LMFDB - Embedded newform 231.2.n.a.89.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(89,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("231.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.n (of order $6$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.18
Character	$\chi$	$=$	231.89
Dual form			231.2.n.a.122.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.942161 + 0.543957i) q^{2} +(1.70755 - 0.290278i) q^{3} +(-0.408222 - 0.707062i) q^{4} +(-1.52055 + 2.63367i) q^{5} +(1.76669 + 0.655346i) q^{6} +(2.61395 + 0.408977i) q^{7} -3.06405i q^{8} +(2.83148 - 0.991331i) q^{9} +O(q^{10})$	\(q+(0.942161 + 0.543957i) q^{2} +(1.70755 - 0.290278i) q^{3} +(-0.408222 - 0.707062i) q^{4} +(-1.52055 + 2.63367i) q^{5} +(1.76669 + 0.655346i) q^{6} +(2.61395 + 0.408977i) q^{7} -3.06405i q^{8} +(2.83148 - 0.991331i) q^{9} +(-2.86521 + 1.65423i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-0.902306 - 1.08885i) q^{12} +4.07958i q^{13} +(2.24030 + 1.80720i) q^{14} +(-1.83193 + 4.93852i) q^{15} +(0.850264 - 1.47270i) q^{16} +(-0.631497 - 1.09378i) q^{17} +(3.20695 + 0.606208i) q^{18} +(-6.20991 - 3.58529i) q^{19} +2.48289 q^{20} +(4.58218 - 0.0604233i) q^{21} +1.08791 q^{22} +(-6.74021 - 3.89146i) q^{23} +(-0.889426 - 5.23202i) q^{24} +(-2.12415 - 3.67914i) q^{25} +(-2.21911 + 3.84362i) q^{26} +(4.54714 - 2.51467i) q^{27} +(-0.777901 - 2.01518i) q^{28} -0.671342i q^{29} +(-4.41231 + 3.65639i) q^{30} +(-3.18173 + 1.83697i) q^{31} +(-3.70492 + 2.13903i) q^{32} +(1.33365 - 1.10516i) q^{33} -1.37403i q^{34} +(-5.05176 + 6.26242i) q^{35} +(-1.85680 - 1.59735i) q^{36} +(-1.00915 + 1.74789i) q^{37} +(-3.90049 - 6.75584i) q^{38} +(1.18421 + 6.96609i) q^{39} +(8.06970 + 4.65904i) q^{40} +3.14262 q^{41} +(4.35001 + 2.43558i) q^{42} -0.803886 q^{43} +(-0.707062 - 0.408222i) q^{44} +(-1.69457 + 8.96455i) q^{45} +(-4.23357 - 7.33276i) q^{46} +(-2.08317 + 3.60816i) q^{47} +(1.02438 - 2.76153i) q^{48} +(6.66548 + 2.13809i) q^{49} -4.62179i q^{50} +(-1.39582 - 1.68439i) q^{51} +(2.88451 - 1.66537i) q^{52} +(2.65499 - 1.53286i) q^{53} +(5.65200 + 0.104226i) q^{54} +3.04110i q^{55} +(1.25312 - 8.00927i) q^{56} +(-11.6445 - 4.31948i) q^{57} +(0.365181 - 0.632512i) q^{58} +(-3.66585 - 6.34944i) q^{59} +(4.23967 - 0.720729i) q^{60} +(12.6751 + 7.31800i) q^{61} -3.99693 q^{62} +(7.80677 - 1.43328i) q^{63} -8.05522 q^{64} +(-10.7443 - 6.20321i) q^{65} +(1.85767 - 0.315797i) q^{66} +(-0.222443 - 0.385283i) q^{67} +(-0.515582 + 0.893015i) q^{68} +(-12.6389 - 4.68834i) q^{69} +(-8.16605 + 3.15227i) q^{70} -2.98265i q^{71} +(-3.03748 - 8.67578i) q^{72} +(6.34549 - 3.66357i) q^{73} +(-1.90155 + 1.09786i) q^{74} +(-4.69508 - 5.66574i) q^{75} +5.85439i q^{76} +(2.46824 - 0.952791i) q^{77} +(-2.67354 + 7.20734i) q^{78} +(1.19783 - 2.07470i) q^{79} +(2.58574 + 4.47864i) q^{80} +(7.03453 - 5.61386i) q^{81} +(2.96085 + 1.70945i) q^{82} +5.99088 q^{83} +(-1.91327 - 3.21522i) q^{84} +3.84089 q^{85} +(-0.757390 - 0.437279i) q^{86} +(-0.194876 - 1.14635i) q^{87} +(-1.53202 - 2.65354i) q^{88} +(-7.74735 + 13.4188i) q^{89} +(-6.47288 + 7.52428i) q^{90} +(-1.66845 + 10.6638i) q^{91} +6.35432i q^{92} +(-4.89974 + 4.06031i) q^{93} +(-3.92537 + 2.26631i) q^{94} +(18.8850 - 10.9032i) q^{95} +(-5.70543 + 4.72797i) q^{96} -7.83644i q^{97} +(5.11692 + 5.64015i) q^{98} +(1.95647 - 2.27426i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9	$ 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) $ 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9 - 30 * q^12 - 4 * q^15 - 20 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^21 + 36 * q^24 - 22 * q^25 - 40 * q^28 - 20 * q^30 - 54 * q^31 + 36 * q^36 + 2 * q^37 + 20 * q^39 + 60 * q^40 - 36 * q^42 + 36 * q^43 - 54 * q^45 + 4 * q^46 + 22 * q^49 - 16 * q^51 + 12 * q^52 + 66 * q^54 - 44 * q^57 - 16 * q^58 + 20 * q^60 - 36 * q^61 - 24 * q^63 - 48 * q^64 - 30 * q^66 - 6 * q^67 - 116 * q^70 + 36 * q^72 - 6 * q^73 + 72 * q^75 + 112 * q^78 + 14 * q^79 + 52 * q^81 - 84 * q^82 + 8 * q^84 + 8 * q^85 + 18 * q^87 - 12 * q^88 + 46 * q^91 + 6 * q^93 + 48 * q^94 - 18 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.942161	+	0.543957i	0.666208	+	0.384635i	0.794638	−	0.607083i	$-0.207661\pi$
$2$	0.942161	+	0.543957i	0.666208	+	0.384635i	−0.128430	+	0.991719i	$0.540994\pi$
$3$	1.70755	−	0.290278i	0.985856	−	0.167592i
$3$	1.70755	−	0.290278i	0.985856	−	0.167592i
$4$	−0.408222	−	0.707062i	−0.204111	−	0.353531i
$5$	−1.52055	+	2.63367i	−0.680011	+	1.17781i	0.294966	+	0.955508i	$0.404692\pi$
$5$	−1.52055	+	2.63367i	−0.680011	+	1.17781i	−0.974977	+	0.222306i	$0.928642\pi$
$6$	1.76669	+	0.655346i	0.721247	+	0.267544i
$7$	2.61395	+	0.408977i	0.987980	+	0.154579i
$7$	2.61395	+	0.408977i	0.987980	+	0.154579i
$8$		−	3.06405i		−	1.08330i
$9$	2.83148	−	0.991331i	0.943826	−	0.330444i
$10$	−2.86521	+	1.65423i	−0.906058	+	0.523113i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	−0.902306	−	1.08885i	−0.260473	−	0.314323i
$13$			4.07958i			1.13147i	0.824587	+	0.565735i	$0.191408\pi$
$13$			4.07958i			1.13147i	−0.824587	+	0.565735i	$0.808592\pi$
$14$	2.24030	+	1.80720i	0.598744	+	0.482994i
$15$	−1.83193	+	4.93852i	−0.473001	+	1.27512i
$16$	0.850264	−	1.47270i	0.212566	−	0.368175i
$17$	−0.631497	−	1.09378i	−0.153160	−	0.265282i	0.779227	−	0.626742i	$-0.215612\pi$
$17$	−0.631497	−	1.09378i	−0.153160	−	0.265282i	−0.932388	+	0.361460i	$0.882278\pi$
$18$	3.20695	+	0.606208i	0.755885	+	0.142885i
$19$	−6.20991	−	3.58529i	−1.42465	−	0.822522i	−0.427959	−	0.903798i	$-0.640767\pi$
$19$	−6.20991	−	3.58529i	−1.42465	−	0.822522i	−0.996692	+	0.0812757i	$0.974101\pi$
$20$	2.48289			0.555192
$21$	4.58218	−	0.0604233i	0.999913	−	0.0131854i
$22$	1.08791			0.231944
$23$	−6.74021	−	3.89146i	−1.40543	−	0.811425i	−0.410487	−	0.911866i	$-0.634641\pi$
$23$	−6.74021	−	3.89146i	−1.40543	−	0.811425i	−0.994943	+	0.100441i	$0.967975\pi$
$24$	−0.889426	−	5.23202i	−0.181553	−	1.06798i
$25$	−2.12415	−	3.67914i	−0.424831	−	0.735829i
$26$	−2.21911	+	3.84362i	−0.435204	+	0.753795i
$27$	4.54714	−	2.51467i	0.875097	−	0.483948i
$28$	−0.777901	−	2.01518i	−0.147010	−	0.380833i
$29$		−	0.671342i		−	0.124665i	−0.998055	−	0.0623325i	$-0.980146\pi$
$29$		−	0.671342i		−	0.124665i	0.998055	−	0.0623325i	$-0.0198539\pi$
$30$	−4.41231	+	3.65639i	−0.805574	+	0.667562i
$31$	−3.18173	+	1.83697i	−0.571455	+	0.329930i	−0.757730	−	0.652568i	$-0.773692\pi$
$31$	−3.18173	+	1.83697i	−0.571455	+	0.329930i	0.186275	+	0.982498i	$0.440358\pi$
$32$	−3.70492	+	2.13903i	−0.654943	+	0.378131i
$33$	1.33365	−	1.10516i	0.232158	−	0.192385i
$34$		−	1.37403i		−	0.235644i
$35$	−5.05176	+	6.26242i	−0.853903	+	1.05854i
$36$	−1.85680	−	1.59735i	−0.309467	−	0.266224i
$37$	−1.00915	+	1.74789i	−0.165902	+	0.287351i	−0.936975	−	0.349395i	$-0.886387\pi$
$37$	−1.00915	+	1.74789i	−0.165902	+	0.287351i	0.771073	+	0.636747i	$0.219720\pi$
$38$	−3.90049	−	6.75584i	−0.632743	−	1.09594i
$39$	1.18421	+	6.96609i	0.189626	+	1.11547i
$40$	8.06970	+	4.65904i	1.27593	+	0.736659i
$41$	3.14262			0.490795			0.245397	−	0.969423i	$-0.421082\pi$
$41$	3.14262			0.490795			0.245397	+	0.969423i	$0.421082\pi$
$42$	4.35001	+	2.43558i	0.671222	+	0.375818i
$43$	−0.803886			−0.122591			−0.0612957	−	0.998120i	$-0.519523\pi$
$43$	−0.803886			−0.122591			−0.0612957	+	0.998120i	$0.519523\pi$
$44$	−0.707062	−	0.408222i	−0.106594	−	0.0615418i
$45$	−1.69457	+	8.96455i	−0.252611	+	1.33636i
$46$	−4.23357	−	7.33276i	−0.624206	−	1.08116i
$47$	−2.08317	+	3.60816i	−0.303862	+	0.526304i	−0.977007	−	0.213206i	$-0.931609\pi$
$47$	−2.08317	+	3.60816i	−0.303862	+	0.526304i	0.673145	+	0.739510i	$0.264943\pi$
$48$	1.02438	−	2.76153i	0.147856	−	0.398592i
$49$	6.66548	+	2.13809i	0.952211	+	0.305441i
$50$		−	4.62179i		−	0.653620i
$51$	−1.39582	−	1.68439i	−0.195453	−	0.235861i
$52$	2.88451	−	1.66537i	0.400010	−	0.230946i
$53$	2.65499	−	1.53286i	0.364691	−	0.210554i	−0.306446	−	0.951888i	$-0.599140\pi$
$53$	2.65499	−	1.53286i	0.364691	−	0.210554i	0.671137	+	0.741334i	$0.265806\pi$
$54$	5.65200	+	0.104226i	0.769140	+	0.0141833i
$55$			3.04110i			0.410062i
$56$	1.25312	−	8.00927i	0.167456	−	1.07028i
$57$	−11.6445	−	4.31948i	−1.54235	−	0.572129i
$58$	0.365181	−	0.632512i	0.0479506	−	0.0830528i
$59$	−3.66585	−	6.34944i	−0.477253	−	0.826626i	0.522407	−	0.852696i	$-0.325034\pi$
$59$	−3.66585	−	6.34944i	−0.477253	−	0.826626i	−0.999660	+	0.0260699i	$0.991701\pi$
$60$	4.23967	−	0.720729i	0.547339	−	0.0930458i
$61$	12.6751	+	7.31800i	1.62289	+	0.936974i	0.986143	+	0.165898i	$0.0530522\pi$
$61$	12.6751	+	7.31800i	1.62289	+	0.936974i	0.636743	+	0.771076i	$0.280281\pi$
$62$	−3.99693			−0.507611
$63$	7.80677	−	1.43328i	0.983561	−	0.180577i
$64$	−8.05522			−1.00690
$65$	−10.7443	−	6.20321i	−1.33266	−	0.769413i
$66$	1.85767	−	0.315797i	0.228663	−	0.0388720i
$67$	−0.222443	−	0.385283i	−0.0271758	−	0.0470699i	0.852118	−	0.523350i	$-0.175318\pi$
$67$	−0.222443	−	0.385283i	−0.0271758	−	0.0470699i	−0.879293	+	0.476280i	$0.841985\pi$
$68$	−0.515582	+	0.893015i	−0.0625235	+	0.108294i
$69$	−12.6389	−	4.68834i	−1.52154	−	0.564410i
$70$	−8.16605	+	3.15227i	−0.976030	+	0.376768i
$71$		−	2.98265i		−	0.353975i	−0.984213	−	0.176988i	$-0.943365\pi$
$71$		−	2.98265i		−	0.353975i	0.984213	−	0.176988i	$-0.0566352\pi$
$72$	−3.03748	−	8.67578i	−0.357971	−	1.02245i
$73$	6.34549	−	3.66357i	0.742684	−	0.428789i	−0.0803606	−	0.996766i	$-0.525607\pi$
$73$	6.34549	−	3.66357i	0.742684	−	0.428789i	0.823044	+	0.567977i	$0.192274\pi$
$74$	−1.90155	+	1.09786i	−0.221051	+	0.127624i
$75$	−4.69508	−	5.66574i	−0.542141	−	0.654223i
$76$			5.85439i			0.671544i
$77$	2.46824	−	0.952791i	0.281282	−	0.108581i
$78$	−2.67354	+	7.20734i	−0.302718	+	0.816070i
$79$	1.19783	−	2.07470i	0.134766	−	0.233422i	−0.790742	−	0.612150i	$-0.790305\pi$
$79$	1.19783	−	2.07470i	0.134766	−	0.233422i	0.925508	+	0.378728i	$0.123638\pi$
$80$	2.58574	+	4.47864i	0.289095	+	0.500727i
$81$	7.03453	−	5.61386i	0.781614	−	0.623762i
$82$	2.96085	+	1.70945i	0.326971	+	0.188777i
$83$	5.99088			0.657585			0.328792	−	0.944402i	$-0.393358\pi$
$83$	5.99088			0.657585			0.328792	+	0.944402i	$0.393358\pi$
$84$	−1.91327	−	3.21522i	−0.208755	−	0.350809i
$85$	3.84089			0.416603
$86$	−0.757390	−	0.437279i	−0.0816714	−	0.0471530i
$87$	−0.194876	−	1.14635i	−0.0208929	−	0.122902i
$88$	−1.53202	−	2.65354i	−0.163314	−	0.282869i
$89$	−7.74735	+	13.4188i	−0.821218	+	1.42239i	0.0835580	+	0.996503i	$0.473372\pi$
$89$	−7.74735	+	13.4188i	−0.821218	+	1.42239i	−0.904776	+	0.425888i	$0.859962\pi$
$90$	−6.47288	+	7.52428i	−0.682302	+	0.793129i
$91$	−1.66845	+	10.6638i	−0.174901	+	1.11787i
$92$			6.35432i			0.662484i
$93$	−4.89974	+	4.06031i	−0.508079	+	0.421035i
$94$	−3.92537	+	2.26631i	−0.404871	+	0.233752i
$95$	18.8850	−	10.9032i	1.93756	−	1.11865i
$96$	−5.70543	+	4.72797i	−0.582308	+	0.482546i
$97$		−	7.83644i		−	0.795670i	−0.917457	−	0.397835i	$-0.869762\pi$
$97$		−	7.83644i		−	0.795670i	0.917457	−	0.397835i	$-0.130238\pi$
$98$	5.11692	+	5.64015i	0.516887	+	0.569742i
$99$	1.95647	−	2.27426i	0.196632	−	0.228571i
$100$	−1.73425	+	3.00382i	−0.173425	+	0.300382i
$101$	9.13110	+	15.8155i	0.908578	+	1.57370i	0.816041	+	0.577994i	$0.196164\pi$
$101$	9.13110	+	15.8155i	0.908578	+	1.57370i	0.0925369	+	0.995709i	$0.470502\pi$
$102$	−0.398850	−	2.34623i	−0.0394920	−	0.232311i
$103$	−13.1750	−	7.60662i	−1.29818	−	0.749502i	−0.318087	−	0.948062i	$-0.603040\pi$
$103$	−13.1750	−	7.60662i	−1.29818	−	0.749502i	−0.980089	+	0.198559i	$0.936374\pi$
$104$	12.5000			1.22573
$105$	−6.80830	+	12.1598i	−0.664422	+	1.18668i
$106$	3.33524			0.323947
$107$	12.2982	+	7.10035i	1.18891	+	0.686417i	0.958059	−	0.286572i	$-0.0925157\pi$
$107$	12.2982	+	7.10035i	1.18891	+	0.686417i	0.230851	+	0.972989i	$0.425849\pi$
$108$	−3.63427	−	2.18856i	−0.349708	−	0.210595i
$109$	2.38951	+	4.13876i	0.228874	+	0.396421i	0.957475	−	0.288518i	$-0.0931623\pi$
$109$	2.38951	+	4.13876i	0.228874	+	0.396421i	−0.728601	+	0.684939i	$0.759829\pi$
$110$	−1.65423	+	2.86521i	−0.157724	+	0.273187i
$111$	−1.21579	+	3.27755i	−0.115398	+	0.311091i
$112$	2.82485	−	3.50183i	0.266923	−	0.330892i
$113$		−	14.9311i		−	1.40460i	−0.711882	−	0.702299i	$-0.752157\pi$
$113$		−	14.9311i		−	1.40460i	0.711882	−	0.702299i	$-0.247843\pi$
$114$	−8.62136	−	10.4037i	−0.807465	−	0.974399i
$115$	20.4977	−	11.8343i	1.91142	−	1.10356i
$116$	−0.474680	+	0.274057i	−0.0440729	+	0.0254455i
$117$	4.04421	+	11.5512i	0.373887	+	1.06791i
$118$		−	7.97625i		−	0.734273i
$119$	−1.20337	−	3.11737i	−0.110313	−	0.285768i
$120$	15.1319	+	5.61311i	1.38134	+	0.512404i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	7.96135	+	13.7895i	0.720787	+	1.24844i
$123$	5.36619	−	0.912234i	0.483853	−	0.0822533i
$124$	2.59771	+	1.49979i	0.233281	+	0.134685i
$125$	−2.28597			−0.204464
$126$	8.13488	+	2.89616i	0.724712	+	0.258011i
$127$	0.433546			0.0384709			0.0192355	−	0.999815i	$-0.493877\pi$
$127$	0.433546			0.0384709			0.0192355	+	0.999815i	$0.493877\pi$
$128$	−0.179483	−	0.103624i	−0.0158642	−	0.00915920i
$129$	−1.37268	+	0.233351i	−0.120858	+	0.0205454i
$130$	−6.74855	−	11.6888i	−0.591887	−	1.02518i
$131$	4.28519	−	7.42216i	0.374398	−	0.648477i	−0.615838	−	0.787872i	$-0.711183\pi$
$131$	4.28519	−	7.42216i	0.374398	−	0.648477i	0.990237	+	0.139395i	$0.0445159\pi$
$132$	−1.32584	−	0.491817i	−0.115400	−	0.0428072i
$133$	−14.7661	−	11.9115i	−1.28038	−	1.03286i
$134$		−	0.483998i		−	0.0418111i
$135$	−0.291348	+	15.7993i	−0.0250753	+	1.35979i
$136$	−3.35141	+	1.93494i	−0.287381	+	0.165919i
$137$	−17.5844	+	10.1524i	−1.50234	+	0.867374i	−0.502340	+	0.864670i	$0.667527\pi$
$137$	−17.5844	+	10.1524i	−1.50234	+	0.867374i	−0.999996	+	0.00270418i	$0.999139\pi$
$138$	−9.35759	−	11.2922i	−0.796571	−	0.961253i
$139$			6.39716i			0.542600i	0.962495	+	0.271300i	$0.0874536\pi$
$139$			6.39716i			0.542600i	−0.962495	+	0.271300i	$0.912546\pi$
$140$	6.49016	+	1.01545i	0.548519	+	0.0858208i
$141$	−2.50976	+	6.76583i	−0.211360	+	0.569785i
$142$	1.62243	−	2.81013i	0.136151	−	0.235821i
$143$	2.03979	+	3.53302i	0.170576	+	0.295446i
$144$	0.947570	−	5.01281i	0.0789642	−	0.417734i
$145$	1.76809	+	1.02081i	0.146832	+	0.0847736i
$146$	7.97130			0.659709
$147$	12.0023	+	1.71606i	0.989933	+	0.141538i
$148$	1.64782			0.135450
$149$	4.58268	+	2.64581i	0.375428	+	0.216753i	0.675827	−	0.737060i	$-0.263787\pi$
$149$	4.58268	+	2.64581i	0.375428	+	0.216753i	−0.300399	+	0.953814i	$0.597120\pi$
$150$	−1.34160	−	7.89195i	−0.109542	−	0.644375i
$151$	2.45595	+	4.25383i	0.199862	+	0.346172i	0.948484	−	0.316826i	$-0.102617\pi$
$151$	2.45595	+	4.25383i	0.199862	+	0.346172i	−0.748621	+	0.662998i	$0.769284\pi$
$152$	−10.9855	+	19.0275i	−0.891042	+	1.54333i
$153$	−2.87237	−	2.47100i	−0.232217	−	0.199769i
$154$	2.84375	+	0.444931i	0.229156	+	0.0358536i
$155$		−	11.1728i		−	0.897424i
$156$	4.44204	−	3.68103i	0.355648	−	0.294718i
$157$	0.766494	−	0.442536i	0.0611729	−	0.0353182i	−0.469102	−	0.883144i	$-0.655422\pi$
$157$	0.766494	−	0.442536i	0.0611729	−	0.0353182i	0.530275	+	0.847826i	$0.322089\pi$
$158$	2.25709	−	1.30313i	0.179565	−	0.103672i
$159$	4.08858	−	3.38812i	0.324246	−	0.268696i
$160$		−	13.0100i		−	1.02853i
$161$	−16.0270	−	12.9287i	−1.26311	−	1.01892i
$162$	9.68135	−	1.46268i	0.760639	−	0.114919i
$163$	−12.6907	+	21.9809i	−0.994012	+	1.72168i	−0.402376	+	0.915474i	$0.631816\pi$
$163$	−12.6907	+	21.9809i	−0.994012	+	1.72168i	−0.591636	+	0.806205i	$0.701518\pi$
$164$	−1.28289	−	2.22203i	−0.100177	−	0.173511i
$165$	0.882766	+	5.19285i	0.0687232	+	0.404263i
$166$	5.64437	+	3.25878i	0.438088	+	0.252930i
$167$	0.559579			0.0433015			0.0216508	−	0.999766i	$-0.493108\pi$
$167$	0.559579			0.0433015			0.0216508	+	0.999766i	$0.493108\pi$
$168$	−0.185140	−	14.0400i	−0.0142838	−	1.08321i
$169$	−3.64295			−0.280227
$170$	3.61874	+	2.08928i	0.277545	+	0.160240i
$171$	−21.1374	−	3.99560i	−1.61642	−	0.305551i
$172$	0.328164	+	0.568397i	0.0250223	+	0.0433399i
$173$	4.25655	−	7.37256i	0.323619	−	0.560525i	−0.657613	−	0.753356i	$-0.728434\pi$
$173$	4.25655	−	7.37256i	0.323619	−	0.560525i	0.981232	+	0.192831i	$0.0617670\pi$
$174$	0.439961	−	1.18605i	0.0333534	−	0.0899143i
$175$	−4.04775	−	10.4858i	−0.305981	−	0.792654i
$176$		−	1.70053i		−	0.128182i
$177$	−8.10273	−	9.77789i	−0.609039	−	0.734951i
$178$	−14.5985	+	8.42845i	−1.09420	+	0.631739i
$179$	19.0300	−	10.9870i	1.42237	−	0.821204i	0.425867	−	0.904786i	$-0.359969\pi$
$179$	19.0300	−	10.9870i	1.42237	−	0.821204i	0.996501	+	0.0835817i	$0.0266359\pi$
$180$	7.03025	−	2.46137i	0.524004	−	0.183460i
$181$			14.9644i			1.11230i	0.831083	+	0.556149i	$0.187722\pi$
$181$			14.9644i			1.11230i	−0.831083	+	0.556149i	$0.812278\pi$
$182$	−7.37260	+	9.13946i	−0.546494	+	0.677462i
$183$	23.7677	+	8.81656i	1.75696	+	0.651739i
$184$	−11.9236	+	20.6523i	−0.879021	+	1.52251i
$185$	−3.06891	−	5.31552i	−0.225631	−	0.390805i
$186$	−6.82498	+	1.16022i	−0.500432	+	0.0850716i
$187$	−1.09378	−	0.631497i	−0.0799854	−	0.0461796i
$188$	3.40159			0.248086
$189$	12.9144	−	4.71354i	0.939387	−	0.342860i
$190$	23.7236			1.72109
$191$	15.3827	+	8.88118i	1.11305	+	0.642620i	0.939618	−	0.342226i	$-0.111181\pi$
$191$	15.3827	+	8.88118i	1.11305	+	0.642620i	0.173432	+	0.984846i	$0.444514\pi$
$192$	−13.7547	+	2.33826i	−0.992662	+	0.168749i
$193$	2.03448	+	3.52383i	0.146445	+	0.253651i	0.929911	−	0.367784i	$-0.119883\pi$
$193$	2.03448	+	3.52383i	0.146445	+	0.253651i	−0.783466	+	0.621435i	$0.786550\pi$
$194$	4.26268	−	7.38318i	0.306043	−	0.530082i
$195$	−20.1471	−	7.47348i	−1.44276	−	0.535187i
$196$	−1.20923	−	5.58572i	−0.0863739	−	0.398980i
$197$		−	4.64326i		−	0.330819i	−0.986225	−	0.165409i	$-0.947105\pi$
$197$		−	4.64326i		−	0.330819i	0.986225	−	0.165409i	$-0.0528945\pi$
$198$	3.08040	−	1.07848i	0.218915	−	0.0766444i
$199$	15.8797	−	9.16815i	1.12568	−	0.649913i	0.182837	−	0.983143i	$-0.441472\pi$
$199$	15.8797	−	9.16815i	1.12568	−	0.649913i	0.942846	+	0.333230i	$0.108139\pi$
$200$	−11.2731	+	6.50851i	−0.797126	+	0.460221i
$201$	−0.491673	−	0.593321i	−0.0346800	−	0.0418497i
$202$			19.8677i			1.39789i
$203$	0.274563	−	1.75485i	0.0192705	−	0.123167i
$204$	−0.621162	+	1.67453i	−0.0434900	+	0.117241i
$205$	−4.77851	+	8.27663i	−0.333746	+	0.578065i
$206$	−8.27534	−	14.3333i	−0.576570	−	0.998649i
$207$	−22.9425	−	4.33680i	−1.59461	−	0.301429i
$208$	6.00800	+	3.46872i	0.416580	+	0.240512i
$209$	−7.17058			−0.496000
$210$	−13.0289	+	7.75309i	−0.899082	+	0.535014i
$211$	−17.7066			−1.21897			−0.609485	−	0.792797i	$-0.708624\pi$
$211$	−17.7066			−1.21897			−0.609485	+	0.792797i	$0.708624\pi$
$212$	−2.16765	−	1.25149i	−0.148875	−	0.0859530i
$213$	−0.865797	−	5.09303i	−0.0593234	−	0.348969i
$214$	7.72457	+	13.3793i	0.528041	+	0.914593i
$215$	1.22235	−	2.11717i	0.0833636	−	0.144390i
$216$	−7.70506	−	13.9326i	−0.524263	−	0.947996i
$217$	−9.06816	+	3.50050i	−0.615587	+	0.237630i
$218$			5.19917i			0.352132i
$219$	9.77181	−	8.09770i	0.660318	−	0.547192i
$220$	2.15025	−	1.24145i	0.144970	−	0.0836983i
$221$	4.46218	−	2.57624i	0.300159	−	0.173297i
$222$	−2.92832	+	2.42664i	−0.196536	+	0.162865i
$223$		−	14.8752i		−	0.996118i	−0.867143	−	0.498059i	$-0.834046\pi$
$223$		−	14.8752i		−	0.996118i	0.867143	−	0.498059i	$-0.165954\pi$
$224$	−10.5593	+	4.07611i	−0.705522	+	0.272346i
$225$	−9.66174	−	8.31167i	−0.644116	−	0.554111i
$226$	8.12186	−	14.0675i	0.540258	−	0.935755i
$227$	5.89242	+	10.2060i	0.391094	+	0.677395i	0.992594	−	0.121478i	$-0.0387634\pi$
$227$	5.89242	+	10.2060i	0.391094	+	0.677395i	−0.601500	+	0.798873i	$0.705430\pi$
$228$	1.69940	+	9.99668i	0.112546	+	0.662046i
$229$	−9.08148	−	5.24320i	−0.600121	−	0.346480i	0.168968	−	0.985622i	$-0.445957\pi$
$229$	−9.08148	−	5.24320i	−0.600121	−	0.346480i	−0.769089	+	0.639141i	$0.779290\pi$
$230$	25.7494			1.69787
$231$	3.93807	−	2.34342i	0.259106	−	0.154186i
$232$	−2.05702			−0.135050
$233$	−17.4429	−	10.0707i	−1.14272	−	0.659751i	−0.195619	−	0.980680i	$-0.562672\pi$
$233$	−17.4429	−	10.0707i	−1.14272	−	0.659751i	−0.947103	+	0.320929i	$0.896005\pi$
$234$	−2.47307	+	13.0830i	−0.161670	+	0.855262i
$235$	−6.33514	−	10.9728i	−0.413259	−	0.715786i
$236$	−2.99296	+	5.18396i	−0.194825	+	0.337447i
$237$	1.44312	−	3.89036i	0.0937405	−	0.252706i
$238$	0.561945	−	3.59164i	0.0364255	−	0.232811i
$239$		−	18.1414i		−	1.17347i	−0.809779	−	0.586735i	$-0.800413\pi$
$239$		−	18.1414i		−	1.17347i	0.809779	−	0.586735i	$-0.199587\pi$
$240$	5.71534	+	6.89692i	0.368924	+	0.445195i
$241$	−14.7430	+	8.51185i	−0.949677	+	0.548296i	−0.892981	−	0.450095i	$-0.851390\pi$
$241$	−14.7430	+	8.51185i	−0.949677	+	0.548296i	−0.0566964	+	0.998391i	$0.518057\pi$
$242$	0.942161	−	0.543957i	0.0605644	−	0.0349669i
$243$	10.3822	−	11.6279i	0.666022	−	0.745933i
$244$		−	11.9495i		−	0.764987i
$245$	−15.7662	+	14.3036i	−1.00727	+	0.913824i
$246$	5.55203	+	2.05950i	0.353984	+	0.131309i
$247$	14.6265	−	25.3338i	0.930660	−	1.61195i
$248$	5.62857	+	9.74897i	0.357415	+	0.619060i
$249$	10.2298	−	1.73902i	0.648284	−	0.110206i
$250$	−2.15375	−	1.24347i	−0.136215	−	0.0786440i
$251$	−7.25375			−0.457853			−0.228926	−	0.973444i	$-0.573521\pi$
$251$	−7.25375			−0.457853			−0.228926	+	0.973444i	$0.573521\pi$
$252$	−4.20032	−	4.93477i	−0.264595	−	0.310862i
$253$	−7.78292			−0.489308
$254$	0.408470	+	0.235830i	0.0256297	+	0.0147973i
$255$	6.55853	−	1.11493i	0.410711	−	0.0698195i
$256$	7.94249	+	13.7568i	0.496406	+	0.859800i
$257$	−1.51901	+	2.63101i	−0.0947534	+	0.164118i	−0.909506	−	0.415692i	$-0.863540\pi$
$257$	−1.51901	+	2.63101i	−0.0947534	+	0.164118i	0.814752	+	0.579809i	$0.196873\pi$
$258$	−1.42022	−	0.526824i	−0.0884188	−	0.0327986i
$259$	−3.35270	+	4.15618i	−0.208327	+	0.258253i
$260$			10.1292i			0.628183i
$261$	−0.665522	−	1.90089i	−0.0411948	−	0.117662i
$262$	8.07466	−	4.66191i	0.498854	−	0.288014i
$263$	−0.361906	+	0.208947i	−0.0223161	+	0.0128842i	−0.511117	−	0.859511i	$-0.670768\pi$
$263$	−0.361906	+	0.208947i	−0.0223161	+	0.0128842i	0.488800	+	0.872396i	$0.337435\pi$
$264$	−3.38628	−	4.08635i	−0.208411	−	0.251498i
$265$			9.32317i			0.572718i
$266$	−7.43270	−	19.2546i	−0.455728	−	1.18058i
$267$	−9.33383	+	25.1622i	−0.571221	+	1.53990i
$268$	−0.181613	+	0.314563i	−0.0110938	+	0.0192150i
$269$	−2.55738	−	4.42952i	−0.155926	−	0.270072i	0.777470	−	0.628921i	$-0.216503\pi$
$269$	−2.55738	−	4.42952i	−0.155926	−	0.270072i	−0.933396	+	0.358848i	$0.883170\pi$
$270$	−8.86866	+	14.7270i	−0.539729	+	0.896259i
$271$	−12.7290	−	7.34911i	−0.773234	−	0.446427i	0.0607930	−	0.998150i	$-0.480637\pi$
$271$	−12.7290	−	7.34911i	−0.773234	−	0.446427i	−0.834027	+	0.551723i	$0.813970\pi$
$272$	−2.14776			−0.130227
$273$	0.246501	+	18.6933i	0.0149189	+	1.13137i
$274$	−22.0898			−1.33449
$275$	−3.67914	−	2.12415i	−0.221861	−	0.128091i
$276$	1.84452	+	10.8503i	0.111027	+	0.653114i
$277$	5.18187	+	8.97526i	0.311348	+	0.539271i	0.978654	−	0.205513i	$-0.0658861\pi$
$277$	5.18187	+	8.97526i	0.311348	+	0.539271i	−0.667306	+	0.744783i	$0.732553\pi$
$278$	−3.47978	+	6.02716i	−0.208703	+	0.361485i
$279$	−7.18795	+	8.35549i	−0.430331	+	0.500230i
$280$	19.1884	+	15.4788i	1.14672	+	0.925037i
$281$		−	14.1296i		−	0.842903i	−0.906851	−	0.421452i	$-0.861521\pi$
$281$		−	14.1296i		−	0.842903i	0.906851	−	0.421452i	$-0.138479\pi$
$282$	−6.04491	+	5.00929i	−0.359969	+	0.298299i
$283$	−3.65008	+	2.10737i	−0.216974	+	0.125270i	−0.604549	−	0.796568i	$-0.706646\pi$
$283$	−3.65008	+	2.10737i	−0.216974	+	0.125270i	0.387574	+	0.921839i	$0.373313\pi$
$284$	−2.10892	+	1.21758i	−0.125141	+	0.0722503i
$285$	29.0821	−	24.0998i	1.72268	−	1.42755i
$286$			4.43823i			0.262438i
$287$	8.21465	+	1.28526i	0.484896	+	0.0758664i
$288$	−8.36989	+	9.72942i	−0.493201	+	0.573312i
$289$	7.70242	−	13.3410i	0.453084	−	0.784764i
$290$	1.11055	+	1.92353i	0.0652139	+	0.112954i
$291$	−2.27475	−	13.3811i	−0.133348	−	0.784416i
$292$	−5.18074	−	2.99110i	−0.303180	−	0.175041i
$293$	−3.23825			−0.189181			−0.0945904	−	0.995516i	$-0.530154\pi$
$293$	−3.23825			−0.189181			−0.0945904	+	0.995516i	$0.530154\pi$
$294$	10.3746	+	8.14553i	0.605061	+	0.475057i
$295$	22.2964			1.29815
$296$	5.35562	+	3.09207i	0.311289	+	0.179723i
$297$	2.68060	−	4.45133i	0.155544	−	0.258293i
$298$	2.87841	+	4.98556i	0.166742	+	0.288806i
$299$	15.8755	−	27.4972i	0.918104	−	1.59020i
$300$	−2.08939	+	5.63259i	−0.120631	+	0.325198i
$301$	−2.10132	−	0.328771i	−0.121118	−	0.0189500i
$302$			5.34372i			0.307497i
$303$	20.1827	+	24.3553i	1.15947	+	1.39917i
$304$	−10.5601	+	6.09689i	−0.605665	+	0.349681i
$305$	−38.5464	+	22.2548i	−2.20716	+	1.27431i
$306$	−1.36212	−	3.89053i	−0.0778670	−	0.222407i
$307$			4.40667i			0.251502i	0.992062	+	0.125751i	$0.0401340\pi$
$307$			4.40667i			0.251502i	−0.992062	+	0.125751i	$0.959866\pi$
$308$	−1.68127	−	1.35624i	−0.0957993	−	0.0772792i
$309$	−24.7051	−	9.16427i	−1.40543	−	0.521337i
$310$	6.07754	−	10.5266i	0.345181	−	0.597871i
$311$	−12.3220	−	21.3424i	−0.698718	−	1.21021i	−0.968911	−	0.247409i	$-0.920421\pi$
$311$	−12.3220	−	21.3424i	−0.698718	−	1.21021i	0.270193	−	0.962806i	$-0.412912\pi$
$312$	21.3444	−	3.62848i	1.20839	−	0.205422i
$313$	−9.33732	−	5.39090i	−0.527776	−	0.304712i	0.212334	−	0.977197i	$-0.431893\pi$
$313$	−9.33732	−	5.39090i	−0.527776	−	0.304712i	−0.740110	+	0.672485i	$0.765227\pi$
$314$	0.962881			0.0543385
$315$	−8.09581	+	22.7399i	−0.456147	+	1.28125i
$316$	−1.95592			−0.110029
$317$	17.4243	+	10.0599i	0.978643	+	0.565020i	0.901860	−	0.432028i	$-0.142202\pi$
$317$	17.4243	+	10.0599i	0.978643	+	0.565020i	0.0767831	+	0.997048i	$0.475535\pi$
$318$	5.69509	−	0.968146i	0.319365	−	0.0542909i
$319$	−0.335671	−	0.581399i	−0.0187940	−	0.0325521i
$320$	12.2484	−	21.2148i	0.684705	−	1.18594i
$321$	23.0609	+	8.55434i	1.28713	+	0.477457i
$322$	−8.06742	−	20.8989i	−0.449580	−	1.16465i
$323$			9.05640i			0.503912i
$324$	−6.84100	−	2.68214i	−0.380055	−	0.149008i
$325$	15.0093	−	8.66565i	0.832569	−	0.480684i
$326$	−23.9133	+	13.8064i	−1.32444	+	0.764665i
$327$	5.28161	+	6.37353i	0.292074	+	0.352457i
$328$		−	9.62914i		−	0.531680i
$329$	−6.92096	+	8.57958i	−0.381565	+	0.473008i
$330$	−1.99298	+	5.37268i	−0.109710	+	0.295756i
$331$	6.27608	−	10.8705i	0.344965	−	0.597496i	−0.640383	−	0.768056i	$-0.721224\pi$
$331$	6.27608	−	10.8705i	0.344965	−	0.597496i	0.985347	+	0.170560i	$0.0545575\pi$
$332$	−2.44561	−	4.23592i	−0.134220	−	0.232477i
$333$	−1.12463	+	5.94951i	−0.0616295	+	0.326031i
$334$	0.527213	+	0.304387i	0.0288478	+	0.0166553i
$335$	1.35295			0.0739194
$336$	3.80708	−	6.79955i	0.207693	−	0.370946i
$337$	11.2513			0.612898			0.306449	−	0.951887i	$-0.400859\pi$
$337$	11.2513			0.612898			0.306449	+	0.951887i	$0.400859\pi$
$338$	−3.43224	−	1.98160i	−0.186689	−	0.107785i
$339$	−4.33417	−	25.4956i	−0.235400	−	1.38473i
$340$	−1.56794	−	2.71575i	−0.0850334	−	0.147282i
$341$	−1.83697	+	3.18173i	−0.0994776	+	0.172300i
$342$	−17.7414	−	15.2623i	−0.959346	−	0.825293i
$343$	16.5488	+	8.31488i	0.893551	+	0.448962i
$344$			2.46315i			0.132804i
$345$	31.5656	−	26.1578i	1.69943	−	1.40829i
$346$	8.02070	−	4.63075i	0.431196	−	0.248951i
$347$	12.4959	−	7.21450i	0.670814	−	0.387295i	−0.125571	−	0.992085i	$-0.540076\pi$
$347$	12.4959	−	7.21450i	0.670814	−	0.387295i	0.796385	+	0.604790i	$0.206743\pi$
$348$	−0.730989	+	0.605756i	−0.0391851	+	0.0324719i
$349$		−	27.4253i		−	1.46804i	−0.679125	−	0.734022i	$-0.737641\pi$
$349$		−	27.4253i		−	1.46804i	0.679125	−	0.734022i	$-0.262359\pi$
$350$	1.89020	−	12.0811i	0.101036	−	0.645764i
$351$	10.2588	+	18.5504i	0.547573	+	0.990147i
$352$	−2.13903	+	3.70492i	−0.114011	+	0.197473i
$353$	10.8849	+	18.8532i	0.579344	+	1.00345i	0.995555	+	0.0941855i	$0.0300247\pi$
$353$	10.8849	+	18.8532i	0.579344	+	1.00345i	−0.416210	+	0.909268i	$0.636642\pi$
$354$	−2.31533	−	13.6199i	−0.123058	−	0.723888i
$355$	7.85531	+	4.53527i	0.416917	+	0.240707i
$356$	12.6506			0.670479
$357$	−2.95972	−	4.97376i	−0.156645	−	0.263239i
$358$	23.9057			1.26346
$359$	30.6280	+	17.6831i	1.61649	+	0.933279i	0.987820	+	0.155604i	$0.0497324\pi$
$359$	30.6280	+	17.6831i	1.61649	+	0.933279i	0.628667	+	0.777675i	$0.283601\pi$
$360$	27.4678	+	5.19223i	1.44768	+	0.273655i
$361$	16.2086	+	28.0742i	0.853086	+	1.47759i
$362$	−8.14000	+	14.0989i	−0.427829	+	0.741022i
$363$	0.602388	−	1.62392i	0.0316172	−	0.0852339i
$364$	8.22107	−	3.17351i	0.430901	−	0.166337i
$365$			22.2826i			1.16632i
$366$	17.5972	+	21.2352i	0.919821	+	1.10998i
$367$	−17.2267	+	9.94583i	−0.899226	+	0.519168i	−0.876949	−	0.480584i	$-0.840425\pi$
$367$	−17.2267	+	9.94583i	−0.899226	+	0.519168i	−0.0222769	+	0.999752i	$0.507092\pi$
$368$	−11.4619	+	6.61754i	−0.597493	+	0.344963i
$369$	8.89825	−	3.11538i	0.463225	−	0.162180i
$370$		−	6.67743i		−	0.347143i
$371$	7.56692	−	2.92099i	0.392855	−	0.151650i
$372$	4.87108	+	1.80691i	0.252554	+	0.0936838i
$373$	−1.80027	+	3.11816i	−0.0932145	+	0.161452i	−0.908862	−	0.417097i	$-0.863048\pi$
$373$	−1.80027	+	3.11816i	−0.0932145	+	0.161452i	0.815648	+	0.578549i	$0.196381\pi$
$374$	−0.687014	−	1.18994i	−0.0355246	−	0.0615305i
$375$	−3.90342	+	0.663568i	−0.201572	+	0.0342665i
$376$	11.0556	+	6.38294i	0.570148	+	0.329175i
$377$	2.73879			0.141055
$378$	14.7314	+	2.58398i	0.757703	+	0.132906i
$379$	−31.1521			−1.60018			−0.800088	−	0.599883i	$-0.795214\pi$
$379$	−31.1521			−1.60018			−0.800088	+	0.599883i	$0.795214\pi$
$380$	−15.4185	−	8.90190i	−0.790954	−	0.456658i
$381$	0.740302	−	0.125849i	0.0379268	−	0.00644743i
$382$	9.66196	+	16.7350i	0.494349	+	0.856237i
$383$	−8.38277	+	14.5194i	−0.428339	+	0.741906i	−0.996726	−	0.0808562i	$-0.974235\pi$
$383$	−8.38277	+	14.5194i	−0.428339	+	0.741906i	0.568386	+	0.822762i	$0.307568\pi$
$384$	−0.336556	−	0.124844i	−0.0171748	−	0.00637094i
$385$	−1.24374	+	7.94929i	−0.0633869	+	0.405134i
$386$			4.42668i			0.225312i
$387$	−2.27619	+	0.796917i	−0.115705	+	0.0405096i
$388$	−5.54085	+	3.19901i	−0.281294	+	0.162405i
$389$	−5.66254	+	3.26927i	−0.287102	+	0.165758i	−0.636634	−	0.771166i	$-0.719674\pi$
$389$	−5.66254	+	3.26927i	−0.287102	+	0.165758i	0.349532	+	0.936924i	$0.386341\pi$
$390$	−14.9165	−	18.0003i	−0.755328	−	0.911483i
$391$			9.82978i			0.497113i
$392$	6.55121	−	20.4233i	0.330886	−	1.03153i
$393$	5.16269	−	13.9176i	0.260423	−	0.702051i
$394$	2.52573	−	4.37470i	0.127245	−	0.220394i
$395$	3.64272	+	6.30938i	0.183285	+	0.317459i
$396$	−2.40671	−	0.454940i	−0.120942	−	0.0228616i
$397$	3.53939	+	2.04347i	0.177637	+	0.102559i	0.586182	−	0.810179i	$-0.300630\pi$
$397$	3.53939	+	2.04347i	0.177637	+	0.102559i	−0.408545	+	0.912738i	$0.633964\pi$
$398$	19.9483			0.999919
$399$	−28.6715	−	16.0532i	−1.43537	−	0.803666i
$400$	−7.22437			−0.361218
$401$	10.9873	+	6.34355i	0.548682	+	0.316782i	0.748590	−	0.663033i	$-0.230731\pi$
$401$	10.9873	+	6.34355i	0.548682	+	0.316782i	−0.199908	+	0.979815i	$0.564064\pi$
$402$	−0.140494	−	0.826453i	−0.00700721	−	0.0412197i
$403$	−7.49407	−	12.9801i	−0.373306	−	0.646585i
$404$	7.45503	−	12.9125i	0.370902	−	0.642421i
$405$	4.08871	+	27.0628i	0.203170	+	1.34476i
$406$	1.21325	−	1.50400i	0.0602124	−	0.0746424i
$407$			2.01829i			0.100043i
$408$	−5.16104	+	4.27685i	−0.255509	+	0.211735i
$409$	12.4882	−	7.21004i	0.617500	−	0.356514i	−0.158395	−	0.987376i	$-0.550632\pi$
$409$	12.4882	−	7.21004i	0.617500	−	0.356514i	0.775895	+	0.630862i	$0.217299\pi$
$410$	−9.00426	+	5.19861i	−0.444688	+	0.256741i
$411$	−27.0793	+	22.4401i	−1.33572	+	1.10689i
$412$			12.4208i			0.611927i
$413$	−6.98558	−	18.0964i	−0.343738	−	0.890464i
$414$	−19.2564	−	16.5657i	−0.946403	−	0.814158i
$415$	−9.10944	+	15.7780i	−0.447165	+	0.774513i
$416$	−8.72635	−	15.1145i	−0.427845	−	0.741049i
$417$	1.85696	+	10.9235i	0.0909356	+	0.534926i
$418$	−6.75584	−	3.90049i	−0.330439	−	0.190779i
$419$	−24.6482			−1.20415			−0.602073	−	0.798441i	$-0.705658\pi$
$419$	−24.6482			−1.20415			−0.602073	+	0.798441i	$0.705658\pi$
$420$	11.3771	−	0.150025i	0.555143	−	0.00732045i
$421$	7.81687			0.380971			0.190485	−	0.981690i	$-0.438994\pi$
$421$	7.81687			0.380971			0.190485	+	0.981690i	$0.438994\pi$
$422$	−16.6824	−	9.63161i	−0.812088	−	0.468859i
$423$	−2.32157	+	12.2815i	−0.112879	+	0.597149i
$424$	−4.69675	−	8.13502i	−0.228095	−	0.395071i
$425$	−2.68279	+	4.64673i	−0.130135	+	0.225400i
$426$	1.95467	−	5.26941i	0.0947039	−	0.255304i
$427$	30.1393	+	24.3127i	1.45854	+	1.17658i
$428$		−	11.5941i		−	0.560422i
$429$	4.50861	+	5.44071i	0.217678	+	0.262680i
$430$	2.30330	−	1.32981i	0.111075	−	0.0641292i
$431$	−19.8324	+	11.4502i	−0.955292	+	0.551538i	−0.894721	−	0.446626i	$-0.852626\pi$
$431$	−19.8324	+	11.4502i	−0.955292	+	0.551538i	−0.0605714	+	0.998164i	$0.519292\pi$
$432$	0.162917	−	8.83470i	0.00783833	−	0.425060i
$433$			8.78970i			0.422406i	0.977442	+	0.211203i	$0.0677381\pi$
$433$			8.78970i			0.422406i	−0.977442	+	0.211203i	$0.932262\pi$
$434$	−10.4478	−	1.63465i	−0.501510	−	0.0784658i
$435$	3.31543	+	1.22985i	0.158963	+	0.0589667i
$436$	1.95091	−	3.37907i	0.0934314	−	0.161828i
$437$	27.9040	+	48.3312i	1.33483	+	2.31200i
$438$	13.6114	−	2.31389i	0.650379	−	0.110562i
$439$	−17.4830	−	10.0938i	−0.834418	−	0.481752i	0.0209448	−	0.999781i	$-0.493333\pi$
$439$	−17.4830	−	10.0938i	−0.834418	−	0.481752i	−0.855363	+	0.518029i	$0.826666\pi$
$440$	9.31808			0.444222
$441$	20.9927	−	0.553740i	0.999652	−	0.0263686i
$442$	5.60545			0.266624
$443$	−21.3785	−	12.3429i	−1.01572	−	0.586427i	−0.102860	−	0.994696i	$-0.532799\pi$
$443$	−21.3785	−	12.3429i	−1.01572	−	0.586427i	−0.912862	+	0.408269i	$0.866133\pi$
$444$	2.81375	−	0.478327i	0.133534	−	0.0227004i
$445$	−23.5605	−	40.8080i	−1.11687	−	1.93448i
$446$	8.09147	−	14.0148i	0.383142	−	0.663622i
$447$	8.59320	+	3.18761i	0.406444	+	0.150769i
$448$	−21.0560	−	3.29440i	−0.994800	−	0.155646i
$449$		−	13.1021i		−	0.618325i	−0.951009	−	0.309162i	$-0.899951\pi$
$449$		−	13.1021i		−	0.618325i	0.951009	−	0.309162i	$-0.100049\pi$
$450$	−4.58172	−	13.0865i	−0.215985	−	0.616903i
$451$	2.72159	−	1.57131i	0.128155	−	0.0739901i
$452$	−10.5572	+	6.09520i	−0.496569	+	0.286694i
$453$	5.42846	+	6.55074i	0.255051	+	0.307780i
$454$			12.8209i			0.601714i
$455$	−25.5480	−	20.6090i	−1.19771	−	0.966166i
$456$	−13.2351	+	35.6792i	−0.619790	+	1.67083i
$457$	−12.8115	+	22.1901i	−0.599295	+	1.03801i	0.393630	+	0.919269i	$0.371219\pi$
$457$	−12.8115	+	22.1901i	−0.599295	+	1.03801i	−0.992925	+	0.118741i	$0.962114\pi$
$458$	−5.70414	−	9.87986i	−0.266537	−	0.461656i
$459$	−5.62201	−	3.38558i	−0.262413	−	0.158026i
$460$	−16.7352	−	9.66208i	−0.780283	−	0.450497i
$461$	−25.3531			−1.18081			−0.590407	−	0.807106i	$-0.701033\pi$
$461$	−25.3531			−1.18081			−0.590407	+	0.807106i	$0.701033\pi$
$462$	4.98501	−	0.0657353i	0.231924	−	0.00305828i
$463$	28.1915			1.31017			0.655084	−	0.755556i	$-0.272633\pi$
$463$	28.1915			1.31017			0.655084	+	0.755556i	$0.272633\pi$
$464$	−0.988685	−	0.570818i	−0.0458986	−	0.0264995i
$465$	−3.24323	−	19.0782i	−0.150401	−	0.884732i
$466$	−10.9560	−	18.9764i	−0.507527	−	0.879063i
$467$	−9.17883	+	15.8982i	−0.424745	+	0.735681i	−0.996397	−	0.0848161i	$-0.972970\pi$
$467$	−9.17883	+	15.8982i	−0.424745	+	0.735681i	0.571651	+	0.820497i	$0.306303\pi$
$468$	6.51650	−	7.57498i	0.301225	−	0.350153i
$469$	−0.423884	−	1.09809i	−0.0195732	−	0.0507049i
$470$		−	13.7842i		−	0.635816i
$471$	1.18037	−	0.978150i	0.0543887	−	0.0450708i
$472$	−19.4550	+	11.2323i	−0.895488	+	0.517010i
$473$	−0.696186	+	0.401943i	−0.0320107	+	0.0184814i
$474$	3.47584	−	2.88035i	0.159650	−	0.132299i
$475$			30.4629i			1.39773i
$476$	−1.71293	+	2.12344i	−0.0785120	+	0.0973275i
$477$	5.99797	−	6.97223i	0.274628	−	0.319236i
$478$	9.86813	−	17.0921i	0.451358	−	0.781775i
$479$	3.85023	+	6.66879i	0.175921	+	0.304705i	0.940480	−	0.339850i	$-0.110376\pi$
$479$	3.85023	+	6.66879i	0.175921	+	0.304705i	−0.764558	+	0.644555i	$0.777043\pi$
$480$	−3.77653	−	22.2153i	−0.172374	−	1.01399i
$481$	−7.13065	−	4.11689i	−0.325130	−	0.187714i
$482$	−18.5203			−0.843577
$483$	−31.1199	−	17.4241i	−1.41601	−	0.792824i
$484$	−0.816445			−0.0371111
$485$	20.6386	+	11.9157i	0.937151	+	0.541064i
$486$	16.1068	−	5.30789i	0.730621	−	0.240771i
$487$	−14.4354	−	25.0028i	−0.654130	−	1.13299i	−0.982111	−	0.188302i	$-0.939702\pi$
$487$	−14.4354	−	25.0028i	−0.654130	−	1.13299i	0.327981	−	0.944684i	$-0.393632\pi$
$488$	22.4227	−	38.8373i	1.01503	−	1.75808i
$489$	−15.2895	+	41.2175i	−0.691413	+	1.86392i
$490$	−22.6349	+	4.90015i	−1.02254	+	0.221366i
$491$		−	17.4448i		−	0.787275i	−0.919266	−	0.393637i	$-0.871217\pi$
$491$		−	17.4448i		−	0.787275i	0.919266	−	0.393637i	$-0.128783\pi$
$492$	−2.83560	−	3.42183i	−0.127839	−	0.154268i
$493$	−0.734303	+	0.423950i	−0.0330713	+	0.0190938i
$494$	27.5610	−	15.9123i	1.24003	−	0.715930i
$495$	3.01474	+	8.61081i	0.135502	+	0.387027i
$496$			6.24765i			0.280528i
$497$	1.21983	−	7.79649i	0.0547170	−	0.349720i
$498$	10.5840	+	3.92610i	0.474281	+	0.175933i
$499$	11.1496	−	19.3116i	0.499123	−	0.864507i	−0.500876	−	0.865519i	$-0.666989\pi$
$499$	11.1496	−	19.3116i	0.499123	−	0.864507i	0.999999	+	0.00101219i	$0.000322189\pi$
$500$	0.933185	+	1.61632i	0.0417333	+	0.0722842i
$501$	0.955511	−	0.162434i	0.0426891	−	0.00725700i
$502$	−6.83420	−	3.94572i	−0.305025	−	0.176106i
$503$	−16.6763			−0.743560			−0.371780	−	0.928321i	$-0.621252\pi$
$503$	−16.6763			−0.743560			−0.371780	+	0.928321i	$0.621252\pi$
$504$	−4.39164	−	23.9203i	−0.195619	−	1.06550i
$505$	−55.5372			−2.47137
$506$	−7.33276	−	4.23357i	−0.325981	−	0.188205i
$507$	−6.22052	+	1.05747i	−0.276263	+	0.0469638i
$508$	−0.176983	−	0.306544i	−0.00785235	−	0.0136007i
$509$	0.323631	−	0.560546i	0.0143447	−	0.0248458i	−0.858764	−	0.512371i	$-0.828767\pi$
$509$	0.323631	−	0.560546i	0.0143447	−	0.0248458i	0.873109	+	0.487526i	$0.162100\pi$
$510$	6.78566	+	2.51712i	0.300474	+	0.111460i
$511$	18.0851	−	6.98124i	0.800039	−	0.308832i
$512$			17.6960i			0.782059i
$513$	−37.2531	−	0.686967i	−1.64477	−	0.0303303i
$514$	−2.86231	+	1.65255i	−0.126251	+	0.0728910i
$515$	40.0667	−	23.1325i	1.76555	−	1.01934i
$516$	0.725351	+	0.875310i	0.0319318	+	0.0385334i
$517$			4.16634i			0.183236i
$518$	−5.41957	+	2.09207i	−0.238122	+	0.0919202i
$519$	5.12819	−	13.8246i	0.225103	−	0.606833i
$520$	−19.0069	+	32.9210i	−0.833509	+	1.44368i
$521$	−10.4553	−	18.1091i	−0.458056	−	0.793376i	0.540802	−	0.841150i	$-0.318121\pi$
$521$	−10.4553	−	18.1091i	−0.458056	−	0.793376i	−0.998858	+	0.0477736i	$0.984787\pi$
$522$	0.406973	−	2.15296i	0.0178127	−	0.0942324i
$523$	9.65787	+	5.57597i	0.422309	+	0.243820i	0.696065	−	0.717979i	$-0.254933\pi$
$523$	9.65787	+	5.57597i	0.422309	+	0.243820i	−0.273756	+	0.961799i	$0.588266\pi$
$524$	−6.99723			−0.305676
$525$	−9.95556	−	16.7301i	−0.434496	−	0.730163i
$526$	−0.454632			−0.0198229
$527$	4.01850	+	2.32008i	0.175049	+	0.101064i
$528$	−0.493626	−	2.90374i	−0.0214823	−	0.126369i
$529$	18.7869	+	32.5399i	0.816822	+	1.41478i
$530$	−5.07140	+	8.78392i	−0.220287	+	0.381549i
$531$	−16.6742	−	14.3442i	−0.723597	−	0.622486i
$532$	−2.39431	+	15.3031i	−0.103806	+	0.663473i
$533$			12.8206i			0.555320i
$534$	−22.4811	+	18.6297i	−0.972853	+	0.806184i
$535$	−37.4000	+	21.5929i	−1.61694	+	0.933543i
$536$	−1.18053	+	0.681577i	−0.0509910	+	0.0294397i
$537$	29.3054	−	24.2848i	1.26462	−	1.04797i
$538$		−	5.56442i		−	0.239899i
$539$	6.84152	−	1.48110i	0.294685	−	0.0637954i
$540$	11.2901	−	6.24365i	0.485847	−	0.268684i
$541$	19.3155	−	33.4555i	0.830440	−	1.43836i	−0.0672499	−	0.997736i	$-0.521422\pi$
$541$	19.3155	−	33.4555i	0.830440	−	1.43836i	0.897690	−	0.440628i	$-0.145244\pi$
$542$	−7.99520	−	13.8481i	−0.343423	−	0.594826i
$543$	4.34385	+	25.5526i	0.186412	+	1.09657i
$544$	4.67928	+	2.70159i	0.200623	+	0.115830i
$545$	−14.5335			−0.622547
$546$	−9.93612	+	17.7462i	−0.425227	+	0.759468i
$547$	36.6422			1.56671			0.783353	−	0.621577i	$-0.213508\pi$
$547$	36.6422			1.56671			0.783353	+	0.621577i	$0.213508\pi$
$548$	14.3567	+	8.28884i	0.613287	+	0.354082i
$549$	43.1439	+	8.15548i	1.84134	+	0.348068i
$550$	−2.31090	−	4.00259i	−0.0985369	−	0.170671i
$551$	−2.40696	+	4.16897i	−0.102540	+	0.177604i
$552$	−14.3653	+	38.7261i	−0.611428	+	1.64829i
$553$	3.97957	−	4.93328i	0.169228	−	0.209784i
$554$			11.2748i			0.479022i
$555$	−6.78331	−	8.18569i	−0.287936	−	0.347463i
$556$	4.52319	−	2.61147i	0.191826	−	0.110751i
$557$	−6.66926	+	3.85050i	−0.282586	+	0.163151i	−0.634593	−	0.772846i	$-0.718832\pi$
$557$	−6.66926	+	3.85050i	−0.282586	+	0.163151i	0.352008	+	0.935997i	$0.385499\pi$
$558$	−11.3172	+	3.96228i	−0.479096	+	0.167737i
$559$		−	3.27951i		−	0.138709i
$560$	4.92734	+	12.7644i	0.208218	+	0.539396i
$561$	−2.05101	−	0.760813i	−0.0865935	−	0.0321215i
$562$	7.68591	−	13.3124i	0.324210	−	0.561549i
$563$	7.77677	+	13.4698i	0.327752	+	0.567683i	0.982065	−	0.188541i	$-0.0603757\pi$
$563$	7.77677	+	13.4698i	0.327752	+	0.567683i	−0.654314	+	0.756223i	$0.727042\pi$
$564$	5.80840	−	0.987407i	0.244578	−	0.0415773i
$565$	39.3236	+	22.7035i	1.65436	+	0.955143i
$566$	−4.58528			−0.192734
$567$	20.6838	−	11.7974i	0.868640	−	0.495444i
$568$	−9.13897			−0.383463
$569$	13.2097	+	7.62662i	0.553779	+	0.319725i	0.750645	−	0.660706i	$-0.229743\pi$
$569$	13.2097	+	7.62662i	0.553779	+	0.319725i	−0.196866	+	0.980430i	$0.563076\pi$
$570$	40.5093	−	6.88643i	1.69675	−	0.288441i
$571$	4.42324	+	7.66127i	0.185107	+	0.320614i	0.943612	−	0.331052i	$-0.107404\pi$
$571$	4.42324	+	7.66127i	0.185107	+	0.320614i	−0.758506	+	0.651666i	$0.774070\pi$
$572$	1.66537	−	2.88451i	0.0696328	−	0.120608i
$573$	28.8447	+	10.6998i	1.20501	+	0.446992i
$574$	7.04040	+	5.67933i	0.293860	+	0.237051i
$575$			33.0642i			1.37887i
$576$	−22.8082	+	7.98539i	−0.950341	+	0.332725i
$577$	−17.7859	+	10.2687i	−0.740436	+	0.427491i	−0.822228	−	0.569159i	$-0.807269\pi$
$577$	−17.7859	+	10.2687i	−0.740436	+	0.427491i	0.0817920	+	0.996649i	$0.473936\pi$
$578$	14.5138	−	8.37957i	0.603696	−	0.348544i
$579$	4.49688	+	5.42656i	0.186884	+	0.225520i
$580$		−	1.66687i		−	0.0692130i
$581$	15.6599	+	2.45013i	0.649681	+	0.101649i
$582$	5.13558	−	13.8445i	0.212877	−	0.573875i
$583$	1.53286	−	2.65499i	0.0634845	−	0.109958i
$584$	−11.2254	−	19.4429i	−0.464509	−	0.804552i
$585$	−36.5716	−	6.91311i	−1.51205	−	0.285822i
$586$	−3.05095	−	1.76147i	−0.126034	−	0.0727656i
$587$	21.7709			0.898580			0.449290	−	0.893386i	$-0.351677\pi$
$587$	21.7709			0.898580			0.449290	+	0.893386i	$0.351677\pi$
$588$	−3.68625	−	9.18690i	−0.152018	−	0.378861i
$589$	26.3443			1.08550
$590$	21.0068	+	12.1283i	0.864838	+	0.499314i
$591$	−1.34784	−	7.92862i	−0.0554426	−	0.326140i
$592$	1.71608	+	2.97234i	0.0705305	+	0.122162i
$593$	−17.9554	+	31.0996i	−0.737338	+	1.27711i	0.216352	+	0.976315i	$0.430584\pi$
$593$	−17.9554	+	31.0996i	−0.737338	+	1.27711i	−0.953690	+	0.300791i	$0.902749\pi$
$594$	4.94689	−	2.73574i	0.202973	−	0.112249i
$595$	10.0399	+	1.57084i	0.411596	+	0.0643980i
$596$		−	4.32032i		−	0.176967i
$597$	24.4541	−	20.2646i	1.00084	−	0.829377i
$598$	29.9145	−	17.2712i	1.22330	−	0.706271i
$599$	32.0098	−	18.4808i	1.30788	−	0.755107i	0.326141	−	0.945321i	$-0.394252\pi$
$599$	32.0098	−	18.4808i	1.30788	−	0.755107i	0.981743	+	0.190214i	$0.0609182\pi$
$600$	−17.3601	+	14.3860i	−0.708723	+	0.587304i
$601$		−	34.1262i		−	1.39204i	−0.718023	−	0.696019i	$-0.754953\pi$
$601$		−	34.1262i		−	1.39204i	0.718023	−	0.696019i	$-0.245047\pi$
$602$	−1.80094	−	1.45278i	−0.0734009	−	0.0592109i
$603$	−1.01179	−	0.870406i	−0.0412031	−	0.0354457i
$604$	2.00515	−	3.47302i	0.0815883	−	0.141315i
$605$	1.52055	+	2.63367i	0.0618192	+	0.107074i
$606$	5.76715	+	33.9251i	0.234275	+	1.37811i
$607$	−12.3918	−	7.15442i	−0.502969	−	0.290389i	0.226970	−	0.973902i	$-0.427118\pi$
$607$	−12.3918	−	7.15442i	−0.502969	−	0.290389i	−0.729939	+	0.683513i	$0.760451\pi$
$608$	30.6762			1.24409
$609$	−0.0405647	−	3.07621i	−0.00164376	−	0.124654i
$610$	−48.4226			−1.96057
$611$	−14.7198	−	8.49846i	−0.595498	−	0.343811i
$612$	−0.574586	+	3.03966i	−0.0232263	+	0.122871i
$613$	−4.04550	−	7.00701i	−0.163396	−	0.283011i	0.772688	−	0.634786i	$-0.218912\pi$
$613$	−4.04550	−	7.00701i	−0.163396	−	0.283011i	−0.936085	+	0.351775i	$0.885578\pi$
$614$	−2.39704	+	4.15179i	−0.0967366	+	0.167553i
$615$	−5.75704	+	15.5199i	−0.232146	+	0.625822i
$616$	−2.91940	−	7.56279i	−0.117626	−	0.304714i
$617$		−	35.8527i		−	1.44337i	−0.692220	−	0.721687i	$-0.743367\pi$
$617$		−	35.8527i		−	1.44337i	0.692220	−	0.721687i	$-0.256633\pi$
$618$	−18.2912	−	22.0727i	−0.735781	−	0.887896i
$619$	−10.9454	+	6.31931i	−0.439931	+	0.253994i	−0.703569	−	0.710627i	$-0.748411\pi$
$619$	−10.9454	+	6.31931i	−0.439931	+	0.253994i	0.263637	+	0.964622i	$0.415078\pi$
$620$	−7.89989	+	4.56101i	−0.317267	+	0.183174i
$621$	−40.4344	−	0.745631i	−1.62257	−	0.0299211i
$622$		−	26.8106i		−	1.07501i
$623$	−25.7392	+	31.9076i	−1.03122	+	1.27835i
$624$	11.2659	+	4.17903i	0.450996	+	0.167295i
$625$	14.0967	−	24.4162i	0.563868	−	0.976649i
$626$	−5.86483	−	10.1582i	−0.234406	−	0.406003i
$627$	−12.2442	+	2.08146i	−0.488984	+	0.0831257i
$628$	−0.625800	−	0.361306i	−0.0249722	−	0.0144177i
$629$	2.54909			0.101639
$630$	−19.9970	+	17.0208i	−0.796701	+	0.678126i
$631$	−3.42781			−0.136459			−0.0682295	−	0.997670i	$-0.521735\pi$
$631$	−3.42781			−0.136459			−0.0682295	+	0.997670i	$0.521735\pi$
$632$	−6.35698	−	3.67020i	−0.252867	−	0.145993i
$633$	−30.2349	+	5.13983i	−1.20173	+	0.204290i
$634$	10.9443	+	18.9561i	0.434653	+	0.752842i
$635$	−0.659228	+	1.14182i	−0.0261607	+	0.0453116i
$636$	−4.06466	−	1.50777i	−0.161174	−	0.0597871i
$637$	−8.72250	+	27.1923i	−0.345598	+	1.07740i
$638$		−	0.730361i		−	0.0289153i
$639$	−2.95679	−	8.44530i	−0.116969	−	0.334091i
$640$	0.545826	−	0.315133i	0.0215757	−	0.0124567i
$641$	19.9707	−	11.5301i	0.788797	−	0.455412i	−0.0507421	−	0.998712i	$-0.516159\pi$
$641$	19.9707	−	11.5301i	0.788797	−	0.455412i	0.839539	+	0.543300i	$0.182825\pi$
$642$	17.0738	+	20.6037i	0.673851	+	0.813162i
$643$			2.48064i			0.0978268i	0.998803	+	0.0489134i	$0.0155758\pi$
$643$			2.48064i			0.0978268i	−0.998803	+	0.0489134i	$0.984424\pi$
$644$	−2.59877	+	16.6099i	−0.102406	+	0.654521i
$645$	1.47266	−	3.97001i	0.0579859	−	0.156319i
$646$	−4.92629	+	8.53258i	−0.193822	+	0.335710i
$647$	0.546278	+	0.946182i	0.0214764	+	0.0371983i	0.876564	−	0.481286i	$-0.159830\pi$
$647$	0.546278	+	0.946182i	0.0214764	+	0.0371983i	−0.855087	+	0.518484i	$0.826497\pi$
$648$	−17.2011	−	21.5541i	−0.675725	−	0.846726i
$649$	−6.34944	−	3.66585i	−0.249237	−	0.143897i
$650$	18.8549			0.739552
$651$	−14.4683	+	8.60958i	−0.567056	+	0.337436i
$652$	20.7225			0.811556
$653$	11.4885	+	6.63287i	0.449578	+	0.259564i	0.707652	−	0.706561i	$-0.249754\pi$
$653$	11.4885	+	6.63287i	0.449578	+	0.259564i	−0.258074	+	0.966125i	$0.583088\pi$
$654$	1.50920	+	8.87785i	0.0590145	+	0.347151i
$655$	13.0317	+	22.5715i	0.509190	+	0.881943i
$656$	2.67206	−	4.62814i	0.104326	−	0.180698i
$657$	14.3353	−	16.6638i	0.559273	−	0.650117i
$658$	−11.1876	+	4.31864i	−0.436137	+	0.168358i
$659$			10.1599i			0.395773i	0.980225	+	0.197886i	$0.0634077\pi$
$659$			10.1599i			0.395773i	−0.980225	+	0.197886i	$0.936592\pi$
$660$	3.31130	−	2.74401i	0.128892	−	0.106810i
$661$	−17.6263	+	10.1766i	−0.685584	+	0.395822i	−0.801956	−	0.597384i	$-0.796207\pi$
$661$	−17.6263	+	10.1766i	−0.685584	+	0.395822i	0.116371	+	0.993206i	$0.462874\pi$
$662$	11.8262	−	6.82783i	0.459637	−	0.265371i
$663$	6.87158	−	5.69434i	0.266870	−	0.221150i
$664$		−	18.3563i		−	0.712364i
$665$	53.8236	−	20.7770i	2.08719	−	0.805699i
$666$	−4.29586	+	4.99364i	−0.166461	+	0.193500i
$667$	−2.61250	+	4.52498i	−0.101156	+	0.175208i
$668$	−0.228433	−	0.395657i	−0.00883833	−	0.0153084i
$669$	−4.31795	−	25.4002i	−0.166942	−	0.982029i
$670$	1.27469	+	0.735945i	0.0492457	+	0.0284320i
$671$	14.6360			0.565016
$672$	−16.8473	+	10.0253i	−0.649900	+	0.386734i
$673$	−18.8590			−0.726962			−0.363481	−	0.931602i	$-0.618412\pi$
$673$	−18.8590			−0.726962			−0.363481	+	0.931602i	$0.618412\pi$
$674$	10.6005	+	6.12022i	0.408317	+	0.235742i
$675$	−18.9106	−	11.3880i	−0.727871	−	0.438325i
$676$	1.48713	+	2.57579i	0.0571974	+	0.0990688i
$677$	−14.4986	+	25.1124i	−0.557228	+	0.965148i	0.440498	+	0.897754i	$0.354802\pi$
$677$	−14.4986	+	25.1124i	−0.557228	+	0.965148i	−0.997726	+	0.0673941i	$0.978532\pi$
$678$	9.78503	−	26.3786i	0.375792	−	1.01306i
$679$	3.20492	−	20.4841i	0.122994	−	0.786106i
$680$		−	11.7687i		−	0.451308i
$681$	13.0242	+	15.7168i	0.499088	+	0.602269i
$682$	−3.46145	+	1.99847i	−0.132546	+	0.0765252i
$683$	−23.1653	+	13.3745i	−0.886395	+	0.511760i	−0.872761	−	0.488147i	$-0.837673\pi$
$683$	−23.1653	+	13.3745i	−0.886395	+	0.511760i	−0.0136331	+	0.999907i	$0.504340\pi$
$684$	5.80363	+	16.5766i	0.221907	+	0.633821i
$685$		−	61.7487i		−	2.35930i
$686$	11.0687	+	16.8358i	0.422604	+	0.642793i
$687$	−17.0291	−	6.31688i	−0.649701	−	0.241004i
$688$	−0.683516	+	1.18388i	−0.0260588	+	0.0451351i
$689$	6.25342	+	10.8312i	0.238236	+	0.412637i
$690$	43.9686	−	7.47450i	1.67385	−	0.284549i
$691$	31.2204	+	18.0251i	1.18768	+	0.685708i	0.957779	−	0.287505i	$-0.0928259\pi$
$691$	31.2204	+	18.0251i	1.18768	+	0.685708i	0.229903	+	0.973214i	$0.426159\pi$
$692$	−6.95047			−0.264217
$693$	6.04422	−	5.14464i	0.229601	−	0.195429i
$694$	15.6975			0.595869
$695$	−16.8480	−	9.72722i	−0.639082	−	0.368974i
$696$	−3.51248	+	0.597109i	−0.133140	+	0.0226333i
$697$	−1.98455	−	3.43735i	−0.0751703	−	0.130199i
$698$	14.9182	−	25.8391i	0.564662	−	0.978023i
$699$	−32.7080	−	12.1329i	−1.23713	−	0.458909i
$700$	−5.76175	+	7.14256i	−0.217774	+	0.269963i
$701$		−	19.3154i		−	0.729532i	−0.931099	−	0.364766i	$-0.881149\pi$
$701$		−	19.3154i		−	0.729532i	0.931099	−	0.364766i	$-0.118851\pi$
$702$	−0.425198	+	23.0578i	−0.0160480	+	0.870260i
$703$	12.5334	−	7.23616i	0.472706	−	0.272917i
$704$	−6.97603	+	4.02761i	−0.262919	+	0.151796i
$705$	−14.0028	−	16.8977i	−0.527374	−	0.636403i
$706$			23.6836i			0.891345i
$707$	17.4001	+	45.0754i	0.654396	+	1.69523i
$708$	−3.60585	+	9.72069i	−0.135516	+	0.365326i
$709$	−4.75386	+	8.23392i	−0.178535	+	0.309231i	−0.941379	−	0.337351i	$-0.890469\pi$
$709$	−4.75386	+	8.23392i	−0.178535	+	0.309231i	0.762844	+	0.646582i	$0.223802\pi$
$710$	4.93398	+	8.54590i	0.185169	+	0.320722i
$711$	1.33491	−	7.06191i	0.0500630	−	0.264842i
$712$	41.1159	+	23.7383i	1.54088	+	0.889629i
$713$	28.5940			1.07085
$714$	−0.0830232	−	6.29604i	−0.00310707	−	0.235623i
$715$	−12.4064			−0.463974
$716$	−15.5369	−	8.97025i	−0.580642	−	0.335234i
$717$	−5.26605	−	30.9774i	−0.196664	−	1.15687i
$718$	19.2377	+	33.3207i	0.717944	+	1.24352i
$719$	−6.62688	+	11.4781i	−0.247141	+	0.428061i	−0.962731	−	0.270459i	$-0.912824\pi$
$719$	−6.62688	+	11.4781i	−0.247141	+	0.428061i	0.715590	+	0.698520i	$0.246158\pi$
$720$	11.7613	+	10.1178i	0.438317	+	0.377069i
$721$	−31.3280	−	25.2716i	−1.16672	−	0.941164i
$722$			35.2672i			1.31251i
$723$	−22.7036	+	18.8140i	−0.844355	+	0.699700i
$724$	10.5808	−	6.10882i	0.393232	−	0.227032i
$725$	−2.46996	+	1.42603i	−0.0917321	+	0.0529615i
$726$	1.45089	−	1.20232i	0.0538476	−	0.0446224i
$727$		−	6.06456i		−	0.224922i	−0.993656	−	0.112461i	$-0.964127\pi$
$727$		−	6.06456i		−	0.224922i	0.993656	−	0.112461i	$-0.0358733\pi$
$728$	32.6744	+	5.11221i	1.21099	+	0.189471i
$729$	14.3529	−	22.8691i	0.531589	−	0.847002i
$730$	−12.1208	+	20.9938i	−0.448610	+	0.777015i
$731$	0.507651	+	0.879278i	0.0187762	+	0.0325213i
$732$	−3.46867	−	20.4044i	−0.128206	−	0.754168i
$733$	−30.0097	−	17.3261i	−1.10843	−	0.639954i	−0.170009	−	0.985442i	$-0.554380\pi$
$733$	−30.0097	−	17.3261i	−1.10843	−	0.639954i	−0.938423	+	0.345489i	$0.887713\pi$
$734$	−21.6404			−0.798762
$735$	−22.7697	+	29.0008i	−0.839871	+	1.06971i
$736$	33.2959			1.22730
$737$	−0.385283	−	0.222443i	−0.0141921	−	0.00819381i
$738$	10.0782	+	1.90508i	0.370984	+	0.0701270i
$739$	15.9331	+	27.5969i	0.586109	+	1.01517i	0.994736	+	0.102469i	$0.0326741\pi$
$739$	15.9331	+	27.5969i	0.586109	+	1.01517i	−0.408628	+	0.912701i	$0.633993\pi$
$740$	−2.50560	+	4.33983i	−0.0921077	+	0.159535i
$741$	17.6216	−	47.5046i	0.647347	−	1.74512i
$742$	8.71814	+	1.36403i	0.320053	+	0.0500752i
$743$			52.3397i			1.92016i	0.279730	+	0.960079i	$0.409755\pi$
$743$			52.3397i			1.92016i	−0.279730	+	0.960079i	$0.590245\pi$
$744$	12.4410	+	15.0130i	0.456109	+	0.550405i
$745$	−13.9364	+	8.04619i	−0.510590	+	0.294790i
$746$	−3.39229	+	1.95854i	−0.124200	+	0.0717072i
$747$	16.9630	−	5.93895i	0.620645	−	0.217295i
$748$			1.03116i			0.0377031i
$749$	29.2429	+	23.5896i	1.06851	+	0.861947i
$750$	−4.03860	−	1.49810i	−0.147469	−	0.0547030i
$751$	−16.5556	+	28.6751i	−0.604121	+	1.04637i	0.388068	+	0.921631i	$0.373143\pi$
$751$	−16.5556	+	28.6751i	−0.604121	+	1.04637i	−0.992190	+	0.124738i	$0.960191\pi$
$752$	3.54249	+	6.13578i	0.129181	+	0.223749i
$753$	−12.3862	+	2.10560i	−0.451377	+	0.0767325i
$754$	2.58038	+	1.48978i	0.0939719	+	0.0542547i
$755$	−14.9376			−0.543635
$756$	−8.60472	−	7.20713i	−0.312951	−	0.262121i
$757$	−7.30268			−0.265420			−0.132710	−	0.991155i	$-0.542368\pi$
$757$	−7.30268			−0.265420			−0.132710	+	0.991155i	$0.542368\pi$
$758$	−29.3503	−	16.9454i	−1.06605	−	0.615484i
$759$	−13.2897	+	2.25921i	−0.482387	+	0.0820042i
$760$	−33.4081	−	57.8645i	−1.21184	−	2.09896i
$761$	13.1037	−	22.6962i	0.475007	−	0.822737i	−0.524583	−	0.851359i	$-0.675779\pi$
$761$	13.1037	−	22.6962i	0.475007	−	0.822737i	0.999590	+	0.0286224i	$0.00911203\pi$
$762$	0.765940	+	0.284123i	0.0277471	+	0.0102927i
$763$	4.55341	+	11.7958i	0.164845	+	0.427035i
$764$		−	14.5020i		−	0.524664i
$765$	10.8754	−	3.80760i	0.393201	−	0.137664i
$766$	−15.7958	+	9.11972i	−0.570726	+	0.329509i
$767$	25.9030	−	14.9551i	0.935303	−	0.539998i
$768$	17.5555	+	21.1849i	0.633480	+	0.764445i
$769$		−	27.2898i		−	0.984097i	−0.870568	−	0.492049i	$-0.836248\pi$
$769$		−	27.2898i		−	0.984097i	0.870568	−	0.492049i	$-0.163752\pi$
$770$	−5.49587	+	6.81297i	−0.198058	+	0.245522i
$771$	−1.83007	+	4.93352i	−0.0659084	+	0.177676i
$772$	1.66104	−	2.87701i	0.0597822	−	0.103546i
$773$	11.6572	+	20.1908i	0.419280	+	0.726214i	0.995867	−	0.0908216i	$-0.0289493\pi$
$773$	11.6572	+	20.1908i	0.419280	+	0.726214i	−0.576587	+	0.817035i	$0.695616\pi$
$774$	−2.57802	−	0.487322i	−0.0926650	−	0.0175164i
$775$	13.5170	+	7.80402i	0.485544	+	0.280329i
$776$	−24.0112			−0.861952
$777$	−4.51847	+	8.07012i	−0.162099	+	0.289514i
$778$	−7.11336			−0.255026
$779$	−19.5154	−	11.2672i	−0.699211	−	0.403690i
$780$	2.94027	+	17.2961i	0.105279	+	0.619299i
$781$	−1.49132	−	2.58305i	−0.0533637	−	0.0924287i
$782$	−5.34697	+	9.26123i	−0.191207	+	0.331181i
$783$	−1.68820	−	3.05268i	−0.0603313	−	0.109094i
$784$	8.81618	−	7.99831i	0.314864	−	0.285654i
$785$			2.69159i			0.0960671i
$786$	12.4347	−	10.3044i	0.443530	−	0.367544i
$787$	5.90178	−	3.40739i	0.210376	−	0.121460i	−0.391110	−	0.920344i	$-0.627909\pi$
$787$	5.90178	−	3.40739i	0.210376	−	0.121460i	0.601486	+	0.798883i	$0.294576\pi$
$788$	−3.28307	+	1.89548i	−0.116955	+	0.0675238i
$789$	−0.557322	+	0.461841i	−0.0198412	+	0.0164420i
$790$			7.92593i			0.281992i
$791$	6.10646	−	39.0291i	0.217121	−	1.38772i
$792$	−6.96843	−	5.99470i	−0.247612	−	0.213013i
$793$	−29.8543	+	51.7092i	−1.06016	+	1.83625i
$794$	2.22312	+	3.85055i	0.0788955	+	0.136651i
$795$	2.70631	+	15.9198i	0.0959830	+	0.564617i
$796$	−12.9649	−	7.48529i	−0.459529	−	0.265309i
$797$	−6.86978			−0.243340			−0.121670	−	0.992571i	$-0.538825\pi$
$797$	−6.86978			−0.243340			−0.121670	+	0.992571i	$0.538825\pi$
$798$	−18.2809	−	30.7208i	−0.647138	−	1.08750i
$799$	5.26207			0.186159
$800$	15.7396	+	9.08727i	0.556480	+	0.321284i
$801$	−8.63397	+	45.6752i	−0.305066	+	1.61386i
$802$	6.90123	+	11.9533i	0.243691	+	0.422085i
$803$	3.66357	−	6.34549i	0.129285	−	0.223928i
$804$	−0.218803	+	0.589851i	−0.00771658	+	0.0208024i
$805$	58.4198	−	22.5513i	2.05903	−	0.794828i
$806$		−	16.3058i		−	0.574347i
$807$	−5.65266	−	6.82128i	−0.198983	−	0.240121i
$808$	48.4595	−	27.9781i	1.70480	−	0.984266i
$809$	17.2631	−	9.96687i	0.606939	−	0.350417i	−0.164827	−	0.986322i	$-0.552707\pi$
$809$	17.2631	−	9.96687i	0.606939	−	0.350417i	0.771767	+	0.635906i	$0.219373\pi$
$810$	−10.8688	+	27.7216i	−0.381890	+	0.974037i
$811$		−	24.6220i		−	0.864594i	−0.901731	−	0.432297i	$-0.857703\pi$
$811$		−	24.6220i		−	0.864594i	0.901731	−	0.432297i	$-0.142297\pi$
$812$	−1.35287	+	0.522238i	−0.0474765	+	0.0183269i
$813$	−23.8688	−	8.85404i	−0.837115	−	0.310525i
$814$	−1.09786	+	1.90155i	−0.0384801	+	0.0666494i
$815$	−38.5937	−	66.8463i	−1.35188	−	2.34152i
$816$	−3.66741	+	0.623447i	−0.128385	+	0.0218250i
$817$	4.99206	+	2.88217i	0.174650	+	0.100834i
$818$	15.6878			0.548511
$819$	5.84718	+	31.8483i	0.204317	+	1.11287i
$820$	7.80279			0.272485
$821$	−9.58441	−	5.53356i	−0.334498	−	0.193123i	0.323338	−	0.946283i	$-0.395195\pi$
$821$	−9.58441	−	5.53356i	−0.334498	−	0.193123i	−0.657836	+	0.753161i	$0.728528\pi$
$822$	−37.7195	+	6.41218i	−1.31562	+	0.223650i
$823$	−5.33069	−	9.23302i	−0.185816	−	0.321843i	0.758035	−	0.652214i	$-0.226160\pi$
$823$	−5.33069	−	9.23302i	−0.185816	−	0.321843i	−0.943851	+	0.330371i	$0.892826\pi$
$824$	−23.3070	+	40.3690i	−0.811939	+	1.40632i
$825$	−6.89893	−	2.55913i	−0.240190	−	0.0890975i
$826$	3.26210	−	20.8495i	0.113503	−	0.725448i
$827$		−	12.3424i		−	0.429187i	−0.976703	−	0.214594i	$-0.931157\pi$
$827$		−	12.3424i		−	0.429187i	0.976703	−	0.214594i	$-0.0688427\pi$
$828$	6.29924	+	17.9921i	0.218914	+	0.625269i
$829$	24.9730	−	14.4182i	0.867349	−	0.500764i	0.000882726	−	1.00000i	$-0.499719\pi$
$829$	24.9730	−	14.4182i	0.867349	−	0.500764i	0.866466	+	0.499235i	$0.166386\pi$
$830$	−17.1651	+	9.91029i	−0.595810	+	0.343991i
$831$	11.4536	+	13.8215i	0.397322	+	0.479464i
$832$		−	32.8619i		−	1.13928i
$833$	−1.87062	−	8.64079i	−0.0648131	−	0.299386i
$834$	−4.19236	+	11.3018i	−0.145170	+	0.391349i
$835$	−0.850869	+	1.47375i	−0.0294455	+	0.0510012i
$836$	2.92719	+	5.07005i	0.101239	+	0.175351i
$837$	−9.84839	+	16.3540i	−0.340410	+	0.565275i
$838$	−23.2226	−	13.4076i	−0.802212	−	0.463157i
$839$	−11.5744			−0.399594			−0.199797	−	0.979837i	$-0.564028\pi$
$839$	−11.5744			−0.399594			−0.199797	+	0.979837i	$0.564028\pi$
$840$	37.2583	+	20.8610i	1.28553	+	0.719772i
$841$	28.5493			0.984459
$842$	7.36474	+	4.25204i	0.253806	+	0.146535i
$843$	−4.10152	−	24.1271i	−0.141264	−	0.830982i
$844$	7.22822	+	12.5196i	0.248806	+	0.430944i
$845$	5.53929	−	9.59433i	0.190557	−	0.330055i
$846$	−8.86792	+	10.3083i	−0.304885	+	0.354408i
$847$	1.66116	−	2.05926i	0.0570781	−	0.0707570i
$848$		−	5.21334i		−	0.179027i
$849$	−5.62097	+	4.65799i	−0.192911	+	0.159862i
$850$	−5.05524	+	2.91865i	−0.173393	+	0.100109i
$851$	13.6037	−	7.85410i	0.466329	−	0.269235i
$852$	−3.24765	+	2.69126i	−0.111263	+	0.0922011i
$853$			4.93920i			0.169115i	0.996419	+	0.0845574i	$0.0269476\pi$
$853$			4.93920i			0.169115i	−0.996419	+	0.0845574i	$0.973052\pi$
$854$	15.1710	+	39.3010i	0.519141	+	1.34485i
$855$	42.6636	−	49.5935i	1.45907	−	1.69606i
$856$	21.7558	−	37.6822i	0.743599	−	1.28795i
$857$	−3.01484	−	5.22185i	−0.102985	−	0.178375i	0.809928	−	0.586529i	$-0.199506\pi$
$857$	−3.01484	−	5.22185i	−0.102985	−	0.178375i	−0.912913	+	0.408154i	$0.866173\pi$
$858$	1.28832	+	7.57851i	0.0439825	+	0.258726i
$859$	5.17382	+	2.98711i	0.176528	+	0.101919i	0.585661	−	0.810556i	$-0.300835\pi$
$859$	5.17382	+	2.98711i	0.176528	+	0.101919i	−0.409132	+	0.912475i	$0.634168\pi$
$860$	−1.99596			−0.0680618
$861$	14.4000	−	0.189887i	0.490752	−	0.00647134i
$862$	−24.9137			−0.848565
$863$	−38.8105	−	22.4073i	−1.32113	−	0.762752i	−0.337218	−	0.941427i	$-0.609486\pi$
$863$	−38.8105	−	22.4073i	−1.32113	−	0.762752i	−0.983908	+	0.178674i	$0.942819\pi$
$864$	−11.4678	+	19.0431i	−0.390142	+	0.647860i
$865$	12.9446	+	22.4207i	0.440130	+	0.762327i
$866$	−4.78122	+	8.28131i	−0.162472	+	0.281410i
$867$	9.27970	−	25.0163i	0.315155	−	0.849598i
$868$	6.17690	+	4.98277i	0.209658	+	0.169126i
$869$		−	2.39566i		−	0.0812671i
$870$	2.45469	+	2.96217i	0.0832217	+	0.100427i
$871$	1.57179	−	0.907475i	0.0532582	−	0.0307486i
$872$	12.6813	−	7.32158i	0.429445	−	0.247940i
$873$	−7.76850	−	22.1887i	−0.262924	−	0.750973i
$874$			60.7143i			2.05369i
$875$	−5.97542	−	0.934910i	−0.202006	−	0.0316057i
$876$	−9.71465	−	3.60361i	−0.328228	−	0.121755i
$877$	−14.3206	+	24.8040i	−0.483571	+	0.837570i	−0.999822	−	0.0188676i	$-0.993994\pi$
$877$	−14.3206	+	24.8040i	−0.483571	+	0.837570i	0.516251	+	0.856437i	$0.327327\pi$
$878$	−10.9812	−	19.0200i	−0.370597	−	0.641894i
$879$	−5.52949	+	0.939994i	−0.186505	+	0.0317052i
$880$	4.47864	+	2.58574i	0.150975	+	0.0871653i
$881$	−20.6566			−0.695938			−0.347969	−	0.937506i	$-0.613128\pi$
$881$	−20.6566			−0.695938			−0.347969	+	0.937506i	$0.613128\pi$
$882$	20.0797	+	10.8974i	0.676119	+	0.366935i
$883$	−1.65718			−0.0557687			−0.0278843	−	0.999611i	$-0.508877\pi$
$883$	−1.65718			−0.0557687			−0.0278843	+	0.999611i	$0.508877\pi$
$884$	−3.64312	−	2.10336i	−0.122531	−	0.0707436i
$885$	38.0724	−	6.47217i	1.27979	−	0.217560i
$886$	−13.4280	−	23.2579i	−0.451121	−	0.781365i
$887$	11.7444	−	20.3419i	0.394338	−	0.683013i	−0.598679	−	0.800989i	$-0.704307\pi$
$887$	11.7444	−	20.3419i	0.394338	−	0.683013i	0.993016	+	0.117976i	$0.0376406\pi$
$888$	10.0426	+	3.72525i	0.337007	+	0.125011i
$889$	1.13327	+	0.177310i	0.0380085	+	0.00594679i
$890$		−	51.2636i		−	1.71836i
$891$	3.28515	−	8.37901i	0.110057	−	0.280707i
$892$	−10.5177	+	6.07240i	−0.352159	+	0.203319i
$893$	25.8726	−	14.9376i	0.865794	−	0.499866i
$894$	6.36225	+	7.67757i	0.212785	+	0.256776i
$895$			66.8250i			2.23371i
$896$	−0.426779	−	0.344274i	−0.0142577	−	0.0115014i
$897$	19.1264	−	51.5612i	0.638613	−	1.72158i
$898$	7.12696	−	12.3442i	0.237830	−	0.411933i
$899$	1.23324	+	2.13603i	0.0411307	+	0.0712405i
$900$	−1.93273	+	10.2245i	−0.0644242	+	0.340815i
$901$	−3.35324	−	1.93599i	−0.111712	−	0.0644972i
$902$	3.41890			0.113837
$903$	−3.68355	+	0.0485734i	−0.122581	+	0.00161642i
$904$	−45.7496			−1.52161
$905$	−39.4114	−	22.7542i	−1.31008	−	0.756375i
$906$	1.55117	+	9.12469i	0.0515340	+	0.303148i
$907$	−26.1933	−	45.3681i	−0.869733	−	1.50642i	−0.862269	−	0.506450i	$-0.830958\pi$
$907$	−26.1933	−	45.3681i	−0.869733	−	1.50642i	−0.00746381	−	0.999972i	$-0.502376\pi$
$908$	4.81084	−	8.33262i	0.159653	−	0.276528i
$909$	41.5329	+	35.7294i	1.37756	+	1.18507i
$910$	−12.8599	−	33.3140i	−0.426302	−	1.10435i
$911$			13.5119i			0.447670i	0.974627	+	0.223835i	$0.0718576\pi$
$911$			13.5119i			0.447670i	−0.974627	+	0.223835i	$0.928142\pi$
$912$	−16.2622	+	13.4761i	−0.538495	+	0.446240i
$913$	5.18826	−	2.99544i	0.171706	−	0.0991346i
$914$	−24.1409	+	13.9378i	−0.798510	+	0.461020i
$915$	−59.3600	+	49.1904i	−1.96238	+	1.62619i
$916$			8.56156i			0.282882i
$917$	14.2368	−	17.6486i	0.470139	−	0.582809i
$918$	−3.45522	−	6.24789i	−0.114039	−	0.206211i
$919$	−7.34579	+	12.7233i	−0.242315	+	0.419702i	−0.961373	−	0.275248i	$-0.911240\pi$
$919$	−7.34579	+	12.7233i	−0.242315	+	0.419702i	0.719058	+	0.694950i	$0.244574\pi$
$920$	−36.2609	−	62.8058i	−1.19549	−	2.07065i
$921$	1.27916	+	7.52463i	0.0421498	+	0.247945i
$922$	−23.8867	−	13.7910i	−0.786667	−	0.454183i
$923$	12.1679			0.400512
$924$	−3.26455	−	1.82782i	−0.107396	−	0.0601310i
$925$	8.57432			0.281922
$926$	26.5609	+	15.3349i	0.872845	+	0.503937i
$927$	−44.8455	−	8.47713i	−1.47292	−	0.278425i
$928$	1.43602	+	2.48726i	0.0471397	+	0.0816484i
$929$	0.991980	−	1.71816i	0.0325458	−	0.0563710i	−0.849294	−	0.527921i	$-0.822972\pi$
$929$	0.991980	−	1.71816i	0.0325458	−	0.0563710i	0.881840	+	0.471550i	$0.156305\pi$
$930$	7.32208	−	19.7389i	0.240101	−	0.647265i
$931$	−33.7263	−	37.1750i	−1.10534	−	1.21836i
$932$			16.4443i			0.538650i
$933$	−27.2357	−	32.8664i	−0.891658	−	1.07600i
$934$	−17.2959	+	9.98577i	−0.565938	+	0.326744i
$935$	3.32631	−	1.92045i	0.108782	−	0.0628053i
$936$	35.3935	−	12.3917i	1.15687	−	0.405034i
$937$		−	11.3329i		−	0.370228i	−0.982717	−	0.185114i	$-0.940735\pi$
$937$		−	11.3329i		−	0.370228i	0.982717	−	0.185114i	$-0.0592655\pi$
$938$	0.197944	−	1.26515i	0.00646310	−	0.0413085i
$939$	−17.5088	−	6.49483i	−0.571379	−	0.211951i
$940$	−5.17229	+	8.95867i	−0.168702	+	0.292200i
$941$	16.5231	+	28.6188i	0.538636	+	0.932945i	0.998978	+	0.0452033i	$0.0143936\pi$
$941$	16.5231	+	28.6188i	0.538636	+	0.932945i	−0.460342	+	0.887742i	$0.652273\pi$
$942$	1.64417	−	0.279503i	0.0535700	−	0.00910671i
$943$	−21.1819	−	12.2294i	−0.689778	−	0.398243i
$944$	−12.4678			−0.405791
$945$	−7.22314	+	41.1796i	−0.234969	+	1.33957i
$946$	−0.874558			−0.0284343
$947$	15.1475	+	8.74539i	0.492226	+	0.284187i	0.725498	−	0.688225i	$-0.241610\pi$
$947$	15.1475	+	8.74539i	0.492226	+	0.284187i	−0.233271	+	0.972412i	$0.574943\pi$
$948$	−3.33984	+	0.567761i	−0.108473	+	0.0184400i
$949$	14.9458	+	25.8869i	0.485162	+	0.840325i
$950$	−16.5705	+	28.7009i	−0.537617	+	0.931180i
$951$	32.6730	+	12.1199i	1.05949	+	0.393016i
$952$	−9.55176	+	3.68718i	−0.309574	+	0.119502i
$953$		−	5.28859i		−	0.171314i	−0.996325	−	0.0856571i	$-0.972701\pi$
$953$		−	5.28859i		−	0.171314i	0.996325	−	0.0856571i	$-0.0272990\pi$
$954$	9.44364	−	3.30632i	0.305749	−	0.107046i
$955$	−46.7802	+	27.0086i	−1.51377	+	0.873977i
$956$	−12.8271	+	7.40572i	−0.414858	+	0.239518i
$957$	−0.741943	−	0.895332i	−0.0239836	−	0.0289420i
$958$			8.37743i			0.270663i
$959$	−50.1168	+	19.3462i	−1.61836	+	0.624720i
$960$	14.7566	−	39.7809i	0.476266	−	1.28392i
$961$	−8.75106	+	15.1573i	−0.282292	+	0.488945i
$962$	−4.47881	−	7.75753i	−0.144403	−	0.250113i
$963$	41.8608	+	7.91293i	1.34895	+	0.254991i
$964$	12.0368	+	6.94945i	0.387679	+	0.223827i
$965$	−12.3741			−0.398338
$966$	−19.8420	−	33.3442i	−0.638407	−	1.07283i
$967$	37.6644			1.21120			0.605602	−	0.795768i	$-0.292932\pi$
$967$	37.6644			1.21120			0.605602	+	0.795768i	$0.292932\pi$
$968$	−2.65354	−	1.53202i	−0.0852881	−	0.0492411i
$969$	2.62888	+	15.4643i	0.0844517	+	0.496785i
$970$	12.9633	+	22.4530i	0.416225	+	0.720923i
$971$	−1.19511	+	2.06998i	−0.0383528	+	0.0664289i	−0.884565	−	0.466418i	$-0.845544\pi$
$971$	−1.19511	+	2.06998i	−0.0383528	+	0.0664289i	0.846212	+	0.532847i	$0.178878\pi$
$972$	−12.4599	−	2.59411i	−0.399653	−	0.0832060i
$973$	−2.61629	+	16.7219i	−0.0838744	+	0.536079i
$974$		−	31.4089i		−	1.00641i
$975$	23.1138	−	19.1539i	0.740234	−	0.613417i
$976$	21.5544	−	12.4445i	0.689941	−	0.398338i
$977$	−35.3417	+	20.4045i	−1.13068	+	0.652799i	−0.944106	−	0.329642i	$-0.893072\pi$
$977$	−35.3417	+	20.4045i	−1.13068	+	0.652799i	−0.186575	+	0.982441i	$0.559739\pi$
$978$	−36.8256	+	30.5167i	−1.17755	+	0.975815i
$979$			15.4947i			0.495213i
$980$	16.5497	+	5.30865i	0.528660	+	0.169579i
$981$	10.8687	+	9.35000i	0.347012	+	0.298523i
$982$	9.48924	−	16.4358i	0.302814	−	0.524489i
$983$	−6.08188	−	10.5341i	−0.193982	−	0.335986i	0.752584	−	0.658496i	$-0.228807\pi$
$983$	−6.08188	−	10.5341i	−0.193982	−	0.335986i	−0.946566	+	0.322509i	$0.895474\pi$
$984$	−2.79513	−	16.4423i	−0.0891054	−	0.524160i
$985$	12.2288	+	7.06032i	0.389643	+	0.224960i
$986$	−0.922442			−0.0293765
$987$	−9.32745	+	16.6591i	−0.296896	+	0.530265i
$988$	−23.8834			−0.759833
$989$	5.41836	+	3.12829i	0.172294	+	0.0994738i
$990$	−1.84354	+	9.75266i	−0.0585916	+	0.309960i
$991$	−0.893809	−	1.54812i	−0.0283928	−	0.0491778i	0.851480	−	0.524387i	$-0.175706\pi$
$991$	−0.893809	−	1.54812i	−0.0283928	−	0.0491778i	−0.879873	+	0.475210i	$0.842372\pi$
$992$	7.85869	−	13.6117i	0.249514	−	0.432170i
$993$	7.56128	−	20.3838i	0.239950	−	0.646859i
$994$	5.39023	−	6.68201i	0.170968	−	0.211940i
$995$			55.7626i			1.76779i
$996$	−5.40561	−	6.52316i	−0.171283	−	0.206694i
$997$	0.581157	−	0.335531i	0.0184054	−	0.0106264i	−0.490769	−	0.871290i	$-0.663284\pi$
$997$	0.581157	−	0.335531i	0.0184054	−	0.0106264i	0.509174	+	0.860663i	$0.329951\pi$
$998$	21.0094	−	12.1298i	0.665040	−	0.383961i
$999$	−0.193359	+	10.4856i	−0.00611762	+	0.331749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.n.a.89.18	yes	52
3.2	odd	2	inner	231.2.n.a.89.9	✓	52
7.3	odd	6	inner	231.2.n.a.122.9	yes	52
21.17	even	6	inner	231.2.n.a.122.18	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.n.a.89.9	✓	52	3.2	odd	2	inner
231.2.n.a.89.18	yes	52	1.1	even	1	trivial
231.2.n.a.122.9	yes	52	7.3	odd	6	inner
231.2.n.a.122.18	yes	52	21.17	even	6	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.942161 + 0.543957i) q^{2} +(1.70755 - 0.290278i) q^{3} +(-0.408222 - 0.707062i) q^{4} +(-1.52055 + 2.63367i) q^{5} +(1.76669 + 0.655346i) q^{6} +(2.61395 + 0.408977i) q^{7} -3.06405i q^{8} +(2.83148 - 0.991331i) q^{9} +O(q^{10})\)	\(q+(0.942161 + 0.543957i) q^{2} +(1.70755 - 0.290278i) q^{3} +(-0.408222 - 0.707062i) q^{4} +(-1.52055 + 2.63367i) q^{5} +(1.76669 + 0.655346i) q^{6} +(2.61395 + 0.408977i) q^{7} -3.06405i q^{8} +(2.83148 - 0.991331i) q^{9} +(-2.86521 + 1.65423i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-0.902306 - 1.08885i) q^{12} +4.07958i q^{13} +(2.24030 + 1.80720i) q^{14} +(-1.83193 + 4.93852i) q^{15} +(0.850264 - 1.47270i) q^{16} +(-0.631497 - 1.09378i) q^{17} +(3.20695 + 0.606208i) q^{18} +(-6.20991 - 3.58529i) q^{19} +2.48289 q^{20} +(4.58218 - 0.0604233i) q^{21} +1.08791 q^{22} +(-6.74021 - 3.89146i) q^{23} +(-0.889426 - 5.23202i) q^{24} +(-2.12415 - 3.67914i) q^{25} +(-2.21911 + 3.84362i) q^{26} +(4.54714 - 2.51467i) q^{27} +(-0.777901 - 2.01518i) q^{28} -0.671342i q^{29} +(-4.41231 + 3.65639i) q^{30} +(-3.18173 + 1.83697i) q^{31} +(-3.70492 + 2.13903i) q^{32} +(1.33365 - 1.10516i) q^{33} -1.37403i q^{34} +(-5.05176 + 6.26242i) q^{35} +(-1.85680 - 1.59735i) q^{36} +(-1.00915 + 1.74789i) q^{37} +(-3.90049 - 6.75584i) q^{38} +(1.18421 + 6.96609i) q^{39} +(8.06970 + 4.65904i) q^{40} +3.14262 q^{41} +(4.35001 + 2.43558i) q^{42} -0.803886 q^{43} +(-0.707062 - 0.408222i) q^{44} +(-1.69457 + 8.96455i) q^{45} +(-4.23357 - 7.33276i) q^{46} +(-2.08317 + 3.60816i) q^{47} +(1.02438 - 2.76153i) q^{48} +(6.66548 + 2.13809i) q^{49} -4.62179i q^{50} +(-1.39582 - 1.68439i) q^{51} +(2.88451 - 1.66537i) q^{52} +(2.65499 - 1.53286i) q^{53} +(5.65200 + 0.104226i) q^{54} +3.04110i q^{55} +(1.25312 - 8.00927i) q^{56} +(-11.6445 - 4.31948i) q^{57} +(0.365181 - 0.632512i) q^{58} +(-3.66585 - 6.34944i) q^{59} +(4.23967 - 0.720729i) q^{60} +(12.6751 + 7.31800i) q^{61} -3.99693 q^{62} +(7.80677 - 1.43328i) q^{63} -8.05522 q^{64} +(-10.7443 - 6.20321i) q^{65} +(1.85767 - 0.315797i) q^{66} +(-0.222443 - 0.385283i) q^{67} +(-0.515582 + 0.893015i) q^{68} +(-12.6389 - 4.68834i) q^{69} +(-8.16605 + 3.15227i) q^{70} -2.98265i q^{71} +(-3.03748 - 8.67578i) q^{72} +(6.34549 - 3.66357i) q^{73} +(-1.90155 + 1.09786i) q^{74} +(-4.69508 - 5.66574i) q^{75} +5.85439i q^{76} +(2.46824 - 0.952791i) q^{77} +(-2.67354 + 7.20734i) q^{78} +(1.19783 - 2.07470i) q^{79} +(2.58574 + 4.47864i) q^{80} +(7.03453 - 5.61386i) q^{81} +(2.96085 + 1.70945i) q^{82} +5.99088 q^{83} +(-1.91327 - 3.21522i) q^{84} +3.84089 q^{85} +(-0.757390 - 0.437279i) q^{86} +(-0.194876 - 1.14635i) q^{87} +(-1.53202 - 2.65354i) q^{88} +(-7.74735 + 13.4188i) q^{89} +(-6.47288 + 7.52428i) q^{90} +(-1.66845 + 10.6638i) q^{91} +6.35432i q^{92} +(-4.89974 + 4.06031i) q^{93} +(-3.92537 + 2.26631i) q^{94} +(18.8850 - 10.9032i) q^{95} +(-5.70543 + 4.72797i) q^{96} -7.83644i q^{97} +(5.11692 + 5.64015i) q^{98} +(1.95647 - 2.27426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9	\( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) \) 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9 - 30 * q^12 - 4 * q^15 - 20 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^21 + 36 * q^24 - 22 * q^25 - 40 * q^28 - 20 * q^30 - 54 * q^31 + 36 * q^36 + 2 * q^37 + 20 * q^39 + 60 * q^40 - 36 * q^42 + 36 * q^43 - 54 * q^45 + 4 * q^46 + 22 * q^49 - 16 * q^51 + 12 * q^52 + 66 * q^54 - 44 * q^57 - 16 * q^58 + 20 * q^60 - 36 * q^61 - 24 * q^63 - 48 * q^64 - 30 * q^66 - 6 * q^67 - 116 * q^70 + 36 * q^72 - 6 * q^73 + 72 * q^75 + 112 * q^78 + 14 * q^79 + 52 * q^81 - 84 * q^82 + 8 * q^84 + 8 * q^85 + 18 * q^87 - 12 * q^88 + 46 * q^91 + 6 * q^93 + 48 * q^94 - 18 * q^96

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