LMFDB - Embedded newform 880.2.bk.b.243.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(243,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.243"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bk (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [236] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$236$
Relative dimension:	$118$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.10
Character	$\chi$	$=$	880.243
Dual form			880.2.bk.b.507.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38402 + 0.290657i) q^{2} -3.12744 q^{3} +(1.83104 - 0.804551i) q^{4} +(-2.12238 + 0.703930i) q^{5} +(4.32844 - 0.909011i) q^{6} +(-1.29734 + 1.29734i) q^{7} +(-2.30035 + 1.64572i) q^{8} +6.78086 q^{9} +(2.73281 - 1.59114i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(-5.72645 + 2.51618i) q^{12} -3.20391i q^{13} +(1.41847 - 2.17263i) q^{14} +(6.63760 - 2.20150i) q^{15} +(2.70539 - 2.94633i) q^{16} +(1.17807 - 1.17807i) q^{17} +(-9.38486 + 1.97090i) q^{18} +(-1.88116 - 1.88116i) q^{19} +(-3.31980 + 2.99648i) q^{20} +(4.05736 - 4.05736i) q^{21} +(1.18418 + 0.773126i) q^{22} +(-1.75494 - 1.75494i) q^{23} +(7.19419 - 5.14689i) q^{24} +(4.00896 - 2.98801i) q^{25} +(0.931239 + 4.43429i) q^{26} -11.8244 q^{27} +(-1.33170 + 3.41926i) q^{28} +(-1.26211 + 1.26211i) q^{29} +(-8.54670 + 4.97618i) q^{30} -5.20499i q^{31} +(-2.88796 + 4.86412i) q^{32} +(2.21143 + 2.21143i) q^{33} +(-1.28806 + 1.97288i) q^{34} +(1.84021 - 3.66669i) q^{35} +(12.4160 - 5.45555i) q^{36} -7.64715i q^{37} +(3.15034 + 2.05680i) q^{38} +10.0200i q^{39} +(3.72373 - 5.11212i) q^{40} +3.94872i q^{41} +(-4.43617 + 6.79477i) q^{42} -1.55976i q^{43} +(-1.86364 - 0.725835i) q^{44} +(-14.3915 + 4.77325i) q^{45} +(2.93896 + 1.91879i) q^{46} +(5.58809 + 5.58809i) q^{47} +(-8.46095 + 9.21445i) q^{48} +3.63381i q^{49} +(-4.68001 + 5.30071i) q^{50} +(-3.68433 + 3.68433i) q^{51} +(-2.57771 - 5.86648i) q^{52} +13.1110 q^{53} +(16.3652 - 3.43684i) q^{54} +(1.99850 + 1.00299i) q^{55} +(0.849276 - 5.11940i) q^{56} +(5.88321 + 5.88321i) q^{57} +(1.37995 - 2.11364i) q^{58} +(-7.71886 + 7.71886i) q^{59} +(10.3825 - 9.37131i) q^{60} +(-2.84893 - 2.84893i) q^{61} +(1.51287 + 7.20382i) q^{62} +(-8.79709 + 8.79709i) q^{63} +(2.58321 - 7.57146i) q^{64} +(2.25533 + 6.79991i) q^{65} +(-3.70344 - 2.41790i) q^{66} +14.6133i q^{67} +(1.20927 - 3.10490i) q^{68} +(5.48846 + 5.48846i) q^{69} +(-1.48114 + 5.60965i) q^{70} -12.4924 q^{71} +(-15.5983 + 11.1594i) q^{72} +(-4.44604 + 4.44604i) q^{73} +(2.22270 + 10.5838i) q^{74} +(-12.5378 + 9.34481i) q^{75} +(-4.95796 - 1.93098i) q^{76} +1.83472 q^{77} +(-2.91239 - 13.8679i) q^{78} +15.6086 q^{79} +(-3.66786 + 8.15762i) q^{80} +16.6374 q^{81} +(-1.14772 - 5.46511i) q^{82} -17.4779 q^{83} +(4.16482 - 10.6935i) q^{84} +(-1.67102 + 3.32958i) q^{85} +(0.453354 + 2.15874i) q^{86} +(3.94718 - 3.94718i) q^{87} +(2.79029 + 0.462892i) q^{88} -6.24849 q^{89} +(18.5308 - 10.7893i) q^{90} +(4.15657 + 4.15657i) q^{91} +(-4.62530 - 1.80142i) q^{92} +16.2783i q^{93} +(-9.35827 - 6.10983i) q^{94} +(5.31673 + 2.66832i) q^{95} +(9.03190 - 15.2122i) q^{96} +(1.98576 - 1.98576i) q^{97} +(-1.05619 - 5.02927i) q^{98} +(-4.79479 - 4.79479i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) $ 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.38402	+	0.290657i	−0.978652	+	0.205525i
$2$	−1.38402	+	0.290657i	−0.978652	+	0.205525i
$3$	−3.12744			−1.80563			−0.902813	−	0.430033i	$-0.858502\pi$
$3$	−3.12744			−1.80563			−0.902813	+	0.430033i	$0.858502\pi$
$4$	1.83104	−	0.804551i	0.915519	−	0.402276i
$5$	−2.12238	+	0.703930i	−0.949156	+	0.314807i
$5$	−2.12238	+	0.703930i	−0.949156	+	0.314807i
$6$	4.32844	−	0.909011i	1.76708	−	0.371102i
$7$	−1.29734	+	1.29734i	−0.490349	+	0.490349i	−0.908416	−	0.418067i	$-0.862708\pi$
$7$	−1.29734	+	1.29734i	−0.490349	+	0.490349i	0.418067	+	0.908416i	$0.362708\pi$
$8$	−2.30035	+	1.64572i	−0.813296	+	0.581850i
$9$	6.78086			2.26029
$10$	2.73281	−	1.59114i	0.864192	−	0.503162i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$12$	−5.72645	+	2.51618i	−1.65308	+	0.726359i
$13$		−	3.20391i		−	0.888605i	−0.895877	−	0.444303i	$-0.853452\pi$
$13$		−	3.20391i		−	0.888605i	0.895877	−	0.444303i	$-0.146548\pi$
$14$	1.41847	−	2.17263i	0.379102	−	0.580660i
$15$	6.63760	−	2.20150i	1.71382	−	0.568424i
$16$	2.70539	−	2.94633i	0.676349	−	0.736582i
$17$	1.17807	−	1.17807i	0.285723	−	0.285723i	−0.549663	−	0.835386i	$-0.685244\pi$
$17$	1.17807	−	1.17807i	0.285723	−	0.285723i	0.835386	+	0.549663i	$0.185244\pi$
$18$	−9.38486	+	1.97090i	−2.21203	+	0.464546i
$19$	−1.88116	−	1.88116i	−0.431568	−	0.431568i	0.457594	−	0.889161i	$-0.348711\pi$
$19$	−1.88116	−	1.88116i	−0.431568	−	0.431568i	−0.889161	+	0.457594i	$0.848711\pi$
$20$	−3.31980	+	2.99648i	−0.742330	+	0.670034i
$21$	4.05736	−	4.05736i	0.885387	−	0.885387i
$22$	1.18418	+	0.773126i	0.252467	+	0.164831i
$23$	−1.75494	−	1.75494i	−0.365930	−	0.365930i	0.500060	−	0.865991i	$-0.333311\pi$
$23$	−1.75494	−	1.75494i	−0.365930	−	0.365930i	−0.865991	+	0.500060i	$0.833311\pi$
$24$	7.19419	−	5.14689i	1.46851	−	1.05060i
$25$	4.00896	−	2.98801i	0.801793	−	0.597602i
$26$	0.931239	+	4.43429i	0.182631	+	0.869635i
$27$	−11.8244			−2.27560
$28$	−1.33170	+	3.41926i	−0.251668	+	0.646180i
$29$	−1.26211	+	1.26211i	−0.234369	+	0.234369i	−0.814513	−	0.580145i	$-0.802996\pi$
$29$	−1.26211	+	1.26211i	−0.234369	+	0.234369i	0.580145	+	0.814513i	$0.302996\pi$
$30$	−8.54670	+	4.97618i	−1.56041	+	0.908523i
$31$		−	5.20499i		−	0.934843i	−0.884035	−	0.467422i	$-0.845183\pi$
$31$		−	5.20499i		−	0.934843i	0.884035	−	0.467422i	$-0.154817\pi$
$32$	−2.88796	+	4.86412i	−0.510523	+	0.859864i
$33$	2.21143	+	2.21143i	0.384961	+	0.384961i
$34$	−1.28806	+	1.97288i	−0.220900	+	0.338347i
$35$	1.84021	−	3.66669i	0.311052	−	0.619783i
$36$	12.4160	−	5.45555i	2.06933	−	0.909258i
$37$		−	7.64715i		−	1.25718i	−0.777735	−	0.628592i	$-0.783632\pi$
$37$		−	7.64715i		−	1.25718i	0.777735	−	0.628592i	$-0.216368\pi$
$38$	3.15034	+	2.05680i	0.511053	+	0.333656i
$39$			10.0200i			1.60449i
$40$	3.72373	−	5.11212i	0.588774	−	0.808298i
$41$			3.94872i			0.616686i	0.951275	+	0.308343i	$0.0997744\pi$
$41$			3.94872i			0.616686i	−0.951275	+	0.308343i	$0.900226\pi$
$42$	−4.43617	+	6.79477i	−0.684516	+	1.04846i
$43$		−	1.55976i		−	0.237861i	−0.992903	−	0.118930i	$-0.962053\pi$
$43$		−	1.55976i		−	0.237861i	0.992903	−	0.118930i	$-0.0379465\pi$
$44$	−1.86364	−	0.725835i	−0.280955	−	0.109424i
$45$	−14.3915	+	4.77325i	−2.14536	+	0.711554i
$46$	2.93896	+	1.91879i	0.433326	+	0.282910i
$47$	5.58809	+	5.58809i	0.815107	+	0.815107i	0.985394	−	0.170287i	$-0.0544695\pi$
$47$	5.58809	+	5.58809i	0.815107	+	0.815107i	−0.170287	+	0.985394i	$0.554470\pi$
$48$	−8.46095	+	9.21445i	−1.22123	+	1.32999i
$49$			3.63381i			0.519115i
$50$	−4.68001	+	5.30071i	−0.661854	+	0.749633i
$51$	−3.68433	+	3.68433i	−0.515909	+	0.515909i
$52$	−2.57771	−	5.86648i	−0.357464	−	0.813534i
$53$	13.1110			1.80093			0.900466	−	0.434926i	$-0.143225\pi$
$53$	13.1110			1.80093			0.900466	+	0.434926i	$0.143225\pi$
$54$	16.3652	−	3.43684i	2.22702	−	0.467694i
$55$	1.99850	+	1.00299i	0.269478	+	0.135244i
$56$	0.849276	−	5.11940i	0.113489	−	0.684109i
$57$	5.88321	+	5.88321i	0.779250	+	0.779250i
$58$	1.37995	−	2.11364i	0.181197	−	0.277534i
$59$	−7.71886	+	7.71886i	−1.00491	+	1.00491i	−0.00492145	+	0.999988i	$0.501567\pi$
$59$	−7.71886	+	7.71886i	−1.00491	+	1.00491i	−0.999988	+	0.00492145i	$0.998433\pi$
$60$	10.3825	−	9.37131i	1.34037	−	1.20983i
$61$	−2.84893	−	2.84893i	−0.364769	−	0.364769i	0.500797	−	0.865565i	$-0.333040\pi$
$61$	−2.84893	−	2.84893i	−0.364769	−	0.364769i	−0.865565	+	0.500797i	$0.833040\pi$
$62$	1.51287	+	7.20382i	0.192134	+	0.914886i
$63$	−8.79709	+	8.79709i	−1.10833	+	1.10833i
$64$	2.58321	−	7.57146i	0.322901	−	0.946433i
$65$	2.25533	+	6.79991i	0.279739	+	0.843425i
$66$	−3.70344	−	2.41790i	−0.455862	−	0.297623i
$67$			14.6133i			1.78530i	0.450754	+	0.892648i	$0.351155\pi$
$67$			14.6133i			1.78530i	−0.450754	+	0.892648i	$0.648845\pi$
$68$	1.20927	−	3.10490i	0.146645	−	0.376524i
$69$	5.48846	+	5.48846i	0.660733	+	0.660733i
$70$	−1.48114	+	5.60965i	−0.177031	+	0.670481i
$71$	−12.4924			−1.48258			−0.741288	−	0.671187i	$-0.765785\pi$
$71$	−12.4924			−1.48258			−0.741288	+	0.671187i	$0.765785\pi$
$72$	−15.5983	+	11.1594i	−1.83828	+	1.31515i
$73$	−4.44604	+	4.44604i	−0.520370	+	0.520370i	−0.917683	−	0.397313i	$-0.869943\pi$
$73$	−4.44604	+	4.44604i	−0.520370	+	0.520370i	0.397313	+	0.917683i	$0.369943\pi$
$74$	2.22270	+	10.5838i	0.258383	+	1.23034i
$75$	−12.5378	+	9.34481i	−1.44774	+	1.07905i
$76$	−4.95796	−	1.93098i	−0.568717	−	0.221499i
$77$	1.83472			0.209086
$78$	−2.91239	−	13.8679i	−0.329763	−	1.57024i
$79$	15.6086			1.75611			0.878054	−	0.478561i	$-0.158842\pi$
$79$	15.6086			1.75611			0.878054	+	0.478561i	$0.158842\pi$
$80$	−3.66786	+	8.15762i	−0.410079	+	0.912050i
$81$	16.6374			1.84860
$82$	−1.14772	−	5.46511i	−0.126745	−	0.603521i
$83$	−17.4779			−1.91845			−0.959226	−	0.282642i	$-0.908789\pi$
$83$	−17.4779			−1.91845			−0.959226	+	0.282642i	$0.908789\pi$
$84$	4.16482	−	10.6935i	0.454419	−	1.16676i
$85$	−1.67102	+	3.32958i	−0.181248	+	0.361143i
$86$	0.453354	+	2.15874i	0.0488864	+	0.232783i
$87$	3.94718	−	3.94718i	0.423182	−	0.423182i
$88$	2.79029	+	0.462892i	0.297446	+	0.0493444i
$89$	−6.24849			−0.662339			−0.331169	−	0.943571i	$-0.607443\pi$
$89$	−6.24849			−0.662339			−0.331169	+	0.943571i	$0.607443\pi$
$90$	18.5308	−	10.7893i	1.95332	−	1.13729i
$91$	4.15657	+	4.15657i	0.435727	+	0.435727i
$92$	−4.62530	−	1.80142i	−0.482221	−	0.187811i
$93$			16.2783i			1.68798i
$94$	−9.35827	−	6.10983i	−0.965231	−	0.630181i
$95$	5.31673	+	2.66832i	0.545485	+	0.273764i
$96$	9.03190	−	15.2122i	0.921814	−	1.55259i
$97$	1.98576	−	1.98576i	0.201623	−	0.201623i	−0.599072	−	0.800695i	$-0.704464\pi$
$97$	1.98576	−	1.98576i	0.201623	−	0.201623i	0.800695	+	0.599072i	$0.204464\pi$
$98$	−1.05619	−	5.02927i	−0.106691	−	0.508033i
$99$	−4.79479	−	4.79479i	−0.481894	−	0.481894i
$100$	4.93655	−	8.69658i	0.493655	−	0.869658i
$101$	1.99304	−	1.99304i	0.198315	−	0.198315i	−0.600962	−	0.799277i	$-0.705216\pi$
$101$	1.99304	−	1.99304i	0.198315	−	0.198315i	0.799277	+	0.600962i	$0.205216\pi$
$102$	4.02832	−	6.17006i	0.398863	−	0.610927i
$103$	−1.93523	−	1.93523i	−0.190684	−	0.190684i	0.605308	−	0.795992i	$-0.293050\pi$
$103$	−1.93523	−	1.93523i	−0.190684	−	0.190684i	−0.795992	+	0.605308i	$0.793050\pi$
$104$	5.27274	+	7.37011i	0.517035	+	0.722699i
$105$	−5.75514	+	11.4673i	−0.561644	+	1.11910i
$106$	−18.1459	+	3.81080i	−1.76249	+	0.370138i
$107$	1.39240			0.134608			0.0673040	−	0.997733i	$-0.478560\pi$
$107$	1.39240			0.134608			0.0673040	+	0.997733i	$0.478560\pi$
$108$	−21.6509	+	9.51332i	−2.08336	+	0.915420i
$109$	−7.96639	+	7.96639i	−0.763042	+	0.763042i	−0.976871	−	0.213829i	$-0.931406\pi$
$109$	−7.96639	+	7.96639i	−0.763042	+	0.763042i	0.213829	+	0.976871i	$0.431406\pi$
$110$	−3.05750	−	0.807287i	−0.291521	−	0.0769718i
$111$			23.9160i			2.27000i
$112$	0.312572	+	7.33222i	0.0295353	+	0.692829i
$113$	−4.66128	−	4.66128i	−0.438496	−	0.438496i	0.453009	−	0.891506i	$-0.350350\pi$
$113$	−4.66128	−	4.66128i	−0.438496	−	0.438496i	−0.891506	+	0.453009i	$0.850350\pi$
$114$	−9.85249	−	6.43250i	−0.922770	−	0.602458i
$115$	4.96000	+	2.48929i	0.462522	+	0.232127i
$116$	−1.29554	+	3.32642i	−0.120288	+	0.308850i
$117$		−	21.7253i		−	2.00850i
$118$	8.43953	−	12.9266i	0.776922	−	1.18999i
$119$			3.05671i			0.280208i
$120$	−11.6457	+	15.9878i	−1.06311	+	1.45948i
$121$			1.00000i			0.0909091i
$122$	4.77105	+	3.11493i	0.431951	+	0.282012i
$123$		−	12.3494i		−	1.11350i
$124$	−4.18768	−	9.53052i	−0.376065	−	0.855866i
$125$	−6.40518	+	9.16371i	−0.572897	+	0.819628i
$126$	9.61844	−	14.7323i	0.856879	−	1.31246i
$127$	4.29487	+	4.29487i	0.381108	+	0.381108i	0.871501	−	0.490393i	$-0.163147\pi$
$127$	4.29487	+	4.29487i	0.381108	+	0.381108i	−0.490393	+	0.871501i	$0.663147\pi$
$128$	−1.37452	+	11.2299i	−0.121491	+	0.992592i
$129$			4.87804i			0.429487i
$130$	−5.09787	−	8.75570i	−0.447113	−	0.767925i
$131$	−0.368265	+	0.368265i	−0.0321755	+	0.0321755i	−0.723011	−	0.690836i	$-0.757243\pi$
$131$	−0.368265	+	0.368265i	−0.0321755	+	0.0321755i	0.690836	+	0.723011i	$0.257243\pi$
$132$	5.82842	+	2.27000i	0.507299	+	0.197578i
$133$	4.88102			0.423238
$134$	−4.24745	−	20.2251i	−0.366924	−	1.74718i
$135$	25.0958	−	8.32354i	2.15990	−	0.716376i
$136$	−0.771194	+	4.64873i	−0.0661294	+	0.398625i
$137$	10.8151	+	10.8151i	0.923996	+	0.923996i	0.997309	−	0.0733129i	$-0.0233572\pi$
$137$	10.8151	+	10.8151i	0.923996	+	0.923996i	−0.0733129	+	0.997309i	$0.523357\pi$
$138$	−9.19142	−	6.00090i	−0.782426	−	0.510830i
$139$	13.7388	−	13.7388i	1.16531	−	1.16531i	0.182011	−	0.983297i	$-0.441739\pi$
$139$	13.7388	−	13.7388i	1.16531	−	1.16531i	0.983297	−	0.182011i	$-0.0582606\pi$
$140$	0.419455	−	8.19438i	0.0354504	−	0.692552i
$141$	−17.4764	−	17.4764i	−1.47178	−	1.47178i
$142$	17.2898	−	3.63100i	1.45093	−	0.304707i
$143$	−2.26551	+	2.26551i	−0.189451	+	0.189451i
$144$	18.3449	−	19.9786i	1.52874	−	1.66488i
$145$	1.79024	−	3.56712i	0.148672	−	0.296234i
$146$	4.86115	−	7.44569i	0.402312	−	0.616210i
$147$		−	11.3645i		−	0.937328i
$148$	−6.15252	−	14.0022i	−0.505734	−	1.15097i
$149$	13.9041	+	13.9041i	1.13907	+	1.13907i	0.988618	+	0.150449i	$0.0480721\pi$
$149$	13.9041	+	13.9041i	1.13907	+	1.13907i	0.150449	+	0.988618i	$0.451928\pi$
$150$	14.6364	−	16.5776i	1.19506	−	1.35356i
$151$	−8.97787			−0.730609			−0.365305	−	0.930888i	$-0.619035\pi$
$151$	−8.97787			−0.730609			−0.365305	+	0.930888i	$0.619035\pi$
$152$	7.42319	+	1.23146i	0.602100	+	0.0998845i
$153$	7.98829	−	7.98829i	0.645815	−	0.645815i
$154$	−2.53929	+	0.533274i	−0.204622	+	0.0429724i
$155$	3.66395	+	11.0469i	0.294295	+	0.887312i
$156$	8.06163	+	18.3470i	0.645447	+	1.46894i
$157$	11.8993			0.949671			0.474835	−	0.880075i	$-0.342508\pi$
$157$	11.8993			0.949671			0.474835	+	0.880075i	$0.342508\pi$
$158$	−21.6027	+	4.53676i	−1.71862	+	0.360925i
$159$	−41.0038			−3.25181
$160$	2.70533	−	12.3564i	0.213875	−	0.976861i
$161$	4.55352			0.358867
$162$	−23.0266	+	4.83579i	−1.80914	+	0.379935i
$163$	−0.629745			−0.0493254			−0.0246627	−	0.999696i	$-0.507851\pi$
$163$	−0.629745			−0.0493254			−0.0246627	+	0.999696i	$0.507851\pi$
$164$	3.17695	+	7.23025i	0.248078	+	0.564588i
$165$	−6.25018	−	3.13680i	−0.486576	−	0.244199i
$166$	24.1898	−	5.08008i	1.87750	−	0.394291i
$167$	−5.38942	+	5.38942i	−0.417046	+	0.417046i	−0.884184	−	0.467138i	$-0.845285\pi$
$167$	−5.38942	+	5.38942i	−0.417046	+	0.417046i	0.467138	+	0.884184i	$0.345285\pi$
$168$	−2.65606	+	16.0106i	−0.204919	+	1.23524i
$169$	2.73495			0.210381
$170$	1.34497	−	5.09390i	0.103154	−	0.390684i
$171$	−12.7559	−	12.7559i	−0.975466	−	0.975466i
$172$	−1.25490	−	2.85597i	−0.0956856	−	0.217766i
$173$			3.62733i			0.275781i	0.990447	+	0.137891i	$0.0440322\pi$
$173$			3.62733i			0.275781i	−0.990447	+	0.137891i	$0.955968\pi$
$174$	−4.31572	+	6.61027i	−0.327174	+	0.501123i
$175$	−1.32453	+	9.07747i	−0.100125	+	0.686192i
$176$	−3.99637	+	0.170365i	−0.301238	+	0.0128418i
$177$	24.1402	−	24.1402i	1.81449	−	1.81449i
$178$	8.64805	−	1.81617i	0.648199	−	0.136127i
$179$	4.71413	+	4.71413i	0.352351	+	0.352351i	0.860984	−	0.508633i	$-0.169849\pi$
$179$	4.71413	+	4.71413i	0.352351	+	0.352351i	−0.508633	+	0.860984i	$0.669849\pi$
$180$	−22.5111	+	20.3187i	−1.67788	+	1.51447i
$181$	−13.3089	+	13.3089i	−0.989239	+	0.989239i	−0.999943	−	0.0107033i	$-0.996593\pi$
$181$	−13.3089	+	13.3089i	−0.989239	+	0.989239i	0.0107033	+	0.999943i	$0.496593\pi$
$182$	−6.96092	−	4.54465i	−0.515978	−	0.336872i
$183$	8.90986	+	8.90986i	0.658636	+	0.658636i
$184$	6.92512	+	1.14883i	0.510526	+	0.0846931i
$185$	5.38306	+	16.2301i	0.395770	+	1.19326i
$186$	−4.73139	−	22.5295i	−0.346922	−	1.65194i
$187$	−1.66604			−0.121833
$188$	14.7279	+	5.73610i	1.07414	+	0.418348i
$189$	15.3403	−	15.3403i	1.11584	−	1.11584i
$190$	−8.13405	−	2.14768i	−0.590106	−	0.155809i
$191$		−	14.7044i		−	1.06397i	−0.846753	−	0.531985i	$-0.821446\pi$
$191$		−	14.7044i		−	1.06397i	0.846753	−	0.531985i	$-0.178554\pi$
$192$	−8.07881	+	23.6793i	−0.583038	+	1.70890i
$193$	−9.11008	−	9.11008i	−0.655758	−	0.655758i	0.298616	−	0.954373i	$-0.403475\pi$
$193$	−9.11008	−	9.11008i	−0.655758	−	0.655758i	−0.954373	+	0.298616i	$0.903475\pi$
$194$	−2.17116	+	3.32551i	−0.155880	+	0.238758i
$195$	−7.05340	−	21.2663i	−0.505105	−	1.52291i
$196$	2.92358	+	6.65363i	0.208827	+	0.475260i
$197$		−	23.8994i		−	1.70276i	−0.524547	−	0.851382i	$-0.675765\pi$
$197$		−	23.8994i		−	1.70276i	0.524547	−	0.851382i	$-0.324235\pi$
$198$	8.02973	+	5.24246i	0.570648	+	0.372565i
$199$		−	5.13846i		−	0.364256i	−0.983275	−	0.182128i	$-0.941702\pi$
$199$		−	5.13846i		−	0.364256i	0.983275	−	0.182128i	$-0.0582985\pi$
$200$	−4.30458	+	13.4711i	−0.304380	+	0.952551i
$201$		−	45.7021i		−	3.22358i
$202$	−2.17912	+	3.33771i	−0.153323	+	0.234840i
$203$		−	3.27479i		−	0.229845i
$204$	−3.78191	+	9.71037i	−0.264787	+	0.679862i
$205$	−2.77962	−	8.38066i	−0.194137	−	0.585331i
$206$	3.24089	+	2.11592i	0.225804	+	0.147423i
$207$	−11.9000	−	11.9000i	−0.827107	−	0.827107i
$208$	−9.43977	−	8.66784i	−0.654530	−	0.601007i
$209$			2.66036i			0.184021i
$210$	4.63219	−	17.5438i	0.319651	−	1.21064i
$211$	−12.0014	+	12.0014i	−0.826208	+	0.826208i	−0.986990	−	0.160782i	$-0.948598\pi$
$211$	−12.0014	+	12.0014i	−0.826208	+	0.826208i	0.160782	+	0.986990i	$0.448598\pi$
$212$	24.0067	−	10.5485i	1.64879	−	0.724471i
$213$	39.0692			2.67698
$214$	−1.92711	+	0.404710i	−0.131734	+	0.0276654i
$215$	1.09796	+	3.31039i	0.0748803	+	0.225767i
$216$	27.2002	−	19.4596i	1.85074	−	1.32406i
$217$	6.75265	+	6.75265i	0.458400	+	0.458400i
$218$	8.71018	−	13.3412i	0.589928	−	0.903577i
$219$	13.9047	−	13.9047i	0.939593	−	0.939593i
$220$	4.46629	+	0.228621i	0.301117	+	0.0154136i
$221$	−3.77442	−	3.77442i	−0.253895	−	0.253895i
$222$	−6.95134	−	33.1002i	−0.466543	−	2.22154i
$223$	16.7638	−	16.7638i	1.12259	−	1.12259i	0.131236	−	0.991351i	$-0.458105\pi$
$223$	16.7638	−	16.7638i	1.12259	−	1.12259i	0.991351	−	0.131236i	$-0.0418947\pi$
$224$	−2.56377	−	10.0571i	−0.171299	−	0.671968i
$225$	27.1842	−	20.2613i	1.81228	−	1.35075i
$226$	7.80615	+	5.09648i	0.519257	+	0.339013i
$227$		−	16.5418i		−	1.09792i	−0.835850	−	0.548958i	$-0.815025\pi$
$227$		−	16.5418i		−	1.09792i	0.835850	−	0.548958i	$-0.184975\pi$
$228$	15.5057	+	6.03903i	1.02689	+	0.399944i
$229$	15.4259	+	15.4259i	1.01937	+	1.01937i	0.999809	+	0.0195630i	$0.00622748\pi$
$229$	15.4259	+	15.4259i	1.01937	+	1.01937i	0.0195630	+	0.999809i	$0.493773\pi$
$230$	−7.58828	−	2.00357i	−0.500356	−	0.132112i
$231$	−5.73797			−0.377530
$232$	0.826215	−	4.98039i	0.0542437	−	0.326979i
$233$	−19.4830	+	19.4830i	−1.27638	+	1.27638i	−0.333695	+	0.942681i	$0.608296\pi$
$233$	−19.4830	+	19.4830i	−1.27638	+	1.27638i	−0.942681	+	0.333695i	$0.891704\pi$
$234$	6.31460	+	30.0683i	0.412798	+	1.96562i
$235$	−15.7937	−	7.92641i	−1.03027	−	0.517062i
$236$	−7.92329	+	20.3437i	−0.515763	+	1.32426i
$237$	−48.8150			−3.17087
$238$	−0.888454	−	4.23056i	−0.0575899	−	0.274226i
$239$	−6.96125			−0.450286			−0.225143	−	0.974326i	$-0.572285\pi$
$239$	−6.96125			−0.450286			−0.225143	+	0.974326i	$0.572285\pi$
$240$	11.4710	−	25.5124i	0.740449	−	1.64682i
$241$	−10.0670			−0.648470			−0.324235	−	0.945977i	$-0.605107\pi$
$241$	−10.0670			−0.648470			−0.324235	+	0.945977i	$0.605107\pi$
$242$	−0.290657	−	1.38402i	−0.0186841	−	0.0889683i
$243$	−16.5594			−1.06228
$244$	−7.50862	−	2.92439i	−0.480690	−	0.187215i
$245$	−2.55795	−	7.71230i	−0.163421	−	0.492721i
$246$	3.58943	+	17.0918i	0.228853	+	1.08973i
$247$	−6.02707	+	6.02707i	−0.383493	+	0.383493i
$248$	8.56596	+	11.9733i	0.543939	+	0.760304i
$249$	54.6611			3.46401
$250$	6.20142	−	14.5445i	0.392212	−	0.919875i
$251$	−4.81883	−	4.81883i	−0.304162	−	0.304162i	0.538478	−	0.842640i	$-0.319000\pi$
$251$	−4.81883	−	4.81883i	−0.304162	−	0.304162i	−0.842640	+	0.538478i	$0.819000\pi$
$252$	−9.03009	+	23.1855i	−0.568842	+	1.46055i
$253$			2.48186i			0.156033i
$254$	−7.19252	−	4.69586i	−0.451299	−	0.294644i
$255$	5.22602	−	10.4130i	0.327266	−	0.652090i
$256$	−1.36169	−	15.9420i	−0.0851053	−	0.996372i
$257$	−11.9925	+	11.9925i	−0.748072	+	0.748072i	−0.974117	−	0.226045i	$-0.927420\pi$
$257$	−11.9925	+	11.9925i	−0.748072	+	0.748072i	0.226045	+	0.974117i	$0.427420\pi$
$258$	−1.41784	−	6.75132i	−0.0882706	−	0.420319i
$259$	9.92097	+	9.92097i	0.616459	+	0.616459i
$260$	9.60047	+	10.6364i	0.595396	+	0.659639i
$261$	−8.55822	+	8.55822i	−0.529740	+	0.529740i
$262$	0.402649	−	0.616726i	0.0248757	−	0.0381015i
$263$	22.1868	+	22.1868i	1.36809	+	1.36809i	0.863155	+	0.504940i	$0.168485\pi$
$263$	22.1868	+	22.1868i	1.36809	+	1.36809i	0.504940	+	0.863155i	$0.331515\pi$
$264$	−8.72646	−	1.44766i	−0.537077	−	0.0890975i
$265$	−27.8265	+	9.22922i	−1.70937	+	0.566947i
$266$	−6.75544	+	1.41870i	−0.414202	+	0.0869861i
$267$	19.5418			1.19594
$268$	11.7571	+	26.7575i	0.718181	+	1.63447i
$269$	−7.49276	+	7.49276i	−0.456842	+	0.456842i	−0.897617	−	0.440775i	$-0.854703\pi$
$269$	−7.49276	+	7.49276i	−0.456842	+	0.456842i	0.440775	+	0.897617i	$0.354703\pi$
$270$	−32.3139	+	18.8142i	−1.96656	+	1.14500i
$271$			17.4269i			1.05861i	0.848432	+	0.529304i	$0.177547\pi$
$271$			17.4269i			1.05861i	−0.848432	+	0.529304i	$0.822453\pi$
$272$	−0.283835	−	6.65810i	−0.0172100	−	0.403707i
$273$	−12.9994	−	12.9994i	−0.786760	−	0.786760i
$274$	−18.1118	−	11.8249i	−1.09418	−	0.714366i
$275$	−4.94761	−	0.721923i	−0.298352	−	0.0435336i
$276$	14.4653	+	5.63383i	0.870711	+	0.339117i
$277$			4.79708i			0.288228i	0.989561	+	0.144114i	$0.0460333\pi$
$277$			4.79708i			0.288228i	−0.989561	+	0.144114i	$0.953967\pi$
$278$	−15.0215	+	23.0080i	−0.900930	+	1.37993i
$279$		−	35.2943i		−	2.11301i
$280$	1.80122	+	11.4631i	0.107643	+	0.685053i
$281$		−	3.68715i		−	0.219957i	−0.993934	−	0.109979i	$-0.964922\pi$
$281$		−	3.68715i		−	0.219957i	0.993934	−	0.109979i	$-0.0350782\pi$
$282$	29.2674	+	19.1081i	1.74285	+	1.13787i
$283$			31.9312i			1.89812i	0.315103	+	0.949058i	$0.397961\pi$
$283$			31.9312i			1.89812i	−0.315103	+	0.949058i	$0.602039\pi$
$284$	−22.8741	+	10.0508i	−1.35733	+	0.596404i
$285$	−16.6277	−	8.34501i	−0.984943	−	0.494316i
$286$	2.47703	−	3.79400i	0.146470	−	0.224344i
$287$	−5.12284	−	5.12284i	−0.302392	−	0.302392i
$288$	−19.5828	+	32.9829i	−1.15393	+	1.94354i
$289$			14.2243i			0.836725i
$290$	−1.44093	+	5.45733i	−0.0846141	+	0.320465i
$291$	−6.21034	+	6.21034i	−0.364056	+	0.364056i
$292$	−4.56380	+	11.7179i	−0.267076	+	0.685740i
$293$	−20.2718			−1.18429			−0.592146	−	0.805831i	$-0.701719\pi$
$293$	−20.2718			−1.18429			−0.592146	+	0.805831i	$0.701719\pi$
$294$	3.30317	+	15.7287i	0.192645	+	0.917317i
$295$	10.9488	−	21.8159i	0.637463	−	1.27017i
$296$	12.5851	+	17.5911i	0.731492	+	1.02246i
$297$	8.36110	+	8.36110i	0.485160	+	0.485160i
$298$	−23.2849	−	15.2023i	−1.34886	−	0.880643i
$299$	−5.62267	+	5.62267i	−0.325168	+	0.325168i
$300$	−15.4388	+	27.1980i	−0.891357	+	1.57028i
$301$	2.02354	+	2.02354i	0.116635	+	0.116635i
$302$	12.4256	−	2.60948i	0.715012	−	0.150159i
$303$	−6.23311	+	6.23311i	−0.358083	+	0.358083i
$304$	−10.6318	+	0.453233i	−0.609775	+	0.0259947i
$305$	8.05196	+	4.04106i	0.461054	+	0.231390i
$306$	−8.73413	+	13.3778i	−0.499297	+	0.764760i
$307$			17.9918i			1.02685i	0.858135	+	0.513424i	$0.171623\pi$
$307$			17.9918i			1.02685i	−0.858135	+	0.513424i	$0.828377\pi$
$308$	3.35944	−	1.47613i	0.191422	−	0.0841101i
$309$	6.05231	+	6.05231i	0.344304	+	0.344304i
$310$	−8.28186	−	14.2243i	−0.470378	−	0.807884i
$311$	18.1036			1.02656			0.513281	−	0.858220i	$-0.328430\pi$
$311$	18.1036			1.02656			0.513281	+	0.858220i	$0.328430\pi$
$312$	−16.4902	−	23.0496i	−0.933572	−	1.30492i
$313$	0.941087	−	0.941087i	0.0531934	−	0.0531934i	−0.680010	−	0.733203i	$-0.738024\pi$
$313$	0.941087	−	0.941087i	0.0531934	−	0.0531934i	0.733203	+	0.680010i	$0.238024\pi$
$314$	−16.4690	+	3.45863i	−0.929397	+	0.195182i
$315$	12.4782	−	24.8633i	0.703067	−	1.40089i
$316$	28.5800	−	12.5579i	1.60775	−	0.706440i
$317$	27.8455			1.56396			0.781980	−	0.623303i	$-0.214210\pi$
$317$	27.8455			1.56396			0.781980	+	0.623303i	$0.214210\pi$
$318$	56.7502	−	11.9180i	3.18239	−	0.668330i
$319$	1.78490			0.0999352
$320$	−0.152753	+	17.8879i	−0.00853916	+	0.999964i
$321$	−4.35463			−0.243052
$322$	−6.30217	+	1.32351i	−0.351206	+	0.0737564i
$323$	−4.43226			−0.246618
$324$	30.4638	−	13.3857i	1.69243	−	0.743648i
$325$	−9.57332	−	12.8444i	−0.531032	−	0.712477i
$326$	0.871581	−	0.183040i	0.0482724	−	0.0101376i
$327$	24.9144	−	24.9144i	1.37777	−	1.37777i
$328$	−6.49849	−	9.08343i	−0.358819	−	0.501548i
$329$	−14.4993			−0.799375
$330$	9.56213	+	2.52474i	0.526378	+	0.138982i
$331$	14.8516	+	14.8516i	0.816316	+	0.816316i	0.985572	−	0.169256i	$-0.0541366\pi$
$331$	14.8516	+	14.8516i	0.816316	+	0.816316i	−0.169256	+	0.985572i	$0.554137\pi$
$332$	−32.0027	+	14.0619i	−1.75638	+	0.771746i
$333$		−	51.8542i		−	2.84159i
$334$	5.89261	−	9.02555i	0.322429	−	0.493856i
$335$	−10.2867	−	31.0149i	−0.562024	−	1.69452i
$336$	−0.977550	−	22.9310i	−0.0533297	−	1.25099i
$337$	−25.6052	+	25.6052i	−1.39481	+	1.39481i	−0.580657	+	0.814148i	$0.697204\pi$
$337$	−25.6052	+	25.6052i	−1.39481	+	1.39481i	−0.814148	+	0.580657i	$0.802796\pi$
$338$	−3.78524	+	0.794933i	−0.205890	+	0.0432386i
$339$	14.5779	+	14.5779i	0.791760	+	0.791760i
$340$	−0.380891	+	7.44100i	−0.0206567	+	0.403545i
$341$	−3.68048	+	3.68048i	−0.199309	+	0.199309i
$342$	21.3620	+	13.9468i	1.15512	+	0.754158i
$343$	−13.7957	−	13.7957i	−0.744897	−	0.744897i
$344$	2.56692	+	3.58798i	0.138399	+	0.193451i
$345$	−15.5121	−	7.78509i	−0.835143	−	0.419135i
$346$	−1.05431	−	5.02031i	−0.0566800	−	0.269894i
$347$	30.4663			1.63552			0.817758	−	0.575562i	$-0.195217\pi$
$347$	30.4663			1.63552			0.817758	+	0.575562i	$0.195217\pi$
$348$	4.05173	−	10.4032i	0.217195	−	0.557667i
$349$	−8.98752	+	8.98752i	−0.481091	+	0.481091i	−0.905480	−	0.424389i	$-0.860489\pi$
$349$	−8.98752	+	8.98752i	−0.481091	+	0.481091i	0.424389	+	0.905480i	$0.360489\pi$
$350$	−0.805254	−	12.9484i	−0.0430427	−	0.692122i
$351$			37.8843i			2.02211i
$352$	5.48155	−	1.39736i	0.292168	−	0.0744796i
$353$	−19.1061	−	19.1061i	−1.01692	−	1.01692i	−0.999854	−	0.0170631i	$-0.994568\pi$
$353$	−19.1061	−	19.1061i	−1.01692	−	1.01692i	−0.0170631	−	0.999854i	$-0.505432\pi$
$354$	−26.3941	+	40.4271i	−1.40283	+	2.14868i
$355$	26.5136	−	8.79378i	1.40719	−	0.466725i
$356$	−11.4412	+	5.02723i	−0.606383	+	0.266443i
$357$		−	9.55966i		−	0.505951i
$358$	−7.89466	−	5.15427i	−0.417246	−	0.272412i
$359$			8.25415i			0.435637i	0.975989	+	0.217819i	$0.0698942\pi$
$359$			8.25415i			0.435637i	−0.975989	+	0.217819i	$0.930106\pi$
$360$	25.2501	−	34.6646i	1.33080	−	1.82698i
$361$		−	11.9225i		−	0.627499i
$362$	14.5514	−	22.2881i	0.764807	−	1.17143i
$363$		−	3.12744i		−	0.164148i
$364$	10.9550	+	4.26666i	0.574198	+	0.223634i
$365$	6.30647	−	12.5659i	0.330096	−	0.657728i
$366$	−14.9212	−	9.74173i	−0.779941	−	0.509208i
$367$	21.4361	+	21.4361i	1.11896	+	1.11896i	0.991895	+	0.127062i	$0.0405548\pi$
$367$	21.4361	+	21.4361i	1.11896	+	1.11896i	0.127062	+	0.991895i	$0.459445\pi$
$368$	−9.91843	+	0.422823i	−0.517034	+	0.0220412i
$369$			26.7757i			1.39389i
$370$	−12.1677	−	20.8982i	−0.632567	−	1.08645i
$371$	−17.0094	+	17.0094i	−0.883086	+	0.883086i
$372$	13.0967	+	29.8061i	0.679032	+	1.54537i
$373$	−21.8545			−1.13158			−0.565792	−	0.824548i	$-0.691429\pi$
$373$	−21.8545			−1.13158			−0.565792	+	0.824548i	$0.691429\pi$
$374$	2.30583	−	0.484245i	0.119232	−	0.0250397i
$375$	20.0318	−	28.6589i	1.03444	−	1.47994i
$376$	−22.0510	−	3.65812i	−1.13719	−	0.188653i
$377$	4.04370	+	4.04370i	0.208261	+	0.208261i
$378$	−16.7725	+	25.6900i	−0.862686	+	1.32135i
$379$	14.7087	−	14.7087i	0.755534	−	0.755534i	−0.219972	−	0.975506i	$-0.570597\pi$
$379$	14.7087	−	14.7087i	0.755534	−	0.755534i	0.975506	+	0.219972i	$0.0705966\pi$
$380$	11.8819	+	0.608214i	0.609531	+	0.0312007i
$381$	−13.4319	−	13.4319i	−0.688138	−	0.688138i
$382$	4.27393	+	20.3512i	0.218673	+	1.04126i
$383$	16.9012	−	16.9012i	0.863611	−	0.863611i	−0.128145	−	0.991755i	$-0.540902\pi$
$383$	16.9012	−	16.9012i	0.863611	−	0.863611i	0.991755	+	0.128145i	$0.0409022\pi$
$384$	4.29872	−	35.1208i	0.219368	−	1.79225i
$385$	−3.89396	+	1.29151i	−0.198455	+	0.0658217i
$386$	15.2565	+	9.96064i	0.776533	+	0.506983i
$387$		−	10.5765i		−	0.537633i
$388$	2.03835	−	5.23365i	0.103482	−	0.265698i
$389$	−3.52495	−	3.52495i	−0.178722	−	0.178722i	0.612076	−	0.790799i	$-0.290334\pi$
$389$	−3.52495	−	3.52495i	−0.178722	−	0.178722i	−0.790799	+	0.612076i	$0.790334\pi$
$390$	15.9433	+	27.3829i	0.807318	+	1.38659i
$391$	−4.13487			−0.209109
$392$	−5.98023	−	8.35902i	−0.302047	−	0.422194i
$393$	1.15173	−	1.15173i	0.0580969	−	0.0580969i
$394$	6.94653	+	33.0773i	0.349961	+	1.66641i
$395$	−33.1274	+	10.9874i	−1.66682	+	0.552836i
$396$	−12.6371	−	4.92178i	−0.635038	−	0.247329i
$397$	0.665941			0.0334226			0.0167113	−	0.999860i	$-0.494680\pi$
$397$	0.665941			0.0334226			0.0167113	+	0.999860i	$0.494680\pi$
$398$	1.49353	+	7.11174i	0.0748638	+	0.356479i
$399$	−15.2651			−0.764209
$400$	2.04217	−	19.8955i	0.102109	−	0.994773i
$401$	30.0842			1.50233			0.751167	−	0.660113i	$-0.229491\pi$
$401$	30.0842			1.50233			0.751167	+	0.660113i	$0.229491\pi$
$402$	13.2836	+	63.2527i	0.662527	+	3.15476i
$403$	−16.6763			−0.830706
$404$	2.04583	−	5.25284i	0.101784	−	0.261338i
$405$	−35.3109	+	11.7116i	−1.75461	+	0.581954i
$406$	0.951840	+	4.53238i	0.0472390	+	0.224938i
$407$	−5.40735	+	5.40735i	−0.268032	+	0.268032i
$408$	2.41186	−	14.5386i	0.119405	−	0.719768i
$409$	−10.5688			−0.522592			−0.261296	−	0.965259i	$-0.584150\pi$
$409$	−10.5688			−0.522592			−0.261296	+	0.965259i	$0.584150\pi$
$410$	6.28296	+	10.7911i	0.310293	+	0.532935i
$411$	−33.8235	−	33.8235i	−1.66839	−	1.66839i
$412$	−5.10047	−	1.98649i	−0.251282	−	0.0978672i
$413$		−	20.0280i		−	0.985513i
$414$	19.9287	+	13.0111i	0.979441	+	0.639458i
$415$	37.0947	−	12.3032i	1.82091	−	0.603942i
$416$	15.5842	+	9.25276i	0.764079	+	0.453654i
$417$	−42.9671	+	42.9671i	−2.10411	+	2.10411i
$418$	−0.773252	−	3.68200i	−0.0378210	−	0.180093i
$419$	4.32327	+	4.32327i	0.211206	+	0.211206i	0.804780	−	0.593574i	$-0.202283\pi$
$419$	4.32327	+	4.32327i	0.211206	+	0.211206i	−0.593574	+	0.804780i	$0.702283\pi$
$420$	−1.31182	+	25.6274i	−0.0640102	+	1.25049i
$421$	−1.30578	+	1.30578i	−0.0636400	+	0.0636400i	−0.738210	−	0.674570i	$-0.764329\pi$
$421$	−1.30578	+	1.30578i	−0.0636400	+	0.0636400i	0.674570	+	0.738210i	$0.264329\pi$
$422$	13.1219	−	20.0984i	0.638763	−	0.978376i
$423$	37.8921	+	37.8921i	1.84237	+	1.84237i
$424$	−30.1598	+	21.5770i	−1.46469	+	1.04787i
$425$	1.20275	−	8.24290i	0.0583420	−	0.399839i
$426$	−54.0726	+	11.3557i	−2.61983	+	0.550187i
$427$	7.39208			0.357728
$428$	2.54953	−	1.12025i	0.123236	−	0.0541496i
$429$	7.08523	−	7.08523i	0.342078	−	0.342078i
$430$	−2.48179	−	4.26253i	−0.119683	−	0.205557i
$431$		−	2.08844i		−	0.100596i	−0.998734	−	0.0502982i	$-0.983983\pi$
$431$		−	2.08844i		−	0.100596i	0.998734	−	0.0502982i	$-0.0160172\pi$
$432$	−31.9896	+	34.8385i	−1.53910	+	1.67617i
$433$	12.7590	+	12.7590i	0.613159	+	0.613159i	0.943768	−	0.330609i	$-0.107254\pi$
$433$	12.7590	+	12.7590i	0.613159	+	0.613159i	−0.330609	+	0.943768i	$0.607254\pi$
$434$	−11.3085	−	7.38312i	−0.542827	−	0.354401i
$435$	−5.59887	+	11.1560i	−0.268445	+	0.534887i
$436$	−8.17739	+	20.9961i	−0.391626	+	1.00553i
$437$			6.60265i			0.315847i
$438$	−15.2029	+	23.2859i	−0.726424	+	1.11264i
$439$		−	17.2571i		−	0.823637i	−0.911266	−	0.411818i	$-0.864894\pi$
$439$		−	17.2571i		−	0.823637i	0.911266	−	0.411818i	$-0.135106\pi$
$440$	−6.24789	+	0.981741i	−0.297857	+	0.0468027i
$441$			24.6403i			1.17335i
$442$	6.32094	+	4.12682i	0.300657	+	0.196293i
$443$			0.239657i			0.0113865i	0.999984	+	0.00569323i	$0.00181222\pi$
$443$			0.239657i			0.0113865i	−0.999984	+	0.00569323i	$0.998188\pi$
$444$	19.2416	+	43.7910i	0.913167	+	2.07823i
$445$	13.2617	−	4.39850i	0.628663	−	0.208509i
$446$	−18.3290	+	28.0740i	−0.867902	+	1.32934i
$447$	−43.4841	−	43.4841i	−2.05673	−	2.05673i
$448$	6.47148	+	13.1741i	0.305749	+	0.622417i
$449$			21.9411i			1.03546i	0.855543	+	0.517732i	$0.173224\pi$
$449$			21.9411i			1.03546i	−0.855543	+	0.517732i	$0.826776\pi$
$450$	−31.7345	+	35.9433i	−1.49598	+	1.69438i
$451$	2.79216	−	2.79216i	0.131478	−	0.131478i
$452$	−12.2852	−	4.78474i	−0.577848	−	0.225055i
$453$	28.0777			1.31921
$454$	4.80798	+	22.8942i	0.225650	+	1.07448i
$455$	−11.7477	−	5.89587i	−0.550743	−	0.276403i
$456$	−23.2155	−	3.85131i	−1.08717	−	0.180354i
$457$	−12.3484	−	12.3484i	−0.577635	−	0.577635i	0.356616	−	0.934251i	$-0.383930\pi$
$457$	−12.3484	−	12.3484i	−0.577635	−	0.577635i	−0.934251	+	0.356616i	$0.883930\pi$
$458$	−25.8334	−	16.8661i	−1.20712	−	0.788103i
$459$	−13.9299	+	13.9299i	−0.650192	+	0.650192i
$460$	11.0847	+	0.567405i	0.516827	+	0.0264554i
$461$	10.0477	+	10.0477i	0.467967	+	0.467967i	0.901255	−	0.433288i	$-0.142647\pi$
$461$	10.0477	+	10.0477i	0.467967	+	0.467967i	−0.433288	+	0.901255i	$0.642647\pi$
$462$	7.94148	−	1.66778i	0.369471	−	0.0775921i
$463$	11.2096	−	11.2096i	0.520952	−	0.520952i	−0.396907	−	0.917859i	$-0.629916\pi$
$463$	11.2096	−	11.2096i	0.520952	−	0.520952i	0.917859	+	0.396907i	$0.129916\pi$
$464$	0.304085	+	7.13312i	0.0141168	+	0.331147i
$465$	−11.4588	−	34.5486i	−0.531387	−	1.60215i
$466$	21.3021	−	32.6278i	0.986800	−	1.51146i
$467$			31.4460i			1.45515i	0.686031	+	0.727573i	$0.259352\pi$
$467$			31.4460i			1.45515i	−0.686031	+	0.727573i	$0.740648\pi$
$468$	−17.4791	−	39.7798i	−0.807971	−	1.83882i
$469$	−18.9584	−	18.9584i	−0.875419	−	0.875419i
$470$	24.1627	+	6.37979i	1.11454	+	0.294278i
$471$	−37.2144			−1.71475
$472$	5.05298	−	30.4591i	0.232582	−	1.40200i
$473$	−1.10291	+	1.10291i	−0.0507121	+	0.0507121i
$474$	67.5611	−	14.1884i	3.10318	−	0.651695i
$475$	−13.1624	−	1.92058i	−0.603934	−	0.0881221i
$476$	2.45928	+	5.59695i	0.112721	+	0.256536i
$477$	88.9037			4.07062
$478$	9.63453	−	2.02334i	0.440673	−	0.0925452i
$479$	−1.10741			−0.0505989			−0.0252994	−	0.999680i	$-0.508054\pi$
$479$	−1.10741			−0.0505989			−0.0252994	+	0.999680i	$0.508054\pi$
$480$	−8.46073	+	38.6439i	−0.386178	+	1.76385i
$481$	−24.5008			−1.11714
$482$	13.9329	−	2.92603i	0.634626	−	0.133277i
$483$	−14.2408			−0.647980
$484$	0.804551	+	1.83104i	0.0365705	+	0.0832290i
$485$	−2.81669	+	5.61237i	−0.127899	+	0.254844i
$486$	22.9185	−	4.81309i	1.03961	−	0.218326i
$487$	10.2044	−	10.2044i	0.462407	−	0.462407i	−0.437037	−	0.899444i	$-0.643972\pi$
$487$	10.2044	−	10.2044i	0.462407	−	0.462407i	0.899444	+	0.437037i	$0.143972\pi$
$488$	11.2421	+	1.86499i	0.508905	+	0.0844241i
$489$	1.96949			0.0890633
$490$	5.78189	+	9.93052i	0.261199	+	0.448615i
$491$	18.3511	+	18.3511i	0.828173	+	0.828173i	0.987264	−	0.159091i	$-0.0508563\pi$
$491$	18.3511	+	18.3511i	0.828173	+	0.828173i	−0.159091	+	0.987264i	$0.550856\pi$
$492$	−9.93569	−	22.6121i	−0.447936	−	1.01943i
$493$			2.97371i			0.133929i
$494$	6.58979	−	10.0934i	0.296489	−	0.454124i
$495$	13.5515	+	6.80115i	0.609097	+	0.305689i
$496$	−15.3356	−	14.0815i	−0.688588	−	0.632280i
$497$	16.2069	−	16.2069i	0.726980	−	0.726980i
$498$	−75.6522	+	15.8876i	−3.39005	+	0.711941i
$499$	15.0666	+	15.0666i	0.674472	+	0.674472i	0.958744	−	0.284271i	$-0.0917517\pi$
$499$	15.0666	+	15.0666i	0.674472	+	0.674472i	−0.284271	+	0.958744i	$0.591752\pi$
$500$	−4.35544	+	21.9324i	−0.194781	+	0.980847i
$501$	16.8551	−	16.8551i	0.753029	−	0.753029i
$502$	8.07000	+	5.26875i	0.360182	+	0.235156i
$503$	−10.9926	−	10.9926i	−0.490138	−	0.490138i	0.418212	−	0.908350i	$-0.362657\pi$
$503$	−10.9926	−	10.9926i	−0.490138	−	0.490138i	−0.908350	+	0.418212i	$0.862657\pi$
$504$	5.75882	−	34.7139i	0.256518	−	1.54628i
$505$	−2.82702	+	5.63295i	−0.125801	+	0.250663i
$506$	−0.721370	−	3.43495i	−0.0320688	−	0.152702i
$507$	−8.55339			−0.379869
$508$	11.3195	+	4.40862i	0.502222	+	0.195601i
$509$	2.41293	−	2.41293i	0.106951	−	0.106951i	−0.651606	−	0.758557i	$-0.725905\pi$
$509$	2.41293	−	2.41293i	0.106951	−	0.106951i	0.758557	+	0.651606i	$0.225905\pi$
$510$	−4.20631	+	15.9309i	−0.186258	+	0.705430i
$511$		−	11.5361i		−	0.510326i
$512$	6.51824	+	21.6682i	0.288068	+	0.957610i
$513$	22.2436	+	22.2436i	0.982077	+	0.982077i
$514$	13.1122	−	20.0836i	0.578354	−	0.885850i
$515$	5.46956	+	2.74502i	0.241018	+	0.120960i
$516$	3.92463	+	8.93187i	0.172772	+	0.393204i
$517$		−	7.90276i		−	0.347563i
$518$	−16.6144	−	10.8472i	−0.729997	−	0.476601i
$519$		−	11.3443i		−	0.497958i
$520$	−16.3788	−	11.9305i	−0.718258	−	0.523187i
$521$			19.8183i			0.868254i	0.900852	+	0.434127i	$0.142943\pi$
$521$			19.8183i			0.868254i	−0.900852	+	0.434127i	$0.857057\pi$
$522$	9.35726	−	14.3323i	0.409556	−	0.627307i
$523$			28.9056i			1.26395i	0.774988	+	0.631976i	$0.217756\pi$
$523$			28.9056i			1.26395i	−0.774988	+	0.631976i	$0.782244\pi$
$524$	−0.378019	+	0.970596i	−0.0165138	+	0.0424007i
$525$	4.14237	−	28.3892i	0.180788	−	1.23901i
$526$	−37.1557	−	24.2582i	−1.62007	−	1.05771i
$527$	−6.13182	−	6.13182i	−0.267106	−	0.267106i
$528$	12.4984	−	0.532806i	0.543923	−	0.0231874i
$529$		−	16.8404i		−	0.732190i
$530$	35.8299	−	20.8614i	1.55635	−	0.906161i
$531$	−52.3404	+	52.3404i	−2.27138	+	2.27138i
$532$	8.93732	−	3.92703i	0.387482	−	0.170258i
$533$	12.6513			0.547990
$534$	−27.0462	+	5.67995i	−1.17040	+	0.245795i
$535$	−2.95519	+	0.980150i	−0.127764	+	0.0423756i
$536$	−24.0494	−	33.6156i	−1.03878	−	1.45197i
$537$	−14.7431	−	14.7431i	−0.636214	−	0.636214i
$538$	8.19233	−	12.5480i	0.353197	−	0.540982i
$539$	2.56949	−	2.56949i	0.110676	−	0.110676i
$540$	39.2546	−	35.4316i	1.68925	−	1.52473i
$541$	14.0775	+	14.0775i	0.605241	+	0.605241i	0.941699	−	0.336458i	$-0.109229\pi$
$541$	14.0775	+	14.0775i	0.605241	+	0.605241i	−0.336458	+	0.941699i	$0.609229\pi$
$542$	−5.06524	−	24.1192i	−0.217571	−	1.03601i
$543$	41.6226	−	41.6226i	1.78620	−	1.78620i
$544$	2.32806	+	9.13246i	0.0998146	+	0.391551i
$545$	11.2999	−	22.5155i	0.484035	−	0.964457i
$546$	21.7698	+	14.2131i	0.931663	+	0.608265i
$547$			19.8842i			0.850186i	0.905150	+	0.425093i	$0.139759\pi$
$547$			19.8842i			0.850186i	−0.905150	+	0.425093i	$0.860241\pi$
$548$	28.5041	+	11.1015i	1.21764	+	0.474234i
$549$	−19.3182	−	19.3182i	−0.824481	−	0.824481i
$550$	7.05743	−	0.438898i	0.300930	−	0.0187147i
$551$	4.74848			0.202292
$552$	−21.6579	−	3.59290i	−0.921820	−	0.152924i
$553$	−20.2497	+	20.2497i	−0.861107	+	0.861107i
$554$	−1.39430	−	6.63926i	−0.0592383	−	0.282075i
$555$	−16.8352	−	50.7587i	−0.714613	−	2.15459i
$556$	14.1027	−	36.2097i	0.598086	−	1.53564i
$557$	20.7494			0.879181			0.439590	−	0.898198i	$-0.355124\pi$
$557$	20.7494			0.879181			0.439590	+	0.898198i	$0.355124\pi$
$558$	10.2585	+	48.8481i	0.434278	+	2.06790i
$559$	−4.99732			−0.211364
$560$	−5.82477	−	15.3417i	−0.246141	−	0.648305i
$561$	5.21042			0.219984
$562$	1.07170	+	5.10310i	0.0452068	+	0.215261i
$563$	42.8815			1.80724			0.903619	−	0.428337i	$-0.140900\pi$
$563$	42.8815			1.80724			0.903619	+	0.428337i	$0.140900\pi$
$564$	−46.0606	−	17.9393i	−1.93950	−	0.755380i
$565$	13.1742	+	6.61178i	0.554243	+	0.278159i
$566$	−9.28103	−	44.1936i	−0.390111	−	1.85759i
$567$	−21.5845	+	21.5845i	−0.906462	+	0.906462i
$568$	28.7369	−	20.5590i	1.20577	−	0.862637i
$569$	−28.1006			−1.17804			−0.589020	−	0.808119i	$-0.700486\pi$
$569$	−28.1006			−1.17804			−0.589020	+	0.808119i	$0.700486\pi$
$570$	25.4387	+	6.71672i	1.06551	+	0.281332i
$571$	18.5052	+	18.5052i	0.774420	+	0.774420i	0.978876	−	0.204456i	$-0.0655425\pi$
$571$	18.5052	+	18.5052i	0.774420	+	0.774420i	−0.204456	+	0.978876i	$0.565543\pi$
$572$	−2.32551	+	5.97095i	−0.0972345	+	0.249658i
$573$			45.9870i			1.92113i
$574$	8.57911	+	5.60114i	0.358085	+	0.233787i
$575$	−12.2793	−	1.79171i	−0.512081	−	0.0747196i
$576$	17.5163	−	51.3410i	0.729848	−	2.13921i
$577$	−0.0182723	+	0.0182723i	−0.000760686	+	0.000760686i	−0.707487	−	0.706726i	$-0.750171\pi$
$577$	−0.0182723	+	0.0182723i	−0.000760686	+	0.000760686i	0.706726	+	0.707487i	$0.250171\pi$
$578$	−4.13440	−	19.6868i	−0.171968	−	0.818862i
$579$	28.4912	+	28.4912i	1.18405	+	1.18405i
$580$	0.408065	−	7.97188i	0.0169440	−	0.331014i
$581$	22.6748	−	22.6748i	0.940711	−	0.940711i
$582$	6.79017	−	10.4003i	0.281462	−	0.431107i
$583$	−9.27087	−	9.27087i	−0.383960	−	0.383960i
$584$	2.91050	−	17.5444i	0.120437	−	0.725992i
$585$	15.2931	+	46.1092i	0.632291	+	1.90638i
$586$	28.0566	−	5.89214i	1.15901	−	0.243402i
$587$	−35.4685			−1.46394			−0.731971	−	0.681336i	$-0.761399\pi$
$587$	−35.4685			−1.46394			−0.731971	+	0.681336i	$0.761399\pi$
$588$	−9.14332	−	20.8088i	−0.377064	−	0.858141i
$589$	−9.79141	+	9.79141i	−0.403448	+	0.403448i
$590$	−8.81243	+	33.3760i	−0.362802	+	1.37407i
$591$			74.7439i			3.07455i
$592$	−22.5310	−	20.6886i	−0.926018	−	0.850294i
$593$	−12.5474	−	12.5474i	−0.515259	−	0.515259i	0.400874	−	0.916133i	$-0.368707\pi$
$593$	−12.5474	−	12.5474i	−0.515259	−	0.515259i	−0.916133	+	0.400874i	$0.868707\pi$
$594$	−14.0022	−	9.14174i	−0.574516	−	0.375090i
$595$	−2.15171	−	6.48749i	−0.0882115	−	0.265961i
$596$	36.6455	+	14.2723i	1.50106	+	0.584618i
$597$			16.0702i			0.657709i
$598$	6.14764	−	9.41618i	0.251396	−	0.385056i
$599$			15.3809i			0.628445i	0.949349	+	0.314223i	$0.101744\pi$
$599$			15.3809i			0.628445i	−0.949349	+	0.314223i	$0.898256\pi$
$600$	13.4623	−	42.1300i	0.549597	−	1.71995i
$601$			2.96821i			0.121076i	0.998166	+	0.0605378i	$0.0192816\pi$
$601$			2.96821i			0.121076i	−0.998166	+	0.0605378i	$0.980718\pi$
$602$	−3.38878	−	2.21247i	−0.138116	−	0.0901734i
$603$			99.0906i			4.03528i
$604$	−16.4388	+	7.22316i	−0.668886	+	0.293906i
$605$	−0.703930	−	2.12238i	−0.0286188	−	0.0862869i
$606$	6.81507	−	10.4385i	0.276843	−	0.424034i
$607$	−15.9801	−	15.9801i	−0.648612	−	0.648612i	0.304046	−	0.952657i	$-0.401662\pi$
$607$	−15.9801	−	15.9801i	−0.648612	−	0.648612i	−0.952657	+	0.304046i	$0.901662\pi$
$608$	14.5829	−	3.71749i	0.591415	−	0.150764i
$609$			10.2417i			0.415014i
$610$	−12.3187	−	3.25256i	−0.498768	−	0.131692i
$611$	17.9038	−	17.9038i	0.724308	−	0.724308i
$612$	8.19987	−	21.0539i	0.331460	−	0.851052i
$613$	13.0443			0.526853			0.263426	−	0.964679i	$-0.415147\pi$
$613$	13.0443			0.526853			0.263426	+	0.964679i	$0.415147\pi$
$614$	−5.22944	−	24.9011i	−0.211043	−	1.00493i
$615$	8.69309	+	26.2100i	0.350539	+	1.05689i
$616$	−4.22049	+	3.01944i	−0.170049	+	0.121657i
$617$	21.6531	+	21.6531i	0.871723	+	0.871723i	0.992660	−	0.120937i	$-0.0385900\pi$
$617$	21.6531	+	21.6531i	0.871723	+	0.871723i	−0.120937	+	0.992660i	$0.538590\pi$
$618$	−10.1357	−	6.61739i	−0.407717	−	0.266191i
$619$	1.89622	−	1.89622i	0.0762156	−	0.0762156i	−0.667971	−	0.744187i	$-0.732837\pi$
$619$	1.89622	−	1.89622i	0.0762156	−	0.0762156i	0.744187	+	0.667971i	$0.232837\pi$
$620$	15.5967	+	17.2795i	0.626377	+	0.693962i
$621$	20.7511	+	20.7511i	0.832713	+	0.832713i
$622$	−25.0558	+	5.26195i	−1.00465	+	0.210985i
$623$	8.10643	−	8.10643i	0.324777	−	0.324777i
$624$	29.5223	+	27.1081i	1.18184	+	1.08519i
$625$	7.14359	−	23.9577i	0.285744	−	0.958306i
$626$	−1.02895	+	1.57602i	−0.0411252	+	0.0629904i
$627$		−	8.32011i		−	0.332273i
$628$	21.7881	−	9.57363i	0.869441	−	0.382029i
$629$	−9.00885	−	9.00885i	−0.359206	−	0.359206i
$630$	−10.0434	+	38.0382i	−0.400140	+	1.51548i
$631$	5.24625			0.208850			0.104425	−	0.994533i	$-0.466700\pi$
$631$	5.24625			0.208850			0.104425	+	0.994533i	$0.466700\pi$
$632$	−35.9053	+	25.6875i	−1.42824	+	1.02179i
$633$	37.5335	−	37.5335i	1.49182	−	1.49182i
$634$	−38.5388	+	8.09349i	−1.53057	+	0.321434i
$635$	−12.1386	−	6.09204i	−0.481706	−	0.241755i
$636$	−75.0794	+	32.9896i	−2.97709	+	1.30812i
$637$	11.6424			0.461288
$638$	−2.47034	+	0.518793i	−0.0978018	+	0.0205392i
$639$	−84.7092			−3.35104
$640$	−4.98782	−	24.8016i	−0.197161	−	0.980371i
$641$	0.705767			0.0278761			0.0139381	−	0.999903i	$-0.495563\pi$
$641$	0.705767			0.0278761			0.0139381	+	0.999903i	$0.495563\pi$
$642$	6.02691	−	1.26570i	0.237863	−	0.0499533i
$643$	−14.8964			−0.587458			−0.293729	−	0.955889i	$-0.594896\pi$
$643$	−14.8964			−0.587458			−0.293729	+	0.955889i	$0.594896\pi$
$644$	8.33766	−	3.66354i	0.328550	−	0.144364i
$645$	−3.43380	−	10.3530i	−0.135206	−	0.407650i
$646$	6.13435	−	1.28827i	0.241353	−	0.0506862i
$647$	6.10216	−	6.10216i	0.239901	−	0.239901i	−0.576908	−	0.816809i	$-0.695741\pi$
$647$	6.10216	−	6.10216i	0.239901	−	0.239901i	0.816809	+	0.576908i	$0.195741\pi$
$648$	−38.2719	+	27.3806i	−1.50346	+	1.07561i
$649$	10.9161			0.428495
$650$	16.9830	+	14.9943i	0.666128	+	0.588126i
$651$	−21.1185	−	21.1185i	−0.827698	−	0.827698i
$652$	−1.15309	+	0.506662i	−0.0451583	+	0.0198424i
$653$			5.47114i			0.214102i	0.994254	+	0.107051i	$0.0341408\pi$
$653$			5.47114i			0.214102i	−0.994254	+	0.107051i	$0.965859\pi$
$654$	−27.2405	+	41.7236i	−1.06519	+	1.63152i
$655$	0.522365	−	1.04083i	0.0204105	−	0.0406686i
$656$	11.6342	+	10.6828i	0.454240	+	0.417095i
$657$	−30.1480	+	30.1480i	−1.17618	+	1.17618i
$658$	20.0674	−	4.21433i	0.782309	−	0.164292i
$659$	−26.5608	−	26.5608i	−1.03466	−	1.03466i	−0.999377	−	0.0352834i	$-0.988767\pi$
$659$	−26.5608	−	26.5608i	−1.03466	−	1.03466i	−0.0352834	−	0.999377i	$-0.511233\pi$
$660$	−13.9680	−	0.714997i	−0.543705	−	0.0278312i
$661$	10.9139	−	10.9139i	0.424501	−	0.424501i	−0.462249	−	0.886750i	$-0.652957\pi$
$661$	10.9139	−	10.9139i	0.424501	−	0.424501i	0.886750	+	0.462249i	$0.152957\pi$
$662$	−24.8716	−	16.2382i	−0.966662	−	0.631115i
$663$	11.8043	+	11.8043i	0.458439	+	0.458439i
$664$	40.2053	−	28.7638i	1.56027	−	1.11625i
$665$	−10.3594	+	3.43590i	−0.401719	+	0.133238i
$666$	15.0718	+	71.7674i	0.584020	+	2.78093i
$667$	4.42987			0.171525
$668$	−5.53216	+	14.2043i	−0.214046	+	0.549581i
$669$	−52.4277	+	52.4277i	−2.02697	+	2.02697i
$670$	23.2518	+	39.9354i	0.898294	+	1.54284i
$671$			4.02900i			0.155538i
$672$	8.01802	+	31.4529i	0.309302	+	1.21332i
$673$	−3.50554	−	3.50554i	−0.135129	−	0.135129i	0.636307	−	0.771436i	$-0.280461\pi$
$673$	−3.50554	−	3.50554i	−0.135129	−	0.135129i	−0.771436	+	0.636307i	$0.780461\pi$
$674$	27.9959	−	42.8805i	1.07836	−	1.65170i
$675$	−47.4035	+	35.3314i	−1.82456	+	1.35991i
$676$	5.00780	−	2.20041i	0.192608	−	0.0846311i
$677$			5.13452i			0.197336i	0.995120	+	0.0986679i	$0.0314581\pi$
$677$			5.13452i			0.197336i	−0.995120	+	0.0986679i	$0.968542\pi$
$678$	−24.4132	−	15.9389i	−0.937585	−	0.612131i
$679$			5.15242i			0.197732i
$680$	−1.63562	−	10.4092i	−0.0627230	−	0.399175i
$681$			51.7334i			1.98243i
$682$	4.02411	−	6.16363i	0.154091	−	0.236017i
$683$		−	40.9851i		−	1.56825i	−0.620603	−	0.784125i	$-0.713112\pi$
$683$		−	40.9851i		−	1.56825i	0.620603	−	0.784125i	$-0.286888\pi$
$684$	−33.6192	−	13.0937i	−1.28546	−	0.500651i
$685$	−30.5668	−	15.3406i	−1.16790	−	0.586135i
$686$	23.1034	+	15.0837i	0.882090	+	0.575900i
$687$	−48.2435	−	48.2435i	−1.84060	−	1.84060i
$688$	−4.59555	−	4.21976i	−0.175204	−	0.160877i
$689$		−	42.0064i		−	1.60032i
$690$	23.7319	+	6.26605i	0.903457	+	0.238544i
$691$	18.1112	−	18.1112i	0.688983	−	0.688983i	−0.273024	−	0.962007i	$-0.588024\pi$
$691$	18.1112	−	18.1112i	0.688983	−	0.688983i	0.962007	+	0.273024i	$0.0880240\pi$
$692$	2.91838	+	6.64178i	0.110940	+	0.252483i
$693$	12.4410			0.472593
$694$	−42.1660	+	8.85524i	−1.60060	+	0.336140i
$695$	−19.4877	+	38.8300i	−0.739211	+	1.47291i
$696$	−2.58394	+	15.5759i	−0.0979438	+	0.590401i
$697$	4.65185	+	4.65185i	0.176201	+	0.176201i
$698$	9.82664	−	15.0512i	0.371944	−	0.569697i
$699$	60.9320	−	60.9320i	2.30466	−	2.30466i
$700$	4.87803	+	17.6868i	0.184372	+	0.668500i
$701$	−24.6087	−	24.6087i	−0.929458	−	0.929458i	0.0682125	−	0.997671i	$-0.478270\pi$
$701$	−24.6087	−	24.6087i	−0.929458	−	0.929458i	−0.997671	+	0.0682125i	$0.978270\pi$
$702$	−11.0113	−	52.4327i	−0.415596	−	1.97894i
$703$	−14.3855	+	14.3855i	−0.542560	+	0.542560i
$704$	−7.18043	+	3.52723i	−0.270623	+	0.132937i
$705$	49.3937	+	24.7893i	1.86027	+	0.933621i
$706$	31.9967	+	20.8900i	1.20421	+	0.786206i
$707$			5.17132i			0.194487i
$708$	24.7796	−	63.6237i	0.931274	−	2.39113i
$709$	−3.93083	−	3.93083i	−0.147625	−	0.147625i	0.629431	−	0.777056i	$-0.283288\pi$
$709$	−3.93083	−	3.93083i	−0.147625	−	0.147625i	−0.777056	+	0.629431i	$0.783288\pi$
$710$	−34.1394	+	19.8771i	−1.28123	+	0.745976i
$711$	105.840			3.96931
$712$	14.3737	−	10.2833i	0.538677	−	0.385382i
$713$	−9.13444	+	9.13444i	−0.342088	+	0.342088i
$714$	2.77858	+	13.2308i	0.103986	+	0.495150i
$715$	3.21350	−	6.40302i	0.120178	−	0.239459i
$716$	12.4245	+	4.83899i	0.464326	+	0.180841i
$717$	21.7709			0.813048
$718$	−2.39913	−	11.4239i	−0.0895346	−	0.426337i
$719$	8.25572			0.307886			0.153943	−	0.988080i	$-0.450803\pi$
$719$	8.25572			0.307886			0.153943	+	0.988080i	$0.450803\pi$
$720$	−24.8712	+	55.3157i	−0.926895	+	2.06149i
$721$	5.02132			0.187004
$722$	3.46535	+	16.5010i	0.128967	+	0.614103i
$723$	31.4838			1.17089
$724$	−13.6614	+	35.0767i	−0.507720	+	1.30361i
$725$	−1.28856	+	8.83099i	−0.0478560	+	0.327975i
$726$	0.909011	+	4.32844i	0.0337366	+	0.160644i
$727$	−26.8683	+	26.8683i	−0.996490	+	0.996490i	−0.999994	−	0.00350418i	$-0.998885\pi$
$727$	−26.8683	+	26.8683i	−0.996490	+	0.996490i	0.00350418	+	0.999994i	$0.498885\pi$
$728$	−16.4021	−	2.72101i	−0.607903	−	0.100847i
$729$	1.87605			0.0694832
$730$	−5.07594	+	19.2245i	−0.187869	+	0.711530i
$731$	−1.83750	−	1.83750i	−0.0679623	−	0.0679623i
$732$	23.4827	+	9.14584i	0.867946	+	0.338040i
$733$			43.7072i			1.61436i	0.590305	+	0.807181i	$0.299008\pi$
$733$			43.7072i			1.61436i	−0.590305	+	0.807181i	$0.700992\pi$
$734$	−35.8986	−	23.4375i	−1.32504	−	0.865095i
$735$	7.99981	+	24.1197i	0.295078	+	0.889670i
$736$	13.6044	−	3.46806i	0.501466	−	0.127834i
$737$	10.3332	−	10.3332i	0.380627	−	0.380627i
$738$	−7.78254	−	37.0581i	−0.286479	−	1.36413i
$739$	17.6623	+	17.6623i	0.649718	+	0.649718i	0.952925	−	0.303207i	$-0.0980574\pi$
$739$	17.6623	+	17.6623i	0.649718	+	0.649718i	−0.303207	+	0.952925i	$0.598057\pi$
$740$	22.9146	+	25.3870i	0.842356	+	0.933245i
$741$	18.8493	−	18.8493i	0.692445	−	0.692445i
$742$	18.5975	−	28.4854i	0.682737	−	1.04573i
$743$	−18.7255	−	18.7255i	−0.686973	−	0.686973i	0.274589	−	0.961562i	$-0.411458\pi$
$743$	−18.7255	−	18.7255i	−0.686973	−	0.686973i	−0.961562	+	0.274589i	$0.911458\pi$
$744$	−26.7895	−	37.4457i	−0.982150	−	1.37283i
$745$	−39.2972	−	19.7222i	−1.43974	−	0.722565i
$746$	30.2471	−	6.35216i	1.10743	−	0.232569i
$747$	−118.515			−4.33625
$748$	−3.05058	+	1.34041i	−0.111540	+	0.0490103i
$749$	−1.80642	+	1.80642i	−0.0660050	+	0.0660050i
$750$	−19.3945	+	45.4870i	−0.708188	+	1.66095i
$751$		−	1.03484i		−	0.0377619i	−0.999822	−	0.0188809i	$-0.993990\pi$
$751$		−	1.03484i		−	0.0377619i	0.999822	−	0.0188809i	$-0.00601035\pi$
$752$	31.5823	−	1.34636i	1.15169	−	0.0490965i
$753$	15.0706	+	15.0706i	0.549203	+	0.549203i
$754$	−6.77191	−	4.42125i	−0.246618	−	0.161012i
$755$	19.0544	−	6.31980i	0.693462	−	0.230001i
$756$	15.7466	−	40.4306i	0.572697	−	1.47045i
$757$		−	20.8912i		−	0.759304i	−0.925129	−	0.379652i	$-0.876044\pi$
$757$		−	20.8912i		−	0.759304i	0.925129	−	0.379652i	$-0.123956\pi$
$758$	−16.0820	+	24.6323i	−0.584123	+	0.894686i
$759$		−	7.76186i		−	0.281738i
$760$	−16.6217	+	2.61179i	−0.602931	+	0.0947394i
$761$		−	17.7736i		−	0.644291i	−0.946690	−	0.322146i	$-0.895596\pi$
$761$		−	17.7736i		−	0.644291i	0.946690	−	0.322146i	$-0.104404\pi$
$762$	22.4942	+	14.6860i	0.814877	+	0.532018i
$763$		−	20.6703i		−	0.748314i
$764$	−11.8304	−	26.9242i	−0.428010	−	0.974085i
$765$	−11.3310	+	22.5774i	−0.409672	+	0.816287i
$766$	−18.4792	+	28.3041i	−0.667680	+	1.02267i
$767$	24.7305	+	24.7305i	0.892968	+	0.892968i
$768$	4.25858	+	49.8574i	0.153668	+	1.79908i
$769$			43.5416i			1.57015i	0.619402	+	0.785074i	$0.287375\pi$
$769$			43.5416i			1.57015i	−0.619402	+	0.785074i	$0.712625\pi$
$770$	5.01395	−	2.91929i	0.180690	−	0.105204i
$771$	37.5058	−	37.5058i	1.35074	−	1.35074i
$772$	−24.0104	−	9.35136i	−0.864154	−	0.336563i
$773$	40.0291			1.43975			0.719874	−	0.694105i	$-0.244200\pi$
$773$	40.0291			1.43975			0.719874	+	0.694105i	$0.244200\pi$
$774$	3.07413	+	14.6381i	0.110497	+	0.526155i
$775$	−15.5526	−	20.8666i	−0.558664	−	0.749551i
$776$	−1.29993	+	7.83595i	−0.0466649	+	0.281294i
$777$	−31.0272	−	31.0272i	−1.11309	−	1.11309i
$778$	5.90317	+	3.85406i	0.211639	+	0.138175i
$779$	7.42817	−	7.42817i	0.266142	−	0.266142i
$780$	−30.0248	−	33.2645i	−1.07506	−	1.19106i
$781$	8.83346	+	8.83346i	0.316086	+	0.316086i
$782$	5.72276	−	1.20183i	0.204645	−	0.0429773i
$783$	14.9237	−	14.9237i	0.533331	−	0.533331i
$784$	10.7064	+	9.83088i	0.382371	+	0.351103i
$785$	−25.2549	+	8.37631i	−0.901385	+	0.298963i
$786$	−1.25926	+	1.92877i	−0.0449162	+	0.0687970i
$787$			2.74573i			0.0978746i	0.998802	+	0.0489373i	$0.0155835\pi$
$787$			2.74573i			0.0978746i	−0.998802	+	0.0489373i	$0.984417\pi$
$788$	−19.2283	−	43.7607i	−0.684980	−	1.55891i
$789$	−69.3877	−	69.3877i	−2.47027	−	2.47027i
$790$	42.6555	−	24.8355i	1.51761	−	0.883607i
$791$	12.0946			0.430033
$792$	18.9206	+	3.13880i	0.672313	+	0.111532i
$793$	−9.12773	+	9.12773i	−0.324135	+	0.324135i
$794$	−0.921677	+	0.193560i	−0.0327091	+	0.00686920i
$795$	87.0255	−	28.8638i	3.08647	−	1.02369i
$796$	−4.13415	−	9.40871i	−0.146531	−	0.333483i
$797$	−24.0697			−0.852593			−0.426297	−	0.904583i	$-0.640182\pi$
$797$	−24.0697			−0.852593			−0.426297	+	0.904583i	$0.640182\pi$
$798$	21.1272	−	4.43690i	0.747895	−	0.157064i
$799$	13.1663			0.465790
$800$	2.95634	+	28.1293i	0.104522	+	0.994523i
$801$	−42.3701			−1.49707
$802$	−41.6372	+	8.74418i	−1.47026	+	0.308768i
$803$	6.28765			0.221886
$804$	−36.7697	−	83.6823i	−1.29677	−	2.95125i
$805$	−9.66428	+	3.20536i	−0.340621	+	0.112974i
$806$	23.0804	−	4.84709i	0.812972	−	0.170731i
$807$	23.4331	−	23.4331i	0.824886	−	0.824886i
$808$	−1.30470	+	7.86468i	−0.0458992	+	0.276679i
$809$	27.5189			0.967513			0.483756	−	0.875203i	$-0.339272\pi$
$809$	27.5189			0.967513			0.483756	+	0.875203i	$0.339272\pi$
$810$	45.4670	−	26.4725i	1.59755	−	0.930148i
$811$	−21.3826	−	21.3826i	−0.750846	−	0.750846i	0.223791	−	0.974637i	$-0.428157\pi$
$811$	−21.3826	−	21.3826i	−0.750846	−	0.750846i	−0.974637	+	0.223791i	$0.928157\pi$
$812$	−2.63474	−	5.99626i	−0.0924611	−	0.210428i
$813$		−	54.5014i		−	1.91145i
$814$	5.91221	−	9.05558i	0.207223	−	0.317398i
$815$	1.33656	−	0.443296i	0.0468175	−	0.0155280i
$816$	0.887675	+	20.8228i	0.0310748	+	0.728943i
$817$	−2.93415	+	2.93415i	−0.102653	+	0.102653i
$818$	14.6274	−	3.07189i	0.511436	−	0.107406i
$819$	28.1851	+	28.1851i	0.984867	+	0.984867i
$820$	−11.8323	−	13.1090i	−0.413201	−	0.457785i
$821$	−4.75637	+	4.75637i	−0.165999	+	0.165999i	−0.785218	−	0.619219i	$-0.787449\pi$
$821$	−4.75637	+	4.75637i	−0.165999	+	0.165999i	0.619219	+	0.785218i	$0.287449\pi$
$822$	56.6436	+	36.9815i	1.97567	+	1.28988i
$823$	3.36779	+	3.36779i	0.117394	+	0.117394i	0.763363	−	0.645969i	$-0.223547\pi$
$823$	3.36779	+	3.36779i	0.117394	+	0.117394i	−0.645969	+	0.763363i	$0.723547\pi$
$824$	7.63656	+	1.26686i	0.266032	+	0.0441330i
$825$	15.4733	+	2.25777i	0.538712	+	0.0786054i
$826$	5.82127	+	27.7192i	0.202548	+	0.964474i
$827$	23.2574			0.808739			0.404370	−	0.914596i	$-0.367491\pi$
$827$	23.2574			0.808739			0.404370	+	0.914596i	$0.367491\pi$
$828$	−31.3635	−	12.2152i	−1.08996	−	0.424507i
$829$	27.9374	−	27.9374i	0.970304	−	0.970304i	−0.0292673	−	0.999572i	$-0.509317\pi$
$829$	27.9374	−	27.9374i	0.970304	−	0.970304i	0.999572	+	0.0292673i	$0.00931740\pi$
$830$	−47.7639	+	27.8098i	−1.65791	+	0.965292i
$831$		−	15.0025i		−	0.520433i
$832$	−24.2583	−	8.27636i	−0.841005	−	0.286931i
$833$	4.28086	+	4.28086i	0.148323	+	0.148323i
$834$	46.9788	−	71.9562i	1.62674	−	2.49164i
$835$	7.64460	−	15.2322i	0.264552	−	0.527130i
$836$	2.14040	+	4.87122i	0.0740272	+	0.168475i
$837$			61.5458i			2.12733i
$838$	−7.24010	−	4.72692i	−0.250105	−	0.163289i
$839$		−	51.3963i		−	1.77440i	−0.461387	−	0.887199i	$-0.652648\pi$
$839$		−	51.3963i		−	1.77440i	0.461387	−	0.887199i	$-0.347352\pi$
$840$	−5.63320	−	35.8502i	−0.194364	−	1.23695i
$841$			25.8141i			0.890142i
$842$	1.42770	−	2.18677i	0.0492018	−	0.0753611i
$843$			11.5313i			0.397160i
$844$	−12.3192	+	31.6306i	−0.424045	+	1.08877i
$845$	−5.80460	+	1.92522i	−0.199684	+	0.0662294i
$846$	−63.4571	−	41.4299i	−2.18170	−	1.42439i
$847$	−1.29734	−	1.29734i	−0.0445772	−	0.0445772i
$848$	35.4704	−	38.6293i	1.21806	−	1.32653i
$849$		−	99.8629i		−	3.42729i
$850$	0.731220	+	11.7579i	0.0250806	+	0.403294i
$851$	−13.4203	+	13.4203i	−0.460042	+	0.460042i
$852$	71.5371	−	31.4332i	2.45082	−	1.07688i
$853$	6.54869			0.224223			0.112111	−	0.993696i	$-0.464239\pi$
$853$	6.54869			0.224223			0.112111	+	0.993696i	$0.464239\pi$
$854$	−10.2308	+	2.14856i	−0.350091	+	0.0735222i
$855$	36.0520	+	18.0935i	1.23295	+	0.618785i
$856$	−3.20300	+	2.29150i	−0.109476	+	0.0783217i
$857$	−10.1187	−	10.1187i	−0.345647	−	0.345647i	0.512838	−	0.858485i	$-0.328594\pi$
$857$	−10.1187	−	10.1187i	−0.345647	−	0.345647i	−0.858485	+	0.512838i	$0.828594\pi$
$858$	−7.74675	+	11.8655i	−0.264470	+	0.405081i
$859$	−15.6518	+	15.6518i	−0.534032	+	0.534032i	−0.921770	−	0.387737i	$-0.873257\pi$
$859$	−15.6518	+	15.6518i	−0.534032	+	0.534032i	0.387737	+	0.921770i	$0.373257\pi$
$860$	4.67379	+	5.17808i	0.159375	+	0.176571i
$861$	16.0213	+	16.0213i	0.546006	+	0.546006i
$862$	0.607018	+	2.89044i	0.0206751	+	0.0984488i
$863$	−4.24837	+	4.24837i	−0.144616	+	0.144616i	−0.775708	−	0.631092i	$-0.782607\pi$
$863$	−4.24837	+	4.24837i	−0.144616	+	0.144616i	0.631092	+	0.775708i	$0.282607\pi$
$864$	34.1483	−	57.5153i	1.16175	−	1.95671i
$865$	−2.55339	−	7.69857i	−0.0868179	−	0.261759i
$866$	−21.3673	−	13.9503i	−0.726089	−	0.474050i
$867$		−	44.4857i		−	1.51081i
$868$	17.7972	+	6.93150i	0.604077	+	0.235270i
$869$	−11.0370	−	11.0370i	−0.374404	−	0.374404i
$870$	4.50641	−	17.0674i	0.152781	−	0.578640i
$871$	46.8197			1.58642
$872$	5.21502	−	31.4359i	0.176603	−	1.06456i
$873$	13.4651	−	13.4651i	0.455726	−	0.455726i
$874$	−1.91910	−	9.13821i	−0.0649147	−	0.309105i
$875$	−3.57876	−	20.1982i	−0.120984	−	0.682823i
$876$	14.2730	−	36.6471i	0.482240	−	1.23819i
$877$	−48.7044			−1.64463			−0.822316	−	0.569031i	$-0.807318\pi$
$877$	−48.7044			−1.64463			−0.822316	+	0.569031i	$0.807318\pi$
$878$	5.01590	+	23.8842i	0.169278	+	0.806054i
$879$	63.3988			2.13839
$880$	8.36188	−	3.17475i	0.281879	−	0.107021i
$881$	−7.93702			−0.267405			−0.133703	−	0.991022i	$-0.542687\pi$
$881$	−7.93702			−0.267405			−0.133703	+	0.991022i	$0.542687\pi$
$882$	−7.16188	−	34.1027i	−0.241153	−	1.14830i
$883$	0.857373			0.0288529			0.0144264	−	0.999896i	$-0.495408\pi$
$883$	0.857373			0.0288529			0.0144264	+	0.999896i	$0.495408\pi$
$884$	−9.94781	−	3.87439i	−0.334581	−	0.130310i
$885$	−34.2416	+	68.2277i	−1.15102	+	2.29345i
$886$	−0.0696580	−	0.331691i	−0.00234021	−	0.0111434i
$887$	−22.1584	+	22.1584i	−0.744005	+	0.744005i	−0.973346	−	0.229341i	$-0.926343\pi$
$887$	−22.1584	+	22.1584i	−0.744005	+	0.744005i	0.229341	+	0.973346i	$0.426343\pi$
$888$	−39.3590	−	55.0151i	−1.32080	−	1.84618i
$889$	−11.1438			−0.373752
$890$	−17.0760	+	9.94222i	−0.572388	+	0.333264i
$891$	−11.7644	−	11.7644i	−0.394124	−	0.394124i
$892$	17.2078	−	44.1825i	0.576160	−	1.47934i
$893$		−	21.0242i		−	0.703548i
$894$	72.8220	+	47.5441i	2.43553	+	1.59011i
$895$	−13.3236	−	6.68674i	−0.445358	−	0.223513i
$896$	−12.7858	−	16.3522i	−0.427144	−	0.546290i
$897$	17.5846	−	17.5846i	0.587131	−	0.587131i
$898$	−6.37733	−	30.3670i	−0.212814	−	1.01336i
$899$	6.56929	+	6.56929i	0.219098	+	0.219098i
$900$	33.4741	−	58.9702i	1.11580	−	1.96567i
$901$	15.4456	−	15.4456i	0.514568	−	0.514568i
$902$	−3.05286	+	4.67598i	−0.101649	+	0.155693i
$903$	−6.32849	−	6.32849i	−0.210599	−	0.210599i
$904$	18.3937	+	3.05140i	0.611767	+	0.101488i
$905$	18.8779	−	37.6149i	0.627522	−	1.25036i
$906$	−38.8602	+	8.16098i	−1.29104	+	0.271131i
$907$	9.02465			0.299659			0.149829	−	0.988712i	$-0.452128\pi$
$907$	9.02465			0.299659			0.149829	+	0.988712i	$0.452128\pi$
$908$	−13.3087	−	30.2886i	−0.441665	−	1.00516i
$909$	13.5145	−	13.5145i	0.448249	−	0.448249i
$910$	17.9728	+	4.74546i	0.595793	+	0.157310i
$911$			4.40115i			0.145817i	0.997339	+	0.0729084i	$0.0232281\pi$
$911$			4.40115i			0.145817i	−0.997339	+	0.0729084i	$0.976772\pi$
$912$	33.2502	−	1.41746i	1.10103	−	0.0469367i
$913$	12.3588	+	12.3588i	0.409015	+	0.409015i
$914$	20.6797	+	13.5013i	0.684022	+	0.446585i
$915$	−25.1820	−	12.6382i	−0.832491	−	0.417804i
$916$	40.6563	+	15.8345i	1.34332	+	0.523185i
$917$		−	0.955532i		−	0.0315545i
$918$	15.2305	−	23.3281i	0.502681	−	0.769943i
$919$		−	47.4495i		−	1.56522i	−0.622515	−	0.782608i	$-0.713889\pi$
$919$		−	47.4495i		−	1.56522i	0.622515	−	0.782608i	$-0.286111\pi$
$920$	−15.5064	+	2.43654i	−0.511231	+	0.0803305i
$921$		−	56.2682i		−	1.85410i
$922$	−16.8266	−	10.9858i	−0.554156	−	0.361798i
$923$			40.0245i			1.31742i
$924$	−10.5064	+	4.61649i	−0.345636	+	0.151871i
$925$	−22.8498	−	30.6571i	−0.751295	−	1.00800i
$926$	−12.2561	+	18.7724i	−0.402762	+	0.616900i
$927$	−13.1225	−	13.1225i	−0.431000	−	0.431000i
$928$	−2.49415	−	9.78402i	−0.0818745	−	0.321176i
$929$		−	16.2390i		−	0.532786i	−0.963865	−	0.266393i	$-0.914168\pi$
$929$		−	16.2390i		−	0.532786i	0.963865	−	0.266393i	$-0.0858319\pi$
$930$	25.9010	+	44.4855i	0.849326	+	1.45874i
$931$	6.83577	−	6.83577i	0.224033	−	0.224033i
$932$	−19.9991	+	51.3493i	−0.655091	+	1.68200i
$933$	−56.6179			−1.85359
$934$	−9.13998	−	43.5219i	−0.299069	−	1.42408i
$935$	3.53596	−	1.17277i	0.115638	−	0.0383538i
$936$	35.7537	+	49.9757i	1.16865	+	1.63351i
$937$	40.5572	+	40.5572i	1.32495	+	1.32495i	0.909717	+	0.415228i	$0.136298\pi$
$937$	40.5572	+	40.5572i	1.32495	+	1.32495i	0.415228	+	0.909717i	$0.363702\pi$
$938$	31.7493	+	20.7285i	1.03665	+	0.676809i
$939$	−2.94319	+	2.94319i	−0.0960474	+	0.0960474i
$940$	−35.2960	−	1.80674i	−1.15123	−	0.0589292i
$941$	0.131577	+	0.131577i	0.00428929	+	0.00428929i	0.709248	−	0.704959i	$-0.249035\pi$
$941$	0.131577	+	0.131577i	0.00428929	+	0.00428929i	−0.704959	+	0.709248i	$0.749035\pi$
$942$	51.5056	−	10.8166i	1.67814	−	0.352425i
$943$	6.92976	−	6.92976i	0.225664	−	0.225664i
$944$	1.85973	+	43.6248i	0.0605289	+	1.41987i
$945$	−21.7594	+	43.3563i	−0.707832	+	1.41038i
$946$	1.20589	−	1.84703i	0.0392068	−	0.0600521i
$947$		−	10.9079i		−	0.354460i	−0.984170	−	0.177230i	$-0.943286\pi$
$947$		−	10.9079i		−	0.354460i	0.984170	−	0.177230i	$-0.0567136\pi$
$948$	−89.3821	+	39.2742i	−2.90299	+	1.27557i
$949$	14.2447	+	14.2447i	0.462403	+	0.462403i
$950$	18.7753	−	1.16763i	0.609152	−	0.0378828i
$951$	−87.0851			−2.82393
$952$	−5.03049	−	7.03150i	−0.163039	−	0.227892i
$953$	−4.38476	+	4.38476i	−0.142036	+	0.142036i	−0.774550	−	0.632513i	$-0.782023\pi$
$953$	−4.38476	+	4.38476i	−0.142036	+	0.142036i	0.632513	+	0.774550i	$0.282023\pi$
$954$	−123.045	+	25.8405i	−3.98372	+	0.836616i
$955$	10.3509	+	31.2082i	0.334946	+	1.00987i
$956$	−12.7463	+	5.60068i	−0.412245	+	0.181139i
$957$	−5.58216			−0.180446
$958$	1.53268	−	0.321876i	0.0495187	−	0.0103994i
$959$	−28.0618			−0.906162
$960$	0.477726	−	55.9432i	0.0154185	−	1.80556i
$961$	3.90811			0.126068
$962$	33.9096	−	7.12132i	1.09329	−	0.229601i
$963$	9.44164			0.304253
$964$	−18.4330	+	8.09938i	−0.593686	+	0.260864i
$965$	25.7479	+	12.9222i	0.828853	+	0.415979i
$966$	19.7096	−	4.13920i	0.634147	−	0.133176i
$967$	−8.97319	+	8.97319i	−0.288558	+	0.288558i	−0.836510	−	0.547952i	$-0.815408\pi$
$967$	−8.97319	+	8.97319i	−0.288558	+	0.288558i	0.547952	+	0.836510i	$0.315408\pi$
$968$	−1.64572	−	2.30035i	−0.0528955	−	0.0739360i
$969$	13.8616			0.445299
$970$	2.26709	−	8.58633i	0.0727920	−	0.275691i
$971$	14.4338	+	14.4338i	0.463203	+	0.463203i	0.899704	−	0.436501i	$-0.143782\pi$
$971$	14.4338	+	14.4338i	0.463203	+	0.463203i	−0.436501	+	0.899704i	$0.643782\pi$
$972$	−30.3208	+	13.3229i	−0.972541	+	0.427331i
$973$			35.6478i			1.14282i
$974$	−11.1572	+	17.0892i	−0.357499	+	0.547572i
$975$	29.9399	+	40.1699i	0.958846	+	1.28647i
$976$	−16.1014	+	0.686402i	−0.515392	+	0.0219712i
$977$	−4.47592	+	4.47592i	−0.143198	+	0.143198i	−0.775071	−	0.631874i	$-0.782286\pi$
$977$	−4.47592	+	4.47592i	−0.143198	+	0.143198i	0.631874	+	0.775071i	$0.282286\pi$
$978$	−2.72581	+	0.572445i	−0.0871619	+	0.0183048i
$979$	4.41835	+	4.41835i	0.141211	+	0.141211i
$980$	−10.8886	−	12.0635i	−0.347825	−	0.385355i
$981$	−54.0190	+	54.0190i	−1.72469	+	1.72469i
$982$	−30.7322	−	20.0645i	−0.980704	−	0.640282i
$983$	−11.7746	−	11.7746i	−0.375553	−	0.375553i	0.493942	−	0.869495i	$-0.335555\pi$
$983$	−11.7746	−	11.7746i	−0.375553	−	0.375553i	−0.869495	+	0.493942i	$0.835555\pi$
$984$	20.3236	+	28.4078i	0.647893	+	0.905609i
$985$	16.8235	+	50.7236i	0.536042	+	1.61619i
$986$	−0.864329	−	4.11568i	−0.0275258	−	0.131070i
$987$	45.3458			1.44337
$988$	−6.18670	+	15.8849i	−0.196825	+	0.505365i
$989$	−2.73728	+	2.73728i	−0.0870405	+	0.0870405i
$990$	−20.7324	−	5.47410i	−0.658920	−	0.173978i
$991$			25.2216i			0.801192i	0.916255	+	0.400596i	$0.131197\pi$
$991$			25.2216i			0.801192i	−0.916255	+	0.400596i	$0.868803\pi$
$992$	25.3177	+	15.0318i	0.803838	+	0.477259i
$993$	−46.4473	−	46.4473i	−1.47396	−	1.47396i
$994$	−17.7201	+	27.1414i	−0.562047	+	0.860873i
$995$	3.61712	+	10.9057i	0.114670	+	0.345735i
$996$	100.086	−	43.9776i	3.17136	−	1.39349i
$997$			29.2093i			0.925067i	0.886602	+	0.462534i	$0.153060\pi$
$997$			29.2093i			0.925067i	−0.886602	+	0.462534i	$0.846940\pi$
$998$	−25.2317	−	16.4733i	−0.798695	−	0.521452i
$999$			90.4228i			2.86085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bk.b.243.10	yes	236
5.2	odd	4		880.2.s.b.67.51	✓	236
16.11	odd	4		880.2.s.b.683.51	yes	236
80.27	even	4	inner	880.2.bk.b.507.10	yes	236

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.s.b.67.51	✓	236	5.2	odd	4
880.2.s.b.683.51	yes	236	16.11	odd	4
880.2.bk.b.243.10	yes	236	1.1	even	1	trivial
880.2.bk.b.507.10	yes	236	80.27	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38402 + 0.290657i) q^{2} -3.12744 q^{3} +(1.83104 - 0.804551i) q^{4} +(-2.12238 + 0.703930i) q^{5} +(4.32844 - 0.909011i) q^{6} +(-1.29734 + 1.29734i) q^{7} +(-2.30035 + 1.64572i) q^{8} +6.78086 q^{9} +(2.73281 - 1.59114i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(-5.72645 + 2.51618i) q^{12} -3.20391i q^{13} +(1.41847 - 2.17263i) q^{14} +(6.63760 - 2.20150i) q^{15} +(2.70539 - 2.94633i) q^{16} +(1.17807 - 1.17807i) q^{17} +(-9.38486 + 1.97090i) q^{18} +(-1.88116 - 1.88116i) q^{19} +(-3.31980 + 2.99648i) q^{20} +(4.05736 - 4.05736i) q^{21} +(1.18418 + 0.773126i) q^{22} +(-1.75494 - 1.75494i) q^{23} +(7.19419 - 5.14689i) q^{24} +(4.00896 - 2.98801i) q^{25} +(0.931239 + 4.43429i) q^{26} -11.8244 q^{27} +(-1.33170 + 3.41926i) q^{28} +(-1.26211 + 1.26211i) q^{29} +(-8.54670 + 4.97618i) q^{30} -5.20499i q^{31} +(-2.88796 + 4.86412i) q^{32} +(2.21143 + 2.21143i) q^{33} +(-1.28806 + 1.97288i) q^{34} +(1.84021 - 3.66669i) q^{35} +(12.4160 - 5.45555i) q^{36} -7.64715i q^{37} +(3.15034 + 2.05680i) q^{38} +10.0200i q^{39} +(3.72373 - 5.11212i) q^{40} +3.94872i q^{41} +(-4.43617 + 6.79477i) q^{42} -1.55976i q^{43} +(-1.86364 - 0.725835i) q^{44} +(-14.3915 + 4.77325i) q^{45} +(2.93896 + 1.91879i) q^{46} +(5.58809 + 5.58809i) q^{47} +(-8.46095 + 9.21445i) q^{48} +3.63381i q^{49} +(-4.68001 + 5.30071i) q^{50} +(-3.68433 + 3.68433i) q^{51} +(-2.57771 - 5.86648i) q^{52} +13.1110 q^{53} +(16.3652 - 3.43684i) q^{54} +(1.99850 + 1.00299i) q^{55} +(0.849276 - 5.11940i) q^{56} +(5.88321 + 5.88321i) q^{57} +(1.37995 - 2.11364i) q^{58} +(-7.71886 + 7.71886i) q^{59} +(10.3825 - 9.37131i) q^{60} +(-2.84893 - 2.84893i) q^{61} +(1.51287 + 7.20382i) q^{62} +(-8.79709 + 8.79709i) q^{63} +(2.58321 - 7.57146i) q^{64} +(2.25533 + 6.79991i) q^{65} +(-3.70344 - 2.41790i) q^{66} +14.6133i q^{67} +(1.20927 - 3.10490i) q^{68} +(5.48846 + 5.48846i) q^{69} +(-1.48114 + 5.60965i) q^{70} -12.4924 q^{71} +(-15.5983 + 11.1594i) q^{72} +(-4.44604 + 4.44604i) q^{73} +(2.22270 + 10.5838i) q^{74} +(-12.5378 + 9.34481i) q^{75} +(-4.95796 - 1.93098i) q^{76} +1.83472 q^{77} +(-2.91239 - 13.8679i) q^{78} +15.6086 q^{79} +(-3.66786 + 8.15762i) q^{80} +16.6374 q^{81} +(-1.14772 - 5.46511i) q^{82} -17.4779 q^{83} +(4.16482 - 10.6935i) q^{84} +(-1.67102 + 3.32958i) q^{85} +(0.453354 + 2.15874i) q^{86} +(3.94718 - 3.94718i) q^{87} +(2.79029 + 0.462892i) q^{88} -6.24849 q^{89} +(18.5308 - 10.7893i) q^{90} +(4.15657 + 4.15657i) q^{91} +(-4.62530 - 1.80142i) q^{92} +16.2783i q^{93} +(-9.35827 - 6.10983i) q^{94} +(5.31673 + 2.66832i) q^{95} +(9.03190 - 15.2122i) q^{96} +(1.98576 - 1.98576i) q^{97} +(-1.05619 - 5.02927i) q^{98} +(-4.79479 - 4.79479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) \) 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

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