LMFDB - Embedded newform 180.2.q.a.11.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,2,Mod(11,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 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("180.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	180.11
Dual form			180.2.q.a.131.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.660227 + 1.25064i) q^{2} +(-1.67907 + 0.425108i) q^{3} +(-1.12820 - 1.65141i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.576911 - 2.38058i) q^{6} +(-1.87435 - 1.08216i) q^{7} +(2.81019 - 0.320666i) q^{8} +(2.63857 - 1.42758i) q^{9} +(-0.0535467 - 1.41320i) q^{10} +(1.44632 - 2.50510i) q^{11} +(2.59636 + 2.29323i) q^{12} +(-3.30299 - 5.72095i) q^{13} +(2.59089 - 1.62967i) q^{14} +(1.24156 - 1.20769i) q^{15} +(-1.45433 + 3.72625i) q^{16} +5.08829i q^{17} +(0.0433305 + 4.24242i) q^{18} -4.66790i q^{19} +(1.80276 + 0.866065i) q^{20} +(3.60721 + 1.02022i) q^{21} +(2.17808 + 3.46277i) q^{22} +(-1.44720 - 2.50662i) q^{23} +(-4.58220 + 1.73306i) q^{24} +(0.500000 - 0.866025i) q^{25} +(9.33557 - 0.353728i) q^{26} +(-3.82347 + 3.51868i) q^{27} +(0.327557 + 4.31623i) q^{28} +(-5.99593 - 3.46175i) q^{29} +(0.690672 + 2.35010i) q^{30} +(-4.51887 + 2.60897i) q^{31} +(-3.70001 - 4.27901i) q^{32} +(-1.36354 + 4.82109i) q^{33} +(-6.36361 - 3.35942i) q^{34} +2.16432 q^{35} +(-5.33435 - 2.74677i) q^{36} +4.58347 q^{37} +(5.83787 + 3.08188i) q^{38} +(7.97798 + 8.20175i) q^{39} +(-2.27336 + 1.68280i) q^{40} +(-4.18802 + 2.41795i) q^{41} +(-3.65751 + 3.83775i) q^{42} +(-3.81468 - 2.20241i) q^{43} +(-5.76870 + 0.437785i) q^{44} +(-1.57128 + 2.55560i) q^{45} +(4.09035 - 0.154985i) q^{46} +(0.00969237 - 0.0167877i) q^{47} +(0.857858 - 6.87489i) q^{48} +(-1.15786 - 2.00548i) q^{49} +(0.752973 + 1.19709i) q^{50} +(-2.16307 - 8.54360i) q^{51} +(-5.72121 + 11.9090i) q^{52} -3.21239i q^{53} +(-1.87624 - 7.10491i) q^{54} +2.89264i q^{55} +(-5.61431 - 2.44003i) q^{56} +(1.98436 + 7.83775i) q^{57} +(8.28807 - 5.21320i) q^{58} +(4.02651 + 6.97412i) q^{59} +(-3.39513 - 0.687818i) q^{60} +(-0.321400 + 0.556681i) q^{61} +(-0.279404 - 7.37400i) q^{62} +(-6.49047 - 0.179566i) q^{63} +(7.79435 - 1.80227i) q^{64} +(5.72095 + 3.30299i) q^{65} +(-5.12921 - 4.88831i) q^{66} +(8.19888 - 4.73363i) q^{67} +(8.40286 - 5.74061i) q^{68} +(3.49553 + 3.59357i) q^{69} +(-1.42894 + 2.70678i) q^{70} +1.17635 q^{71} +(6.95710 - 4.85786i) q^{72} +2.32539 q^{73} +(-3.02613 + 5.73228i) q^{74} +(-0.471381 + 1.66667i) q^{75} +(-7.70863 + 5.26633i) q^{76} +(-5.42184 + 3.13030i) q^{77} +(-15.5247 + 4.56256i) q^{78} +(14.6983 + 8.48606i) q^{79} +(-0.603641 - 3.95419i) q^{80} +(4.92406 - 7.53350i) q^{81} +(-0.258947 - 6.83410i) q^{82} +(-0.950613 + 1.64651i) q^{83} +(-2.38486 - 7.10801i) q^{84} +(-2.54414 - 4.40658i) q^{85} +(5.27297 - 3.31670i) q^{86} +(11.5392 + 3.26361i) q^{87} +(3.26114 - 7.50361i) q^{88} -3.72649i q^{89} +(-2.15874 - 3.65238i) q^{90} +14.2974i q^{91} +(-2.50673 + 5.21788i) q^{92} +(6.47842 - 6.30166i) q^{93} +(0.0145962 + 0.0232054i) q^{94} +(2.33395 + 4.04252i) q^{95} +(8.03163 + 5.61186i) q^{96} +(5.78082 - 10.0127i) q^{97} +(3.27258 - 0.123999i) q^{98} +(0.239992 - 8.67461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 4 q^{9} - 22 q^{12} - 30 q^{14} - 16 q^{18} - 4 q^{21} - 28 q^{24} + 24 q^{25} - 12 q^{29} + 16 q^{30} - 44 q^{33} - 6 q^{34} + 42 q^{36} + 60 q^{38} - 6 q^{40} - 60 q^{41} - 18 q^{42}+ \cdots - 12 q^{97}+O(q^{100}) $ 48 * q + 6 * q^6 + 4 * q^9 - 22 * q^12 - 30 * q^14 - 16 * q^18 - 4 * q^21 - 28 * q^24 + 24 * q^25 - 12 * q^29 + 16 * q^30 - 44 * q^33 - 6 * q^34 + 42 * q^36 + 60 * q^38 - 6 * q^40 - 60 * q^41 - 18 * q^42 - 8 * q^45 - 12 * q^46 - 12 * q^48 + 24 * q^49 - 18 * q^52 - 32 * q^54 - 42 * q^56 - 12 * q^57 - 18 * q^58 + 14 * q^60 - 48 * q^64 + 16 * q^66 + 48 * q^68 + 36 * q^69 + 60 * q^72 - 24 * q^73 + 84 * q^74 + 6 * q^76 + 48 * q^77 + 38 * q^78 - 36 * q^82 + 50 * q^84 - 54 * q^86 - 18 * q^90 + 60 * q^92 - 32 * q^93 + 18 * q^94 - 18 * q^96 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.660227	+	1.25064i	−0.466851	+	0.884336i
$2$	−0.660227	+	1.25064i	−0.466851	+	0.884336i
$3$	−1.67907	+	0.425108i	−0.969413	+	0.245436i
$3$	−1.67907	+	0.425108i	−0.969413	+	0.245436i
$4$	−1.12820	−	1.65141i	−0.564100	−	0.825706i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	0.576911	−	2.38058i	0.235523	−	0.971869i
$7$	−1.87435	−	1.08216i	−0.708440	−	0.409018i	0.102043	−	0.994780i	$-0.467462\pi$
$7$	−1.87435	−	1.08216i	−0.708440	−	0.409018i	−0.810483	+	0.585762i	$0.800795\pi$
$8$	2.81019	−	0.320666i	0.993553	−	0.113373i
$9$	2.63857	−	1.42758i	0.879522	−	0.475858i
$10$	−0.0535467	−	1.41320i	−0.0169329	−	0.446893i
$11$	1.44632	−	2.50510i	0.436083	−	0.755317i	−0.561301	−	0.827612i	$-0.689699\pi$
$11$	1.44632	−	2.50510i	0.436083	−	0.755317i	0.997383	+	0.0722948i	$0.0230322\pi$
$12$	2.59636	+	2.29323i	0.749504	+	0.661999i
$13$	−3.30299	−	5.72095i	−0.916085	−	1.58671i	−0.805306	−	0.592860i	$-0.797999\pi$
$13$	−3.30299	−	5.72095i	−0.916085	−	1.58671i	−0.110779	−	0.993845i	$-0.535335\pi$
$14$	2.59089	−	1.62967i	0.692445	−	0.435548i
$15$	1.24156	−	1.20769i	0.320571	−	0.311824i
$16$	−1.45433	+	3.72625i	−0.363582	+	0.931562i
$17$			5.08829i			1.23409i	0.786928	+	0.617045i	$0.211670\pi$
$17$			5.08829i			1.23409i	−0.786928	+	0.617045i	$0.788330\pi$
$18$	0.0433305	+	4.24242i	0.0102131	+	0.999948i
$19$		−	4.66790i		−	1.07089i	−0.844570	−	0.535445i	$-0.820144\pi$
$19$		−	4.66790i		−	1.07089i	0.844570	−	0.535445i	$-0.179856\pi$
$20$	1.80276	+	0.866065i	0.403109	+	0.193658i
$21$	3.60721	+	1.02022i	0.787158	+	0.222630i
$22$	2.17808	+	3.46277i	0.464369	+	0.738264i
$23$	−1.44720	−	2.50662i	−0.301761	−	0.522666i	0.674774	−	0.738025i	$-0.264241\pi$
$23$	−1.44720	−	2.50662i	−0.301761	−	0.522666i	−0.976535	+	0.215359i	$0.930908\pi$
$24$	−4.58220	+	1.73306i	−0.935337	+	0.353759i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	9.33557	−	0.353728i	1.83086	−	0.0693718i
$27$	−3.82347	+	3.51868i	−0.735827	+	0.677170i
$28$	0.327557	+	4.31623i	0.0619025	+	0.815690i
$29$	−5.99593	−	3.46175i	−1.11342	−	0.642831i	−0.173704	−	0.984798i	$-0.555573\pi$
$29$	−5.99593	−	3.46175i	−1.11342	−	0.642831i	−0.939712	+	0.341967i	$0.888907\pi$
$30$	0.690672	+	2.35010i	0.126099	+	0.429068i
$31$	−4.51887	+	2.60897i	−0.811613	+	0.468585i	−0.847516	−	0.530770i	$-0.821903\pi$
$31$	−4.51887	+	2.60897i	−0.811613	+	0.468585i	0.0359024	+	0.999355i	$0.488569\pi$
$32$	−3.70001	−	4.27901i	−0.654076	−	0.756429i
$33$	−1.36354	+	4.82109i	−0.237362	+	0.839245i
$34$	−6.36361	−	3.35942i	−1.09135	−	0.576136i
$35$	2.16432			0.365837
$36$	−5.33435	−	2.74677i	−0.889058	−	0.457795i
$37$	4.58347			0.753518			0.376759	−	0.926311i	$-0.377038\pi$
$37$	4.58347			0.753518			0.376759	+	0.926311i	$0.377038\pi$
$38$	5.83787	+	3.08188i	0.947027	+	0.499946i
$39$	7.97798	+	8.20175i	1.27750	+	1.31333i
$40$	−2.27336	+	1.68280i	−0.359450	+	0.266074i
$41$	−4.18802	+	2.41795i	−0.654059	+	0.377621i	−0.790009	−	0.613095i	$-0.789924\pi$
$41$	−4.18802	+	2.41795i	−0.654059	+	0.377621i	0.135951	+	0.990716i	$0.456591\pi$
$42$	−3.65751	+	3.83775i	−0.564365	+	0.592177i
$43$	−3.81468	−	2.20241i	−0.581733	−	0.335864i	0.180089	−	0.983650i	$-0.442361\pi$
$43$	−3.81468	−	2.20241i	−0.581733	−	0.335864i	−0.761822	+	0.647787i	$0.775695\pi$
$44$	−5.76870	+	0.437785i	−0.869664	+	0.0659986i
$45$	−1.57128	+	2.55560i	−0.234232	+	0.380966i
$46$	4.09035	−	0.154985i	0.603089	−	0.0228513i
$47$	0.00969237	−	0.0167877i	0.00141378	−	0.00244874i	−0.865318	−	0.501224i	$-0.832883\pi$
$47$	0.00969237	−	0.0167877i	0.00141378	−	0.00244874i	0.866731	+	0.498775i	$0.166217\pi$
$48$	0.857858	−	6.87489i	0.123821	−	0.992305i
$49$	−1.15786	−	2.00548i	−0.165409	−	0.286497i
$50$	0.752973	+	1.19709i	0.106486	+	0.169295i
$51$	−2.16307	−	8.54360i	−0.302891	−	1.19634i
$52$	−5.72121	+	11.9090i	−0.793389	+	1.65148i
$53$		−	3.21239i		−	0.441256i	−0.975358	−	0.220628i	$-0.929189\pi$
$53$		−	3.21239i		−	0.441256i	0.975358	−	0.220628i	$-0.0708107\pi$
$54$	−1.87624	−	7.10491i	−0.255324	−	0.966855i
$55$			2.89264i			0.390044i
$56$	−5.61431	−	2.44003i	−0.750243	−	0.326063i
$57$	1.98436	+	7.83775i	0.262836	+	1.03813i
$58$	8.28807	−	5.21320i	1.08828	−	0.684527i
$59$	4.02651	+	6.97412i	0.524207	+	0.907953i	0.999603	+	0.0281811i	$0.00897150\pi$
$59$	4.02651	+	6.97412i	0.524207	+	0.907953i	−0.475396	+	0.879772i	$0.657695\pi$
$60$	−3.39513	−	0.687818i	−0.438309	−	0.0887969i
$61$	−0.321400	+	0.556681i	−0.0411510	+	0.0712757i	−0.885867	−	0.463939i	$-0.846436\pi$
$61$	−0.321400	+	0.556681i	−0.0411510	+	0.0712757i	0.844716	+	0.535214i	$0.179769\pi$
$62$	−0.279404	−	7.37400i	−0.0354843	−	0.936499i
$63$	−6.49047	−	0.179566i	−0.817723	−	0.0226232i
$64$	7.79435	−	1.80227i	0.974293	−	0.225283i
$65$	5.72095	+	3.30299i	0.709596	+	0.409685i
$66$	−5.12921	−	4.88831i	−0.631362	−	0.601710i
$67$	8.19888	−	4.73363i	1.00165	−	0.578304i	0.0929158	−	0.995674i	$-0.470381\pi$
$67$	8.19888	−	4.73363i	1.00165	−	0.578304i	0.908737	+	0.417370i	$0.137048\pi$
$68$	8.40286	−	5.74061i	1.01900	−	0.696151i
$69$	3.49553	+	3.59357i	0.420812	+	0.432615i
$70$	−1.42894	+	2.70678i	−0.170791	+	0.323523i
$71$	1.17635			0.139607			0.0698035	−	0.997561i	$-0.477763\pi$
$71$	1.17635			0.139607			0.0698035	+	0.997561i	$0.477763\pi$
$72$	6.95710	−	4.85786i	0.819902	−	0.572504i
$73$	2.32539			0.272166			0.136083	−	0.990697i	$-0.456549\pi$
$73$	2.32539			0.272166			0.136083	+	0.990697i	$0.456549\pi$
$74$	−3.02613	+	5.73228i	−0.351781	+	0.666364i
$75$	−0.471381	+	1.66667i	−0.0544304	+	0.192451i
$76$	−7.70863	+	5.26633i	−0.884241	+	0.604090i
$77$	−5.42184	+	3.13030i	−0.617876	+	0.356731i
$78$	−15.5247	+	4.56256i	−1.75783	+	0.516609i
$79$	14.6983	+	8.48606i	1.65369	+	0.954756i	0.975538	+	0.219830i	$0.0705503\pi$
$79$	14.6983	+	8.48606i	1.65369	+	0.954756i	0.678148	+	0.734926i	$0.262783\pi$
$80$	−0.603641	−	3.95419i	−0.0674892	−	0.442092i
$81$	4.92406	−	7.53350i	0.547118	−	0.837056i
$82$	−0.258947	−	6.83410i	−0.0285959	−	0.754700i
$83$	−0.950613	+	1.64651i	−0.104343	+	0.180728i	−0.913470	−	0.406907i	$-0.866607\pi$
$83$	−0.950613	+	1.64651i	−0.104343	+	0.180728i	0.809126	+	0.587635i	$0.199941\pi$
$84$	−2.38486	−	7.10801i	−0.260209	−	0.775547i
$85$	−2.54414	−	4.40658i	−0.275951	−	0.477961i
$86$	5.27297	−	3.31670i	0.568599	−	0.357649i
$87$	11.5392	+	3.26361i	1.23713	+	0.349896i
$88$	3.26114	−	7.50361i	0.347639	−	0.799887i
$89$		−	3.72649i		−	0.395007i	−0.980302	−	0.197503i	$-0.936717\pi$
$89$		−	3.72649i		−	0.395007i	0.980302	−	0.197503i	$-0.0632834\pi$
$90$	−2.15874	−	3.65238i	−0.227551	−	0.384994i
$91$			14.2974i			1.49878i
$92$	−2.50673	+	5.21788i	−0.261345	+	0.544002i
$93$	6.47842	−	6.30166i	0.671780	−	0.653452i
$94$	0.0145962	+	0.0232054i	0.00150548	+	0.00239345i
$95$	2.33395	+	4.04252i	0.239458	+	0.414754i
$96$	8.03163	+	5.61186i	0.819725	+	0.572758i
$97$	5.78082	−	10.0127i	0.586953	−	1.01663i	−0.407675	−	0.913127i	$-0.633661\pi$
$97$	5.78082	−	10.0127i	0.586953	−	1.01663i	0.994629	−	0.103506i	$-0.0330062\pi$
$98$	3.27258	−	0.123999i	0.330581	−	0.0125258i
$99$	0.239992	−	8.67461i	0.0241201	−	0.871831i
$100$	−1.99427	+	0.151344i	−0.199427	+	0.0151344i
$101$	−9.46327	−	5.46362i	−0.941630	−	0.543650i	−0.0511591	−	0.998691i	$-0.516292\pi$
$101$	−9.46327	−	5.46362i	−0.941630	−	0.543650i	−0.890471	+	0.455040i	$0.849625\pi$
$102$	12.1131	+	2.93549i	1.19937	+	0.290657i
$103$	0.550211	−	0.317664i	0.0542139	−	0.0313004i	−0.472648	−	0.881251i	$-0.656702\pi$
$103$	0.550211	−	0.317664i	0.0542139	−	0.0313004i	0.526862	+	0.849951i	$0.323368\pi$
$104$	−11.1165	−	15.0178i	−1.09007	−	1.47262i
$105$	−3.63405	+	0.920070i	−0.354647	+	0.0897896i
$106$	4.01755	+	2.12091i	0.390219	+	0.206001i
$107$	−18.8050			−1.81795			−0.908975	−	0.416850i	$-0.863134\pi$
$107$	−18.8050			−1.81795			−0.908975	+	0.416850i	$0.863134\pi$
$108$	10.1244	+	2.34435i	0.974224	+	0.225585i
$109$	−3.39053			−0.324754			−0.162377	−	0.986729i	$-0.551916\pi$
$109$	−3.39053			−0.324754			−0.162377	+	0.986729i	$0.551916\pi$
$110$	−3.61766	−	1.90980i	−0.344930	−	0.182092i
$111$	−7.69598	+	1.94847i	−0.730470	+	0.184941i
$112$	6.75832	−	5.41050i	0.638601	−	0.511244i
$113$	−0.864471	+	0.499103i	−0.0813226	+	0.0469516i	−0.540110	−	0.841595i	$-0.681617\pi$
$113$	−0.864471	+	0.499103i	−0.0813226	+	0.0469516i	0.458787	+	0.888546i	$0.348284\pi$
$114$	−11.1123	−	2.69296i	−1.04077	−	0.252219i
$115$	2.50662	+	1.44720i	0.233743	+	0.134952i
$116$	1.04783	+	13.8073i	0.0972888	+	1.28198i
$117$	−16.8822	−	10.3798i	−1.56076	−	0.959615i
$118$	−11.3805	+	0.431213i	−1.04766	+	0.0396963i
$119$	5.50634	−	9.53725i	0.504765	−	0.874279i
$120$	3.10177	−	3.79197i	0.283151	−	0.346158i
$121$	1.31630	+	2.27991i	0.119664	+	0.207264i
$122$	−0.484010	−	0.769491i	−0.0438202	−	0.0696665i
$123$	6.00409	−	5.84028i	0.541371	−	0.526600i
$124$	9.40668	+	4.51908i	0.844745	+	0.405825i
$125$			1.00000i			0.0894427i
$126$	4.50976	−	7.99869i	0.401761	−	0.712580i
$127$		−	8.78450i		−	0.779498i	−0.920921	−	0.389749i	$-0.872562\pi$
$127$		−	8.78450i		−	0.779498i	0.920921	−	0.389749i	$-0.127438\pi$
$128$	−2.89205	+	10.9378i	−0.255624	+	0.966776i
$129$	7.34138	+	2.07635i	0.646372	+	0.182812i
$130$	−7.90797	+	4.97412i	−0.693575	+	0.436259i
$131$	7.06346	+	12.2343i	0.617137	+	1.06891i	0.990005	+	0.141029i	$0.0450411\pi$
$131$	7.06346	+	12.2343i	0.617137	+	1.06891i	−0.372868	+	0.927884i	$0.621626\pi$
$132$	9.49996	−	3.18740i	0.826865	−	0.277427i
$133$	−5.05142	+	8.74931i	−0.438013	+	0.758661i
$134$	0.506940	+	13.3791i	0.0437929	+	1.15578i
$135$	1.55188	−	4.95900i	0.133565	−	0.426803i
$136$	1.63164	+	14.2991i	0.139912	+	1.22613i
$137$	13.1658	+	7.60127i	1.12483	+	0.649420i	0.942629	−	0.333841i	$-0.108345\pi$
$137$	13.1658	+	7.60127i	1.12483	+	0.649420i	0.182200	+	0.983262i	$0.441678\pi$
$138$	−6.80211	+	1.99907i	−0.579034	+	0.170172i
$139$	−2.20036	+	1.27038i	−0.186632	+	0.107752i	−0.590405	−	0.807107i	$-0.701032\pi$
$139$	−2.20036	+	1.27038i	−0.186632	+	0.107752i	0.403773	+	0.914859i	$0.367699\pi$
$140$	−2.44179	−	3.57418i	−0.206369	−	0.302074i
$141$	−0.00913761	+	0.0323080i	−0.000769525	+	0.00272083i
$142$	−0.776658	+	1.47119i	−0.0651757	+	0.123460i
$143$	−19.1087			−1.59795
$144$	1.48217	+	11.9081i	0.123514	+	0.992343i
$145$	6.92350			0.574965
$146$	−1.53529	+	2.90823i	−0.127061	+	0.240686i
$147$	2.79668	+	2.87512i	0.230666	+	0.237136i
$148$	−5.17108	−	7.56921i	−0.425060	−	0.622185i
$149$	5.98481	−	3.45533i	0.490294	−	0.283072i	−0.234402	−	0.972140i	$-0.575313\pi$
$149$	5.98481	−	3.45533i	0.490294	−	0.283072i	0.724697	+	0.689068i	$0.241980\pi$
$150$	−1.77319	−	1.68991i	−0.144780	−	0.137981i
$151$	−18.4571	−	10.6562i	−1.50202	−	0.867191i	−0.999997	−	0.00233576i	$-0.999257\pi$
$151$	−18.4571	−	10.6562i	−1.50202	−	0.867191i	−0.502021	−	0.864855i	$-0.667410\pi$
$152$	−1.49684	−	13.1177i	−0.121410	−	1.06399i
$153$	7.26391	+	13.4258i	0.587252	+	1.08541i
$154$	−0.335235	−	8.84748i	−0.0270140	−	0.712950i
$155$	2.60897	−	4.51887i	0.209558	−	0.362965i
$156$	4.54371	−	22.4282i	0.363788	−	1.79569i
$157$	−5.83484	−	10.1062i	−0.465671	−	0.806566i	0.533560	−	0.845762i	$-0.320854\pi$
$157$	−5.83484	−	10.1062i	−0.465671	−	0.806566i	−0.999232	+	0.0391957i	$0.987520\pi$
$158$	−20.3172	+	12.7795i	−1.61635	+	1.01669i
$159$	1.36561	+	5.39384i	0.108300	+	0.427759i
$160$	5.34381	+	1.85572i	0.422465	+	0.146708i
$161$			6.26438i			0.493703i
$162$	6.17070	+	11.1320i	0.484816	+	0.874616i
$163$			0.438006i			0.0343073i	0.999853	+	0.0171536i	$0.00546044\pi$
$163$			0.438006i			0.0343073i	−0.999853	+	0.0171536i	$0.994540\pi$
$164$	8.71796	+	4.18821i	0.680759	+	0.327044i
$165$	−1.22969	−	4.85696i	−0.0957310	−	0.378114i
$166$	−1.43157	−	2.27594i	−0.111111	−	0.176648i
$167$	−2.08280	−	3.60751i	−0.161172	−	0.279157i	0.774118	−	0.633042i	$-0.218194\pi$
$167$	−2.08280	−	3.60751i	−0.161172	−	0.279157i	−0.935289	+	0.353884i	$0.884861\pi$
$168$	10.4641	+	1.71030i	0.807323	+	0.131953i
$169$	−15.3195	+	26.5341i	−1.17842	+	2.04109i
$170$	7.19076	−	0.272461i	0.551506	−	0.0208968i
$171$	−6.66378	−	12.3166i	−0.509592	−	0.941872i
$172$	0.666643	+	8.78436i	0.0508311	+	0.669801i
$173$	7.75332	+	4.47638i	0.589474	+	0.340333i	0.764889	−	0.644162i	$-0.222794\pi$
$173$	7.75332	+	4.47638i	0.589474	+	0.340333i	−0.175416	+	0.984494i	$0.556127\pi$
$174$	−11.7001	+	12.2767i	−0.886982	+	0.930692i
$175$	−1.87435	+	1.08216i	−0.141688	+	0.0818036i
$176$	7.23122	+	9.03259i	0.545073	+	0.680857i
$177$	−9.72556	−	9.99835i	−0.731018	−	0.751522i
$178$	4.66049	+	2.46033i	0.349319	+	0.184409i
$179$	−10.5263			−0.786776			−0.393388	−	0.919373i	$-0.628697\pi$
$179$	−10.5263			−0.786776			−0.393388	+	0.919373i	$0.628697\pi$
$180$	5.99306	−	0.288402i	0.446697	−	0.0214962i
$181$	−9.50854			−0.706765			−0.353382	−	0.935479i	$-0.614968\pi$
$181$	−9.50854			−0.706765			−0.353382	+	0.935479i	$0.614968\pi$
$182$	−17.8810	−	9.43956i	−1.32542	−	0.699707i
$183$	0.303004	−	1.07134i	0.0223987	−	0.0791955i
$184$	−4.87068	−	6.58000i	−0.359071	−	0.485084i
$185$	−3.96940	+	2.29174i	−0.291836	+	0.168492i
$186$	3.60389	+	12.2627i	0.264250	+	0.899144i
$187$	12.7467	+	7.35930i	0.932130	+	0.538165i
$188$	−0.0386583	+	0.00293377i	−0.00281945	+	0.000213967i
$189$	10.9743	−	2.45765i	0.798263	−	0.178768i
$190$	−6.59668	+	0.249951i	−0.478573	+	0.0181333i
$191$	6.08040	−	10.5316i	0.439963	−	0.762038i	−0.557723	−	0.830027i	$-0.688325\pi$
$191$	6.08040	−	10.5316i	0.439963	−	0.762038i	0.997686	+	0.0679893i	$0.0216584\pi$
$192$	−12.3211	+	6.33958i	−0.889200	+	0.457519i
$193$	7.01439	+	12.1493i	0.504907	+	0.874525i	0.999984	+	0.00567551i	$0.00180658\pi$
$193$	7.01439	+	12.1493i	0.504907	+	0.874525i	−0.495077	+	0.868849i	$0.664860\pi$
$194$	8.70560	+	13.8404i	0.625026	+	0.993680i
$195$	−11.0100	−	3.11394i	−0.788443	−	0.222994i
$196$	−2.00557	+	4.17469i	−0.143255	+	0.298192i
$197$			7.21555i			0.514086i	0.966400	+	0.257043i	$0.0827483\pi$
$197$			7.21555i			0.514086i	−0.966400	+	0.257043i	$0.917252\pi$
$198$	10.6904	+	6.02736i	0.759731	+	0.428346i
$199$		−	8.63093i		−	0.611830i	−0.952059	−	0.305915i	$-0.901038\pi$
$199$		−	8.63093i		−	0.611830i	0.952059	−	0.305915i	$-0.0989624\pi$
$200$	1.12739	−	2.59403i	0.0797186	−	0.183426i
$201$	−11.7542	+	11.4335i	−0.829078	+	0.806458i
$202$	13.0809	−	8.22791i	0.920370	−	0.578914i
$203$	7.49233	+	12.9771i	0.525858	+	0.910814i
$204$	−11.6686	+	13.2110i	−0.816967	+	0.924956i
$205$	2.41795	−	4.18802i	0.168877	−	0.292504i
$206$	0.0340198	+	0.897846i	0.00237027	+	0.0625559i
$207$	−7.39690	−	4.54789i	−0.514120	−	0.316100i
$208$	26.1213	−	3.98764i	1.81119	−	0.276493i
$209$	−11.6936	−	6.75129i	−0.808862	−	0.466997i
$210$	1.24862	−	5.15234i	0.0861629	−	0.355545i
$211$	16.1103	−	9.30130i	1.10908	−	0.640328i	0.170490	−	0.985359i	$-0.445465\pi$
$211$	16.1103	−	9.30130i	1.10908	−	0.640328i	0.938591	+	0.345031i	$0.112132\pi$
$212$	−5.30498	+	3.62422i	−0.364348	+	0.248913i
$213$	−1.97518	+	0.500076i	−0.135337	+	0.0342647i
$214$	12.4156	−	23.5183i	0.848712	−	1.60768i
$215$	4.40481			0.300406
$216$	−9.61635	+	11.1142i	−0.654310	+	0.756226i
$217$	11.2933			0.766639
$218$	2.23852	−	4.24033i	0.151612	−	0.287192i
$219$	−3.90450	+	0.988543i	−0.263841	+	0.0667995i
$220$	4.77695	−	3.26348i	0.322062	−	0.220024i
$221$	29.1098	−	16.8066i	1.95814	−	1.13053i
$222$	2.64426	−	10.9113i	0.177471	−	0.732321i
$223$	−10.6900	−	6.17187i	−0.715854	−	0.413299i	0.0973706	−	0.995248i	$-0.468957\pi$
$223$	−10.6900	−	6.17187i	−0.715854	−	0.413299i	−0.813225	+	0.581949i	$0.802290\pi$
$224$	2.30457	+	12.0244i	0.153980	+	0.803413i
$225$	0.0829664	−	2.99885i	0.00553110	−	0.199924i
$226$	−0.0534506	−	1.41066i	−0.00355548	−	0.0938359i
$227$	0.372024	−	0.644365i	0.0246921	−	0.0427680i	−0.853415	−	0.521232i	$-0.825473\pi$
$227$	0.372024	−	0.644365i	0.0246921	−	0.0427680i	0.878107	+	0.478464i	$0.158806\pi$
$228$	10.7046	−	12.1196i	0.708929	−	0.802637i
$229$	13.0783	+	22.6523i	0.864238	+	1.49690i	0.867801	+	0.496911i	$0.165532\pi$
$229$	13.0783	+	22.6523i	0.864238	+	1.49690i	−0.00356308	+	0.999994i	$0.501134\pi$
$230$	−3.46486	+	2.17940i	−0.228466	+	0.143705i
$231$	7.77295	−	7.56087i	0.511422	−	0.497469i
$232$	−17.9598	−	7.80549i	−1.17912	−	0.512455i
$233$		−	25.8264i		−	1.69195i	−0.533226	−	0.845973i	$-0.679021\pi$
$233$		−	25.8264i		−	1.69195i	0.533226	−	0.845973i	$-0.320979\pi$
$234$	24.1275	−	14.2606i	1.57727	−	0.932242i
$235$			0.0193847i			0.00126452i
$236$	6.97444	−	14.5176i	0.453997	−	0.945018i
$237$	−28.2870	−	8.00034i	−1.83744	−	0.519678i
$238$	8.29224	+	13.1832i	0.537506	+	0.854540i
$239$	−4.11600	−	7.12913i	−0.266242	−	0.461145i	0.701646	−	0.712526i	$-0.252449\pi$
$239$	−4.11600	−	7.12913i	−0.266242	−	0.461145i	−0.967888	+	0.251381i	$0.919115\pi$
$240$	2.69452	+	6.38276i	0.173930	+	0.412005i
$241$	0.0705544	−	0.122204i	0.00454481	−	0.00787184i	−0.863744	−	0.503931i	$-0.831887\pi$
$241$	0.0705544	−	0.122204i	0.00454481	−	0.00787184i	0.868289	+	0.496059i	$0.165220\pi$
$242$	−3.72040	+	0.140967i	−0.239156	+	0.00906173i
$243$	−5.06529	+	14.7426i	−0.324939	+	0.945735i
$244$	1.28191	−	0.0972841i	0.0820661	−	0.00622797i
$245$	2.00548	+	1.15786i	0.128125	+	0.0739731i
$246$	3.34002	+	11.3649i	0.212952	+	0.724597i
$247$	−26.7048	+	15.4180i	−1.69919	+	0.981026i
$248$	−11.8623	+	8.78076i	−0.753256	+	0.557579i
$249$	0.896202	−	3.16872i	0.0567945	−	0.200810i
$250$	−1.25064	−	0.660227i	−0.0790974	−	0.0417564i
$251$	9.50499			0.599950			0.299975	−	0.953947i	$-0.403022\pi$
$251$	9.50499			0.599950			0.299975	+	0.953947i	$0.403022\pi$
$252$	7.02602	+	10.9210i	0.442598	+	0.687960i
$253$	−8.37244			−0.526371
$254$	10.9862	+	5.79976i	0.689338	+	0.363909i
$255$	6.14507	+	6.31744i	0.384820	+	0.395613i
$256$	−11.7699	−	10.8384i	−0.735617	−	0.677398i
$257$	22.5033	−	12.9923i	1.40372	−	0.810436i	0.408945	−	0.912559i	$-0.365897\pi$
$257$	22.5033	−	12.9923i	1.40372	−	0.810436i	0.994772	+	0.102123i	$0.0325636\pi$
$258$	−7.44374	+	7.81056i	−0.463427	+	0.486264i
$259$	−8.59106	−	4.96005i	−0.533822	−	0.308202i
$260$	−0.999777	−	13.1741i	−0.0620036	−	0.817022i
$261$	−20.7626	−	0.574418i	−1.28517	−	0.0355556i
$262$	−19.9642	+	0.756450i	−1.23339	+	0.0467336i
$263$	13.4383	−	23.2758i	0.828640	−	1.43525i	−0.0704654	−	0.997514i	$-0.522448\pi$
$263$	13.4383	−	23.2758i	0.828640	−	1.43525i	0.899105	−	0.437732i	$-0.144218\pi$
$264$	−2.28584	+	13.9854i	−0.140684	+	0.860744i
$265$	1.60620	+	2.78201i	0.0986678	+	0.170898i
$266$	−7.60715	−	12.0940i	−0.466425	−	0.741533i
$267$	1.58416	+	6.25704i	0.0969491	+	0.382925i
$268$	−17.0672	−	8.19925i	−1.04254	−	0.500849i
$269$		−	16.4030i		−	1.00011i	−0.865995	−	0.500053i	$-0.833314\pi$
$269$		−	16.4030i		−	1.00011i	0.865995	−	0.500053i	$-0.166686\pi$
$270$	5.17733	+	5.21491i	0.315082	+	0.317369i
$271$			16.0484i			0.974873i	0.873158	+	0.487437i	$0.162068\pi$
$271$			16.0484i			0.974873i	−0.873158	+	0.487437i	$0.837932\pi$
$272$	−18.9602	−	7.40003i	−1.14963	−	0.448692i
$273$	−6.07796	−	24.0064i	−0.367855	−	1.45294i
$274$	−18.1989	+	11.4471i	−1.09943	+	0.691544i
$275$	−1.44632	−	2.50510i	−0.0872165	−	0.151063i
$276$	1.99081	−	9.82683i	0.119833	−	0.591506i
$277$	12.1659	−	21.0720i	0.730978	−	1.26609i	−0.225488	−	0.974246i	$-0.572398\pi$
$277$	12.1659	−	21.0720i	0.730978	−	1.26609i	0.956466	−	0.291845i	$-0.0942691\pi$
$278$	−0.136049	−	3.59060i	−0.00815969	−	0.215350i
$279$	−8.19884	+	13.3350i	−0.490852	+	0.798344i
$280$	6.08215	−	0.694023i	0.363478	−	0.0414758i
$281$	9.04166	+	5.22020i	0.539380	+	0.311411i	0.744828	−	0.667257i	$-0.232532\pi$
$281$	9.04166	+	5.22020i	0.539380	+	0.311411i	−0.205448	+	0.978668i	$0.565865\pi$
$282$	−0.0343728	−	0.0327585i	−0.00204687	−	0.00195074i
$283$	12.8943	−	7.44455i	0.766489	−	0.442533i	−0.0651317	−	0.997877i	$-0.520747\pi$
$283$	12.8943	−	7.44455i	0.766489	−	0.442533i	0.831621	+	0.555344i	$0.187413\pi$
$284$	−1.32716	−	1.94264i	−0.0787524	−	0.115274i
$285$	−5.63738	−	5.79550i	−0.333930	−	0.343296i
$286$	12.6161	−	23.8982i	0.746006	−	1.41313i
$287$	10.4664			0.617815
$288$	−15.8713	−	6.00840i	−0.935227	−	0.354048i
$289$	−8.89065			−0.522979
$290$	−4.57108	+	8.65881i	−0.268423	+	0.508463i
$291$	−5.44994	+	19.2695i	−0.319481	+	1.12960i
$292$	−2.62351	−	3.84018i	−0.153529	−	0.224729i
$293$	−22.6187	+	13.0589i	−1.32140	+	0.762911i	−0.983952	−	0.178433i	$-0.942897\pi$
$293$	−22.6187	+	13.0589i	−1.32140	+	0.762911i	−0.337449	+	0.941344i	$0.609564\pi$
$294$	−5.44219	+	1.59941i	−0.317395	+	0.0932792i
$295$	−6.97412	−	4.02651i	−0.406049	−	0.234432i
$296$	12.8804	−	1.46976i	0.748660	−	0.0854283i
$297$	3.28469	+	14.6673i	0.190597	+	0.851084i
$298$	0.370043	+	9.76614i	0.0214360	+	0.565737i
$299$	−9.56014	+	16.5587i	−0.552877	+	0.957612i
$300$	3.28418	−	1.10190i	0.189612	−	0.0636181i
$301$	4.76671	+	8.25618i	0.274748	+	0.475878i
$302$	25.5130	−	16.0477i	1.46811	−	0.923440i
$303$	18.2121	+	5.15090i	1.04626	+	0.295911i
$304$	17.3938	+	6.78865i	0.997601	+	0.389356i
$305$		−	0.642800i		−	0.0368066i
$306$	−21.5866	+	0.220478i	−1.23403	+	0.0126039i
$307$		−	28.5542i		−	1.62967i	−0.579690	−	0.814837i	$-0.696826\pi$
$307$		−	28.5542i		−	1.62967i	0.579690	−	0.814837i	$-0.303174\pi$
$308$	11.2863	+	5.42209i	0.643099	+	0.308952i
$309$	−0.788802	+	0.767281i	−0.0448734	+	0.0436491i
$310$	3.92897	+	6.24637i	0.223150	+	0.354770i
$311$	−0.0440224	−	0.0762490i	−0.00249628	−	0.00432369i	0.864775	−	0.502160i	$-0.167461\pi$
$311$	−0.0440224	−	0.0762490i	−0.00249628	−	0.00432369i	−0.867271	+	0.497837i	$0.834128\pi$
$312$	25.0497	+	20.4902i	1.41816	+	1.16003i
$313$	−7.60804	+	13.1775i	−0.430032	+	0.744837i	−0.996876	−	0.0789885i	$-0.974831\pi$
$313$	−7.60804	+	13.1775i	−0.430032	+	0.744837i	0.566844	+	0.823825i	$0.308164\pi$
$314$	16.4916	−	0.624873i	0.930675	−	0.0352636i
$315$	5.71070	−	3.08973i	0.321761	−	0.174086i
$316$	−2.56863	−	33.8469i	−0.144497	−	1.90404i
$317$	6.20554	+	3.58277i	0.348538	+	0.201228i	0.664041	−	0.747696i	$-0.268840\pi$
$317$	6.20554	+	3.58277i	0.348538	+	0.201228i	−0.315503	+	0.948925i	$0.602173\pi$
$318$	−7.64736	−	1.85326i	−0.428843	−	0.103926i
$319$	−17.3441	+	10.0136i	−0.971082	+	0.560655i
$320$	−5.84897	+	5.45798i	−0.326967	+	0.305110i
$321$	31.5750	−	7.99417i	1.76234	−	0.446191i
$322$	−7.83449	−	4.13591i	−0.436599	−	0.230486i
$323$	23.7516			1.32158
$324$	−17.9962	+	0.367652i	−0.999791	+	0.0204251i
$325$	−6.60598			−0.366434
$326$	−0.547788	−	0.289183i	−0.0303392	−	0.0160164i
$327$	5.69295	−	1.44134i	0.314821	−	0.0797065i
$328$	−10.9938	+	8.13787i	−0.607030	+	0.449338i
$329$	−0.0363339	+	0.0209774i	−0.00200315	+	0.00115652i
$330$	6.88618	+	1.66880i	0.379072	+	0.0918643i
$331$	0.709837	+	0.409824i	0.0390161	+	0.0225260i	0.519381	−	0.854543i	$-0.326162\pi$
$331$	0.709837	+	0.409824i	0.0390161	+	0.0225260i	−0.480365	+	0.877069i	$0.659496\pi$
$332$	3.79155	−	0.287740i	0.208088	−	0.0157918i
$333$	12.0938	−	6.54325i	0.662736	−	0.358568i
$334$	5.88681	−	0.223054i	0.322112	−	0.0122050i
$335$	−4.73363	+	8.19888i	−0.258626	+	0.447953i
$336$	−9.04765	+	11.9576i	−0.493590	+	0.652343i
$337$	1.53390	+	2.65680i	0.0835571	+	0.144725i	0.904775	−	0.425889i	$-0.140039\pi$
$337$	1.53390	+	2.65680i	0.0835571	+	0.144725i	−0.821218	+	0.570614i	$0.806705\pi$
$338$	−23.0703	−	36.6777i	−1.25486	−	1.99500i
$339$	1.23934	−	1.20552i	0.0673115	−	0.0654750i
$340$	−4.40678	+	9.17294i	−0.238991	+	0.497473i
$341$			15.0937i			0.817367i
$342$	19.8032	−	0.202263i	1.07083	−	0.0109371i
$343$			20.1622i			1.08866i
$344$	−11.4262	−	4.96594i	−0.616060	−	0.267746i
$345$	−4.82400	−	1.36436i	−0.259716	−	0.0734548i
$346$	−10.7173	+	6.74118i	−0.576165	+	0.362408i
$347$	11.1564	+	19.3234i	0.598906	+	1.03734i	0.992983	+	0.118258i	$0.0377311\pi$
$347$	11.1564	+	19.3234i	0.598906	+	1.03734i	−0.394077	+	0.919078i	$0.628936\pi$
$348$	−7.62898	−	22.7380i	−0.408956	−	1.21888i
$349$	5.01965	−	8.69429i	0.268696	−	0.465395i	−0.699829	−	0.714310i	$-0.746741\pi$
$349$	5.01965	−	8.69429i	0.268696	−	0.465395i	0.968525	+	0.248915i	$0.0800740\pi$
$350$	−0.115892	−	3.05861i	−0.00619469	−	0.163490i
$351$	32.7590	+	10.2517i	1.74855	+	0.547195i
$352$	−16.0708	+	3.08009i	−0.856575	+	0.164169i
$353$	−11.0265	−	6.36616i	−0.586882	−	0.338836i	0.176982	−	0.984214i	$-0.443367\pi$
$353$	−11.0265	−	6.36616i	−0.586882	−	0.338836i	−0.763864	+	0.645378i	$0.776700\pi$
$354$	18.9254	−	5.56199i	1.00587	−	0.295617i
$355$	−1.01875	+	0.588175i	−0.0540696	+	0.0312171i
$356$	−6.15397	+	4.20423i	−0.326160	+	0.222824i
$357$	−5.19117	+	18.3545i	−0.274746	+	0.971424i
$358$	6.94978	−	13.1647i	0.367307	−	0.695774i
$359$	5.93304			0.313134			0.156567	−	0.987667i	$-0.449957\pi$
$359$	5.93304			0.313134			0.156567	+	0.987667i	$0.449957\pi$
$360$	−3.59610	+	7.68558i	−0.189531	+	0.405065i
$361$	−2.78932			−0.146806
$362$	6.27780	−	11.8918i	0.329954	−	0.625017i
$363$	−3.17938	−	3.26855i	−0.166874	−	0.171555i
$364$	23.6110	−	16.1304i	1.23755	−	0.845462i
$365$	−2.01385	+	1.16270i	−0.105410	+	0.0608582i
$366$	1.13981	+	1.08627i	0.0595786	+	0.0567805i
$367$	23.0370	+	13.3004i	1.20252	+	0.694277i	0.961115	−	0.276147i	$-0.0890576\pi$
$367$	23.0370	+	13.3004i	1.20252	+	0.694277i	0.241407	+	0.970424i	$0.422391\pi$
$368$	11.4450	−	1.74717i	0.596610	−	0.0910777i
$369$	−7.59855	+	12.3586i	−0.395565	+	0.643365i
$370$	−0.245430	−	6.47736i	−0.0127593	−	0.336742i
$371$	−3.47632	+	6.02116i	−0.180482	+	0.312603i
$372$	−17.7156	−	3.58900i	−0.918511	−	0.186081i
$373$	13.2294	+	22.9141i	0.684995	+	1.18645i	0.973438	+	0.228949i	$0.0735288\pi$
$373$	13.2294	+	22.9141i	0.684995	+	1.18645i	−0.288444	+	0.957497i	$0.593138\pi$
$374$	−17.6195	+	11.0827i	−0.911085	+	0.573073i
$375$	−0.425108	−	1.67907i	−0.0219525	−	0.0867069i
$376$	0.0218542	−	0.0502846i	0.00112704	−	0.00259323i
$377$			45.7365i			2.35555i
$378$	−4.17190	+	15.3475i	−0.214579	+	0.789391i
$379$		−	21.3357i		−	1.09594i	−0.836497	−	0.547972i	$-0.815400\pi$
$379$		−	21.3357i		−	1.09594i	0.836497	−	0.547972i	$-0.184600\pi$
$380$	4.04271	−	8.41509i	0.207386	−	0.431685i
$381$	3.73436	+	14.7498i	0.191317	+	0.755655i
$382$	9.15675	+	14.5576i	0.468500	+	0.744833i
$383$	−1.57676	−	2.73103i	−0.0805688	−	0.139549i	0.822926	−	0.568149i	$-0.192340\pi$
$383$	−1.57676	−	2.73103i	−0.0805688	−	0.139549i	−0.903494	+	0.428600i	$0.859007\pi$
$384$	0.206203	−	19.5948i	0.0105227	−	0.999945i
$385$	3.13030	−	5.42184i	0.159535	−	0.276323i
$386$	−19.8255	+	0.751195i	−1.00909	+	0.0382348i
$387$	−13.2094	−	0.365451i	−0.671470	−	0.0185769i
$388$	−23.0570	+	1.74979i	−1.17054	+	0.0888321i
$389$	12.9948	+	7.50253i	0.658860	+	0.380393i	0.791843	−	0.610725i	$-0.209122\pi$
$389$	12.9948	+	7.50253i	0.658860	+	0.380393i	−0.132982	+	0.991118i	$0.542455\pi$
$390$	11.1635	−	11.7137i	0.565287	−	0.593144i
$391$	12.7544	−	7.36374i	0.645017	−	0.372400i
$392$	−3.89690	−	5.26448i	−0.196823	−	0.265897i
$393$	−17.0610	−	17.5395i	−0.860611	−	0.884750i
$394$	−9.02405	−	4.76390i	−0.454625	−	0.240002i
$395$	−16.9721			−0.853960
$396$	−14.5961	+	9.39038i	−0.733483	+	0.471884i
$397$	−10.0474			−0.504266			−0.252133	−	0.967693i	$-0.581132\pi$
$397$	−10.0474			−0.504266			−0.252133	+	0.967693i	$0.581132\pi$
$398$	10.7942	+	5.69837i	0.541064	+	0.285634i
$399$	4.76229	−	16.8381i	0.238412	−	0.842960i
$400$	2.49986	+	3.12261i	0.124993	+	0.156130i
$401$	−6.85153	+	3.95573i	−0.342149	+	0.197540i	−0.661222	−	0.750190i	$-0.729962\pi$
$401$	−6.85153	+	3.95573i	−0.342149	+	0.197540i	0.319073	+	0.947730i	$0.396629\pi$
$402$	−6.53876	−	22.2490i	−0.326124	−	1.10968i
$403$	29.8516	+	17.2348i	1.48701	+	0.858527i
$404$	1.65378	+	21.7918i	0.0822784	+	1.08418i
$405$	−0.497608	+	8.98623i	−0.0247264	+	0.446530i
$406$	−21.1763	+	0.802379i	−1.05096	+	0.0398214i
$407$	6.62918	−	11.4821i	0.328596	−	0.569145i
$408$	−8.81829	−	23.3155i	−0.436570	−	1.15429i
$409$	−13.5824	−	23.5255i	−0.671608	−	1.16326i	−0.977448	−	0.211177i	$-0.932270\pi$
$409$	−13.5824	−	23.5255i	−0.671608	−	1.16326i	0.305840	−	0.952083i	$-0.401063\pi$
$410$	3.64131	+	5.78903i	0.179831	+	0.285900i
$411$	−25.3377	−	7.16619i	−1.24981	−	0.353482i
$412$	−1.14534	−	0.550236i	−0.0564270	−	0.0271082i
$413$		−	17.4293i		−	0.857640i
$414$	10.5714	−	6.24822i	0.519556	−	0.307083i
$415$		−	1.90123i		−	0.0933275i
$416$	−12.2589	+	35.3011i	−0.601041	+	1.73078i
$417$	3.15452	−	3.06845i	0.154477	−	0.150263i
$418$	16.1639	−	10.1671i	0.790600	−	0.497288i
$419$	−4.28527	−	7.42230i	−0.209349	−	0.362603i	0.742161	−	0.670222i	$-0.233801\pi$
$419$	−4.28527	−	7.42230i	−0.209349	−	0.362603i	−0.951510	+	0.307619i	$0.900468\pi$
$420$	5.61935	+	4.96329i	0.274196	+	0.242184i
$421$	3.41504	−	5.91502i	0.166439	−	0.288280i	−0.770727	−	0.637166i	$-0.780107\pi$
$421$	3.41504	−	5.91502i	0.166439	−	0.288280i	0.937165	+	0.348886i	$0.113440\pi$
$422$	0.996108	+	26.2892i	0.0484898	+	1.27974i
$423$	0.00160828	−	0.0581320i	7.81974e−5	−	0.00282647i
$424$	−1.03010	−	9.02743i	−0.0500263	−	0.438411i
$425$	4.40658	+	2.54414i	0.213751	+	0.123409i
$426$	0.678649	−	2.80040i	0.0328807	−	0.135680i
$427$	1.20483	−	0.695612i	0.0583060	−	0.0336630i
$428$	21.2158	+	31.0549i	1.02551	+	1.50109i
$429$	32.0850	−	8.12329i	1.54908	−	0.392196i
$430$	−2.90817	+	5.50883i	−0.140245	+	0.265659i
$431$	−26.5552			−1.27912			−0.639559	−	0.768742i	$-0.720883\pi$
$431$	−26.5552			−1.27912			−0.639559	+	0.768742i	$0.720883\pi$
$432$	−7.55090	−	19.3645i	−0.363293	−	0.931675i
$433$	−12.4714			−0.599339			−0.299669	−	0.954043i	$-0.596876\pi$
$433$	−12.4714			−0.599339			−0.299669	+	0.954043i	$0.596876\pi$
$434$	−7.45614	+	14.1238i	−0.357906	+	0.677966i
$435$	−11.6251	+	2.94324i	−0.557379	+	0.141117i
$436$	3.82520	+	5.59917i	0.183194	+	0.268151i
$437$	−11.7006	+	6.75537i	−0.559718	+	0.323153i
$438$	1.34154	−	5.53578i	0.0641014	−	0.264510i
$439$	−12.8412	−	7.41389i	−0.612879	−	0.353846i	0.161212	−	0.986920i	$-0.448460\pi$
$439$	−12.8412	−	7.41389i	−0.612879	−	0.353846i	−0.774091	+	0.633074i	$0.781793\pi$
$440$	0.927573	+	8.12888i	0.0442203	+	0.387529i
$441$	−5.91806	−	3.63865i	−0.281813	−	0.173269i
$442$	1.79987	+	47.5020i	0.0856111	+	2.25944i
$443$	−19.7625	+	34.2297i	−0.938945	+	1.62630i	−0.171501	+	0.985184i	$0.554862\pi$
$443$	−19.7625	+	34.2297i	−0.938945	+	1.62630i	−0.767444	+	0.641117i	$0.778472\pi$
$444$	11.9003	+	10.5110i	0.564765	+	0.498829i
$445$	1.86324	+	3.22723i	0.0883262	+	0.152986i
$446$	14.7766	−	9.29449i	0.699692	−	0.440107i
$447$	−8.58003	+	8.34594i	−0.405822	+	0.394749i
$448$	−16.5597	−	5.05664i	−0.782373	−	0.238904i
$449$		−	22.8395i		−	1.07786i	−0.842349	−	0.538932i	$-0.818828\pi$
$449$		−	22.8395i		−	1.07786i	0.842349	−	0.538932i	$-0.181172\pi$
$450$	3.69571	+	2.08368i	0.174217	+	0.0982258i
$451$			13.9886i			0.658695i
$452$	1.79952	+	0.864510i	0.0846424	+	0.0406631i
$453$	35.5209	+	10.0463i	1.66892	+	0.472016i
$454$	0.560248	+	0.890696i	0.0262938	+	0.0418024i
$455$	−7.14872	−	12.3820i	−0.335137	−	0.580475i
$456$	8.08974	+	21.3892i	0.378837	+	1.00164i
$457$	−0.416241	+	0.720950i	−0.0194709	+	0.0337246i	−0.875597	−	0.483043i	$-0.839532\pi$
$457$	−0.416241	+	0.720950i	−0.0194709	+	0.0337246i	0.856126	+	0.516768i	$0.172865\pi$
$458$	−36.9645	+	1.40060i	−1.72724	+	0.0654457i
$459$	−17.9040	−	19.4549i	−0.835689	−	0.908077i
$460$	−0.438050	−	5.77218i	−0.0204242	−	0.269129i
$461$	−30.9887	−	17.8913i	−1.44329	−	0.833281i	−0.445218	−	0.895422i	$-0.646874\pi$
$461$	−30.9887	−	17.8913i	−1.44329	−	0.833281i	−0.998067	+	0.0621408i	$0.980207\pi$
$462$	4.32402	+	14.7130i	0.201172	+	0.684513i
$463$	−7.21179	+	4.16373i	−0.335160	+	0.193505i	−0.658130	−	0.752904i	$-0.728652\pi$
$463$	−7.21179	+	4.16373i	−0.335160	+	0.193505i	0.322969	+	0.946409i	$0.395319\pi$
$464$	21.6194	−	17.3078i	1.00365	−	0.803495i
$465$	−2.45964	+	8.69661i	−0.114063	+	0.403296i
$466$	32.2996	+	17.0513i	1.49625	+	0.789886i
$467$	16.8607			0.780220			0.390110	−	0.920768i	$-0.372437\pi$
$467$	16.8607			0.780220			0.390110	+	0.920768i	$0.372437\pi$
$468$	1.90518	+	39.5901i	0.0880669	+	1.83005i
$469$	−20.4901			−0.946147
$470$	−0.0242433	−	0.0127983i	−0.00111826	−	0.000590343i
$471$	14.0934	+	14.4887i	0.649388	+	0.667603i
$472$	13.5516	+	18.3074i	0.623764	+	0.842668i
$473$	−11.0345	+	6.37077i	−0.507367	+	0.292929i
$474$	28.6814	−	30.0948i	1.31738	−	1.38230i
$475$	−4.04252	−	2.33395i	−0.185484	−	0.107089i
$476$	−21.9622	+	1.66671i	−1.00664	+	0.0763933i
$477$	−4.58593	−	8.47611i	−0.209975	−	0.388094i
$478$	11.6335	−	0.440797i	0.532102	−	0.0201616i
$479$	2.64691	−	4.58458i	0.120940	−	0.209475i	−0.799198	−	0.601067i	$-0.794742\pi$
$479$	2.64691	−	4.58458i	0.120940	−	0.209475i	0.920139	+	0.391593i	$0.128076\pi$
$480$	−9.76152	−	0.844197i	−0.445551	−	0.0385322i
$481$	−15.1392	−	26.2218i	−0.690287	−	1.19561i
$482$	0.106251	+	0.168920i	0.00483960	+	0.00769411i
$483$	−2.66304	−	10.5184i	−0.121173	−	0.478602i
$484$	2.28001	−	4.74595i	0.103637	−	0.215725i
$485$			11.5616i			0.524987i
$486$	−15.0934	−	16.0683i	−0.684650	−	0.728872i
$487$			19.8270i			0.898449i	0.893419	+	0.449225i	$0.148300\pi$
$487$			19.8270i			0.898449i	−0.893419	+	0.449225i	$0.851700\pi$
$488$	−0.724686	+	1.66744i	−0.0328050	+	0.0754815i
$489$	−0.186200	−	0.735444i	−0.00842026	−	0.0332579i
$490$	−2.77214	+	1.74368i	−0.125232	+	0.0787713i
$491$	−14.2239	−	24.6365i	−0.641916	−	1.11183i	−0.985005	−	0.172528i	$-0.944807\pi$
$491$	−14.2239	−	24.6365i	−0.641916	−	1.11183i	0.343089	−	0.939303i	$-0.388527\pi$
$492$	−16.4185	−	3.32622i	−0.740205	−	0.149958i
$493$	17.6144	−	30.5090i	0.793311	−	1.37406i
$494$	−1.65117	−	43.5775i	−0.0742896	−	1.96065i
$495$	4.12947	+	7.63243i	0.185606	+	0.343052i
$496$	−3.14977	−	20.6327i	−0.141429	−	0.926438i
$497$	−2.20490	−	1.27300i	−0.0989031	−	0.0571018i
$498$	3.37123	+	3.21290i	0.151069	+	0.143974i
$499$	−4.89300	+	2.82497i	−0.219041	+	0.126463i	−0.605506	−	0.795841i	$-0.707029\pi$
$499$	−4.89300	+	2.82497i	−0.219041	+	0.126463i	0.386465	+	0.922304i	$0.373696\pi$
$500$	1.65141	−	1.12820i	0.0738534	−	0.0504547i
$501$	5.03075	+	5.17185i	0.224757	+	0.231061i
$502$	−6.27545	+	11.8873i	−0.280087	+	0.530557i
$503$	32.7730			1.46128			0.730638	−	0.682765i	$-0.239223\pi$
$503$	32.7730			1.46128			0.730638	+	0.682765i	$0.239223\pi$
$504$	−18.2970	+	1.57666i	−0.815015	+	0.0702300i
$505$	10.9272			0.486256
$506$	5.52771	−	10.4709i	0.245737	−	0.465489i
$507$	14.4426	−	51.0652i	0.641420	−	2.26788i
$508$	−14.5068	+	9.91068i	−0.643636	+	0.439715i
$509$	−10.8656	+	6.27327i	−0.481610	+	0.278058i	−0.721087	−	0.692844i	$-0.756357\pi$
$509$	−10.8656	+	6.27327i	−0.481610	+	0.278058i	0.239477	+	0.970902i	$0.423024\pi$
$510$	−11.9580	+	3.51433i	−0.529508	+	0.155617i
$511$	−4.35861	−	2.51644i	−0.192813	−	0.111321i
$512$	21.3257	−	7.56409i	0.942471	−	0.334289i
$513$	16.4248	+	17.8476i	0.725175	+	0.787990i
$514$	1.39139	+	36.7214i	0.0613715	+	1.61971i
$515$	−0.317664	+	0.550211i	−0.0139980	+	0.0242452i
$516$	−4.85365	−	14.4662i	−0.213670	−	0.636838i
$517$	−0.0280366	−	0.0485608i	−0.00123305	−	0.00213570i
$518$	11.8753	−	7.46956i	0.521770	−	0.328194i
$519$	−14.9213	−	4.22016i	−0.654974	−	0.185245i
$520$	17.1361	+	7.44752i	0.751468	+	0.326595i
$521$		−	11.7475i		−	0.514665i	−0.966323	−	0.257333i	$-0.917156\pi$
$521$		−	11.7475i		−	0.514665i	0.966323	−	0.257333i	$-0.0828436\pi$
$522$	14.4264	−	25.5872i	0.631426	−	1.11992i
$523$		−	20.5196i		−	0.897261i	−0.893717	−	0.448630i	$-0.851912\pi$
$523$		−	20.5196i		−	0.897261i	0.893717	−	0.448630i	$-0.148088\pi$
$524$	12.2348	−	25.4674i	0.534481	−	1.11255i
$525$	2.68714	−	2.61383i	0.117276	−	0.114077i
$526$	20.2373	+	32.1738i	0.882389	+	1.40284i
$527$	−13.2752	−	22.9933i	−0.578277	−	1.00160i
$528$	−15.9816	−	12.0923i	−0.695508	−	0.526251i
$529$	7.31125	−	12.6635i	0.317881	−	0.550585i
$530$	−4.53975	+	0.172013i	−0.197194	+	0.00747177i
$531$	20.5803	+	12.6535i	0.893109	+	0.549116i
$532$	20.1477	−	1.52901i	0.873515	−	0.0662908i
$533$	27.6660	+	15.9730i	1.19835	+	0.691865i
$534$	−8.87121	−	2.14985i	−0.383895	−	0.0930332i
$535$	16.2856	−	9.40251i	0.704089	−	0.406506i
$536$	21.5225	−	15.9315i	0.929631	−	0.688136i
$537$	17.6745	−	4.47484i	0.762711	−	0.193104i
$538$	20.5142	+	10.8297i	0.884429	+	0.466900i
$539$	−6.69857			−0.288528
$540$	−9.94019	+	3.03195i	−0.427757	+	0.130474i
$541$	19.0464			0.818871			0.409435	−	0.912339i	$-0.365726\pi$
$541$	19.0464			0.818871			0.409435	+	0.912339i	$0.365726\pi$
$542$	−20.0708	−	10.5956i	−0.862116	−	0.455121i
$543$	15.9655	−	4.04216i	0.685147	−	0.173466i
$544$	21.7728	−	18.8267i	0.933502	−	0.807189i
$545$	2.93629	−	1.69527i	0.125777	−	0.0726172i
$546$	34.0363	+	8.24835i	1.45662	+	0.352997i
$547$	−21.7291	−	12.5453i	−0.929071	−	0.536399i	−0.0425534	−	0.999094i	$-0.513549\pi$
$547$	−21.7291	−	12.5453i	−0.929071	−	0.536399i	−0.886518	+	0.462695i	$0.846883\pi$
$548$	−2.30082	−	30.3179i	−0.0982861	−	1.29512i
$549$	−0.0533308	+	1.92766i	−0.00227610	+	0.0822706i
$550$	4.08788	−	0.154892i	0.174308	−	0.00660460i
$551$	−16.1591	+	27.9884i	−0.688401	+	1.19235i
$552$	10.9754	+	8.97773i	0.467146	+	0.382118i
$553$	−18.3665	−	31.8118i	−0.781024	−	1.35277i
$554$	18.3212	+	29.1274i	0.778392	+	1.23751i
$555$	5.69068	−	5.53542i	0.241556	−	0.234965i
$556$	4.58037	+	2.20046i	0.194251	+	0.0933204i
$557$		−	4.13922i		−	0.175384i	−0.996148	−	0.0876922i	$-0.972051\pi$
$557$		−	4.13922i		−	0.175384i	0.996148	−	0.0876922i	$-0.0279492\pi$
$558$	−11.2642	−	19.0579i	−0.476850	−	0.806785i
$559$			29.0981i			1.23072i
$560$	−3.14763	+	8.06479i	−0.133011	+	0.340800i
$561$	−24.5311	−	6.93807i	−1.03570	−	0.292926i
$562$	−12.4981	+	7.86134i	−0.527202	+	0.331611i
$563$	−14.9335	−	25.8656i	−0.629372	−	1.09010i	−0.987678	−	0.156500i	$-0.949979\pi$
$563$	−14.9335	−	25.8656i	−0.629372	−	1.09010i	0.358306	−	0.933604i	$-0.383354\pi$
$564$	0.0636630	−	0.0213600i	0.00268069	−	0.000899418i
$565$	0.499103	−	0.864471i	0.0209974	−	0.0363686i
$566$	0.797262	+	21.0413i	0.0335114	+	0.884431i
$567$	−17.3819	+	8.79184i	−0.729970	+	0.369223i
$568$	3.30577	−	0.377215i	0.138707	−	0.0158276i
$569$	−35.2116	−	20.3294i	−1.47615	−	0.852253i	−0.476507	−	0.879170i	$-0.658097\pi$
$569$	−35.2116	−	20.3294i	−1.47615	−	0.852253i	−0.999638	+	0.0269176i	$0.991431\pi$
$570$	10.9700	−	3.22399i	0.459485	−	0.135038i
$571$	34.7953	−	20.0891i	1.45614	−	0.840702i	0.457320	−	0.889302i	$-0.348809\pi$
$571$	34.7953	−	20.0891i	1.45614	−	0.840702i	0.998818	+	0.0486002i	$0.0154760\pi$
$572$	21.5585	+	31.5564i	0.901406	+	1.31944i
$573$	−5.73238	+	20.2681i	−0.239474	+	0.846712i
$574$	−6.91023	+	13.0898i	−0.288427	+	0.546356i
$575$	−2.89439			−0.120704
$576$	17.9930	−	15.8824i	0.749709	−	0.661767i
$577$	33.5865			1.39822			0.699112	−	0.715013i	$-0.253579\pi$
$577$	33.5865			1.39822			0.699112	+	0.715013i	$0.253579\pi$
$578$	5.86984	−	11.1190i	0.244153	−	0.462489i
$579$	−16.9424	−	17.4176i	−0.704104	−	0.723853i
$580$	−7.81110	−	11.4336i	−0.324338	−	0.474752i
$581$	3.56357	−	2.05743i	0.147842	−	0.0853565i
$582$	−20.5010	−	19.5381i	−0.849793	−	0.809882i
$583$	−8.04737	−	4.64615i	−0.333288	−	0.192424i
$584$	6.53479	−	0.745674i	0.270412	−	0.0308562i
$585$	19.8104	+	0.548075i	0.819058	+	0.0226601i
$586$	−1.39853	−	36.9098i	−0.0577726	−	1.52473i
$587$	−18.6898	+	32.3717i	−0.771410	+	1.33612i	0.165380	+	0.986230i	$0.447115\pi$
$587$	−18.6898	+	32.3717i	−0.771410	+	1.33612i	−0.936790	+	0.349892i	$0.886218\pi$
$588$	1.59280	−	7.86219i	0.0656858	−	0.324231i
$589$	12.1784	+	21.0937i	0.501803	+	0.869149i
$590$	9.64022	−	6.06370i	0.396881	−	0.249639i
$591$	−3.06739	−	12.1154i	−0.126176	−	0.498362i
$592$	−6.66587	+	17.0792i	−0.273965	+	0.701949i
$593$			11.3789i			0.467275i	0.972324	+	0.233638i	$0.0750630\pi$
$593$			11.3789i			0.467275i	−0.972324	+	0.233638i	$0.924937\pi$
$594$	−20.5122	−	5.57580i	−0.841625	−	0.228778i
$595$			11.0127i			0.451475i
$596$	−12.4582	−	5.98508i	−0.510309	−	0.245158i
$597$	3.66908	+	14.4920i	0.150165	+	0.593116i
$598$	−14.3971	−	22.8888i	−0.588739	−	0.935991i
$599$	−1.12135	−	1.94223i	−0.0458170	−	0.0793574i	0.842207	−	0.539154i	$-0.181256\pi$
$599$	−1.12135	−	1.94223i	−0.0458170	−	0.0793574i	−0.888024	+	0.459796i	$0.847922\pi$
$600$	−0.790226	+	4.83483i	−0.0322608	+	0.197381i
$601$	−8.67140	+	15.0193i	−0.353714	+	0.612650i	−0.986897	−	0.161352i	$-0.948415\pi$
$601$	−8.67140	+	15.0193i	−0.353714	+	0.612650i	0.633183	+	0.774002i	$0.281748\pi$
$602$	−13.4726	+	0.510483i	−0.549103	+	0.0208057i
$603$	14.8757	−	24.1945i	0.605784	−	0.985276i
$604$	3.22552	+	42.5027i	0.131244	+	1.72941i
$605$	−2.27991	−	1.31630i	−0.0926914	−	0.0535154i
$606$	−18.4661	+	19.3761i	−0.750132	+	0.787099i
$607$	−14.7319	+	8.50549i	−0.597951	+	0.345227i	−0.768235	−	0.640168i	$-0.778865\pi$
$607$	−14.7319	+	8.50549i	−0.597951	+	0.345227i	0.170284	+	0.985395i	$0.445531\pi$
$608$	−19.9740	+	17.2713i	−0.810053	+	0.700444i
$609$	−18.0968	−	18.6044i	−0.733321	−	0.753889i
$610$	0.803911	+	0.424394i	0.0325494	+	0.0171832i
$611$	−0.128055			−0.00518056
$612$	13.9763	−	27.1427i	0.564960	−	1.09718i
$613$	6.23696			0.251908			0.125954	−	0.992036i	$-0.459801\pi$
$613$	6.23696			0.251908			0.125954	+	0.992036i	$0.459801\pi$
$614$	35.7110	+	18.8523i	1.44118	+	0.760815i
$615$	−2.27956	+	8.05988i	−0.0919206	+	0.325006i
$616$	−14.2326	+	10.5353i	−0.573449	+	0.424481i
$617$	−7.25716	+	4.18992i	−0.292162	+	0.168680i	−0.638917	−	0.769276i	$-0.720617\pi$
$617$	−7.25716	+	4.18992i	−0.292162	+	0.168680i	0.346754	+	0.937956i	$0.387284\pi$
$618$	−0.438804	−	1.49309i	−0.0176513	−	0.0600607i
$619$	31.5019	+	18.1876i	1.26617	+	0.731021i	0.974260	−	0.225426i	$-0.0723773\pi$
$619$	31.5019	+	18.1876i	1.26617	+	0.731021i	0.291906	+	0.956447i	$0.405711\pi$
$620$	−10.4060	+	0.789706i	−0.417914	+	0.0317154i
$621$	14.3533	+	4.49175i	0.575977	+	0.180248i
$622$	0.124425	−	0.00471451i	0.00498898	−	0.000189034i
$623$	−4.03265	+	6.98476i	−0.161565	+	0.279839i
$624$	−42.1644	+	17.7999i	−1.68793	+	0.712567i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−11.4573	−	18.2151i	−0.457925	−	0.728020i
$627$	22.5044	+	6.36487i	0.898739	+	0.254188i
$628$	−10.1067	+	21.0376i	−0.403301	+	0.839492i
$629$			23.3220i			0.929910i
$630$	0.0937810	+	9.18195i	0.00373632	+	0.365818i
$631$		−	42.3747i		−	1.68691i	−0.537199	−	0.843455i	$-0.680518\pi$
$631$		−	42.3747i		−	1.68691i	0.537199	−	0.843455i	$-0.319482\pi$
$632$	44.0262	+	19.1342i	1.75127	+	0.761118i
$633$	−23.0963	+	22.4662i	−0.917997	+	0.892951i
$634$	−8.57782	+	5.39546i	−0.340669	+	0.214281i
$635$	4.39225	+	7.60760i	0.174301	+	0.301898i
$636$	7.36676	−	8.34052i	0.292111	−	0.330723i
$637$	−7.64881	+	13.2481i	−0.303057	+	0.524910i
$638$	−1.07239	−	28.3025i	−0.0424564	−	1.12051i
$639$	3.10388	−	1.67933i	0.122787	−	0.0664332i
$640$	−2.96432	−	10.9185i	−0.117175	−	0.431590i
$641$	−9.58349	−	5.53303i	−0.378525	−	0.218542i	0.298651	−	0.954362i	$-0.403463\pi$
$641$	−9.58349	−	5.53303i	−0.378525	−	0.218542i	−0.677176	+	0.735821i	$0.736797\pi$
$642$	−10.8488	+	44.7669i	−0.428169	+	1.76681i
$643$	−10.5557	+	6.09436i	−0.416278	+	0.240338i	−0.693484	−	0.720472i	$-0.743925\pi$
$643$	−10.5557	+	6.09436i	−0.416278	+	0.240338i	0.277206	+	0.960811i	$0.410592\pi$
$644$	10.3451	−	7.06748i	0.407653	−	0.278498i
$645$	−7.39599	+	1.87252i	−0.291217	+	0.0737305i
$646$	−15.6815	+	29.7047i	−0.616979	+	1.16872i
$647$	13.5692			0.533460			0.266730	−	0.963771i	$-0.414057\pi$
$647$	13.5692			0.533460			0.266730	+	0.963771i	$0.414057\pi$
$648$	11.4218	−	22.7496i	0.448691	−	0.893687i
$649$	23.2945			0.914390
$650$	4.36145	−	8.26170i	0.171070	−	0.324051i
$651$	−18.9623	+	4.80087i	−0.743189	+	0.188161i
$652$	0.723329	−	0.494159i	0.0283277	−	0.0193528i
$653$	9.93280	−	5.73470i	0.388700	−	0.224416i	−0.292896	−	0.956144i	$-0.594619\pi$
$653$	9.93280	−	5.73470i	0.388700	−	0.224416i	0.681597	+	0.731728i	$0.261286\pi$
$654$	−1.95603	+	8.07144i	−0.0764870	+	0.315618i
$655$	−12.2343	−	7.06346i	−0.478033	−	0.275992i
$656$	−2.91915	−	19.1221i	−0.113974	−	0.746592i
$657$	6.13569	−	3.31967i	0.239376	−	0.129513i
$658$	−0.00224654	−	0.0592905i	−8.75792e−5	−	0.00231138i
$659$	8.46548	−	14.6626i	0.329768	−	0.571175i	−0.652698	−	0.757619i	$-0.726363\pi$
$659$	8.46548	−	14.6626i	0.329768	−	0.571175i	0.982466	+	0.186443i	$0.0596961\pi$
$660$	−6.63351	+	7.51034i	−0.258209	+	0.292340i
$661$	6.92555	+	11.9954i	0.269373	+	0.466567i	0.968700	−	0.248234i	$-0.0798503\pi$
$661$	6.92555	+	11.9954i	0.269373	+	0.466567i	−0.699327	+	0.714802i	$0.746517\pi$
$662$	−0.981196	+	0.617173i	−0.0381353	+	0.0239871i
$663$	−41.7329	+	40.5942i	−1.62077	+	1.57655i
$664$	−2.14342	+	4.93184i	−0.0831810	+	0.191392i
$665$		−	10.1028i		−	0.391771i
$666$	0.198604	+	19.4450i	0.00769576	+	0.753479i
$667$			20.0393i			0.775925i
$668$	−3.60767	+	7.50955i	−0.139585	+	0.290553i
$669$	20.5730	+	5.81860i	0.795397	+	0.224960i
$670$	−7.12858	−	11.3332i	−0.275401	−	0.437839i
$671$	0.929695	+	1.61028i	0.0358905	+	0.0621642i
$672$	−8.98120	−	19.2101i	−0.346457	−	0.741046i
$673$	7.68786	−	13.3158i	0.296345	−	0.513285i	−0.678952	−	0.734183i	$-0.737565\pi$
$673$	7.68786	−	13.3158i	0.296345	−	0.513285i	0.975297	+	0.220898i	$0.0708988\pi$
$674$	−4.33542	+	0.164271i	−0.166994	+	0.00632748i
$675$	1.13553	+	5.07056i	0.0437066	+	0.195166i
$676$	61.1022	−	4.63703i	2.35009	−	0.178347i
$677$	−34.4057	−	19.8641i	−1.32232	−	0.763441i	−0.338221	−	0.941067i	$-0.609825\pi$
$677$	−34.4057	−	19.8641i	−1.32232	−	0.763441i	−0.984098	+	0.177626i	$0.943158\pi$
$678$	0.689432	+	2.34588i	0.0264775	+	0.0900931i
$679$	−21.6706	+	12.5115i	−0.831642	+	0.480149i
$680$	−8.56257	−	11.5675i	−0.328360	−	0.443594i
$681$	−0.350731	+	1.24009i	−0.0134400	+	0.0475202i
$682$	−18.8767	−	9.96524i	−0.722827	−	0.381589i
$683$	−21.6572			−0.828690			−0.414345	−	0.910120i	$-0.635989\pi$
$683$	−21.6572			−0.828690			−0.414345	+	0.910120i	$0.635989\pi$
$684$	−12.8217	+	24.9002i	−0.490248	+	0.952084i
$685$	−15.2025			−0.580859
$686$	−25.2156	−	13.3116i	−0.962738	−	0.508240i
$687$	−31.5891	−	32.4751i	−1.20520	−	1.23900i
$688$	13.7545	−	11.0114i	0.524385	−	0.419807i
$689$	−18.3779	+	10.6105i	−0.700143	+	0.404228i
$690$	4.89126	−	5.13230i	0.186207	−	0.195383i
$691$	−15.3770	−	8.87791i	−0.584968	−	0.337732i	0.178137	−	0.984006i	$-0.442993\pi$
$691$	−15.3770	−	8.87791i	−0.584968	−	0.337732i	−0.763105	+	0.646274i	$0.776326\pi$
$692$	−1.35495	−	17.8542i	−0.0515075	−	0.678714i
$693$	−9.83715	+	15.9996i	−0.373682	+	0.607774i
$694$	−31.5324	+	1.19477i	−1.19695	+	0.0453530i
$695$	1.27038	−	2.20036i	0.0481883	−	0.0834645i
$696$	33.4739	+	5.47113i	1.26883	+	0.207383i
$697$	−12.3032	−	21.3098i	−0.466018	−	0.807167i
$698$	7.55932	+	12.0180i	0.286125	+	0.454888i
$699$	10.9790	+	43.3644i	0.415265	+	1.64019i
$700$	3.90174	+	1.87444i	0.147472	+	0.0708472i
$701$			38.3642i			1.44900i	0.689277	+	0.724498i	$0.257928\pi$
$701$			38.3642i			1.44900i	−0.689277	+	0.724498i	$0.742072\pi$
$702$	−34.4496	+	34.2013i	−1.30022	+	1.29085i
$703$		−	21.3952i		−	0.806936i
$704$	6.75827	−	22.1323i	0.254712	−	0.834142i
$705$	−0.00824062	−	0.0325484i	−0.000310360	−	0.00122584i
$706$	15.2418	−	9.58708i	0.573631	−	0.360815i
$707$	11.8250	+	20.4815i	0.444725	+	0.770287i
$708$	−5.53901	+	27.3410i	−0.208169	+	1.02754i
$709$	−1.96851	+	3.40955i	−0.0739288	+	0.128049i	−0.900620	−	0.434608i	$-0.856887\pi$
$709$	−1.96851	+	3.40955i	−0.0739288	+	0.128049i	0.826691	+	0.562656i	$0.190220\pi$
$710$	−0.0629896	−	1.66242i	−0.00236396	−	0.0623894i
$711$	50.8969	+	1.40812i	1.90878	+	0.0528085i
$712$	−1.19496	−	10.4721i	−0.0447829	−	0.392460i
$713$	13.0794	+	7.55138i	0.489827	+	0.282802i
$714$	−19.5276	−	18.6104i	−0.730800	−	0.696478i
$715$	16.5487	−	9.55437i	0.618885	−	0.357313i
$716$	11.8758	+	17.3833i	0.443821	+	0.649646i
$717$	9.94172	+	10.2206i	0.371280	+	0.381694i
$718$	−3.91715	+	7.42010i	−0.146187	+	0.276916i
$719$	25.9983			0.969573			0.484787	−	0.874632i	$-0.338897\pi$
$719$	25.9983			0.969573			0.484787	+	0.874632i	$0.338897\pi$
$720$	−7.23765	−	9.57165i	−0.269731	−	0.356714i
$721$	−1.37505			−0.0512097
$722$	1.84159	−	3.48844i	0.0685367	−	0.129826i
$723$	−0.0665161	+	0.235182i	−0.00247376	+	0.00874652i
$724$	10.7275	+	15.7025i	0.398686	+	0.583580i
$725$	−5.99593	+	3.46175i	−0.222683	+	0.128566i
$726$	6.18690	−	1.81827i	0.229617	−	0.0674823i
$727$	23.2282	+	13.4108i	0.861486	+	0.497379i	0.864510	−	0.502616i	$-0.167629\pi$
$727$	23.2282	+	13.4108i	0.861486	+	0.497379i	−0.00302389	+	0.999995i	$0.500963\pi$
$728$	4.58470	+	40.1786i	0.169920	+	1.48912i
$729$	2.23781	−	26.9071i	0.0828818	−	0.996559i
$730$	−0.124517	−	3.28624i	−0.00460858	−	0.121629i
$731$	11.2065	−	19.4102i	0.414486	−	0.717911i
$732$	−2.11107	+	0.708299i	−0.0780273	+	0.0261795i
$733$	−8.00096	−	13.8581i	−0.295522	−	0.511859i	0.679584	−	0.733598i	$-0.262160\pi$
$733$	−8.00096	−	13.8581i	−0.295522	−	0.511859i	−0.975106	+	0.221738i	$0.928827\pi$
$734$	−31.8437	+	20.0297i	−1.17537	+	0.739310i
$735$	−3.85956	−	1.09159i	−0.142362	−	0.0402639i
$736$	−5.37119	+	15.4671i	−0.197985	+	0.570124i
$737$		−	27.3854i		−	1.00875i
$738$	−10.4394	−	17.6626i	−0.384281	−	0.650168i
$739$		−	2.17451i		−	0.0799905i	−0.999200	−	0.0399952i	$-0.987266\pi$
$739$		−	2.17451i		−	0.0799905i	0.999200	−	0.0399952i	$-0.0127343\pi$
$740$	8.26289	+	3.96959i	0.303750	+	0.145925i
$741$	38.2850	−	37.2404i	1.40643	−	1.36806i
$742$	−5.23515	−	8.32296i	−0.192188	−	0.305545i
$743$	9.16604	+	15.8760i	0.336269	+	0.582436i	0.983728	−	0.179665i	$-0.0575014\pi$
$743$	9.16604	+	15.8760i	0.336269	+	0.582436i	−0.647458	+	0.762101i	$0.724168\pi$
$744$	16.1849	−	19.7863i	0.593366	−	0.725400i
$745$	−3.45533	+	5.98481i	−0.126593	+	0.219266i
$746$	−37.3917	+	1.41679i	−1.36901	+	0.0518722i
$747$	−0.157738	+	5.70150i	−0.00577133	+	0.208607i
$748$	−2.22758	−	29.3528i	−0.0814483	−	1.07324i
$749$	35.2473	+	20.3500i	1.28791	+	0.743574i
$750$	2.38058	+	0.576911i	0.0869266	+	0.0210658i
$751$	23.9363	−	13.8196i	0.873449	−	0.504286i	0.00495598	−	0.999988i	$-0.498422\pi$
$751$	23.9363	−	13.8196i	0.873449	−	0.504286i	0.868493	+	0.495702i	$0.165089\pi$
$752$	0.0484592	+	0.0605310i	0.00176713	+	0.00220734i
$753$	−15.9596	+	4.04065i	−0.581599	+	0.147250i
$754$	−57.1999	−	30.1965i	−2.08310	−	1.09969i
$755$	21.3124			0.775639
$756$	−16.4398	−	15.3504i	−0.597910	−	0.558288i
$757$	−47.4098			−1.72314			−0.861570	−	0.507640i	$-0.830518\pi$
$757$	−47.4098			−1.72314			−0.861570	+	0.507640i	$0.830518\pi$
$758$	26.6833	+	14.0864i	0.969182	+	0.511642i
$759$	14.0579	−	3.55920i	0.510271	−	0.129191i
$760$	7.85515	+	10.6118i	0.284936	+	0.384932i
$761$	−19.6920	+	11.3692i	−0.713834	+	0.412132i	−0.812479	−	0.582990i	$-0.801883\pi$
$761$	−19.6920	+	11.3692i	−0.713834	+	0.412132i	0.0986449	+	0.995123i	$0.468549\pi$
$762$	−20.9122	−	5.06787i	−0.757570	−	0.183590i
$763$	6.35506	+	3.66910i	0.230069	+	0.132830i
$764$	−24.2519	+	1.84047i	−0.877402	+	0.0665858i
$765$	−13.0036	−	7.99511i	−0.470147	−	0.289064i
$766$	4.45656	−	0.168861i	0.161022	−	0.00610119i
$767$	26.5990	−	46.0709i	0.960436	−	1.66352i
$768$	24.3699	+	13.1949i	0.879375	+	0.476131i
$769$	−17.4807	−	30.2775i	−0.630371	−	1.09183i	−0.987476	−	0.157770i	$-0.949570\pi$
$769$	−17.4807	−	30.2775i	−0.630371	−	1.09183i	0.357105	−	0.934064i	$-0.383764\pi$
$770$	4.71406	+	7.49453i	0.169883	+	0.270084i
$771$	−32.2615	+	31.3813i	−1.16187	+	1.13017i
$772$	12.1498	−	25.2905i	0.437282	−	0.910225i
$773$			5.74824i			0.206750i	0.994642	+	0.103375i	$0.0329642\pi$
$773$			5.74824i			0.206750i	−0.994642	+	0.103375i	$0.967036\pi$
$774$	9.17823	−	16.2789i	0.329905	−	0.585133i
$775$			5.21794i			0.187434i
$776$	13.0345	−	29.9912i	0.467911	−	1.07662i
$777$	16.5336	+	4.67615i	0.593138	+	0.167756i
$778$	−17.9624	+	11.2984i	−0.643985	+	0.405067i
$779$	11.2868	+	19.5493i	0.404391	+	0.700425i
$780$	7.27911	+	21.6952i	0.260634	+	0.776813i
$781$	1.70138	−	2.94688i	0.0608802	−	0.105448i
$782$	0.788608	+	20.8129i	0.0282006	+	0.744267i
$783$	35.1060	−	7.86185i	1.25459	−	0.280959i
$784$	9.15681	−	1.39787i	0.327029	−	0.0499238i
$785$	10.1062	+	5.83484i	0.360707	+	0.208255i
$786$	33.1997	−	9.75707i	1.18419	−	0.348023i
$787$	−45.9027	+	26.5020i	−1.63626	+	0.944693i	−0.654149	+	0.756366i	$0.726973\pi$
$787$	−45.9027	+	26.5020i	−1.63626	+	0.944693i	−0.982106	+	0.188327i	$0.939694\pi$
$788$	11.9158	−	8.14059i	0.424484	−	0.289996i
$789$	−12.6691	+	44.7944i	−0.451032	+	1.59472i
$790$	11.2054	−	21.2260i	0.398672	−	0.755187i
$791$	2.16043			0.0768162
$792$	−2.10723	−	24.4543i	−0.0748771	−	0.868945i
$793$	4.24632			0.150791
$794$	6.63358	−	12.5657i	0.235417	−	0.445940i
$795$	−3.87958	−	3.98839i	−0.137594	−	0.141454i
$796$	−14.2532	+	9.73742i	−0.505192	+	0.345134i
$797$	12.0190	−	6.93917i	0.425735	−	0.245798i	−0.271793	−	0.962356i	$-0.587617\pi$
$797$	12.0190	−	6.93917i	0.425735	−	0.245798i	0.697528	+	0.716558i	$0.254283\pi$
$798$	17.9142	+	17.0729i	0.634157	+	0.604374i
$799$	0.0854205	+	0.0493176i	0.00302196	+	0.00174473i
$800$	−5.55574	+	1.06480i	−0.196425	+	0.0376463i
$801$	−5.31984	−	9.83258i	−0.187967	−	0.347417i
$802$	−0.423633	−	11.1805i	−0.0149590	−	0.394796i
$803$	3.36326	−	5.82534i	0.118687	−	0.205572i
$804$	32.1425	+	6.51175i	1.13358	+	0.229652i
$805$	−3.13219	−	5.42512i	−0.110395	−	0.191210i
$806$	−41.2634	+	25.9547i	−1.45344	+	0.914215i
$807$	6.97303	+	27.5417i	0.245462	+	0.969515i
$808$	−28.3456	−	12.3193i	−0.997194	−	0.433390i
$809$			46.1210i			1.62153i	0.585372	+	0.810765i	$0.300948\pi$
$809$			46.1210i			1.62153i	−0.585372	+	0.810765i	$0.699052\pi$
$810$	−10.9100	−	6.55528i	−0.383339	−	0.230329i
$811$			31.7719i			1.11566i	0.829954	+	0.557832i	$0.188367\pi$
$811$			31.7719i			1.11566i	−0.829954	+	0.557832i	$0.811633\pi$
$812$	12.9777	−	27.0137i	0.455427	−	0.947995i
$813$	−6.82233	−	26.9465i	−0.239269	−	0.945055i
$814$	9.98318	+	15.8715i	0.349910	+	0.556296i
$815$	−0.219003	−	0.379324i	−0.00767134	−	0.0132872i
$816$	34.9814	+	4.36503i	1.22459	+	0.152807i
$817$	−10.2806	+	17.8065i	−0.359673	+	0.622972i
$818$	38.3894	−	1.45459i	1.34225	−	0.0508585i
$819$	20.4107	+	37.7247i	0.713207	+	1.31821i
$820$	−9.64408	+	0.731887i	−0.336786	+	0.0255586i
$821$	11.7695	+	6.79511i	0.410758	+	0.237151i	0.691115	−	0.722745i	$-0.257120\pi$
$821$	11.7695	+	6.79511i	0.410758	+	0.237151i	−0.280358	+	0.959896i	$0.590453\pi$
$822$	25.6909	−	26.9570i	0.896074	−	0.940233i
$823$	−25.6756	+	14.8238i	−0.894995	+	0.516725i	−0.875573	−	0.483086i	$-0.839516\pi$
$823$	−25.6756	+	14.8238i	−0.894995	+	0.516725i	−0.0194217	+	0.999811i	$0.506182\pi$
$824$	1.44433	−	1.06913i	0.0503157	−	0.0372450i
$825$	3.49342	+	3.59141i	0.121625	+	0.125037i
$826$	21.7978	+	11.5073i	0.758442	+	0.400390i
$827$	24.1020			0.838110			0.419055	−	0.907961i	$-0.362361\pi$
$827$	24.1020			0.838110			0.419055	+	0.907961i	$0.362361\pi$
$828$	0.834748	+	17.3463i	0.0290095	+	0.602825i
$829$	42.6555			1.48149			0.740743	−	0.671789i	$-0.234474\pi$
$829$	42.6555			1.48149			0.740743	+	0.671789i	$0.234474\pi$
$830$	2.37775	+	1.25524i	0.0825329	+	0.0435700i
$831$	−11.4696	+	40.5532i	−0.397874	+	1.40677i
$832$	−36.0553	−	38.6382i	−1.24999	−	1.33954i
$833$	10.2044	−	5.89153i	0.353563	−	0.204130i
$834$	1.75483	+	5.97104i	0.0607648	+	0.206760i
$835$	3.60751	+	2.08280i	0.124843	+	0.0720781i
$836$	2.04354	+	26.9277i	0.0706773	+	0.931315i
$837$	8.09763	−	25.8758i	0.279895	−	0.894398i
$838$	12.1119	−	0.458924i	0.418398	−	0.0158533i
$839$	−9.56807	+	16.5724i	−0.330327	+	0.572142i	−0.982576	−	0.185862i	$-0.940492\pi$
$839$	−9.56807	+	16.5724i	−0.330327	+	0.572142i	0.652249	+	0.758005i	$0.273826\pi$
$840$	−9.91733	+	3.75089i	−0.342180	+	0.129418i
$841$	9.46742	+	16.3981i	0.326463	+	0.565450i
$842$	5.14286	+	8.17624i	0.177235	+	0.281772i
$843$	−17.4007	−	4.92141i	−0.599314	−	0.169502i
$844$	−33.5360	−	16.1111i	−1.15436	−	0.554566i
$845$		−	30.6390i		−	1.05401i
$846$	0.0716404	+	0.0403917i	0.00246305	+	0.00138870i
$847$		−	5.69781i		−	0.195779i
$848$	11.9702	+	4.67187i	0.411057	+	0.160433i
$849$	−18.4858	+	17.9814i	−0.634430	+	0.617121i
$850$	−6.09115	+	3.83134i	−0.208925	+	0.131414i
$851$	−6.63318	−	11.4890i	−0.227383	−	0.393838i
$852$	3.05423	+	2.69764i	0.104636	+	0.0924198i
$853$	−14.4881	+	25.0942i	−0.496064	+	0.859207i	−0.999990	−	0.00453935i	$-0.998555\pi$
$853$	−14.4881	+	25.0942i	−0.496064	+	0.859207i	0.503926	+	0.863747i	$0.331888\pi$
$854$	0.0744954	+	1.96608i	0.00254918	+	0.0672777i
$855$	11.9293	+	7.33457i	0.407973	+	0.250837i
$856$	−52.8457	+	6.03013i	−1.80623	+	0.206106i
$857$	−14.0771	−	8.12743i	−0.480865	−	0.277628i	0.239912	−	0.970795i	$-0.422882\pi$
$857$	−14.0771	−	8.12743i	−0.480865	−	0.277628i	−0.720777	+	0.693167i	$0.756215\pi$
$858$	−11.0240	+	45.4900i	−0.376355	+	1.55300i
$859$	39.4268	−	22.7631i	1.34523	−	0.776666i	0.357657	−	0.933853i	$-0.383576\pi$
$859$	39.4268	−	22.7631i	1.34523	−	0.776666i	0.987569	+	0.157187i	$0.0502425\pi$
$860$	−4.96951	−	7.27416i	−0.169459	−	0.248047i
$861$	−17.5739	+	4.44937i	−0.598917	+	0.151634i
$862$	17.5324	−	33.2110i	0.597157	−	1.13117i
$863$	−14.4497			−0.491875			−0.245937	−	0.969286i	$-0.579096\pi$
$863$	−14.4497			−0.491875			−0.245937	+	0.969286i	$0.579096\pi$
$864$	29.2033	+	3.34150i	0.993517	+	0.113680i
$865$	−8.95276			−0.304403
$866$	8.23397	−	15.5973i	0.279802	−	0.530017i
$867$	14.9280	−	3.77949i	0.506983	−	0.128358i
$868$	−12.7411	−	18.6499i	−0.432461	−	0.633018i
$869$	42.5169	−	24.5471i	1.44229	−	0.832705i
$870$	3.99424	−	16.4820i	0.135418	−	0.558791i
$871$	−54.1616	−	31.2702i	−1.83520	−	1.05955i
$872$	−9.52804	+	1.08723i	−0.322660	+	0.0368182i
$873$	0.959228	−	34.6717i	0.0324650	−	1.17346i
$874$	−0.723455	−	19.0934i	−0.0244712	−	0.645843i
$875$	1.08216	−	1.87435i	0.0365837	−	0.0633648i
$876$	6.03755	+	5.33266i	0.203990	+	0.180174i
$877$	11.9538	+	20.7046i	0.403651	+	0.699144i	0.994163	−	0.107885i	$-0.0344077\pi$
$877$	11.9538	+	20.7046i	0.403651	+	0.699144i	−0.590512	+	0.807029i	$0.701074\pi$
$878$	17.7502	−	11.1649i	0.599042	−	0.376798i
$879$	32.4270	−	31.5423i	1.09374	−	1.06390i
$880$	−10.7787	−	4.20685i	−0.363350	−	0.141813i
$881$		−	51.7852i		−	1.74469i	−0.488893	−	0.872344i	$-0.662599\pi$
$881$		−	51.7852i		−	1.74469i	0.488893	−	0.872344i	$-0.337401\pi$
$882$	8.45790	−	4.99904i	0.284792	−	0.168326i
$883$		−	17.1884i		−	0.578436i	−0.957263	−	0.289218i	$-0.906605\pi$
$883$		−	17.1884i		−	0.578436i	0.957263	−	0.289218i	$-0.0933953\pi$
$884$	−60.5963	−	29.1111i	−2.03807	−	0.979113i
$885$	13.4218	+	3.79604i	0.451167	+	0.127603i
$886$	−29.7612	−	47.3151i	−0.999849	−	1.58958i
$887$	−8.92377	−	15.4564i	−0.299631	−	0.518976i	0.676421	−	0.736515i	$-0.263530\pi$
$887$	−8.92377	−	15.4564i	−0.299631	−	0.518976i	−0.976051	+	0.217540i	$0.930197\pi$
$888$	−21.0024	+	7.94342i	−0.704793	+	0.266564i
$889$	−9.50623	+	16.4653i	−0.318829	+	0.552227i
$890$	−5.26627	+	0.199541i	−0.176526	+	0.00668863i
$891$	−11.7504	−	23.2311i	−0.393654	−	0.778273i
$892$	1.86815	+	24.6167i	0.0625504	+	0.824227i
$893$	−0.0783633	−	0.0452431i	−0.00262233	−	0.00151400i
$894$	−4.77300	−	16.2407i	−0.159633	−	0.543172i
$895$	9.11608	−	5.26317i	0.304717	−	0.175928i
$896$	17.2572	−	17.3717i	0.576523	−	0.580348i
$897$	9.01295	−	31.8673i	0.300934	−	1.06402i
$898$	28.5640	+	15.0793i	0.953195	+	0.503202i
$899$	36.1264			1.20488
$900$	−5.04595	+	3.24630i	−0.168198	+	0.108210i
$901$	16.3456			0.544550
$902$	−17.4947	−	9.23562i	−0.582508	−	0.307513i
$903$	−11.5134	−	11.8364i	−0.383142	−	0.393889i
$904$	−2.26928	+	1.67978i	−0.0754752	+	0.0558687i
$905$	8.23464	−	4.75427i	0.273729	−	0.158037i
$906$	−36.0161	+	37.7910i	−1.19656	+	1.25552i
$907$	−2.04370	−	1.17993i	−0.0678600	−	0.0391790i	0.465686	−	0.884950i	$-0.345808\pi$
$907$	−2.04370	−	1.17993i	−0.0678600	−	0.0391790i	−0.533546	+	0.845771i	$0.679141\pi$
$908$	−1.48383	+	0.112608i	−0.0492427	+	0.00373701i
$909$	−32.7692	−	0.906594i	−1.08688	−	0.0300698i
$910$	20.2051	−	0.765581i	0.669794	−	0.0253788i
$911$	−18.6895	+	32.3712i	−0.619212	+	1.07251i	0.370418	+	0.928865i	$0.379214\pi$
$911$	−18.6895	+	32.3712i	−0.619212	+	1.07251i	−0.989630	+	0.143641i	$0.954119\pi$
$912$	−32.0913	−	4.00440i	−1.06265	−	0.132599i
$913$	2.74978	+	4.76277i	0.0910046	+	0.157625i
$914$	−0.626835	−	0.996557i	−0.0207339	−	0.0329632i
$915$	0.273260	+	1.07931i	0.00903368	+	0.0356808i
$916$	22.6533	−	47.1540i	0.748486	−	1.55801i
$917$		−	30.5752i		−	1.00968i
$918$	36.1518	−	9.54686i	1.19319	−	0.315093i
$919$		−	4.73062i		−	0.156049i	−0.996951	−	0.0780243i	$-0.975139\pi$
$919$		−	4.73062i		−	0.156049i	0.996951	−	0.0780243i	$-0.0248612\pi$
$920$	7.50814	+	3.26311i	0.247536	+	0.107582i
$921$	12.1386	+	47.9446i	0.399982	+	1.57983i
$922$	42.8351	−	26.9433i	1.41070	−	0.887331i
$923$	−3.88547	−	6.72983i	−0.127892	−	0.221515i
$924$	−21.2556	−	4.30616i	−0.699257	−	0.141662i
$925$	2.29174	−	3.96940i	0.0753518	−	0.130513i
$926$	−0.445908	−	11.7684i	−0.0146534	−	0.386732i
$927$	0.998278	−	1.62365i	0.0327877	−	0.0533275i
$928$	7.37214	+	38.4651i	0.242002	+	1.26268i
$929$	25.4661	+	14.7029i	0.835517	+	0.482386i	0.855738	−	0.517410i	$-0.173104\pi$
$929$	25.4661	+	14.7029i	0.835517	+	0.482386i	−0.0202209	+	0.999796i	$0.506437\pi$
$930$	−9.25240	−	8.81786i	−0.303398	−	0.289149i
$931$	−9.36137	+	5.40479i	−0.306806	+	0.177135i
$932$	−42.6501	+	29.1374i	−1.39705	+	0.954427i
$933$	0.106331	+	0.109313i	0.00348112	+	0.00357876i
$934$	−11.1319	+	21.0867i	−0.364246	+	0.689977i
$935$	−14.7186			−0.481350
$936$	−50.7708	−	23.7557i	−1.65949	−	0.776480i
$937$	20.2810			0.662551			0.331276	−	0.943534i	$-0.392521\pi$
$937$	20.2810			0.662551			0.331276	+	0.943534i	$0.392521\pi$
$938$	13.5281	−	25.6258i	0.441710	−	0.836712i
$939$	7.17257	−	25.3602i	0.234068	−	0.827600i
$940$	0.0320122	−	0.0218699i	0.00104412	−	0.000713317i
$941$	−7.09878	+	4.09848i	−0.231413	+	0.133607i	−0.611224	−	0.791458i	$-0.709323\pi$
$941$	−7.09878	+	4.09848i	−0.231413	+	0.133607i	0.379810	+	0.925064i	$0.375989\pi$
$942$	−27.4249	+	8.05992i	−0.893553	+	0.262607i
$943$	12.1218	+	6.99850i	0.394739	+	0.227903i
$944$	−31.8432	+	4.86114i	−1.03641	+	0.158217i
$945$	−8.27520	+	7.61554i	−0.269192	+	0.247734i
$946$	−0.682268	−	18.0064i	−0.0221824	−	0.585437i
$947$	−21.0440	+	36.4493i	−0.683839	+	1.18444i	0.289962	+	0.957038i	$0.406357\pi$
$947$	−21.0440	+	36.4493i	−0.683839	+	1.18444i	−0.973800	+	0.227405i	$0.926976\pi$
$948$	18.7015	+	55.7394i	0.607397	+	1.81033i
$949$	−7.68074	−	13.3034i	−0.249327	−	0.431848i
$950$	5.58792	−	3.51480i	0.181296	−	0.114035i
$951$	−11.9426	−	3.37770i	−0.387266	−	0.109530i
$952$	12.4156	−	28.5672i	0.402391	−	0.925868i
$953$			17.5687i			0.569106i	0.958660	+	0.284553i	$0.0918452\pi$
$953$			17.5687i			0.569106i	−0.958660	+	0.284553i	$0.908155\pi$
$954$	13.6283	−	0.139195i	0.441233	−	0.00450659i
$955$			12.1608i			0.393515i
$956$	−7.12945	+	14.8403i	−0.230583	+	0.479970i
$957$	24.8651	−	24.1867i	0.803774	−	0.781845i
$958$	3.98610	+	6.33719i	0.128785	+	0.204745i
$959$	−16.4516	−	28.4950i	−0.531249	−	0.920150i
$960$	7.50061	−	11.6508i	0.242081	−	0.376028i
$961$	−1.88653	+	3.26756i	−0.0608557	+	0.105405i
$962$	42.7893	−	1.62130i	1.37958	−	0.0522730i
$963$	−49.6183	+	26.8456i	−1.59893	+	0.865087i
$964$	−0.281408	+	0.0213560i	−0.00906356	+	0.000687831i
$965$	−12.1493	−	7.01439i	−0.391099	−	0.225801i
$966$	14.9129	+	3.61399i	0.479814	+	0.116278i
$967$	20.1466	−	11.6316i	0.647870	−	0.374048i	−0.139770	−	0.990184i	$-0.544636\pi$
$967$	20.1466	−	11.6316i	0.647870	−	0.374048i	0.787640	+	0.616136i	$0.211303\pi$
$968$	4.43016	+	5.98488i	0.142391	+	0.192361i
$969$	−39.8807	+	10.0970i	−1.28115	+	0.324363i
$970$	−14.4595	−	7.63331i	−0.464265	−	0.245091i
$971$	25.2618			0.810688			0.405344	−	0.914164i	$-0.367152\pi$
$971$	25.2618			0.810688			0.405344	+	0.914164i	$0.367152\pi$
$972$	30.0607	−	8.26767i	0.964197	−	0.265186i
$973$	5.49901			0.176290
$974$	−24.7965	−	13.0904i	−0.794531	−	0.419442i
$975$	11.0919	−	2.80826i	0.355226	−	0.0899362i
$976$	−1.60691	−	2.00721i	−0.0514360	−	0.0642493i
$977$	21.5806	−	12.4595i	0.690423	−	0.398616i	−0.113347	−	0.993555i	$-0.536157\pi$
$977$	21.5806	−	12.4595i	0.690423	−	0.398616i	0.803771	+	0.594939i	$0.202824\pi$
$978$	1.04271	+	0.252691i	0.0333422	+	0.00808015i
$979$	−9.33524	−	5.38970i	−0.298355	−	0.172256i
$980$	−0.350472	−	4.61817i	−0.0111954	−	0.147522i
$981$	−8.94614	+	4.84024i	−0.285628	+	0.154537i
$982$	40.2024	−	1.52329i	1.28291	−	0.0486100i
$983$	7.99642	−	13.8502i	0.255046	−	0.441753i	−0.709862	−	0.704341i	$-0.751243\pi$
$983$	7.99642	−	13.8502i	0.255046	−	0.441753i	0.964908	+	0.262588i	$0.0845760\pi$
$984$	14.9999	−	18.3376i	0.478178	−	0.584582i
$985$	−3.60777	−	6.24885i	−0.114953	−	0.199105i
$986$	26.5263	+	42.1721i	0.844769	+	1.34303i
$987$	0.0520896	−	0.0506684i	0.00165803	−	0.00161279i
$988$	55.5899	+	26.7060i	1.76855	+	0.849632i
$989$			12.7492i			0.405402i
$990$	−12.2718	+	0.125340i	−0.390024	+	0.00398356i
$991$			29.4708i			0.936171i	0.883683	+	0.468085i	$0.155056\pi$
$991$			29.4708i			0.936171i	−0.883683	+	0.468085i	$0.844944\pi$
$992$	27.8837	+	9.68307i	0.885308	+	0.307438i
$993$	−1.36609	−	0.386367i	−0.0433514	−	0.0122610i
$994$	3.04779	−	1.91706i	0.0966702	−	0.0608056i
$995$	4.31546	+	7.47460i	0.136809	+	0.236961i
$996$	−6.24396	+	2.09495i	−0.197848	+	0.0663812i
$997$	−19.3519	+	33.5185i	−0.612881	+	1.06154i	0.377871	+	0.925858i	$0.376656\pi$
$997$	−19.3519	+	33.5185i	−0.612881	+	1.06154i	−0.990752	+	0.135683i	$0.956677\pi$
$998$	−0.302536	−	7.98451i	−0.00957661	−	0.252745i
$999$	−17.5248	+	16.1278i	−0.554459	+	0.510260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.q.a.11.9	✓	48
3.2	odd	2		540.2.q.a.251.16		48
4.3	odd	2	inner	180.2.q.a.11.17	yes	48
5.2	odd	4		900.2.o.c.299.4		48
5.3	odd	4		900.2.o.b.299.21		48
5.4	even	2		900.2.r.f.551.16		48
9.2	odd	6		1620.2.e.b.971.2		48
9.4	even	3		540.2.q.a.71.8		48
9.5	odd	6	inner	180.2.q.a.131.17	yes	48
9.7	even	3		1620.2.e.b.971.47		48
12.11	even	2		540.2.q.a.251.8		48
20.3	even	4		900.2.o.b.299.5		48
20.7	even	4		900.2.o.c.299.20		48
20.19	odd	2		900.2.r.f.551.8		48
36.7	odd	6		1620.2.e.b.971.1		48
36.11	even	6		1620.2.e.b.971.48		48
36.23	even	6	inner	180.2.q.a.131.9	yes	48
36.31	odd	6		540.2.q.a.71.16		48
45.14	odd	6		900.2.r.f.851.8		48
45.23	even	12		900.2.o.c.599.20		48
45.32	even	12		900.2.o.b.599.5		48
180.23	odd	12		900.2.o.c.599.4		48
180.59	even	6		900.2.r.f.851.16		48
180.167	odd	12		900.2.o.b.599.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.9	✓	48	1.1	even	1	trivial
180.2.q.a.11.17	yes	48	4.3	odd	2	inner
180.2.q.a.131.9	yes	48	36.23	even	6	inner
180.2.q.a.131.17	yes	48	9.5	odd	6	inner
540.2.q.a.71.8		48	9.4	even	3
540.2.q.a.71.16		48	36.31	odd	6
540.2.q.a.251.8		48	12.11	even	2
540.2.q.a.251.16		48	3.2	odd	2
900.2.o.b.299.5		48	20.3	even	4
900.2.o.b.299.21		48	5.3	odd	4
900.2.o.b.599.5		48	45.32	even	12
900.2.o.b.599.21		48	180.167	odd	12
900.2.o.c.299.4		48	5.2	odd	4
900.2.o.c.299.20		48	20.7	even	4
900.2.o.c.599.4		48	180.23	odd	12
900.2.o.c.599.20		48	45.23	even	12
900.2.r.f.551.8		48	20.19	odd	2
900.2.r.f.551.16		48	5.4	even	2
900.2.r.f.851.8		48	45.14	odd	6
900.2.r.f.851.16		48	180.59	even	6
1620.2.e.b.971.1		48	36.7	odd	6
1620.2.e.b.971.2		48	9.2	odd	6
1620.2.e.b.971.47		48	9.7	even	3
1620.2.e.b.971.48		48	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.660227 + 1.25064i) q^{2} +(-1.67907 + 0.425108i) q^{3} +(-1.12820 - 1.65141i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.576911 - 2.38058i) q^{6} +(-1.87435 - 1.08216i) q^{7} +(2.81019 - 0.320666i) q^{8} +(2.63857 - 1.42758i) q^{9} +(-0.0535467 - 1.41320i) q^{10} +(1.44632 - 2.50510i) q^{11} +(2.59636 + 2.29323i) q^{12} +(-3.30299 - 5.72095i) q^{13} +(2.59089 - 1.62967i) q^{14} +(1.24156 - 1.20769i) q^{15} +(-1.45433 + 3.72625i) q^{16} +5.08829i q^{17} +(0.0433305 + 4.24242i) q^{18} -4.66790i q^{19} +(1.80276 + 0.866065i) q^{20} +(3.60721 + 1.02022i) q^{21} +(2.17808 + 3.46277i) q^{22} +(-1.44720 - 2.50662i) q^{23} +(-4.58220 + 1.73306i) q^{24} +(0.500000 - 0.866025i) q^{25} +(9.33557 - 0.353728i) q^{26} +(-3.82347 + 3.51868i) q^{27} +(0.327557 + 4.31623i) q^{28} +(-5.99593 - 3.46175i) q^{29} +(0.690672 + 2.35010i) q^{30} +(-4.51887 + 2.60897i) q^{31} +(-3.70001 - 4.27901i) q^{32} +(-1.36354 + 4.82109i) q^{33} +(-6.36361 - 3.35942i) q^{34} +2.16432 q^{35} +(-5.33435 - 2.74677i) q^{36} +4.58347 q^{37} +(5.83787 + 3.08188i) q^{38} +(7.97798 + 8.20175i) q^{39} +(-2.27336 + 1.68280i) q^{40} +(-4.18802 + 2.41795i) q^{41} +(-3.65751 + 3.83775i) q^{42} +(-3.81468 - 2.20241i) q^{43} +(-5.76870 + 0.437785i) q^{44} +(-1.57128 + 2.55560i) q^{45} +(4.09035 - 0.154985i) q^{46} +(0.00969237 - 0.0167877i) q^{47} +(0.857858 - 6.87489i) q^{48} +(-1.15786 - 2.00548i) q^{49} +(0.752973 + 1.19709i) q^{50} +(-2.16307 - 8.54360i) q^{51} +(-5.72121 + 11.9090i) q^{52} -3.21239i q^{53} +(-1.87624 - 7.10491i) q^{54} +2.89264i q^{55} +(-5.61431 - 2.44003i) q^{56} +(1.98436 + 7.83775i) q^{57} +(8.28807 - 5.21320i) q^{58} +(4.02651 + 6.97412i) q^{59} +(-3.39513 - 0.687818i) q^{60} +(-0.321400 + 0.556681i) q^{61} +(-0.279404 - 7.37400i) q^{62} +(-6.49047 - 0.179566i) q^{63} +(7.79435 - 1.80227i) q^{64} +(5.72095 + 3.30299i) q^{65} +(-5.12921 - 4.88831i) q^{66} +(8.19888 - 4.73363i) q^{67} +(8.40286 - 5.74061i) q^{68} +(3.49553 + 3.59357i) q^{69} +(-1.42894 + 2.70678i) q^{70} +1.17635 q^{71} +(6.95710 - 4.85786i) q^{72} +2.32539 q^{73} +(-3.02613 + 5.73228i) q^{74} +(-0.471381 + 1.66667i) q^{75} +(-7.70863 + 5.26633i) q^{76} +(-5.42184 + 3.13030i) q^{77} +(-15.5247 + 4.56256i) q^{78} +(14.6983 + 8.48606i) q^{79} +(-0.603641 - 3.95419i) q^{80} +(4.92406 - 7.53350i) q^{81} +(-0.258947 - 6.83410i) q^{82} +(-0.950613 + 1.64651i) q^{83} +(-2.38486 - 7.10801i) q^{84} +(-2.54414 - 4.40658i) q^{85} +(5.27297 - 3.31670i) q^{86} +(11.5392 + 3.26361i) q^{87} +(3.26114 - 7.50361i) q^{88} -3.72649i q^{89} +(-2.15874 - 3.65238i) q^{90} +14.2974i q^{91} +(-2.50673 + 5.21788i) q^{92} +(6.47842 - 6.30166i) q^{93} +(0.0145962 + 0.0232054i) q^{94} +(2.33395 + 4.04252i) q^{95} +(8.03163 + 5.61186i) q^{96} +(5.78082 - 10.0127i) q^{97} +(3.27258 - 0.123999i) q^{98} +(0.239992 - 8.67461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 4 q^{9} - 22 q^{12} - 30 q^{14} - 16 q^{18} - 4 q^{21} - 28 q^{24} + 24 q^{25} - 12 q^{29} + 16 q^{30} - 44 q^{33} - 6 q^{34} + 42 q^{36} + 60 q^{38} - 6 q^{40} - 60 q^{41} - 18 q^{42}+ \cdots - 12 q^{97}+O(q^{100}) \) 48 * q + 6 * q^6 + 4 * q^9 - 22 * q^12 - 30 * q^14 - 16 * q^18 - 4 * q^21 - 28 * q^24 + 24 * q^25 - 12 * q^29 + 16 * q^30 - 44 * q^33 - 6 * q^34 + 42 * q^36 + 60 * q^38 - 6 * q^40 - 60 * q^41 - 18 * q^42 - 8 * q^45 - 12 * q^46 - 12 * q^48 + 24 * q^49 - 18 * q^52 - 32 * q^54 - 42 * q^56 - 12 * q^57 - 18 * q^58 + 14 * q^60 - 48 * q^64 + 16 * q^66 + 48 * q^68 + 36 * q^69 + 60 * q^72 - 24 * q^73 + 84 * q^74 + 6 * q^76 + 48 * q^77 + 38 * q^78 - 36 * q^82 + 50 * q^84 - 54 * q^86 - 18 * q^90 + 60 * q^92 - 32 * q^93 + 18 * q^94 - 18 * q^96 - 12 * q^97

Introduction

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