33.4935	+	9.68675i	−1.40535	+	0.406447i
$569$			1.87396i			0.0785604i	0.999228	+	0.0392802i	$0.0125065\pi$
$569$			1.87396i			0.0785604i	−0.999228	+	0.0392802i	$0.987494\pi$
$570$	2.37511	−	2.86866i	0.0994825	−	0.120155i
$571$	7.38060			0.308868			0.154434	−	0.988003i	$-0.450645\pi$
$571$	7.38060			0.308868			0.154434	+	0.988003i	$0.450645\pi$
$572$	4.85283	−	3.38315i	0.202907	−	0.141457i
$573$	2.80696			0.117262
$574$	0.662622	−	0.800314i	0.0276573	−	0.0334045i
$575$		−	3.19730i		−	0.133337i
$576$	−8.97725	−	14.2219i	−0.374052	−	0.592581i
$577$	−2.76000	+	2.76000i	−0.114900	+	0.114900i	−0.762219	−	0.647319i	$-0.775890\pi$
$577$	−2.76000	+	2.76000i	−0.114900	+	0.114900i	0.647319	+	0.762219i	$0.275890\pi$
$578$	6.73556	+	5.57672i	0.280162	+	0.231961i
$579$	−12.0970	+	12.0970i	−0.502734	+	0.502734i
$580$	6.17832	+	4.20609i	0.256541	+	0.174648i
$581$	−50.1416			−2.08022
$582$	−1.67755	−	17.8234i	−0.0695366	−	0.738806i
$583$	4.99886	−	4.99886i	0.207032	−	0.207032i
$584$	−24.9433	+	7.21393i	−1.03216	+	0.298515i
$585$	3.09855	+	6.91765i	0.128109	+	0.286010i
$586$	2.41296	+	25.6369i	0.0996784	+	1.05905i
$587$	5.39425	+	5.39425i	0.222644	+	0.222644i	0.809611	−	0.586967i	$-0.199678\pi$
$587$	5.39425	+	5.39425i	0.222644	+	0.222644i	−0.586967	+	0.809611i	$0.699678\pi$
$588$	1.21613	+	6.40330i	0.0501525	+	0.264068i
$589$			3.28303i			0.135275i
$590$	−6.89226	+	8.32446i	−0.283750	+	0.342713i
$591$	15.5026	+	15.5026i	0.637692	+	0.637692i
$592$	29.4279	+	12.7911i	1.20948	+	0.525710i
$593$	8.41441	+	8.41441i	0.345538	+	0.345538i	0.858445	−	0.512906i	$-0.171431\pi$
$593$	8.41441	+	8.41441i	0.345538	+	0.345538i	−0.512906	+	0.858445i	$0.671431\pi$
$594$	0.525560	+	5.58392i	0.0215640	+	0.229111i
$595$	−15.5571			−0.637779
$596$	6.58383	+	4.48214i	0.269684	+	0.183596i
$597$		−	1.73486i		−	0.0710032i
$598$	14.1887	−	8.02938i	0.580221	−	0.328346i
$599$			40.3593i			1.64904i	0.565835	+	0.824519i	$0.308554\pi$
$599$			40.3593i			1.64904i	−0.565835	+	0.824519i	$0.691446\pi$
$600$	1.29388	−	2.34682i	0.0528225	−	0.0958087i
$601$	−7.27421			−0.296721			−0.148361	−	0.988933i	$-0.547400\pi$
$601$	−7.27421			−0.296721			−0.148361	+	0.988933i	$0.547400\pi$
$602$	27.5329	−	2.59141i	1.12216	−	0.105618i
$603$	−23.1638	−	23.1638i	−0.943303	−	0.943303i
$604$	−38.7843	−	26.4036i	−1.57811	−	1.07435i
$605$	7.30230	+	7.30230i	0.296881	+	0.296881i
$606$	−9.17238	−	7.59430i	−0.372602	−	0.308497i
$607$			6.34744i			0.257635i	0.991668	+	0.128817i	$0.0411181\pi$
$607$			6.34744i			0.257635i	−0.991668	+	0.128817i	$0.958882\pi$
$608$	7.10978	+	14.0237i	0.288340	+	0.568735i
$609$	−8.08958	−	8.08958i	−0.327806	−	0.327806i
$610$	2.07435	−	0.195238i	0.0839879	−	0.00790497i
$611$	3.72402	+	8.31403i	0.150658	+	0.336350i
$612$	−19.8891	+	3.77740i	−0.803969	+	0.152692i
$613$	−8.06926	+	8.06926i	−0.325914	+	0.325914i	−0.851031	−	0.525116i	$-0.824022\pi$
$613$	−8.06926	+	8.06926i	−0.325914	+	0.325914i	0.525116	+	0.851031i	$0.324022\pi$
$614$	28.1652	−	2.65092i	1.13666	−	0.106982i
$615$	0.215446			0.00868764
$616$	−6.56534	−	3.61969i	−0.264525	−	0.145842i
$617$	−2.83828	+	2.83828i	−0.114265	+	0.114265i	−0.761927	−	0.647662i	$-0.775747\pi$
$617$	−2.83828	+	2.83828i	−0.114265	+	0.114265i	0.647662	+	0.761927i	$0.275747\pi$
$618$	7.96935	−	9.62537i	0.320574	−	0.387189i
$619$	15.1420	−	15.1420i	0.608610	−	0.608610i	−0.333973	−	0.942583i	$-0.608389\pi$
$619$	15.1420	−	15.1420i	0.608610	−	0.608610i	0.942583	+	0.333973i	$0.108389\pi$
$620$	0.440786	+	2.32086i	0.0177024	+	0.0932082i
$621$			15.4567i			0.620257i
$622$	−26.3426	−	21.8104i	−1.05624	−	0.874519i
$623$	−37.9001			−1.51844
$624$	13.6639	−	0.151680i	0.546993	−	0.00607208i
$625$	−1.00000			−0.0400000
$626$	−24.6118	−	20.3774i	−0.983687	−	0.814446i
$627$		−	2.16040i		−	0.0862781i
$628$	−6.25115	−	32.9141i	−0.249448	−	1.31342i
$629$	27.3118	−	27.3118i	1.08899	−	1.08899i
$630$	6.12615	−	7.39916i	0.244072	−	0.294790i
$631$	−9.29996	+	9.29996i	−0.370226	+	0.370226i	−0.867559	−	0.497334i	$-0.834312\pi$
$631$	−9.29996	+	9.29996i	−0.370226	+	0.370226i	0.497334	+	0.867559i	$0.334312\pi$
$632$	15.4264	+	8.50511i	0.613630	+	0.338315i
$633$	−8.62929			−0.342984
$634$	21.4450	−	2.01841i	0.851688	−	0.0801612i
$635$	6.70334	−	6.70334i	0.266014	−	0.266014i
$636$	16.0430	−	3.04693i	0.636145	−	0.120819i
$637$	11.5877	+	4.41828i	0.459120	+	0.175059i
$638$	4.31655	−	0.406275i	0.170894	−	0.0160846i
$639$	−18.3246	−	18.3246i	−0.724911	−	0.724911i
$640$	6.90895	+	8.95915i	0.273100	+	0.354142i
$641$			1.74836i			0.0690560i	0.999404	+	0.0345280i	$0.0109928\pi$
$641$			1.74836i			0.0690560i	−0.999404	+	0.0345280i	$0.989007\pi$
$642$	−19.3373	−	16.0104i	−0.763183	−	0.631880i
$643$	−8.60913	−	8.60913i	−0.339511	−	0.339511i	0.516672	−	0.856183i	$-0.327171\pi$
$643$	−8.60913	−	8.60913i	−0.339511	−	0.339511i	−0.856183	+	0.516672i	$0.827171\pi$
$644$	−17.0790	−	11.6271i	−0.673008	−	0.458171i
$645$	4.05477	+	4.05477i	0.159656	+	0.159656i
$646$	18.8429	−	1.77350i	0.741364	−	0.0697775i
$647$	31.3474			1.23239			0.616197	−	0.787592i	$-0.288673\pi$
$647$	31.3474			1.23239			0.616197	+	0.787592i	$0.288673\pi$
$648$	2.35767	−	4.27631i	0.0926182	−	0.167989i
$649$			6.26920i			0.246087i
$650$	−2.51130	−	4.43772i	−0.0985012	−	0.174062i
$651$		−	3.61596i		−	0.141721i
$652$	−1.71774	−	1.16941i	−0.0672720	−	0.0457975i
$653$	−30.1607			−1.18028			−0.590140	−	0.807301i	$-0.700928\pi$
$653$	−30.1607			−1.18028			−0.590140	+	0.807301i	$0.700928\pi$
$654$	−0.858283	−	9.11899i	−0.0335615	−	0.356581i
$655$	−13.2933	−	13.2933i	−0.519411	−	0.519411i
$656$	−0.362577	+	0.834166i	−0.0141563	+	0.0325687i
$657$	−13.6467	−	13.6467i	−0.532410	−	0.532410i
$658$	7.36276	−	8.89274i	0.287030	−	0.346675i
$659$			1.25226i			0.0487813i	0.999703	+	0.0243906i	$0.00776455\pi$
$659$			1.25226i			0.0487813i	−0.999703	+	0.0243906i	$0.992235\pi$
$660$	−0.290060	−	1.52725i	−0.0112906	−	0.0594481i
$661$	9.85365	+	9.85365i	0.383263	+	0.383263i	0.872276	−	0.489014i	$-0.162643\pi$
$661$	9.85365	+	9.85365i	0.383263	+	0.383263i	−0.489014	+	0.872276i	$0.662643\pi$
$662$	−0.820413	−	8.71664i	−0.0318863	−	0.338782i
$663$	5.86017	−	15.3693i	0.227590	−	0.596893i
$664$	42.1657	−	12.1949i	1.63635	−	0.473253i
$665$	−6.35017	+	6.35017i	−0.246249	+	0.246249i
$666$	2.23487	+	23.7448i	0.0865995	+	0.920093i
$667$	11.9486			0.462650
$668$	−8.16883	−	5.56119i	−0.316062	−	0.215169i
$669$	−11.2191	+	11.2191i	−0.433757	+	0.433757i
$670$	16.9740	+	14.0536i	0.655761	+	0.542939i
$671$	0.854618	−	0.854618i	0.0329922	−	0.0329922i
$672$	−7.83079	−	15.4458i	−0.302079	−	0.595836i
$673$		−	43.3273i		−	1.67014i	−0.550141	−	0.835072i	$-0.685426\pi$
$673$		−	43.3273i		−	1.67014i	0.550141	−	0.835072i	$-0.314574\pi$
$674$	−18.6874	+	22.5706i	−0.719810	+	0.869386i
$675$	4.83430			0.186072
$676$	13.3868	−	22.2889i	0.514876	−	0.857265i
$677$	−4.99424			−0.191944			−0.0959721	−	0.995384i	$-0.530596\pi$
$677$	−4.99424			−0.191944			−0.0959721	+	0.995384i	$0.530596\pi$
$678$	11.0045	−	13.2913i	0.422626	−	0.510447i
$679$			43.1681i			1.65664i
$680$	13.0825	−	3.78362i	0.501690	−	0.145095i
$681$	−0.837952	+	0.837952i	−0.0321104	+	0.0321104i
$682$	1.05553	+	0.873927i	0.0404183	+	0.0334644i
$683$	−9.92091	+	9.92091i	−0.379613	+	0.379613i	−0.870963	−	0.491349i	$-0.836504\pi$
$683$	−9.92091	+	9.92091i	−0.379613	+	0.379613i	0.491349	+	0.870963i	$0.336504\pi$
$684$	−6.57655	+	9.66031i	−0.251461	+	0.369371i
$685$	18.5805			0.709924
$686$	1.52451	+	16.1975i	0.0582061	+	0.618422i
$687$	9.90472	−	9.90472i	0.377889	−	0.377889i
$688$	−22.5231	+	8.87545i	−0.858684	+	0.338373i
$689$	11.0697	−	29.0320i	0.421720	−	1.10603i
$690$	−0.401454	−	4.26533i	−0.0152831	−	0.162378i
$691$	13.2727	+	13.2727i	0.504917	+	0.504917i	0.912962	−	0.408045i	$-0.133789\pi$
$691$	13.2727	+	13.2727i	0.504917	+	0.504917i	−0.408045	+	0.912962i	$0.633789\pi$
$692$	12.2689	−	2.33014i	0.466392	−	0.0885786i
$693$		−	5.57234i		−	0.211676i
$694$	16.8428	−	20.3427i	0.639343	−	0.772198i
$695$	9.85622	+	9.85622i	0.373868	+	0.373868i
$696$	8.77025	+	4.83533i	0.332435	+	0.183283i
$697$	0.774182	+	0.774182i	0.0293242	+	0.0293242i
$698$	−1.56614	−	16.6397i	−0.0592791	−	0.629822i
$699$	−8.95421			−0.338679
$700$	−3.63653	+	5.34170i	−0.137448	+	0.201897i
$701$			18.8310i			0.711236i	0.934631	+	0.355618i	$0.115730\pi$
$701$			18.8310i			0.711236i	−0.934631	+	0.355618i	$0.884270\pi$
$702$	12.1404	+	21.4533i	0.458209	+	0.809702i
$703$		−	22.2965i		−	0.840929i
$704$	6.40135	+	1.44717i	0.241260	+	0.0545422i
$705$	2.39394			0.0901611
$706$	−24.3353	+	2.29044i	−0.915870	+	0.0862020i
$707$	20.3043	+	20.3043i	0.763623	+	0.763623i
$708$	−8.14933	+	11.9706i	−0.306270	+	0.449881i
$709$	22.2853	+	22.2853i	0.836942	+	0.836942i	0.988455	−	0.151513i	$-0.0484146\pi$
$709$	22.2853	+	22.2853i	0.836942	+	0.836942i	−0.151513	+	0.988455i	$0.548415\pi$
$710$	13.4279	+	11.1177i	0.503940	+	0.417239i
$711$			13.0932i			0.491033i
$712$	31.8714	−	9.21764i	1.19443	−	0.345446i
$713$	2.67044	+	2.67044i	0.100009	+	0.100009i
$714$	−20.7538	+	1.95335i	−0.776691	+	0.0731024i
$715$	−2.76377	−	1.05380i	−0.103359	−	0.0394100i
$716$	−5.30126	−	27.9127i	−0.198117	−	1.04314i
$717$	−6.19448	+	6.19448i	−0.231337	+	0.231337i
$718$	−8.38907	+	0.789582i	−0.313077	+	0.0294669i
$719$	1.64758			0.0614442			0.0307221	−	0.999528i	$-0.490219\pi$
$719$	1.64758			0.0614442			0.0307221	+	0.999528i	$0.490219\pi$
$720$	−3.35214	+	7.71213i	−0.124927	+	0.287414i
$721$	−21.3071	+	21.3071i	−0.793518	+	0.793518i
$722$	−10.1685	+	12.2815i	−0.378433	+	0.457070i
$723$	−6.50528	+	6.50528i	−0.241934	+	0.241934i
$724$	0.0475696	−	0.00903457i	0.00176791	−	0.000335767i
$725$		−	3.73707i		−	0.138791i
$726$	10.6584	+	8.82468i	0.395572	+	0.327514i
$727$	−47.2764			−1.75339			−0.876693	−	0.481051i	$-0.840255\pi$
$727$	−47.2764			−1.75339			−0.876693	+	0.481051i	$0.840255\pi$
$728$	−32.8374	−	2.72330i	−1.21704	−	0.100932i
$729$	−10.1117			−0.374506
$730$	10.0000	+	8.27956i	0.370118	+	0.306440i
$731$			29.1407i			1.07781i
$732$	2.74275	−	0.520911i	0.101375	−	0.0192534i
$733$	−29.8092	+	29.8092i	−1.10103	+	1.10103i	−0.106740	+	0.994287i	$0.534041\pi$
$733$	−29.8092	+	29.8092i	−1.10103	+	1.10103i	−0.994287	+	0.106740i	$0.965959\pi$
$734$	−6.23964	+	7.53623i	−0.230309	+	0.278167i
$735$	2.30438	−	2.30438i	0.0849982	−	0.0849982i
$736$	17.1901	+	5.62382i	0.633636	+	0.207297i
$737$	12.7832			0.470874
$738$	−0.673073	+	0.0633498i	−0.0247761	+	0.00233194i
$739$	4.32736	−	4.32736i	0.159185	−	0.159185i	−0.623021	−	0.782205i	$-0.714095\pi$
$739$	4.32736	−	4.32736i	0.159185	−	0.159185i	0.782205	+	0.623021i	$0.214095\pi$
$740$	−2.99358	−	15.7620i	−0.110046	−	0.579424i
$741$	−3.88147	−	8.66554i	−0.142589	−	0.318337i
$742$	−39.2032	+	3.68981i	−1.43919	+	0.135457i
$743$	10.5016	+	10.5016i	0.385267	+	0.385267i	0.872995	−	0.487728i	$-0.162174\pi$
$743$	10.5016	+	10.5016i	0.385267	+	0.385267i	−0.487728	+	0.872995i	$0.662174\pi$
$744$	0.879434	+	3.04078i	0.0322416	+	0.111480i
$745$		−	3.98235i		−	0.145902i
$746$	0.792364	+	0.656040i	0.0290105	+	0.0240193i
$747$	23.0693	+	23.0693i	0.844062	+	0.844062i
$748$	4.44570	−	6.53029i	0.162551	−	0.238771i
$749$	42.8058	+	42.8058i	1.56409	+	1.56409i
$750$	−1.33404	+	0.125560i	−0.0487122	+	0.00458481i
$751$	−24.6601			−0.899859			−0.449930	−	0.893064i	$-0.648551\pi$
$751$	−24.6601			−0.899859			−0.449930	+	0.893064i	$0.648551\pi$
$752$	−4.02879	+	9.26888i	−0.146915	+	0.338001i
$753$		−	13.1042i		−	0.477542i
$754$	16.5841	−	9.38490i	0.603957	−	0.341778i
$755$			23.4594i			0.853775i
$756$	17.5801	−	25.8234i	0.639381	−	0.939188i
$757$	15.7562			0.572669			0.286334	−	0.958130i	$-0.407563\pi$
$757$	15.7562			0.572669			0.286334	+	0.958130i	$0.407563\pi$
$758$	4.08894	+	43.4438i	0.148517	+	1.57795i
$759$	−1.75729	−	1.75729i	−0.0637855	−	0.0637855i
$760$	3.79565	−	6.88448i	0.137683	−	0.249726i
$761$	−2.00078	−	2.00078i	−0.0725282	−	0.0725282i	0.669912	−	0.742440i	$-0.266332\pi$
$761$	−2.00078	−	2.00078i	−0.0725282	−	0.0725282i	−0.742440	+	0.669912i	$0.766332\pi$
$762$	8.10085	−	9.78419i	0.293463	−	0.354444i
$763$			22.0861i			0.799570i
$764$	5.82107	−	1.10556i	0.210599	−	0.0399976i
$765$	7.15756	+	7.15756i	0.258782	+	0.258782i
$766$	5.02168	+	53.3539i	0.181441	+	1.92775i
$767$	11.2635	+	25.1462i	0.406702	+	0.907978i
$768$	10.3417	+	11.0844i	0.373175	+	0.399973i
$769$	16.9102	−	16.9102i	0.609797	−	0.609797i	−0.333096	−	0.942893i	$-0.608093\pi$
$769$	16.9102	−	16.9102i	0.609797	−	0.609797i	0.942893	+	0.333096i	$0.108093\pi$
$770$	0.351261	+	3.73204i	0.0126586	+	0.134493i
$771$	11.8904			0.428221
$772$	−20.3222	+	29.8512i	−0.731410	+	1.07437i
$773$	5.61667	−	5.61667i	0.202018	−	0.202018i	−0.598846	−	0.800864i	$-0.704374\pi$
$773$	5.61667	−	5.61667i	0.202018	−	0.202018i	0.800864	+	0.598846i	$0.204374\pi$
$774$	−13.8597	−	11.4752i	−0.498176	−	0.412466i
$775$	0.835217	−	0.835217i	0.0300019	−	0.0300019i
$776$	−10.4989	−	36.3015i	−0.376888	−	1.30315i
$777$			24.5576i			0.881001i
$778$	12.7818	−	15.4379i	0.458251	−	0.553475i
$779$	0.632019			0.0226444
$780$	−3.90737	−	5.60478i	−0.139906	−	0.200683i
$781$	10.1126			0.361858
$782$	13.8844	−	16.7696i	0.496505	−	0.599678i
$783$			18.0661i			0.645631i
$784$	5.04403	+	12.8002i	0.180144	+	0.457148i
$785$	−11.8449	+	11.8449i	−0.422763	+	0.422763i
$786$	−19.4029	−	16.0646i	−0.692077	−	0.573007i
$787$	−2.83112	+	2.83112i	−0.100918	+	0.100918i	−0.755763	−	0.654845i	$-0.772734\pi$
$787$	−2.83112	+	2.83112i	−0.100918	+	0.100918i	0.654845	+	0.755763i	$0.272734\pi$
$788$	38.2552	+	26.0434i	1.36278	+	0.927757i
$789$	17.0317			0.606343
$790$	−0.825348	−	8.76907i	−0.0293646	−	0.311990i
$791$	−29.4220	+	29.4220i	−1.04613	+	1.04613i
$792$	1.35524	+	4.68596i	0.0481565	+	0.166508i
$793$	1.89250	−	4.96339i	0.0672045	−	0.176255i
$794$	−3.31212	−	35.1903i	−0.117543	−	1.24886i
$795$	−5.77344	−	5.77344i	−0.204763	−	0.204763i
$796$	−0.683296	−	3.59775i	−0.0242188	−	0.127519i
$797$		−	56.1153i		−	1.98771i	−0.110705	−	0.993853i	$-0.535311\pi$
$797$		−	56.1153i		−	1.98771i	0.110705	−	0.993853i	$-0.464689\pi$
$798$	−7.67405	+	9.26871i	−0.271659	+	0.328109i
$799$	8.60237	+	8.60237i	0.304330	+	0.304330i
$800$	1.75893	−	5.37645i	0.0621874	−	0.190086i
$801$	17.4372	+	17.4372i	0.616113	+	0.616113i
$802$	0.578023	+	6.14132i	0.0204107	+	0.216858i
$803$	7.53109			0.265766
$804$	24.4085	+	16.6169i	0.860822	+	0.586031i
$805$			10.3306i			0.364105i
$806$	5.80394	+	1.60898i	0.204435	+	0.0566740i
$807$			0.664622i			0.0233958i
$808$	−22.0128	−	12.1364i	−0.774406	−	0.426956i
$809$	−18.7722			−0.659994			−0.329997	−	0.943982i	$-0.607048\pi$
$809$	−18.7722			−0.659994			−0.329997	+	0.943982i	$0.607048\pi$
$810$	−2.43085	+	0.228792i	−0.0854113	+	0.00803894i
$811$	7.14031	+	7.14031i	0.250730	+	0.250730i	0.821270	−	0.570540i	$-0.193266\pi$
$811$	7.14031	+	7.14031i	0.250730	+	0.250730i	−0.570540	+	0.821270i	$0.693266\pi$
$812$	−19.9623	−	13.5900i	−0.700541	−	0.476915i
$813$	−4.01932	−	4.01932i	−0.140964	−	0.140964i
$814$	−7.16857	−	5.93524i	−0.251258	−	0.208030i
$815$			1.03901i			0.0363949i
$816$	16.9775	−	6.69014i	0.594330	−	0.234202i
$817$	11.8948	+	11.8948i	0.416146	+	0.416146i
$818$	48.3307	−	4.54890i	1.68984	−	0.159049i
$819$	−10.0115	−	22.3511i	−0.349831	−	0.781011i
$820$	0.446792	−	0.0848562i	0.0156027	−	0.00296331i
$821$	0.369450	−	0.369450i	0.0128939	−	0.0128939i	−0.700630	−	0.713524i	$-0.747098\pi$
$821$	0.369450	−	0.369450i	0.0128939	−	0.0128939i	0.713524	+	0.700630i	$0.247098\pi$
$822$	24.7871	−	2.33297i	0.864550	−	0.0813717i
$823$	12.4888			0.435331			0.217666	−	0.976023i	$-0.430156\pi$
$823$	12.4888			0.435331			0.217666	+	0.976023i	$0.430156\pi$
$824$	12.7358	−	23.0999i	0.443671	−	0.804723i
$825$	−0.549616	+	0.549616i	−0.0191352	+	0.0191352i
$826$	22.2691	−	26.8966i	0.774840	−	0.935851i
$827$	7.16621	−	7.16621i	0.249194	−	0.249194i	−0.571446	−	0.820640i	$-0.693617\pi$
$827$	7.16621	−	7.16621i	0.249194	−	0.249194i	0.820640	+	0.571446i	$0.193617\pi$
$828$	2.50835	+	13.2072i	0.0871713	+	0.458982i
$829$			13.5183i			0.469509i	0.972055	+	0.234755i	$0.0754287\pi$
$829$			13.5183i			0.469509i	−0.972055	+	0.234755i	$0.924571\pi$
$830$	−16.9047	−	13.9963i	−0.586771	−	0.485818i
$831$	−3.56316			−0.123605
$832$	28.2764	−	5.69624i	0.980307	−	0.197481i
$833$	16.5610			0.573806
$834$	14.3861	+	11.9110i	0.498151	+	0.412445i
$835$			4.94107i			0.170993i
$836$	−0.850900	−	4.48023i	−0.0294290	−	0.154952i
$837$	−4.03769	+	4.03769i	−0.139563	+	0.139563i
$838$	−34.2904	+	41.4159i	−1.18454	+	1.43069i
$839$	30.8850	−	30.8850i	1.06627	−	1.06627i	0.0686251	−	0.997643i	$-0.478139\pi$
$839$	30.8850	−	30.8850i	1.06627	−	1.06627i	0.997643	−	0.0686251i	$-0.0218612\pi$
$840$	−4.18057	+	7.58265i	−0.144243	+	0.261626i
$841$	−15.0343			−0.518424
$842$	−51.8339	+	4.87863i	−1.78631	+	0.168129i
$843$	−3.27312	+	3.27312i	−0.112732	+	0.112732i
$844$	−17.8954	+	3.39875i	−0.615985	+	0.116990i
$845$	−12.9790	+	0.738625i	−0.446491	+	0.0254095i
$846$	−7.47888	+	0.703915i	−0.257129	+	0.0242011i
$847$	−23.5939	−	23.5939i	−0.810696	−	0.810696i
$848$	32.0698	−	12.6374i	1.10128	−	0.433971i
$849$			17.9222i			0.615088i
$850$	−5.24491	−	4.34254i	−0.179899	−	0.148948i
$851$	−18.1362	−	18.1362i	−0.621700	−	0.621700i
$852$	19.3093	+	13.1454i	0.661526	+	0.450354i
$853$	19.6854	+	19.6854i	0.674015	+	0.674015i	0.958639	−	0.284624i	$-0.0918688\pi$
$853$	19.6854	+	19.6854i	0.674015	+	0.674015i	−0.284624	+	0.958639i	$0.591869\pi$
$854$	−6.70227	+	0.630820i	−0.229347	+	0.0215862i
$855$	5.84321			0.199834
$856$	−46.4076	−	25.5861i	−1.58618	−	0.874513i
$857$		−	31.0165i		−	1.05950i	−0.848153	−	0.529751i	$-0.822285\pi$
$857$		−	31.0165i		−	1.05950i	0.848153	−	0.529751i	$-0.177715\pi$
$858$	−3.81929	−	1.05879i	−0.130389	−	0.0361466i
$859$			54.5587i			1.86152i	0.365632	+	0.930759i	$0.380853\pi$
$859$			54.5587i			1.86152i	−0.365632	+	0.930759i	$0.619147\pi$
$860$	10.0058	+	6.81174i	0.341194	+	0.232279i
$861$	−0.696113			−0.0237235
$862$	−2.65650	−	28.2245i	−0.0904808	−	0.961331i
$863$	31.3699	+	31.3699i	1.06784	+	1.06784i	0.997524	+	0.0703205i	$0.0224022\pi$
$863$	31.3699	+	31.3699i	1.06784	+	1.06784i	0.0703205	+	0.997524i	$0.477598\pi$
$864$	−8.50318	+	25.9914i	−0.289284	+	0.884244i
$865$	−4.41524	−	4.41524i	−0.150123	−	0.150123i
$866$	2.59673	−	3.13633i	0.0882406	−	0.106577i
$867$		−	5.85859i		−	0.198968i
$868$	−1.42419	−	7.49878i	−0.0483402	−	0.254525i
$869$	−3.61280	−	3.61280i	−0.122556	−	0.122556i
$870$	−0.469228	−	4.98540i	−0.0159083	−	0.169021i
$871$	51.2743	−	22.9668i	1.73736	−	0.778200i
$872$	−5.37153	−	18.5729i	−0.181903	−	0.628958i
$873$	19.8609	−	19.8609i	0.672191	−	0.672191i
$874$	−1.17768	−	12.5125i	−0.0398356	−	0.423241i
$875$	3.23103			0.109229
$876$	14.3800	+	9.78966i	0.485857	+	0.330762i
$877$	8.00017	−	8.00017i	0.270147	−	0.270147i	−0.559013	−	0.829159i	$-0.688820\pi$
$877$	8.00017	−	8.00017i	0.270147	−	0.270147i	0.829159	+	0.559013i	$0.188820\pi$
$878$	−26.3304	−	21.8004i	−0.888609	−	0.735726i
$879$	12.1989	−	12.1989i	0.411458	−	0.411458i
$880$	−1.20305	−	3.05296i	−0.0405548	−	0.102915i
$881$			8.34832i			0.281262i	0.990062	+	0.140631i	$0.0449131\pi$
$881$			8.34832i			0.281262i	−0.990062	+	0.140631i	$0.955087\pi$
$882$	−6.52149	+	7.87665i	−0.219590	+	0.265220i
$883$	−37.2563			−1.25378			−0.626888	−	0.779109i	$-0.715672\pi$
$883$	−37.2563			−1.25378			−0.626888	+	0.779109i	$0.715672\pi$
$884$	6.09944	−	34.1809i	0.205146	−	1.14963i
$885$	7.24061			0.243391
$886$	−19.7593	+	23.8653i	−0.663828	+	0.801771i
$887$			42.2683i			1.41923i	0.704589	+	0.709616i	$0.251131\pi$
$887$			42.2683i			1.41923i	−0.704589	+	0.709616i	$0.748869\pi$
$888$	−5.97264	−	20.6513i	−0.200429	−	0.693013i
$889$	−21.6587	+	21.6587i	−0.726408	+	0.726408i
$890$	−12.7776	−	10.5793i	−0.428307	−	0.354618i
$891$	−1.00149	+	1.00149i	−0.0335513	+	0.0335513i
$892$	−18.8474	+	27.6850i	−0.631059	+	0.926963i
$893$	7.02271			0.235006
$894$	−0.500025	−	5.31261i	−0.0167233	−	0.177680i
$895$	−10.0450	+	10.0450i	−0.335768	+	0.335768i
$896$	−22.3230	−	28.9473i	−0.745759	−	0.967060i
$897$	−10.2058	−	3.89140i	−0.340763	−	0.129930i
$898$	5.46187	+	58.0307i	0.182265	+	1.93651i
$899$	3.12127	+	3.12127i	0.104100	+	0.104100i
$900$	4.13073	−	0.784522i	0.137691	−	0.0261507i
$901$		−	41.4924i		−	1.38231i
$902$	0.168241	−	0.203201i	0.00560180	−	0.00676585i
$903$	−13.1011	−	13.1011i	−0.435976	−	0.435976i
$904$	17.5862	−	31.8976i	0.584909	−	1.06090i
$905$	−0.0171190	−	0.0171190i	−0.000569056	−	0.000569056i
$906$	2.94557	+	31.2958i	0.0978599	+	1.03973i
$907$	−5.76412			−0.191395			−0.0956973	−	0.995410i	$-0.530508\pi$
$907$	−5.76412			−0.191395			−0.0956973	+	0.995410i	$0.530508\pi$
$908$	−1.40770	+	2.06778i	−0.0467163	+	0.0686217i
$909$		−	18.6834i		−	0.619688i
$910$	8.11407	+	14.3384i	0.268979	+	0.475313i
$911$		−	15.0025i		−	0.497056i	−0.968625	−	0.248528i	$-0.920053\pi$
$911$		−	15.0025i		−	0.497056i	0.968625	−	0.248528i	$-0.0799468\pi$
$912$	4.19913	−	9.66076i	0.139047	−	0.319900i
$913$	−12.7310			−0.421335
$914$	55.9668	−	5.26762i	1.85122	−	0.174237i
$915$	−0.987042	−	0.987042i	−0.0326306	−	0.0326306i
$916$	16.6393	−	24.4415i	0.549777	−	0.807569i
$917$	42.9509	+	42.9509i	1.41836	+	1.41836i
$918$	25.3555	+	20.9931i	0.836855	+	0.692877i
$919$		−	29.5306i		−	0.974125i	−0.873367	−	0.487063i	$-0.838068\pi$
$919$		−	29.5306i		−	0.974125i	0.873367	−	0.487063i	$-0.161932\pi$
$920$	−2.51249	−	8.68731i	−0.0828342	−	0.286412i
$921$	−13.4019	−	13.4019i	−0.441609	−	0.441609i
$922$	33.9470	−	3.19510i	1.11798	−	0.105225i
$923$	40.5625	−	18.1688i	1.33513	−	0.598033i
$924$	0.937191	+	4.93458i	0.0308313	+	0.162336i
$925$	−5.67234	+	5.67234i	−0.186505	+	0.186505i
$926$	36.1532	−	3.40275i	1.18807	−	0.111821i
$927$	19.6061			0.643948
$928$	20.0922	+	6.57323i	0.659558	+	0.215777i
$929$	−3.83565	+	3.83565i	−0.125844	+	0.125844i	−0.767223	−	0.641380i	$-0.778362\pi$
$929$	−3.83565	+	3.83565i	−0.125844	+	0.125844i	0.641380	+	0.767223i	$0.278362\pi$
$930$	1.00934	−	1.21908i	0.0330977	−	0.0399753i
$931$	6.75997	−	6.75997i	0.221549	−	0.221549i
$932$	−18.5692	+	3.52672i	−0.608255	+	0.115522i
$933$			22.9128i			0.750131i
$934$	−20.8304	−	17.2466i	−0.681592	−	0.564326i
$935$	−3.94997			−0.129178
$936$	13.8550	+	16.3609i	0.452865	+	0.534772i
$937$	−36.1439			−1.18077			−0.590384	−	0.807122i	$-0.701024\pi$
$937$	−36.1439			−1.18077			−0.590384	+	0.807122i	$0.701024\pi$
$938$	−54.8433	−	45.4077i	−1.79070	−	1.48261i
$939$			21.4074i			0.698602i
$940$	4.96455	−	0.942884i	0.161926	−	0.0307535i
$941$	−16.7054	+	16.7054i	−0.544581	+	0.544581i	−0.924868	−	0.380288i	$-0.875825\pi$
$941$	−16.7054	+	16.7054i	−0.544581	+	0.544581i	0.380288	+	0.924868i	$0.375825\pi$
$942$	−14.3143	+	17.2888i	−0.466386	+	0.563301i
$943$	0.514090	−	0.514090i	0.0167411	−	0.0167411i
$944$	−12.1853	+	28.0342i	−0.396598	+	0.912436i
$945$	−15.6198			−0.508111
$946$	6.99064	−	0.657962i	0.227285	−	0.0213922i
$947$	−32.2608	+	32.2608i	−1.04834	+	1.04834i	−0.0495658	+	0.998771i	$0.515784\pi$
$947$	−32.2608	+	32.2608i	−1.04834	+	1.04834i	−0.998771	+	0.0495658i	$0.984216\pi$
$948$	−2.20209	−	11.5947i	−0.0715207	−	0.376577i
$949$	30.2078	−	13.5307i	0.980586	−	0.439224i
$950$	−3.91345	+	0.368335i	−0.126969	+	0.0119504i
$951$	−10.2042	−	10.2042i	−0.330894	−	0.330894i
$952$	−42.2698	+	12.2250i	−1.36997	+	0.396214i
$953$			12.5115i			0.405286i	0.979253	+	0.202643i	$0.0649530\pi$
$953$			12.5115i			0.405286i	−0.979253	+	0.202643i	$0.935047\pi$
$954$	19.7343	+	16.3391i	0.638923	+	0.528998i
$955$	−2.09485	−	2.09485i	−0.0677877	−	0.0677877i
$956$	−10.4063	+	15.2859i	−0.336565	+	0.494380i
$957$	−2.05396	−	2.05396i	−0.0663949	−	0.0663949i
$958$	−1.70570	+	0.160541i	−0.0551087	+	0.00518685i
$959$	−60.0341			−1.93860
$960$	1.67141	−	7.39325i	0.0539445	−	0.238616i
$961$		−	29.6048i		−	0.954994i
$962$	−39.4172	−	10.9273i	−1.27086	−	0.352311i
$963$		−	39.3885i		−	1.26928i
$964$	−10.9284	+	16.0528i	−0.351982	+	0.517026i
$965$	18.0561			0.581245
$966$	1.29711	+	13.7814i	0.0417338	+	0.443409i
$967$	−24.4422	−	24.4422i	−0.786009	−	0.786009i	0.194828	−	0.980837i	$-0.437585\pi$
$967$	−24.4422	−	24.4422i	−0.786009	−	0.786009i	−0.980837	+	0.194828i	$0.937585\pi$
$968$	25.5791	+	14.1026i	0.822145	+	0.453276i
$969$	−8.96607	−	8.96607i	−0.288032	−	0.288032i
$970$	−12.0498	+	14.5537i	−0.386894	+	0.467290i
$971$		−	8.74946i		−	0.280784i	−0.990096	−	0.140392i	$-0.955164\pi$
$971$		−	8.74946i		−	0.280784i	0.990096	−	0.140392i	$-0.0448362\pi$
$972$	−31.7105	+	6.02257i	−1.01712	+	0.193174i
$973$	−31.8457	−	31.8457i	−1.02093	−	1.02093i
$974$	3.91996	+	41.6484i	0.125604	+	1.33450i
$975$	−1.21709	+	3.19202i	−0.0389781	+	0.102226i
$976$	5.48274	−	2.16053i	0.175498	−	0.0691569i
$977$	−27.9185	+	27.9185i	−0.893193	+	0.893193i	−0.994822	−	0.101629i	$-0.967595\pi$
$977$	−27.9185	+	27.9185i	−0.893193	+	0.893193i	0.101629	+	0.994822i	$0.467595\pi$
$978$	0.130458	+	1.38608i	0.00417159	+	0.0443219i
$979$	−9.62289			−0.307549
$980$	3.87120	−	5.68642i	0.123661	−	0.181646i
$981$	10.1614	−	10.1614i	0.324430	−	0.324430i
$982$	11.9637	+	9.90541i	0.381778	+	0.316094i
$983$	−16.2132	+	16.2132i	−0.517122	+	0.517122i	−0.916699	−	0.399577i	$-0.869157\pi$
$983$	−16.2132	+	16.2132i	−0.517122	+	0.517122i	0.399577	+	0.916699i	$0.369157\pi$
$984$	0.585384	−	0.169301i	0.0186614	−	0.00539711i
$985$		−	23.1393i		−	0.737281i
$986$	16.2284	−	19.6006i	0.516817	−	0.624211i
$987$	−7.73490			−0.246204
$988$	−11.4624	−	16.4418i	−0.364668	−	0.523084i
$989$	19.3507			0.615315
$990$	1.55544	−	1.87866i	0.0494351	−	0.0597076i
$991$		−	38.6799i		−	1.22871i	−0.789031	−	0.614353i	$-0.789417\pi$
$991$		−	38.6799i		−	1.22871i	0.789031	−	0.614353i	$-0.210583\pi$
$992$	3.02142	+	5.95959i	0.0959301	+	0.189217i
$993$	−4.14766	+	4.14766i	−0.131622	+	0.131622i
$994$	−43.3859	−	35.9215i	−1.37612	−	1.13936i
$995$	−1.29474	+	1.29474i	−0.0410459	+	0.0410459i
$996$	−24.3089	−	16.5491i	−0.770258	−	0.524377i
$997$	−19.8744			−0.629429			−0.314715	−	0.949186i	$-0.601909\pi$
$997$	−19.8744			−0.629429			−0.314715	+	0.949186i	$0.601909\pi$
$998$	−2.94050	−	31.2419i	−0.0930798	−	0.988945i
$999$	27.4218	−	27.4218i	0.867587	−	0.867587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.j.a.31.7	✓	56
4.3	odd	2	inner	260.2.j.a.31.21	yes	56
13.8	odd	4	inner	260.2.j.a.151.21	yes	56
52.47	even	4	inner	260.2.j.a.151.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.j.a.31.7	✓	56	1.1	even	1	trivial
260.2.j.a.31.21	yes	56	4.3	odd	2	inner
260.2.j.a.151.7	yes	56	52.47	even	4	inner
260.2.j.a.151.21	yes	56	13.8	odd	4	inner

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08931 - 0.901894i) q^{2} +0.947478i q^{3} +(0.373176 + 1.96488i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.854524 - 1.03209i) q^{6} +(-2.28468 + 2.28468i) q^{7} +(1.36561 - 2.47692i) q^{8} +2.10229 q^{9} +O(q^{10})\)	\(q+(-1.08931 - 0.901894i) q^{2} +0.947478i q^{3} +(0.373176 + 1.96488i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.854524 - 1.03209i) q^{6} +(-2.28468 + 2.28468i) q^{7} +(1.36561 - 2.47692i) q^{8} +2.10229 q^{9} +(-1.40799 + 0.132521i) q^{10} +(-0.580083 + 0.580083i) q^{11} +(-1.86168 + 0.353575i) q^{12} +(-1.28456 + 3.36896i) q^{13} +(4.54926 - 0.428178i) q^{14} +(0.669968 + 0.669968i) q^{15} +(-3.72148 + 1.46649i) q^{16} +4.81491i q^{17} +(-2.29003 - 1.89604i) q^{18} +(1.96537 + 1.96537i) q^{19} +(1.65325 + 1.12550i) q^{20} +(-2.16468 - 2.16468i) q^{21} +(1.15506 - 0.108715i) q^{22} +3.19730 q^{23} +(2.34682 + 1.29388i) q^{24} -1.00000i q^{25} +(4.43772 - 2.51130i) q^{26} +4.83430i q^{27} +(-5.34170 - 3.63653i) q^{28} +3.73707 q^{29} +(-0.125560 - 1.33404i) q^{30} +(0.835217 + 0.835217i) q^{31} +(5.37645 + 1.75893i) q^{32} +(-0.549616 - 0.549616i) q^{33} +(4.34254 - 5.24491i) q^{34} +3.23103i q^{35} +(0.784522 + 4.13073i) q^{36} +(-5.67234 - 5.67234i) q^{37} +(-0.368335 - 3.91345i) q^{38} +(-3.19202 - 1.21709i) q^{39} +(-0.785814 - 2.71707i) q^{40} +(0.160789 - 0.160789i) q^{41} +(0.405689 + 4.31032i) q^{42} +6.05218 q^{43} +(-1.35627 - 0.923320i) q^{44} +(1.48654 - 1.48654i) q^{45} +(-3.48284 - 2.88363i) q^{46} +(1.78661 - 1.78661i) q^{47} +(-1.38946 - 3.52602i) q^{48} -3.43953i q^{49} +(-0.901894 + 1.08931i) q^{50} -4.56202 q^{51} +(-7.09896 - 1.26678i) q^{52} -8.61749 q^{53} +(4.36003 - 5.26603i) q^{54} +0.820362i q^{55} +(2.53899 + 8.77894i) q^{56} +(-1.86215 + 1.86215i) q^{57} +(-4.07082 - 3.37044i) q^{58} +(5.40370 - 5.40370i) q^{59} +(-1.06639 + 1.56642i) q^{60} -1.47327 q^{61} +(-0.156530 - 1.66308i) q^{62} +(-4.80305 + 4.80305i) q^{63} +(-4.27023 - 6.76499i) q^{64} +(1.47390 + 3.29054i) q^{65} +(0.103005 + 1.09440i) q^{66} +(-11.0184 - 11.0184i) q^{67} +(-9.46070 + 1.79681i) q^{68} +3.02937i q^{69} +(2.91404 - 3.51958i) q^{70} +(-8.71653 - 8.71653i) q^{71} +(2.87090 - 5.20719i) q^{72} +(-6.49138 - 6.49138i) q^{73} +(1.06307 + 11.2948i) q^{74} +0.947478 q^{75} +(-3.12829 + 4.59514i) q^{76} -2.65061i q^{77} +(2.37940 + 4.20464i) q^{78} +6.22808i q^{79} +(-1.59452 + 3.66845i) q^{80} +1.72647 q^{81} +(-0.320162 + 0.0301338i) q^{82} +(10.9734 + 10.9734i) q^{83} +(3.44553 - 5.06114i) q^{84} +(3.40465 + 3.40465i) q^{85} +(-6.59268 - 5.45842i) q^{86} +3.54079i q^{87} +(0.644652 + 2.22898i) q^{88} +(8.29440 + 8.29440i) q^{89} +(-2.96000 + 0.278596i) q^{90} +(-4.76220 - 10.6318i) q^{91} +(1.19315 + 6.28230i) q^{92} +(-0.791350 + 0.791350i) q^{93} +(-3.55750 + 0.334833i) q^{94} +2.77946 q^{95} +(-1.66654 + 5.09406i) q^{96} +(9.44730 - 9.44730i) q^{97} +(-3.10209 + 3.74671i) q^{98} +(-1.21950 + 1.21950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

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