LMFDB - Embedded newform 368.2.i.b.91.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(91,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("368.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			91.15
Character	$\chi$	$=$	368.91
Dual form			368.2.i.b.275.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.750696 - 1.19852i) q^{2} +(0.670749 + 0.670749i) q^{3} +(-0.872910 + 1.79945i) q^{4} +(-1.44943 + 1.44943i) q^{5} +(0.300379 - 1.30744i) q^{6} +2.27607i q^{7} +(2.81197 - 0.304639i) q^{8} -2.10019i q^{9} +(2.82526 + 0.649093i) q^{10} +(-3.32432 - 3.32432i) q^{11} +(-1.79248 + 0.621477i) q^{12} +(-3.84412 + 3.84412i) q^{13} +(2.72792 - 1.70864i) q^{14} -1.94441 q^{15} +(-2.47605 - 3.14152i) q^{16} +1.88583i q^{17} +(-2.51713 + 1.57661i) q^{18} +(-5.20211 + 5.20211i) q^{19} +(-1.34296 - 3.87340i) q^{20} +(-1.52667 + 1.52667i) q^{21} +(-1.48872 + 6.47982i) q^{22} +(0.199226 + 4.79169i) q^{23} +(2.09046 + 1.68179i) q^{24} +0.798301i q^{25} +(7.49304 + 1.72150i) q^{26} +(3.42095 - 3.42095i) q^{27} +(-4.09568 - 1.98681i) q^{28} +(1.10155 - 1.10155i) q^{29} +(1.45966 + 2.33042i) q^{30} -4.06162i q^{31} +(-1.90642 + 5.32593i) q^{32} -4.45956i q^{33} +(2.26021 - 1.41569i) q^{34} +(-3.29901 - 3.29901i) q^{35} +(3.77919 + 1.83328i) q^{36} +(0.370332 - 0.370332i) q^{37} +(10.1400 + 2.32964i) q^{38} -5.15688 q^{39} +(-3.63421 + 4.51731i) q^{40} -4.50895i q^{41} +(2.97582 + 0.683683i) q^{42} +(-1.66897 - 1.66897i) q^{43} +(8.88378 - 3.08012i) q^{44} +(3.04408 + 3.04408i) q^{45} +(5.59339 - 3.83588i) q^{46} +12.9505i q^{47} +(0.446361 - 3.76798i) q^{48} +1.81950 q^{49} +(0.956781 - 0.599282i) q^{50} +(-1.26492 + 1.26492i) q^{51} +(-3.56174 - 10.2729i) q^{52} +(9.19784 - 9.19784i) q^{53} +(-6.66818 - 1.53199i) q^{54} +9.63673 q^{55} +(0.693380 + 6.40025i) q^{56} -6.97862 q^{57} +(-2.14716 - 0.493301i) q^{58} +(-5.82397 + 5.82397i) q^{59} +(1.69729 - 3.49887i) q^{60} +(0.275232 + 0.275232i) q^{61} +(-4.86794 + 3.04904i) q^{62} +4.78019 q^{63} +(7.81439 - 1.71327i) q^{64} -11.1436i q^{65} +(-5.34489 + 3.34778i) q^{66} +(-9.16779 + 9.16779i) q^{67} +(-3.39346 - 1.64616i) q^{68} +(-3.08039 + 3.34765i) q^{69} +(-1.47738 + 6.43049i) q^{70} -1.85029 q^{71} +(-0.639801 - 5.90568i) q^{72} +11.4766i q^{73} +(-0.721858 - 0.165844i) q^{74} +(-0.535460 + 0.535460i) q^{75} +(-4.81997 - 13.9019i) q^{76} +(7.56638 - 7.56638i) q^{77} +(3.87125 + 6.18064i) q^{78} +2.78305 q^{79} +(8.14229 + 0.964547i) q^{80} -1.71138 q^{81} +(-5.40408 + 3.38485i) q^{82} +(4.80163 - 4.80163i) q^{83} +(-1.41453 - 4.07982i) q^{84} +(-2.73338 - 2.73338i) q^{85} +(-0.747407 + 3.25318i) q^{86} +1.47772 q^{87} +(-10.3606 - 8.33517i) q^{88} +15.1990 q^{89} +(1.36322 - 5.93358i) q^{90} +(-8.74950 - 8.74950i) q^{91} +(-8.79633 - 3.82422i) q^{92} +(2.72433 - 2.72433i) q^{93} +(15.5214 - 9.72188i) q^{94} -15.0802i q^{95} +(-4.85109 + 2.29364i) q^{96} -17.2722i q^{97} +(-1.36589 - 2.18071i) q^{98} +(-6.98170 + 6.98170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} - 4 q^{3} - 16 q^{6} - 4 q^{8} + 20 q^{12} - 4 q^{13} - 16 q^{16} + 24 q^{18} + 4 q^{23} + 4 q^{24} - 24 q^{26} + 44 q^{27} - 20 q^{29} - 24 q^{32} + 16 q^{35} + 104 q^{36} - 128 q^{39} - 16 q^{46}+ \cdots - 88 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 - 4 * q^3 - 16 * q^6 - 4 * q^8 + 20 * q^12 - 4 * q^13 - 16 * q^16 + 24 * q^18 + 4 * q^23 + 4 * q^24 - 24 * q^26 + 44 * q^27 - 20 * q^29 - 24 * q^32 + 16 * q^35 + 104 * q^36 - 128 * q^39 - 16 * q^46 + 56 * q^48 - 160 * q^49 + 8 * q^50 - 72 * q^52 + 52 * q^54 - 8 * q^55 - 44 * q^58 + 80 * q^59 - 92 * q^62 - 24 * q^69 - 12 * q^70 - 8 * q^71 - 120 * q^72 - 12 * q^75 + 40 * q^77 + 136 * q^78 + 40 * q^81 + 132 * q^82 - 16 * q^85 - 8 * q^87 + 4 * q^92 - 28 * q^93 - 60 * q^94 + 24 * q^96 - 88 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.750696	−	1.19852i	−0.530822	−	0.847483i
$2$	−0.750696	−	1.19852i	−0.530822	−	0.847483i
$3$	0.670749	+	0.670749i	0.387257	+	0.387257i	0.873708	−	0.486451i	$-0.161709\pi$
$3$	0.670749	+	0.670749i	0.387257	+	0.387257i	−0.486451	+	0.873708i	$0.661709\pi$
$4$	−0.872910	+	1.79945i	−0.436455	+	0.899726i
$5$	−1.44943	+	1.44943i	−0.648205	+	0.648205i	−0.952559	−	0.304354i	$-0.901559\pi$
$5$	−1.44943	+	1.44943i	−0.648205	+	0.648205i	0.304354	+	0.952559i	$0.401559\pi$
$6$	0.300379	−	1.30744i	0.122629	−	0.533759i
$7$			2.27607i			0.860274i	0.902764	+	0.430137i	$0.141535\pi$
$7$			2.27607i			0.860274i	−0.902764	+	0.430137i	$0.858465\pi$
$8$	2.81197	−	0.304639i	0.994183	−	0.107706i
$9$		−	2.10019i		−	0.700064i
$10$	2.82526	+	0.649093i	0.893425	+	0.205261i
$11$	−3.32432	−	3.32432i	−1.00232	−	1.00232i	−0.999997	−	0.00232187i	$-0.999261\pi$
$11$	−3.32432	−	3.32432i	−1.00232	−	1.00232i	−0.00232187	−	0.999997i	$-0.500739\pi$
$12$	−1.79248	+	0.621477i	−0.517446	+	0.179405i
$13$	−3.84412	+	3.84412i	−1.06617	+	1.06617i	−0.0685183	+	0.997650i	$0.521827\pi$
$13$	−3.84412	+	3.84412i	−1.06617	+	1.06617i	−0.997650	+	0.0685183i	$0.978173\pi$
$14$	2.72792	−	1.70864i	0.729068	−	0.456653i
$15$	−1.94441			−0.502044
$16$	−2.47605	−	3.14152i	−0.619014	−	0.785380i
$17$			1.88583i			0.457381i	0.973499	+	0.228690i	$0.0734444\pi$
$17$			1.88583i			0.457381i	−0.973499	+	0.228690i	$0.926556\pi$
$18$	−2.51713	+	1.57661i	−0.593292	+	0.371610i
$19$	−5.20211	+	5.20211i	−1.19345	+	1.19345i	−0.217353	+	0.976093i	$0.569742\pi$
$19$	−5.20211	+	5.20211i	−1.19345	+	1.19345i	−0.976093	+	0.217353i	$0.930258\pi$
$20$	−1.34296	−	3.87340i	−0.300294	−	0.866120i
$21$	−1.52667	+	1.52667i	−0.333147	+	0.333147i
$22$	−1.48872	+	6.47982i	−0.317395	+	1.38150i
$23$	0.199226	+	4.79169i	0.0415414	+	0.999137i
$23$	0.199226	+	4.79169i	0.0415414	+	0.999137i
$24$	2.09046	+	1.68179i	0.426714	+	0.343294i
$25$			0.798301i			0.159660i
$26$	7.49304	+	1.72150i	1.46951	+	0.337614i
$27$	3.42095	−	3.42095i	0.658362	−	0.658362i
$28$	−4.09568	−	1.98681i	−0.774011	−	0.375471i
$29$	1.10155	−	1.10155i	0.204552	−	0.204552i	−0.597395	−	0.801947i	$-0.703798\pi$
$29$	1.10155	−	1.10155i	0.204552	−	0.204552i	0.801947	+	0.597395i	$0.203798\pi$
$30$	1.45966	+	2.33042i	0.266496	+	0.425474i
$31$		−	4.06162i		−	0.729489i	−0.931108	−	0.364744i	$-0.881156\pi$
$31$		−	4.06162i		−	0.729489i	0.931108	−	0.364744i	$-0.118844\pi$
$32$	−1.90642	+	5.32593i	−0.337010	+	0.941501i
$33$		−	4.45956i		−	0.776310i
$34$	2.26021	−	1.41569i	0.387623	−	0.242788i
$35$	−3.29901	−	3.29901i	−0.557634	−	0.557634i
$36$	3.77919	+	1.83328i	0.629866	+	0.305547i
$37$	0.370332	−	0.370332i	0.0608822	−	0.0608822i	−0.676010	−	0.736892i	$-0.736292\pi$
$37$	0.370332	−	0.370332i	0.0608822	−	0.0608822i	0.736892	+	0.676010i	$0.236292\pi$
$38$	10.1400	+	2.32964i	1.64493	+	0.377917i
$39$	−5.15688			−0.825762
$40$	−3.63421	+	4.51731i	−0.574619	+	0.714250i
$41$		−	4.50895i		−	0.704180i	−0.935966	−	0.352090i	$-0.885471\pi$
$41$		−	4.50895i		−	0.704180i	0.935966	−	0.352090i	$-0.114529\pi$
$42$	2.97582	+	0.683683i	0.459179	+	0.105495i
$43$	−1.66897	−	1.66897i	−0.254515	−	0.254515i	0.568304	−	0.822819i	$-0.307600\pi$
$43$	−1.66897	−	1.66897i	−0.254515	−	0.254515i	−0.822819	+	0.568304i	$0.807600\pi$
$44$	8.88378	−	3.08012i	1.33928	−	0.464345i
$45$	3.04408	+	3.04408i	0.453785	+	0.453785i
$46$	5.59339	−	3.83588i	0.824700	−	0.565570i
$47$			12.9505i			1.88902i	0.328480	+	0.944511i	$0.393464\pi$
$47$			12.9505i			1.88902i	−0.328480	+	0.944511i	$0.606536\pi$
$48$	0.446361	−	3.76798i	0.0644266	−	0.543862i
$49$	1.81950			0.259929
$50$	0.956781	−	0.599282i	0.135309	−	0.0847512i
$51$	−1.26492	+	1.26492i	−0.177124	+	0.177124i
$52$	−3.56174	−	10.2729i	−0.493925	−	1.42459i
$53$	9.19784	−	9.19784i	1.26342	−	1.26342i	0.313996	−	0.949424i	$-0.398332\pi$
$53$	9.19784	−	9.19784i	1.26342	−	1.26342i	0.949424	−	0.313996i	$-0.101668\pi$
$54$	−6.66818	−	1.53199i	−0.907424	−	0.208477i
$55$	9.63673			1.29942
$56$	0.693380	+	6.40025i	0.0926569	+	0.855270i
$57$	−6.97862			−0.924341
$58$	−2.14716	−	0.493301i	−0.281935	−	0.0647736i
$59$	−5.82397	+	5.82397i	−0.758217	+	0.758217i	−0.975998	−	0.217781i	$-0.930118\pi$
$59$	−5.82397	+	5.82397i	−0.758217	+	0.758217i	0.217781	+	0.975998i	$0.430118\pi$
$60$	1.69729	−	3.49887i	0.219120	−	0.451702i
$61$	0.275232	+	0.275232i	0.0352398	+	0.0352398i	0.724507	−	0.689267i	$-0.242067\pi$
$61$	0.275232	+	0.275232i	0.0352398	+	0.0352398i	−0.689267	+	0.724507i	$0.742067\pi$
$62$	−4.86794	+	3.04904i	−0.618229	+	0.387229i
$63$	4.78019			0.602247
$64$	7.81439	−	1.71327i	0.976799	−	0.214159i
$65$		−	11.1436i		−	1.38219i
$66$	−5.34489	+	3.34778i	−0.657910	+	0.412083i
$67$	−9.16779	+	9.16779i	−1.12002	+	1.12002i	−0.128286	+	0.991737i	$0.540948\pi$
$67$	−9.16779	+	9.16779i	−1.12002	+	1.12002i	−0.991737	+	0.128286i	$0.959052\pi$
$68$	−3.39346	−	1.64616i	−0.411518	−	0.199626i
$69$	−3.08039	+	3.34765i	−0.370836	+	0.403010i
$70$	−1.47738	+	6.43049i	−0.176581	+	0.768590i
$71$	−1.85029			−0.219589			−0.109795	−	0.993954i	$-0.535019\pi$
$71$	−1.85029			−0.219589			−0.109795	+	0.993954i	$0.535019\pi$
$72$	−0.639801	−	5.90568i	−0.0754012	−	0.695991i
$73$			11.4766i			1.34324i	0.740896	+	0.671620i	$0.234401\pi$
$73$			11.4766i			1.34324i	−0.740896	+	0.671620i	$0.765599\pi$
$74$	−0.721858	−	0.165844i	−0.0839143	−	0.0192790i
$75$	−0.535460	+	0.535460i	−0.0618296	+	0.0618296i
$76$	−4.81997	−	13.9019i	−0.552888	−	1.59466i
$77$	7.56638	−	7.56638i	0.862269	−	0.862269i
$78$	3.87125	+	6.18064i	0.438333	+	0.699820i
$79$	2.78305			0.313118			0.156559	−	0.987669i	$-0.449960\pi$
$79$	2.78305			0.313118			0.156559	+	0.987669i	$0.449960\pi$
$80$	8.14229	+	0.964547i	0.910335	+	0.107840i
$81$	−1.71138			−0.190153
$82$	−5.40408	+	3.38485i	−0.596781	+	0.373794i
$83$	4.80163	−	4.80163i	0.527047	−	0.527047i	−0.392643	−	0.919691i	$-0.628439\pi$
$83$	4.80163	−	4.80163i	0.527047	−	0.527047i	0.919691	+	0.392643i	$0.128439\pi$
$84$	−1.41453	−	4.07982i	−0.154337	−	0.445145i
$85$	−2.73338	−	2.73338i	−0.296477	−	0.296477i
$86$	−0.747407	+	3.25318i	−0.0805950	+	0.350800i
$87$	1.47772			0.158429
$88$	−10.3606	−	8.33517i	−1.10444	−	0.888532i
$89$	15.1990			1.61109			0.805544	−	0.592536i	$-0.201873\pi$
$89$	15.1990			1.61109			0.805544	+	0.592536i	$0.201873\pi$
$90$	1.36322	−	5.93358i	0.143696	−	0.625454i
$91$	−8.74950	−	8.74950i	−0.917197	−	0.917197i
$92$	−8.79633	−	3.82422i	−0.917080	−	0.398703i
$93$	2.72433	−	2.72433i	0.282500	−	0.282500i
$94$	15.5214	−	9.72188i	1.60091	−	1.00273i
$95$		−	15.0802i		−	1.54720i
$96$	−4.85109	+	2.29364i	−0.495113	+	0.234093i
$97$		−	17.2722i		−	1.75372i	−0.480742	−	0.876862i	$-0.659633\pi$
$97$		−	17.2722i		−	1.75372i	0.480742	−	0.876862i	$-0.340367\pi$
$98$	−1.36589	−	2.18071i	−0.137976	−	0.220285i
$99$	−6.98170	+	6.98170i	−0.701687	+	0.701687i
$100$	−1.43650	−	0.696845i	−0.143650	−	0.0696845i
$101$	2.61032	+	2.61032i	0.259736	+	0.259736i	0.824947	−	0.565210i	$-0.191205\pi$
$101$	2.61032	+	2.61032i	0.259736	+	0.259736i	−0.565210	+	0.824947i	$0.691205\pi$
$102$	2.46560	+	0.566463i	0.244131	+	0.0560882i
$103$			5.02316i			0.494947i	0.968895	+	0.247473i	$0.0796003\pi$
$103$			5.02316i			0.494947i	−0.968895	+	0.247473i	$0.920400\pi$
$104$	−9.63850	+	11.9806i	−0.945133	+	1.17480i
$105$		−	4.42561i		−	0.431895i
$106$	−17.9286	−	4.11903i	−1.74138	−	0.400076i
$107$	−6.24164	−	6.24164i	−0.603403	−	0.603403i	0.337811	−	0.941214i	$-0.390313\pi$
$107$	−6.24164	−	6.24164i	−0.603403	−	0.603403i	−0.941214	+	0.337811i	$0.890313\pi$
$108$	3.16965	+	9.14201i	0.305000	+	0.879691i
$109$	7.28329	+	7.28329i	0.697612	+	0.697612i	0.963895	−	0.266283i	$-0.0857954\pi$
$109$	7.28329	+	7.28329i	0.697612	+	0.697612i	−0.266283	+	0.963895i	$0.585795\pi$
$110$	−7.23426	−	11.5498i	−0.689760	−	1.10123i
$111$	0.496800			0.0471542
$112$	7.15032	−	5.63568i	0.675642	−	0.532521i
$113$		−	10.6919i		−	1.00581i	−0.864342	−	0.502905i	$-0.832265\pi$
$113$		−	10.6919i		−	1.00581i	0.864342	−	0.502905i	$-0.167735\pi$
$114$	5.23882	+	8.36403i	0.490661	+	0.783363i
$115$	−7.23399	−	6.65646i	−0.674573	−	0.620718i
$116$	1.02063	+	2.94373i	0.0947630	+	0.273319i
$117$	8.07340	+	8.07340i	0.746386	+	0.746386i
$118$	11.3522	+	2.60813i	1.04505	+	0.240097i
$119$	−4.29228			−0.393473
$120$	−5.46762	+	0.592343i	−0.499124	+	0.0540733i
$121$			11.1022i			1.00929i
$122$	0.123256	−	0.536487i	0.0111591	−	0.0485712i
$123$	3.02437	−	3.02437i	0.272699	−	0.272699i
$124$	7.30869	+	3.54543i	0.656340	+	0.318389i
$125$	−8.40424	−	8.40424i	−0.751698	−	0.751698i
$126$	−3.58847	−	5.72916i	−0.319686	−	0.510394i
$127$		−	0.457843i		−	0.0406270i	−0.999794	−	0.0203135i	$-0.993534\pi$
$127$		−	0.457843i		−	0.0406270i	0.999794	−	0.0203135i	$-0.00646644\pi$
$128$	−7.91963	−	8.07957i	−0.700003	−	0.714140i
$129$		−	2.23892i		−	0.197126i
$130$	−13.3558	+	8.36545i	−1.17138	+	0.733698i
$131$	7.00221	+	7.00221i	0.611786	+	0.611786i	0.943411	−	0.331625i	$-0.107597\pi$
$131$	7.00221	+	7.00221i	0.611786	+	0.611786i	−0.331625	+	0.943411i	$0.607597\pi$
$132$	8.02477	+	3.89280i	0.698467	+	0.338825i
$133$	−11.8404	−	11.8404i	−1.02669	−	1.02669i
$134$	17.8700	+	4.10557i	1.54373	+	0.354667i
$135$			9.91686i			0.853507i
$136$	0.574498	+	5.30290i	0.0492628	+	0.454720i
$137$	13.1770			1.12579			0.562896	−	0.826528i	$-0.309687\pi$
$137$	13.1770			1.12579			0.562896	+	0.826528i	$0.309687\pi$
$138$	6.32467	+	1.17885i	0.538392	+	0.100350i
$139$	0.430791	−	0.430791i	0.0365392	−	0.0365392i	−0.688601	−	0.725140i	$-0.741775\pi$
$139$	0.430791	−	0.430791i	0.0365392	−	0.0365392i	0.725140	+	0.688601i	$0.241775\pi$
$140$	8.81614	−	3.05667i	0.745100	−	0.258336i
$141$	−8.68652	+	8.68652i	−0.731537	+	0.731537i
$142$	1.38901	+	2.21761i	0.116563	+	0.186098i
$143$	25.5582			2.13728
$144$	−6.59780	+	5.20019i	−0.549816	+	0.433349i
$145$			3.19323i			0.265183i
$146$	13.7550	−	8.61547i	1.13837	−	0.713021i
$147$	1.22043	+	1.22043i	0.100659	+	0.100659i
$148$	0.343128	+	0.989662i	0.0282050	+	0.0813497i
$149$	−8.70336	+	8.70336i	−0.713007	+	0.713007i	−0.967163	−	0.254156i	$-0.918202\pi$
$149$	−8.70336	+	8.70336i	−0.713007	+	0.713007i	0.254156	+	0.967163i	$0.418202\pi$
$150$	1.04373	+	0.239793i	0.0852200	+	0.0195790i
$151$	−17.2438			−1.40328			−0.701642	−	0.712529i	$-0.747549\pi$
$151$	−17.2438			−1.40328			−0.701642	+	0.712529i	$0.747549\pi$
$152$	−13.0434	+	16.2130i	−1.05796	+	1.31504i
$153$	3.96060			0.320196
$154$	−14.7485	−	3.38842i	−1.18847	−	0.273047i
$155$	5.88704	+	5.88704i	0.472858	+	0.472858i
$156$	4.50150	−	9.27957i	0.360408	−	0.742960i
$157$	9.59663	+	9.59663i	0.765894	+	0.765894i	0.977381	−	0.211487i	$-0.0678305\pi$
$157$	9.59663	+	9.59663i	0.765894	+	0.765894i	−0.211487	+	0.977381i	$0.567831\pi$
$158$	−2.08923	−	3.33555i	−0.166210	−	0.265362i
$159$	12.3389			0.978537
$160$	−4.95635	−	10.4828i	−0.391834	−	0.828738i
$161$	−10.9062	+	0.453452i	−0.859531	+	0.0357370i
$162$	1.28473	+	2.05113i	0.100938	+	0.161152i
$163$	13.3128	+	13.3128i	1.04274	+	1.04274i	0.999045	+	0.0436956i	$0.0139132\pi$
$163$	13.3128	+	13.3128i	1.04274	+	1.04274i	0.0436956	+	0.999045i	$0.486087\pi$
$164$	8.11364	+	3.93591i	0.633569	+	0.307343i
$165$	6.46383	+	6.46383i	0.503208	+	0.503208i
$166$	−9.35943	−	2.15029i	−0.726432	−	0.166895i
$167$	9.90841			0.766736			0.383368	−	0.923596i	$-0.374764\pi$
$167$	9.90841			0.766736			0.383368	+	0.923596i	$0.374764\pi$
$168$	−3.82788	+	4.75805i	−0.295327	+	0.367091i
$169$		−	16.5546i		−	1.27343i
$170$	−1.22408	+	5.32795i	−0.0938825	+	0.408635i
$171$	10.9254	+	10.9254i	0.835488	+	0.835488i
$172$	4.46009	−	1.54637i	0.340079	−	0.117909i
$173$	−2.92457	+	2.92457i	−0.222351	+	0.222351i	−0.809488	−	0.587137i	$-0.800255\pi$
$173$	−2.92457	+	2.92457i	−0.222351	+	0.222351i	0.587137	+	0.809488i	$0.300255\pi$
$174$	−1.10932	−	1.77108i	−0.0840974	−	0.134265i
$175$	−1.81699			−0.137352
$176$	−2.21222	+	18.6746i	−0.166752	+	1.40765i
$177$	−7.81285			−0.587250
$178$	−11.4098	−	18.2163i	−0.855202	−	1.36537i
$179$	6.79334	+	6.79334i	0.507758	+	0.507758i	0.913838	−	0.406080i	$-0.133104\pi$
$179$	6.79334	+	6.79334i	0.507758	+	0.507758i	−0.406080	+	0.913838i	$0.633104\pi$
$180$	−8.13489	+	2.82047i	−0.606339	+	0.210225i
$181$	−12.5304	+	12.5304i	−0.931377	+	0.931377i	−0.997792	−	0.0664150i	$-0.978844\pi$
$181$	−12.5304	+	12.5304i	−0.931377	+	0.931377i	0.0664150	+	0.997792i	$0.478844\pi$
$182$	−3.91825	+	17.0547i	−0.290440	+	1.26418i
$183$			0.369223i			0.0272937i
$184$	2.01995	+	13.4134i	0.148913	+	0.988850i
$185$			1.07354i			0.0789284i
$186$	−5.31031	−	1.22003i	−0.389371	−	0.0894566i
$187$	6.26910	−	6.26910i	0.458442	−	0.458442i
$188$	−23.3038	−	11.3046i	−1.69960	−	0.824473i
$189$	7.78632	+	7.78632i	0.566372	+	0.566372i
$190$	−18.0739	+	11.3206i	−1.31122	+	0.821286i
$191$	−16.2633			−1.17677			−0.588385	−	0.808581i	$-0.700236\pi$
$191$	−16.2633			−1.17677			−0.588385	+	0.808581i	$0.700236\pi$
$192$	6.39067	+	4.09232i	0.461207	+	0.295338i
$193$	−4.12644			−0.297028			−0.148514	−	0.988910i	$-0.547449\pi$
$193$	−4.12644			−0.297028			−0.148514	+	0.988910i	$0.547449\pi$
$194$	−20.7011	+	12.9662i	−1.48625	+	0.930916i
$195$	7.47455	−	7.47455i	0.535263	−	0.535263i
$196$	−1.58826	+	3.27410i	−0.113447	+	0.233865i
$197$	−7.49535	−	7.49535i	−0.534022	−	0.534022i	0.387745	−	0.921767i	$-0.373254\pi$
$197$	−7.49535	−	7.49535i	−0.534022	−	0.534022i	−0.921767	+	0.387745i	$0.873254\pi$
$198$	13.6089	+	3.12659i	0.967140	+	0.222197i
$199$		−	5.11160i		−	0.362352i	−0.983451	−	0.181176i	$-0.942010\pi$
$199$		−	5.11160i		−	0.362352i	0.983451	−	0.181176i	$-0.0579903\pi$
$200$	0.243194	+	2.24480i	0.0171964	+	0.158731i
$201$	−12.2986			−0.867474
$202$	1.16897	−	5.08808i	0.0822483	−	0.357996i
$203$	2.50720	+	2.50720i	0.175971	+	0.175971i
$204$	−1.17200	−	3.38032i	−0.0820564	−	0.236670i
$205$	6.53541	+	6.53541i	0.456453	+	0.456453i
$206$	6.02037	−	3.77087i	0.419459	−	0.262729i
$207$	10.0635	−	0.418412i	0.699460	−	0.0290817i
$208$	21.5947	+	2.55814i	1.49732	+	0.177375i
$209$	34.5869			2.39243
$210$	−5.30419	+	3.32229i	−0.366024	+	0.229260i
$211$	−8.06042	−	8.06042i	−0.554902	−	0.554902i	0.372949	−	0.927852i	$-0.378346\pi$
$211$	−8.06042	−	8.06042i	−0.554902	−	0.554902i	−0.927852	+	0.372949i	$0.878346\pi$
$212$	8.52218	+	24.5800i	0.585306	+	1.68816i
$213$	−1.24108	−	1.24108i	−0.0850375	−	0.0850375i
$214$	−2.79517	+	12.1663i	−0.191074	+	0.831673i
$215$	4.83811			0.329956
$216$	8.57746	−	10.6618i	0.583622	−	0.725442i
$217$	9.24454			0.627560
$218$	3.26165	−	14.1967i	0.220906	−	0.961523i
$219$	−7.69794	+	7.69794i	−0.520179	+	0.520179i
$220$	−8.41201	+	17.3408i	−0.567137	+	1.16912i
$221$	−7.24936	−	7.24936i	−0.487645	−	0.487645i
$222$	−0.372946	−	0.595426i	−0.0250305	−	0.0399624i
$223$			7.56976i			0.506909i	0.967347	+	0.253454i	$0.0815668\pi$
$223$			7.56976i			0.506909i	−0.967347	+	0.253454i	$0.918433\pi$
$224$	−12.1222	−	4.33914i	−0.809949	−	0.289921i
$225$	1.67659			0.111772
$226$	−12.8145	+	8.02637i	−0.852407	+	0.533906i
$227$	−2.93082	+	2.93082i	−0.194526	+	0.194526i	−0.797648	−	0.603123i	$-0.793923\pi$
$227$	−2.93082	+	2.93082i	−0.194526	+	0.194526i	0.603123	+	0.797648i	$0.293923\pi$
$228$	6.09171	−	12.5577i	0.403433	−	0.831653i
$229$	−0.601957	+	0.601957i	−0.0397785	+	0.0397785i	−0.726716	−	0.686938i	$-0.758954\pi$
$229$	−0.601957	+	0.601957i	−0.0397785	+	0.0397785i	0.686938	+	0.726716i	$0.258954\pi$
$230$	−2.54739	+	13.6671i	−0.167970	+	0.901180i
$231$	10.1503			0.667840
$232$	2.76195	−	3.43309i	0.181331	−	0.225394i
$233$		−	13.7383i		−	0.900028i	−0.893022	−	0.450014i	$-0.851419\pi$
$233$		−	13.7383i		−	0.900028i	0.893022	−	0.450014i	$-0.148581\pi$
$234$	3.61548	−	15.7368i	0.236351	−	1.02875i
$235$	−18.7708	−	18.7708i	−1.22447	−	1.22447i
$236$	−5.39615	−	15.5638i	−0.351260	−	1.01311i
$237$	1.86673	+	1.86673i	0.121257	+	0.121257i
$238$	3.22220	+	5.14440i	0.208864	+	0.333462i
$239$			2.11257i			0.136651i	0.997663	+	0.0683253i	$0.0217656\pi$
$239$			2.11257i			0.136651i	−0.997663	+	0.0683253i	$0.978234\pi$
$240$	4.81446	+	6.10840i	0.310772	+	0.394296i
$241$			19.3136i			1.24410i	0.782979	+	0.622049i	$0.213699\pi$
$241$			19.3136i			1.24410i	−0.782979	+	0.622049i	$0.786301\pi$
$242$	13.3062	−	8.33435i	0.855354	−	0.535752i
$243$	−11.4108	−	11.4108i	−0.732000	−	0.732000i
$244$	−0.735519	+	0.255014i	−0.0470868	+	0.0163256i
$245$	−2.63724	+	2.63724i	−0.168487	+	0.168487i
$246$	−5.89517	−	1.35439i	−0.375862	−	0.0863530i
$247$		−	39.9951i		−	2.54483i
$248$	−1.23733	−	11.4212i	−0.0785705	−	0.725245i
$249$	6.44138			0.408206
$250$	−3.76363	+	16.3817i	−0.238033	+	1.03607i
$251$	−5.08882	−	5.08882i	−0.321204	−	0.321204i	0.528025	−	0.849229i	$-0.322933\pi$
$251$	−5.08882	−	5.08882i	−0.321204	−	0.321204i	−0.849229	+	0.528025i	$0.822933\pi$
$252$	−4.17267	+	8.60171i	−0.262854	+	0.541857i
$253$	15.2668	−	16.5914i	0.959816	−	1.04309i
$254$	−0.548735	+	0.343701i	−0.0344307	+	0.0215657i
$255$		−	3.66682i		−	0.229625i
$256$	−3.73831	+	15.5572i	−0.233644	+	0.972322i
$257$	−24.2743			−1.51419			−0.757095	−	0.653304i	$-0.773382\pi$
$257$	−24.2743			−1.51419			−0.757095	+	0.653304i	$0.773382\pi$
$258$	−2.68339	+	1.68075i	−0.167061	+	0.104639i
$259$	0.842902	+	0.842902i	0.0523754	+	0.0523754i
$260$	20.0523	+	9.72735i	1.24359	+	0.603265i
$261$	−2.31346	−	2.31346i	−0.143200	−	0.143200i
$262$	3.13577	−	13.6488i	0.193729	−	0.843228i
$263$		−	2.50166i		−	0.154259i	−0.997021	−	0.0771295i	$-0.975424\pi$
$263$		−	2.50166i		−	0.154259i	0.997021	−	0.0771295i	$-0.0245755\pi$
$264$	−1.35856	−	12.5402i	−0.0836135	−	0.771794i
$265$			26.6633i			1.63791i
$266$	−5.30242	+	23.0795i	−0.325113	+	1.41509i
$267$	10.1947	+	10.1947i	0.623905	+	0.623905i
$268$	−8.49433	−	24.4996i	−0.518874	−	1.49655i
$269$	−14.3723	+	14.3723i	−0.876294	+	0.876294i	−0.993149	−	0.116855i	$-0.962719\pi$
$269$	−14.3723	+	14.3723i	−0.876294	+	0.876294i	0.116855	+	0.993149i	$0.462719\pi$
$270$	11.8856	−	7.44455i	0.723333	−	0.453061i
$271$			13.8576i			0.841786i	0.907110	+	0.420893i	$0.138283\pi$
$271$			13.8576i			0.841786i	−0.907110	+	0.420893i	$0.861717\pi$
$272$	5.92437	−	4.66942i	0.359218	−	0.283125i
$273$		−	11.7374i		−	0.710382i
$274$	−9.89196	−	15.7930i	−0.597595	−	0.954089i
$275$	2.65381	−	2.65381i	0.160030	−	0.160030i
$276$	−3.33503	−	8.46522i	−0.200745	−	0.509546i
$277$	18.6905	+	18.6905i	1.12300	+	1.12300i	0.991287	+	0.131717i	$0.0420490\pi$
$277$	18.6905	+	18.6905i	1.12300	+	1.12300i	0.131717	+	0.991287i	$0.457951\pi$
$278$	−0.839706	−	0.192919i	−0.0503622	−	0.0115705i
$279$	−8.53018			−0.510689
$280$	−10.2817	−	8.27171i	−0.614451	−	0.494329i
$281$	−2.91403			−0.173836			−0.0869182	−	0.996215i	$-0.527702\pi$
$281$	−2.91403			−0.173836			−0.0869182	+	0.996215i	$0.527702\pi$
$282$	16.9319	+	3.89005i	1.00828	+	0.231649i
$283$	10.3017	+	10.3017i	0.612373	+	0.612373i	0.943564	−	0.331191i	$-0.107450\pi$
$283$	10.3017	+	10.3017i	0.612373	+	0.612373i	−0.331191	+	0.943564i	$0.607450\pi$
$284$	1.61514	−	3.32951i	0.0958408	−	0.197570i
$285$	10.1150	−	10.1150i	0.599162	−	0.599162i
$286$	−19.1864	−	30.6320i	−1.13452	−	1.81131i
$287$	10.2627			0.605788
$288$	11.1855	+	4.00384i	0.659111	+	0.235929i
$289$	13.4436			0.790803
$290$	3.82716	−	2.39715i	0.224738	−	0.140765i
$291$	11.5853	−	11.5853i	0.679142	−	0.679142i
$292$	−20.6517	−	10.0181i	−1.20855	−	0.586264i
$293$	−13.0337	+	13.0337i	−0.761436	+	0.761436i	−0.976582	−	0.215146i	$-0.930977\pi$
$293$	−13.0337	+	13.0337i	−0.761436	+	0.761436i	0.215146	+	0.976582i	$0.430977\pi$
$294$	0.546539	−	2.37888i	0.0318748	−	0.138739i
$295$		−	16.8829i		−	0.982960i
$296$	0.928547	−	1.15418i	0.0539707	−	0.0670855i
$297$	−22.7446			−1.31978
$298$	16.9648	+	3.89759i	0.982742	+	0.225781i
$299$	−19.1857	−	17.6540i	−1.10954	−	1.02096i
$300$	−0.496126	−	1.43094i	−0.0286438	−	0.0826155i
$301$	3.79869	−	3.79869i	0.218953	−	0.218953i
$302$	12.9449	+	20.6671i	0.744895	+	1.18926i
$303$			3.50174i			0.201170i
$304$	29.2232	+	3.46183i	1.67607	+	0.198550i
$305$	−0.797859			−0.0456852
$306$	−2.97321	−	4.74687i	−0.169967	−	0.271361i
$307$	−20.3605	−	20.3605i	−1.16204	−	1.16204i	−0.984029	−	0.178006i	$-0.943035\pi$
$307$	−20.3605	−	20.3605i	−1.16204	−	1.16204i	−0.178006	−	0.984029i	$-0.556965\pi$
$308$	7.01057	+	20.2201i	0.399464	+	1.15215i
$309$	−3.36928	+	3.36928i	−0.191672	+	0.191672i
$310$	2.63637	−	11.4751i	0.149736	−	0.651743i
$311$	−4.15120			−0.235393			−0.117697	−	0.993050i	$-0.537551\pi$
$311$	−4.15120			−0.235393			−0.117697	+	0.993050i	$0.537551\pi$
$312$	−14.5010	+	1.57099i	−0.820959	+	0.0889397i
$313$	3.26556			0.184580			0.0922901	−	0.995732i	$-0.470581\pi$
$313$	3.26556			0.184580			0.0922901	+	0.995732i	$0.470581\pi$
$314$	4.29762	−	18.7059i	0.242529	−	1.05564i
$315$	−6.92855	+	6.92855i	−0.390379	+	0.390379i
$316$	−2.42936	+	5.00797i	−0.136662	+	0.281720i
$317$	−18.9573	+	18.9573i	−1.06475	+	1.06475i	−0.0669963	+	0.997753i	$0.521342\pi$
$317$	−18.9573	+	18.9573i	−1.06475	+	1.06475i	−0.997753	+	0.0669963i	$0.978658\pi$
$318$	−9.26275	−	14.7884i	−0.519429	−	0.829294i
$319$	−7.32378			−0.410053
$320$	−8.84314	+	13.8097i	−0.494347	+	0.771985i
$321$		−	8.37315i		−	0.467344i
$322$	8.73074	+	12.7310i	0.486545	+	0.709468i
$323$	−9.81029	−	9.81029i	−0.545859	−	0.545859i
$324$	1.49388	−	3.07955i	0.0829934	−	0.171086i
$325$	−3.06877	−	3.06877i	−0.170225	−	0.170225i
$326$	5.96183	−	25.9496i	0.330195	−	1.43721i
$327$			9.77052i			0.540311i
$328$	−1.37360	−	12.6791i	−0.0758445	−	0.700083i
$329$	−29.4762			−1.62508
$330$	2.89467	−	12.5994i	0.159346	−	0.693575i
$331$	19.0787	−	19.0787i	1.04866	−	1.04866i	0.0499074	−	0.998754i	$-0.484107\pi$
$331$	19.0787	−	19.0787i	1.04866	−	1.04866i	0.998754	−	0.0499074i	$-0.0158926\pi$
$332$	4.44891	+	12.8317i	0.244166	+	0.704231i
$333$	−0.777769	−	0.777769i	−0.0426215	−	0.0426215i
$334$	−7.43821	−	11.8754i	−0.407001	−	0.649796i
$335$		−	26.5761i		−	1.45201i
$336$	8.57620	+	1.01595i	0.467870	+	0.0554246i
$337$			16.3290i			0.889499i	0.895655	+	0.444749i	$0.146707\pi$
$337$			16.3290i			0.889499i	−0.895655	+	0.444749i	$0.853293\pi$
$338$	−19.8410	+	12.4275i	−1.07921	+	0.675965i
$339$	7.17158	−	7.17158i	0.389507	−	0.389507i
$340$	7.30458	−	2.53259i	0.396147	−	0.137349i
$341$	−13.5021	+	13.5021i	−0.731181	+	0.731181i
$342$	4.89269	−	21.2960i	0.264566	−	1.15156i
$343$			20.0738i			1.08388i
$344$	−5.20153	−	4.18466i	−0.280448	−	0.225622i
$345$	−0.387376	−	9.31701i	−0.0208556	−	0.501611i
$346$	5.70063	+	1.30970i	0.306468	+	0.0704099i
$347$	4.28173	−	4.28173i	0.229855	−	0.229855i	−0.582777	−	0.812632i	$-0.698034\pi$
$347$	4.28173	−	4.28173i	0.229855	−	0.229855i	0.812632	+	0.582777i	$0.198034\pi$
$348$	−1.28992	+	2.65909i	−0.0691470	+	0.142542i
$349$	−3.50723	+	3.50723i	−0.187738	+	0.187738i	−0.794717	−	0.606980i	$-0.792381\pi$
$349$	−3.50723	+	3.50723i	−0.187738	+	0.187738i	0.606980	+	0.794717i	$0.292381\pi$
$350$	1.36401	+	2.17770i	0.0729093	+	0.116403i
$351$			26.3011i			1.40385i
$352$	24.0426	−	11.3676i	1.28148	−	0.605893i
$353$	22.1399			1.17839			0.589193	−	0.807992i	$-0.299446\pi$
$353$	22.1399			1.17839			0.589193	+	0.807992i	$0.299446\pi$
$354$	5.86507	+	9.36387i	0.311725	+	0.497684i
$355$	2.68187	−	2.68187i	0.142339	−	0.142339i
$356$	−13.2673	+	27.3498i	−0.703168	+	1.44954i
$357$	−2.87904	−	2.87904i	−0.152375	−	0.152375i
$358$	3.04223	−	13.2417i	0.160787	−	0.699845i
$359$			3.34064i			0.176312i	0.996107	+	0.0881561i	$0.0280974\pi$
$359$			3.34064i			0.176312i	−0.996107	+	0.0881561i	$0.971903\pi$
$360$	9.48723	+	7.63253i	0.500021	+	0.402270i
$361$		−	35.1239i		−	1.84863i
$362$	24.4245	+	5.61144i	1.28372	+	0.294931i
$363$	−7.44676	+	7.44676i	−0.390854	+	0.390854i
$364$	23.3818	−	8.10677i	1.22554	−	0.424910i
$365$	−16.6346	−	16.6346i	−0.870695	−	0.870695i
$366$	0.442522	−	0.277174i	0.0231310	−	0.0144881i
$367$	−4.97591			−0.259740			−0.129870	−	0.991531i	$-0.541456\pi$
$367$	−4.97591			−0.259740			−0.129870	+	0.991531i	$0.541456\pi$
$368$	14.5599	−	12.4904i	0.758988	−	0.651105i
$369$	−9.46966			−0.492971
$370$	1.28666	−	0.805904i	0.0668904	−	0.0418969i
$371$	20.9349	+	20.9349i	1.08689	+	1.08689i
$372$	2.52420	+	7.28039i	0.130874	+	0.377471i
$373$	−22.0154	+	22.0154i	−1.13991	+	1.13991i	−0.151449	+	0.988465i	$0.548394\pi$
$373$	−22.0154	+	22.0154i	−1.13991	+	1.13991i	−0.988465	+	0.151449i	$0.951606\pi$
$374$	−12.2198	−	2.80746i	−0.631873	−	0.145171i
$375$		−	11.2743i		−	0.582201i
$376$	3.94522	+	36.4164i	0.203459	+	1.87803i
$377$			8.46896i			0.436174i
$378$	3.48692	−	15.1772i	0.179348	−	0.780633i
$379$	−0.0193600	−	0.0193600i	−0.000994457	−	0.000994457i	0.706609	−	0.707604i	$-0.250224\pi$
$379$	−0.0193600	−	0.0193600i	−0.000994457	−	0.000994457i	−0.707604	+	0.706609i	$0.750224\pi$
$380$	27.1361	+	13.1637i	1.39205	+	0.675281i
$381$	0.307098	−	0.307098i	0.0157331	−	0.0157331i
$382$	12.2088	+	19.4919i	0.624656	+	0.997293i
$383$	18.4502			0.942759			0.471380	−	0.881930i	$-0.343756\pi$
$383$	18.4502			0.942759			0.471380	+	0.881930i	$0.343756\pi$
$384$	0.107280	−	10.7314i	0.00547460	−	0.547637i
$385$			21.9339i			1.11785i
$386$	3.09771	+	4.94563i	0.157669	+	0.251726i
$387$	−3.50515	+	3.50515i	−0.178177	+	0.178177i
$388$	31.0805	+	15.0771i	1.57787	+	0.765422i
$389$	17.3891	−	17.3891i	0.881660	−	0.881660i	−0.112043	−	0.993703i	$-0.535740\pi$
$389$	17.3891	−	17.3891i	0.881660	−	0.881660i	0.993703	+	0.112043i	$0.0357395\pi$
$390$	−14.5695	−	3.34730i	−0.737757	−	0.169497i
$391$	−9.03632	+	0.375706i	−0.456986	+	0.0190003i
$392$	5.11639	−	0.554291i	0.258417	−	0.0279959i
$393$			9.39346i			0.473837i
$394$	−3.35661	+	14.6101i	−0.169104	+	0.736045i
$395$	−4.03384	+	4.03384i	−0.202965	+	0.202965i
$396$	−6.46884	−	18.6576i	−0.325071	−	0.937582i
$397$	8.83120	−	8.83120i	0.443225	−	0.443225i	−0.449869	−	0.893094i	$-0.648529\pi$
$397$	8.83120	−	8.83120i	0.443225	−	0.443225i	0.893094	+	0.449869i	$0.148529\pi$
$398$	−6.12637	+	3.83726i	−0.307087	+	0.192344i
$399$		−	15.8838i		−	0.795186i
$400$	2.50788	−	1.97664i	0.125394	−	0.0988319i
$401$		−	1.26312i		−	0.0630771i	−0.999503	−	0.0315385i	$-0.989959\pi$
$401$		−	1.26312i		−	0.0630771i	0.999503	−	0.0315385i	$-0.0100407\pi$
$402$	9.23249	+	14.7401i	0.460475	+	0.735169i
$403$	15.6134	+	15.6134i	0.777758	+	0.777758i
$404$	−6.97572	+	2.41857i	−0.347055	+	0.120328i
$405$	2.48053	−	2.48053i	0.123258	−	0.123258i
$406$	1.12279	−	4.88708i	0.0557231	−	0.242542i
$407$	−2.46220			−0.122047
$408$	−3.17157	+	3.94226i	−0.157016	+	0.195171i
$409$			7.78472i			0.384930i	0.981304	+	0.192465i	$0.0616481\pi$
$409$			7.78472i			0.384930i	−0.981304	+	0.192465i	$0.938352\pi$
$410$	2.92673	−	12.7389i	0.144541	−	0.629132i
$411$	8.83849	+	8.83849i	0.435971	+	0.435971i
$412$	−9.03894	−	4.38477i	−0.445316	−	0.216022i
$413$	−13.2558	−	13.2558i	−0.652274	−	0.652274i
$414$	−8.05609	−	11.7472i	−0.395935	−	0.577343i
$415$			13.9193i			0.683270i
$416$	−13.1450	−	27.8021i	−0.644489	−	1.36311i
$417$	0.577905			0.0283001
$418$	−25.9643	−	41.4532i	−1.26995	−	2.02754i
$419$	−0.940821	+	0.940821i	−0.0459621	+	0.0459621i	−0.729714	−	0.683752i	$-0.760347\pi$
$419$	−0.940821	+	0.940821i	−0.0459621	+	0.0459621i	0.683752	+	0.729714i	$0.260347\pi$
$420$	7.96368	+	3.86316i	0.388588	+	0.188503i
$421$	22.9027	−	22.9027i	1.11621	−	1.11621i	0.123918	−	0.992292i	$-0.460454\pi$
$421$	22.9027	−	22.9027i	1.11621	−	1.11621i	0.992292	−	0.123918i	$-0.0395459\pi$
$422$	−3.60966	+	15.7115i	−0.175716	+	0.764825i
$423$	27.1985			1.32244
$424$	23.0621	−	28.6661i	1.11999	−	1.39215i
$425$	−1.50546			−0.0730255
$426$	−0.555788	+	2.41914i	−0.0269280	+	0.117208i
$427$	−0.626447	+	0.626447i	−0.0303159	+	0.0303159i
$428$	16.6799	−	5.78314i	0.806255	−	0.279539i
$429$	17.1431	+	17.1431i	0.827677	+	0.827677i
$430$	−3.63195	−	5.79858i	−0.175148	−	0.279632i
$431$	−29.0886			−1.40115			−0.700575	−	0.713579i	$-0.747073\pi$
$431$	−29.0886			−1.40115			−0.700575	+	0.713579i	$0.747073\pi$
$432$	−19.2174	−	2.27653i	−0.924599	−	0.109529i
$433$			20.1866i			0.970106i	0.874485	+	0.485053i	$0.161200\pi$
$433$			20.1866i			0.970106i	−0.874485	+	0.485053i	$0.838800\pi$
$434$	−6.93984	−	11.0798i	−0.333123	−	0.531847i
$435$	−2.14186	+	2.14186i	−0.102694	+	0.102694i
$436$	−19.4636	+	6.74827i	−0.932137	+	0.323183i
$437$	−25.9633	−	23.8905i	−1.24199	−	1.14284i
$438$	15.0050	+	3.44734i	0.716965	+	0.164720i
$439$	9.76395			0.466008			0.233004	−	0.972476i	$-0.425145\pi$
$439$	9.76395			0.466008			0.233004	+	0.972476i	$0.425145\pi$
$440$	27.0982	−	2.93573i	1.29186	−	0.139955i
$441$		−	3.82130i		−	0.181967i
$442$	−3.24645	+	14.1306i	−0.154418	+	0.672124i
$443$	−17.3012	+	17.3012i	−0.822006	+	0.822006i	−0.986395	−	0.164390i	$-0.947434\pi$
$443$	−17.3012	+	17.3012i	−0.822006	+	0.822006i	0.164390	+	0.986395i	$0.447434\pi$
$444$	−0.433662	+	0.893967i	−0.0205807	+	0.0424258i
$445$	−22.0299	+	22.0299i	−1.04432	+	1.04432i
$446$	9.07252	−	5.68259i	0.429597	−	0.269078i
$447$	−11.6755			−0.552234
$448$	3.89953	+	17.7861i	0.184236	+	0.840315i
$449$	−5.62283			−0.265358			−0.132679	−	0.991159i	$-0.542358\pi$
$449$	−5.62283			−0.265358			−0.132679	+	0.991159i	$0.542358\pi$
$450$	−1.25861	−	2.00942i	−0.0593313	−	0.0947252i
$451$	−14.9892	+	14.9892i	−0.705813	+	0.705813i
$452$	19.2396	+	9.33307i	0.904953	+	0.438991i
$453$	−11.5663	−	11.5663i	−0.543432	−	0.543432i
$454$	5.71282	+	1.31250i	0.268116	+	0.0615986i
$455$	25.3636			1.18906
$456$	−19.6237	+	2.12596i	−0.918964	+	0.0995572i
$457$	−3.01480			−0.141026			−0.0705131	−	0.997511i	$-0.522464\pi$
$457$	−3.01480			−0.141026			−0.0705131	+	0.997511i	$0.522464\pi$
$458$	1.17335	+	0.269572i	0.0548269	+	0.0125963i
$459$	6.45133	+	6.45133i	0.301122	+	0.301122i
$460$	18.2926	−	7.20672i	0.852897	−	0.336015i
$461$	3.88877	−	3.88877i	0.181118	−	0.181118i	−0.610725	−	0.791843i	$-0.709122\pi$
$461$	3.88877	−	3.88877i	0.181118	−	0.181118i	0.791843	+	0.610725i	$0.209122\pi$
$462$	−7.61978	−	12.1653i	−0.354504	−	0.565983i
$463$		−	9.71786i		−	0.451627i	−0.974171	−	0.225814i	$-0.927496\pi$
$463$		−	9.71786i		−	0.451627i	0.974171	−	0.225814i	$-0.0725041\pi$
$464$	−6.18802	−	0.733042i	−0.287272	−	0.0340306i
$465$			7.89745i			0.366236i
$466$	−16.4657	+	10.3133i	−0.762758	+	0.477755i
$467$	23.4089	−	23.4089i	1.08323	−	1.08323i	0.0870279	−	0.996206i	$-0.472263\pi$
$467$	23.4089	−	23.4089i	1.08323	−	1.08323i	0.996206	−	0.0870279i	$-0.0277369\pi$
$468$	−21.5750	+	7.48034i	−0.997307	+	0.345779i
$469$	−20.8665	−	20.8665i	−0.963527	−	0.963527i
$470$	−8.40606	+	36.5884i	−0.387743	+	1.68770i
$471$			12.8739i			0.593196i
$472$	−14.6026	+	18.1511i	−0.672141	+	0.835471i
$473$			11.0964i			0.510211i
$474$	0.835971	−	3.63867i	0.0383974	−	0.167129i
$475$	−4.15285	−	4.15285i	−0.190546	−	0.190546i
$476$	3.74678	−	7.72376i	0.171733	−	0.354018i
$477$	−19.3172	−	19.3172i	−0.884475	−	0.884475i
$478$	2.53196	−	1.58590i	0.115809	−	0.0725372i
$479$	−11.2386			−0.513507			−0.256753	−	0.966477i	$-0.582653\pi$
$479$	−11.2386			−0.513507			−0.256753	+	0.966477i	$0.582653\pi$
$480$	3.70685	−	10.3558i	0.169194	−	0.472675i
$481$			2.84721i			0.129821i
$482$	23.1478	−	14.4986i	1.05435	−	0.660395i
$483$	−7.61950	−	7.01119i	−0.346699	−	0.319020i
$484$	−19.9778	−	9.69119i	−0.908082	−	0.440509i
$485$	25.0348	+	25.0348i	1.13677	+	1.13677i
$486$	−5.11003	+	22.2420i	−0.231796	+	1.00892i
$487$	−20.3561			−0.922425			−0.461212	−	0.887290i	$-0.652585\pi$
$487$	−20.3561			−0.922425			−0.461212	+	0.887290i	$0.652585\pi$
$488$	0.857791	+	0.690098i	0.0388304	+	0.0312393i
$489$			17.8591i			0.807617i
$490$	5.14056	+	1.18102i	0.232227	+	0.0533533i
$491$	5.63270	−	5.63270i	0.254200	−	0.254200i	−0.568490	−	0.822690i	$-0.692472\pi$
$491$	5.63270	−	5.63270i	0.254200	−	0.254200i	0.822690	+	0.568490i	$0.192472\pi$
$492$	2.80221	+	8.08222i	0.126333	+	0.364375i
$493$	2.07733	+	2.07733i	0.0935582	+	0.0935582i
$494$	−47.9350	+	30.0242i	−2.15670	+	1.35085i
$495$		−	20.2390i		−	0.909675i
$496$	−12.7597	+	10.0568i	−0.572926	+	0.451564i
$497$		−	4.21139i		−	0.188907i
$498$	−4.83552	−	7.72013i	−0.216685	−	0.345947i
$499$	5.93144	+	5.93144i	0.265528	+	0.265528i	0.827295	−	0.561767i	$-0.189878\pi$
$499$	5.93144	+	5.93144i	0.265528	+	0.265528i	−0.561767	+	0.827295i	$0.689878\pi$
$500$	22.4592	−	7.78687i	1.00440	−	0.348240i
$501$	6.64606	+	6.64606i	0.296924	+	0.296924i
$502$	−2.27891	+	9.91923i	−0.101713	+	0.442717i
$503$			2.58202i			0.115127i	0.998342	+	0.0575633i	$0.0183331\pi$
$503$			2.58202i			0.115127i	−0.998342	+	0.0575633i	$0.981667\pi$
$504$	13.4418	−	1.45623i	0.598743	−	0.0648657i
$505$	−7.56695			−0.336725
$506$	−31.3459	−	5.84252i	−1.39349	−	0.259732i
$507$	11.1040	−	11.1040i	0.493144	−	0.493144i
$508$	0.823867	+	0.399656i	0.0365532	+	0.0177319i
$509$	22.0392	−	22.0392i	0.976869	−	0.976869i	−0.0228697	−	0.999738i	$-0.507280\pi$
$509$	22.0392	−	22.0392i	0.976869	−	0.976869i	0.999738	+	0.0228697i	$0.00728027\pi$
$510$	−4.39477	+	2.75267i	−0.194604	+	0.121890i
$511$	−26.1216			−1.15555
$512$	21.4519	−	7.19825i	0.948050	−	0.318121i
$513$			35.5923i			1.57144i
$514$	18.2226	+	29.0933i	0.803766	+	1.28325i
$515$	−7.28072	−	7.28072i	−0.320827	−	0.320827i
$516$	4.02883	+	1.95437i	0.177359	+	0.0860366i
$517$	43.0515	−	43.0515i	1.89340	−	1.89340i
$518$	0.377474	−	1.64300i	0.0165852	−	0.0721893i
$519$	−3.92331			−0.172214
$520$	−3.39477	−	31.3355i	−0.148871	−	1.37415i
$521$	−26.7900			−1.17369			−0.586846	−	0.809699i	$-0.699631\pi$
$521$	−26.7900			−1.17369			−0.586846	+	0.809699i	$0.699631\pi$
$522$	−1.03603	+	4.50944i	−0.0453457	+	0.197373i
$523$	12.8604	+	12.8604i	0.562345	+	0.562345i	0.929973	−	0.367628i	$-0.119830\pi$
$523$	12.8604	+	12.8604i	0.562345	+	0.562345i	−0.367628	+	0.929973i	$0.619830\pi$
$524$	−18.7125	+	6.48784i	−0.817457	+	0.283423i
$525$	−1.21874	−	1.21874i	−0.0531904	−	0.0531904i
$526$	−2.99830	+	1.87799i	−0.130732	+	0.0818842i
$527$	7.65953			0.333654
$528$	−14.0098	+	11.0421i	−0.609699	+	0.480547i
$529$	−22.9206	+	1.90926i	−0.996549	+	0.0830112i
$530$	31.9565	−	20.0160i	1.38810	−	0.869440i
$531$	12.2315	+	12.2315i	0.530800	+	0.530800i
$532$	31.6418	−	10.9706i	1.37184	−	0.475636i
$533$	17.3330	+	17.3330i	0.750774	+	0.750774i
$534$	4.56545	−	19.8717i	0.197566	−	0.859932i
$535$	18.0937			0.782257
$536$	−22.9867	+	28.5724i	−0.992874	+	1.23414i
$537$			9.11325i			0.393266i
$538$	28.0147	+	6.43629i	1.20780	+	0.277488i
$539$	−6.04860	−	6.04860i	−0.260532	−	0.260532i
$540$	−17.8449	−	8.65653i	−0.767922	−	0.372518i
$541$	20.9382	−	20.9382i	0.900204	−	0.900204i	−0.0952497	−	0.995453i	$-0.530365\pi$
$541$	20.9382	−	20.9382i	0.900204	−	0.900204i	0.995453	+	0.0952497i	$0.0303650\pi$
$542$	16.6086	−	10.4028i	0.713400	−	0.446839i
$543$	−16.8095			−0.721365
$544$	−10.0438	−	3.59518i	−0.430625	−	0.154142i
$545$	−21.1132			−0.904392
$546$	−14.0676	+	8.81125i	−0.602037	+	0.377087i
$547$	10.9565	+	10.9565i	0.468465	+	0.468465i	0.901417	−	0.432952i	$-0.142528\pi$
$547$	10.9565	+	10.9565i	0.468465	+	0.468465i	−0.432952	+	0.901417i	$0.642528\pi$
$548$	−11.5024	+	23.7115i	−0.491357	+	1.01290i
$549$	0.578039	−	0.578039i	0.0246701	−	0.0246701i
$550$	−5.17285	−	1.18844i	−0.220571	−	0.0506754i
$551$			11.4607i			0.488244i
$552$	−7.64215	+	10.3519i	−0.325272	+	0.440607i
$553$			6.33443i			0.269367i
$554$	8.37010	−	36.4319i	0.355611	−	1.54784i
$555$	−0.720077	+	0.720077i	−0.0305656	+	0.0305656i
$556$	0.399146	+	1.15123i	0.0169276	+	0.0488230i
$557$	−13.4998	−	13.4998i	−0.572003	−	0.572003i	0.360685	−	0.932688i	$-0.382543\pi$
$557$	−13.4998	−	13.4998i	−0.572003	−	0.572003i	−0.932688	+	0.360685i	$0.882543\pi$
$558$	6.40358	+	10.2236i	0.271085	+	0.432800i
$559$	12.8314			0.542712
$560$	−2.19538	+	18.5324i	−0.0927717	+	0.783138i
$561$	8.40998			0.355070
$562$	2.18755	+	3.49253i	0.0922763	+	0.147323i
$563$	9.17043	−	9.17043i	0.386488	−	0.386488i	−0.486945	−	0.873433i	$-0.661889\pi$
$563$	9.17043	−	9.17043i	0.386488	−	0.386488i	0.873433	+	0.486945i	$0.161889\pi$
$564$	−8.04842	−	23.2135i	−0.338900	−	0.977466i
$565$	15.4972	+	15.4972i	0.651971	+	0.651971i
$566$	4.61337	−	20.0803i	0.193914	−	0.844036i
$567$		−	3.89522i		−	0.163584i
$568$	−5.20297	+	0.563671i	−0.218312	+	0.0236511i
$569$	21.2569			0.891134			0.445567	−	0.895249i	$-0.353002\pi$
$569$	21.2569			0.891134			0.445567	+	0.895249i	$0.353002\pi$
$570$	−19.7164	−	4.52977i	−0.825829	−	0.189731i
$571$	11.1237	+	11.1237i	0.465512	+	0.465512i	0.900457	−	0.434945i	$-0.143232\pi$
$571$	11.1237	+	11.1237i	0.465512	+	0.465512i	−0.434945	+	0.900457i	$0.643232\pi$
$572$	−22.3100	+	45.9907i	−0.932828	+	1.92297i
$573$	−10.9086	−	10.9086i	−0.455713	−	0.455713i
$574$	−7.70416	−	12.3001i	−0.321566	−	0.513395i
$575$	−3.82521	+	0.159042i	−0.159522	+	0.00663252i
$576$	−3.59820	−	16.4117i	−0.149925	−	0.683822i
$577$	−10.8523			−0.451787			−0.225894	−	0.974152i	$-0.572530\pi$
$577$	−10.8523			−0.451787			−0.225894	+	0.974152i	$0.572530\pi$
$578$	−10.0921	−	16.1125i	−0.419776	−	0.670192i
$579$	−2.76781	−	2.76781i	−0.115026	−	0.115026i
$580$	−5.74607	−	2.78741i	−0.238592	−	0.115741i
$581$	10.9289	+	10.9289i	0.453405	+	0.453405i
$582$	−22.5823	−	5.18820i	−0.936065	−	0.215058i
$583$	−61.1531			−2.53270
$584$	3.49623	+	32.2720i	0.144675	+	1.33543i
$585$	−23.4037			−0.967622
$586$	25.4055	+	5.83682i	1.04949	+	0.241117i
$587$	−4.15104	+	4.15104i	−0.171332	+	0.171332i	−0.787564	−	0.616233i	$-0.788658\pi$
$587$	−4.15104	+	4.15104i	−0.171332	+	0.171332i	0.616233	+	0.787564i	$0.288658\pi$
$588$	−3.26143	+	1.13078i	−0.134499	+	0.0466325i
$589$	21.1290	+	21.1290i	0.870605	+	0.870605i
$590$	−20.2345	+	12.6739i	−0.833042	+	0.521777i
$591$		−	10.0550i		−	0.413608i
$592$	−2.08037	−	0.246444i	−0.0855026	−	0.0101288i
$593$	−24.5289			−1.00728			−0.503641	−	0.863913i	$-0.668006\pi$
$593$	−24.5289			−1.00728			−0.503641	+	0.863913i	$0.668006\pi$
$594$	17.0743	+	27.2599i	0.700567	+	1.11849i
$595$	6.22137	−	6.22137i	0.255051	−	0.255051i
$596$	−8.06403	−	23.2585i	−0.330315	−	0.952707i
$597$	3.42860	−	3.42860i	0.140323	−	0.140323i
$598$	−6.75608	+	36.2473i	−0.276277	+	1.48226i
$599$	−24.3488			−0.994865			−0.497432	−	0.867503i	$-0.665724\pi$
$599$	−24.3488			−0.994865			−0.497432	+	0.867503i	$0.665724\pi$
$600$	−1.34258	+	1.66882i	−0.0548104	+	0.0681293i
$601$		−	30.8952i		−	1.26024i	−0.776498	−	0.630120i	$-0.783006\pi$
$601$		−	30.8952i		−	1.26024i	0.776498	−	0.630120i	$-0.216994\pi$
$602$	−7.40448	−	1.70115i	−0.301784	−	0.0693338i
$603$	19.2541	+	19.2541i	0.784088	+	0.784088i
$604$	15.0523	−	31.0295i	0.612471	−	1.26257i
$605$	−16.0918	−	16.0918i	−0.654225	−	0.654225i
$606$	4.19691	−	2.62874i	0.170488	−	0.106785i
$607$		−	5.80970i		−	0.235808i	−0.993025	−	0.117904i	$-0.962382\pi$
$607$		−	5.80970i		−	0.235808i	0.993025	−	0.117904i	$-0.0376176\pi$
$608$	−17.7887	−	37.6235i	−0.721427	−	1.52583i
$609$			3.36340i			0.136292i
$610$	0.598949	+	0.956251i	0.0242507	+	0.0387175i
$611$	−49.7833	−	49.7833i	−2.01401	−	2.01401i
$612$	−3.45725	+	7.12692i	−0.139751	+	0.288089i
$613$	−5.24464	+	5.24464i	−0.211829	+	0.211829i	−0.805044	−	0.593215i	$-0.797858\pi$
$613$	−5.24464	+	5.24464i	−0.211829	+	0.211829i	0.593215	+	0.805044i	$0.297858\pi$
$614$	−9.11796	+	39.6871i	−0.367971	+	1.60164i
$615$			8.76724i			0.353529i
$616$	18.9714	−	23.5815i	0.764381	−	0.950125i
$617$	7.65986			0.308375			0.154187	−	0.988042i	$-0.450724\pi$
$617$	7.65986			0.308375			0.154187	+	0.988042i	$0.450724\pi$
$618$	6.56746	+	1.50885i	0.264182	+	0.0606949i
$619$	−2.24543	−	2.24543i	−0.0902516	−	0.0902516i	0.660540	−	0.750791i	$-0.270328\pi$
$619$	−2.24543	−	2.24543i	−0.0902516	−	0.0902516i	−0.750791	+	0.660540i	$0.770328\pi$
$620$	−15.7323	+	5.45459i	−0.631825	+	0.219061i
$621$	17.0737	+	15.7106i	0.685143	+	0.630444i
$622$	3.11629	+	4.97531i	0.124952	+	0.199492i
$623$			34.5939i			1.38598i
$624$	12.7687	+	16.2005i	0.511158	+	0.648537i
$625$	20.3712			0.814848
$626$	−2.45144	−	3.91384i	−0.0979793	−	0.156429i
$627$	23.1991	+	23.1991i	0.926484	+	0.926484i
$628$	−25.6457	+	8.89167i	−1.02337	+	0.354816i
$629$	0.698384	+	0.698384i	0.0278464	+	0.0278464i
$630$	13.5053	+	3.10278i	0.538062	+	0.123618i
$631$			17.9139i			0.713140i	0.934269	+	0.356570i	$0.116054\pi$
$631$			17.9139i			0.713140i	−0.934269	+	0.356570i	$0.883946\pi$
$632$	7.82588	−	0.847827i	0.311297	−	0.0337248i
$633$		−	10.8130i		−	0.429780i
$634$	36.9520	+	8.48958i	1.46755	+	0.337164i
$635$	0.663612	+	0.663612i	0.0263347	+	0.0263347i
$636$	−10.7707	+	22.2032i	−0.427088	+	0.880415i
$637$	−6.99439	+	6.99439i	−0.277128	+	0.277128i
$638$	5.49793	+	8.77771i	0.217665	+	0.347513i
$639$			3.88597i			0.153726i
$640$	23.1897	+	0.231822i	0.916655	+	0.00916358i
$641$		−	33.4086i		−	1.31956i	−0.751459	−	0.659780i	$-0.770650\pi$
$641$		−	33.4086i		−	1.31956i	0.751459	−	0.659780i	$-0.229350\pi$
$642$	−10.0354	+	6.28569i	−0.396066	+	0.248077i
$643$	14.1808	−	14.1808i	0.559236	−	0.559236i	−0.369854	−	0.929090i	$-0.620592\pi$
$643$	14.1808	−	14.1808i	0.559236	−	0.559236i	0.929090	+	0.369854i	$0.120592\pi$
$644$	8.70420	−	20.0211i	0.342993	−	0.788940i
$645$	3.24516	+	3.24516i	0.127778	+	0.127778i
$646$	−4.39330	+	19.1224i	−0.172852	+	0.752361i
$647$	−28.4190			−1.11727			−0.558634	−	0.829415i	$-0.688674\pi$
$647$	−28.4190			−1.11727			−0.558634	+	0.829415i	$0.688674\pi$
$648$	−4.81235	+	0.521353i	−0.189047	+	0.0204807i
$649$	38.7215			1.51995
$650$	−1.37427	+	5.98170i	−0.0539035	+	0.234622i
$651$	6.20077	+	6.20077i	0.243027	+	0.243027i
$652$	−35.5767	+	12.3349i	−1.39329	+	0.483071i
$653$	12.6424	−	12.6424i	0.494736	−	0.494736i	−0.415058	−	0.909795i	$-0.636239\pi$
$653$	12.6424	−	12.6424i	0.494736	−	0.494736i	0.909795	+	0.415058i	$0.136239\pi$
$654$	11.7102	−	7.33469i	0.457904	−	0.286809i
$655$	−20.2985			−0.793126
$656$	−14.1650	+	11.1644i	−0.553049	+	0.435897i
$657$	24.1031			0.940353
$658$	22.1277	+	35.3279i	0.862627	+	1.37722i
$659$	−22.5169	+	22.5169i	−0.877133	+	0.877133i	−0.993237	−	0.116104i	$-0.962959\pi$
$659$	−22.5169	+	22.5169i	−0.877133	+	0.877133i	0.116104	+	0.993237i	$0.462959\pi$
$660$	−17.2737	+	5.98901i	−0.672378	+	0.233122i
$661$	19.8538	−	19.8538i	0.772222	−	0.772222i	−0.206272	−	0.978495i	$-0.566133\pi$
$661$	19.8538	−	19.8538i	0.772222	−	0.772222i	0.978495	+	0.206272i	$0.0661332\pi$
$662$	−37.1886	−	8.54394i	−1.44538	−	0.332070i
$663$		−	9.72501i		−	0.377688i
$664$	12.0393	−	14.9648i	0.467215	−	0.580748i
$665$	34.3236			1.33101
$666$	−0.348305	+	1.51604i	−0.0134965	+	0.0587454i
$667$	5.49773	+	5.05882i	0.212873	+	0.195878i
$668$	−8.64916	+	17.8297i	−0.334646	+	0.689852i
$669$	−5.07741	+	5.07741i	−0.196304	+	0.196304i
$670$	−31.8521	+	19.9506i	−1.23055	+	0.770759i
$671$		−	1.82991i		−	0.0706431i
$672$	−5.22048	−	11.0414i	−0.201384	−	0.425932i
$673$	6.43354			0.247995			0.123997	−	0.992283i	$-0.460429\pi$
$673$	6.43354			0.247995			0.123997	+	0.992283i	$0.460429\pi$
$674$	19.5707	−	12.2581i	0.753835	−	0.472166i
$675$	2.73095	+	2.73095i	0.105114	+	0.105114i
$676$	29.7892	+	14.4507i	1.14574	+	0.555795i
$677$	31.6248	−	31.6248i	1.21544	−	1.21544i	0.246229	−	0.969212i	$-0.420808\pi$
$677$	31.6248	−	31.6248i	1.21544	−	1.21544i	0.969212	−	0.246229i	$-0.0791917\pi$
$678$	−13.9790	−	3.21162i	−0.536859	−	0.123342i
$679$	39.3127			1.50868
$680$	−8.51889	−	6.85350i	−0.326684	−	0.262820i
$681$	−3.93169			−0.150663
$682$	26.3186	+	6.04660i	1.00779	+	0.231536i
$683$	35.0359	−	35.0359i	1.34061	−	1.34061i	0.445160	−	0.895451i	$-0.353147\pi$
$683$	35.0359	−	35.0359i	1.34061	−	1.34061i	0.895451	−	0.445160i	$-0.146853\pi$
$684$	−29.1967	+	10.1229i	−1.11636	+	0.387057i
$685$	−19.0992	+	19.0992i	−0.729744	+	0.729744i
$686$	24.0589	−	15.0693i	0.918573	−	0.575350i
$687$	−0.807524			−0.0308090
$688$	−1.11064	+	9.37556i	−0.0423428	+	0.357440i
$689$			70.7153i			2.69404i
$690$	−10.8758	+	7.45852i	−0.414036	+	0.283941i
$691$	14.5935	+	14.5935i	0.555164	+	0.555164i	0.927927	−	0.372762i	$-0.121589\pi$
$691$	14.5935	+	14.5935i	0.555164	+	0.555164i	−0.372762	+	0.927927i	$0.621589\pi$
$692$	−2.70974	−	7.81552i	−0.103009	−	0.297101i
$693$	−15.8908	−	15.8908i	−0.603643	−	0.603643i
$694$	−8.34602	−	1.91747i	−0.316811	−	0.0727861i
$695$			1.24880i			0.0473698i
$696$	4.15532	−	0.450172i	0.157507	−	0.0170637i
$697$	8.50312			0.322078
$698$	6.83636	+	1.57063i	0.258760	+	0.0594492i
$699$	9.21497	−	9.21497i	0.348542	−	0.348542i
$700$	1.58607	−	3.26959i	0.0599478	−	0.123579i
$701$	−8.52120	−	8.52120i	−0.321841	−	0.321841i	0.527632	−	0.849473i	$-0.323080\pi$
$701$	−8.52120	−	8.52120i	−0.321841	−	0.321841i	−0.849473	+	0.527632i	$0.823080\pi$
$702$	31.5224	−	19.7441i	1.18974	−	0.745194i
$703$			3.85302i			0.145319i
$704$	−31.6730	−	20.2820i	−1.19372	−	0.764408i
$705$		−	25.1810i		−	0.948372i
$706$	−16.6203	−	26.5351i	−0.625514	−	0.998662i
$707$	−5.94127	+	5.94127i	−0.223444	+	0.223444i
$708$	6.81992	−	14.0588i	0.256308	−	0.528364i
$709$	1.15928	−	1.15928i	0.0435375	−	0.0435375i	−0.685003	−	0.728540i	$-0.740199\pi$
$709$	1.15928	−	1.15928i	0.0435375	−	0.0435375i	0.728540	+	0.685003i	$0.240199\pi$
$710$	−5.22755	−	1.20101i	−0.196186	−	0.0450731i
$711$		−	5.84495i		−	0.219203i
$712$	42.7391	−	4.63020i	1.60172	−	0.173524i
$713$	19.4620	−	0.809180i	0.728859	−	0.0303040i
$714$	−1.28931	+	5.61189i	−0.0482512	+	0.210020i
$715$	−37.0448	+	37.0448i	−1.38540	+	1.38540i
$716$	−18.1543	+	6.29431i	−0.678457	+	0.235229i
$717$	−1.41700	+	1.41700i	−0.0529189	+	0.0529189i
$718$	4.00383	−	2.50780i	0.149422	−	0.0935904i
$719$			3.35579i			0.125150i	0.998040	+	0.0625750i	$0.0199312\pi$
$719$			3.35579i			0.125150i	−0.998040	+	0.0625750i	$0.980069\pi$
$720$	2.02573	−	17.1004i	0.0754947	−	0.637293i
$721$	−11.4331			−0.425790
$722$	−42.0967	+	26.3674i	−1.56668	+	0.981292i
$723$	−12.9546	+	12.9546i	−0.481786	+	0.481786i
$724$	−11.6099	−	33.4858i	−0.431480	−	1.24449i
$725$	0.879366	+	0.879366i	0.0326588	+	0.0326588i
$726$	14.5154	+	3.33485i	0.538716	+	0.123768i
$727$		−	37.3678i		−	1.38590i	−0.720987	−	0.692948i	$-0.756311\pi$
$727$		−	37.3678i		−	1.38590i	0.720987	−	0.692948i	$-0.243689\pi$
$728$	−27.2688	−	21.9379i	−1.01065	−	0.813073i
$729$		−	10.1734i		−	0.376791i
$730$	−7.44940	+	32.4245i	−0.275715	+	1.20008i
$731$	3.14739	−	3.14739i	0.116410	−	0.116410i
$732$	−0.664399	−	0.322298i	−0.0245569	−	0.0119125i
$733$	15.8730	+	15.8730i	0.586284	+	0.586284i	0.936623	−	0.350339i	$-0.113934\pi$
$733$	15.8730	+	15.8730i	0.586284	+	0.586284i	−0.350339	+	0.936623i	$0.613934\pi$
$734$	3.73540	+	5.96374i	0.137876	+	0.220126i
$735$	−3.53785			−0.130496
$736$	−25.9000	−	8.07390i	−0.954688	−	0.297608i
$737$	60.9532			2.24524
$738$	7.10884	+	11.3496i	0.261680	+	0.417784i
$739$	22.8825	+	22.8825i	0.841748	+	0.841748i	0.989086	−	0.147339i	$-0.0470707\pi$
$739$	22.8825	+	22.8825i	0.841748	+	0.841748i	−0.147339	+	0.989086i	$0.547071\pi$
$740$	−1.93179	−	0.937106i	−0.0710139	−	0.0344487i
$741$	26.8267	−	26.8267i	0.985503	−	0.985503i
$742$	9.37521	−	40.8068i	0.344175	−	1.49806i
$743$			35.7928i			1.31311i	0.754277	+	0.656556i	$0.227987\pi$
$743$			35.7928i			1.31311i	−0.754277	+	0.656556i	$0.772013\pi$
$744$	6.83080	−	8.49068i	0.250429	−	0.311283i
$745$		−	25.2298i		−	0.924350i
$746$	42.9128	+	9.85907i	1.57115	+	0.360966i
$747$	−10.0843	−	10.0843i	−0.368967	−	0.368967i
$748$	5.80858	+	16.7533i	0.212383	+	0.612561i
$749$	14.2064	−	14.2064i	0.519092	−	0.519092i
$750$	−13.5125	+	8.46355i	−0.493405	+	0.309045i
$751$	19.5324			0.712747			0.356374	−	0.934344i	$-0.384013\pi$
$751$	19.5324			0.712747			0.356374	+	0.934344i	$0.384013\pi$
$752$	40.6842	−	32.0661i	1.48360	−	1.16933i
$753$		−	6.82665i		−	0.248777i
$754$	10.1502	−	6.35762i	0.369650	−	0.231531i
$755$	24.9938	−	24.9938i	0.909616	−	0.909616i
$756$	−20.8079	+	7.21435i	−0.756775	+	0.262383i
$757$	9.97229	−	9.97229i	0.362449	−	0.362449i	−0.502265	−	0.864714i	$-0.667500\pi$
$757$	9.97229	−	9.97229i	0.362449	−	0.362449i	0.864714	+	0.502265i	$0.167500\pi$
$758$	−0.00866991	+	0.0377369i	−0.000314905	+	0.00137067i
$759$	21.3689	−	0.888460i	0.775640	−	0.0322491i
$760$	−4.59402	−	42.4051i	−0.166643	−	1.53819i
$761$			41.6215i			1.50878i	0.656428	+	0.754388i	$0.272066\pi$
$761$			41.6215i			1.50878i	−0.656428	+	0.754388i	$0.727934\pi$
$762$	−0.598601	−	0.137526i	−0.0216850	−	0.00498206i
$763$	−16.5773	+	16.5773i	−0.600138	+	0.600138i
$764$	14.1964	−	29.2650i	0.513608	−	1.05877i
$765$	−5.74062	+	5.74062i	−0.207553	+	0.207553i
$766$	−13.8505	−	22.1129i	−0.500438	−	0.798972i
$767$		−	44.7761i		−	1.61677i
$768$	−12.9424	+	7.92748i	−0.467019	+	0.286058i
$769$			10.8316i			0.390599i	0.980744	+	0.195299i	$0.0625679\pi$
$769$			10.8316i			0.390599i	−0.980744	+	0.195299i	$0.937432\pi$
$770$	26.2883	−	16.4657i	0.947363	−	0.593382i
$771$	−16.2820	−	16.2820i	−0.586381	−	0.586381i
$772$	3.60202	−	7.42534i	0.129639	−	0.267244i
$773$	−10.7375	+	10.7375i	−0.386200	+	0.386200i	−0.873330	−	0.487129i	$-0.838044\pi$
$773$	−10.7375	+	10.7375i	−0.386200	+	0.386200i	0.487129	+	0.873330i	$0.338044\pi$
$774$	6.83231	+	1.56970i	0.245582	+	0.0564217i
$775$	3.24240			0.116470
$776$	−5.26178	−	48.5689i	−0.188887	−	1.74352i
$777$			1.13075i			0.0405655i
$778$	−33.8951	−	7.78727i	−1.21520	−	0.279187i
$779$	23.4561	+	23.4561i	0.840400	+	0.840400i
$780$	6.92548	+	19.9747i	0.247972	+	0.715209i
$781$	6.15095	+	6.15095i	0.220098	+	0.220098i
$782$	7.23382	+	10.5482i	0.258681	+	0.377202i
$783$		−	7.53667i		−	0.269339i
$784$	−4.50518	−	5.71600i	−0.160899	−	0.204143i
$785$	−27.8193			−0.992913
$786$	11.2583	−	7.05163i	0.401569	−	0.251523i
$787$	1.63965	−	1.63965i	0.0584471	−	0.0584471i	−0.677279	−	0.735726i	$-0.736841\pi$
$787$	1.63965	−	1.63965i	0.0584471	−	0.0584471i	0.735726	+	0.677279i	$0.236841\pi$
$788$	20.0303	−	6.94476i	0.713550	−	0.247397i
$789$	1.67799	−	1.67799i	0.0597379	−	0.0597379i
$790$	7.86284	+	1.80646i	0.279747	+	0.0642710i
$791$	24.3355			0.865272
$792$	−17.5055	+	21.7593i	−0.622029	+	0.773182i
$793$	−2.11605			−0.0751431
$794$	−17.2139	−	3.95484i	−0.610900	−	0.140352i
$795$	−17.8844	+	17.8844i	−0.634293	+	0.634293i
$796$	9.19808	+	4.46197i	0.326017	+	0.158150i
$797$	−20.0013	−	20.0013i	−0.708481	−	0.708481i	0.257735	−	0.966216i	$-0.417024\pi$
$797$	−20.0013	−	20.0013i	−0.708481	−	0.708481i	−0.966216	+	0.257735i	$0.917024\pi$
$798$	−19.0371	+	11.9239i	−0.673907	+	0.422103i
$799$	−24.4224			−0.864003
$800$	−4.25170	−	1.52190i	−0.150320	−	0.0538071i
$801$		−	31.9208i		−	1.12786i
$802$	−1.51387	+	0.948218i	−0.0534568	+	0.0334827i
$803$	38.1520	−	38.1520i	1.34635	−	1.34635i
$804$	10.7355	−	22.1307i	0.378614	−	0.780489i
$805$	15.1506	−	16.4651i	0.533988	−	0.580318i
$806$	6.99208	−	30.4339i	0.246285	−	1.07199i
$807$	−19.2804			−0.678702
$808$	8.13535	+	6.54494i	0.286201	+	0.230250i
$809$			32.7856i			1.15268i	0.817210	+	0.576340i	$0.195520\pi$
$809$			32.7856i			1.15268i	−0.817210	+	0.576340i	$0.804480\pi$
$810$	−4.83509	−	1.11084i	−0.169888	−	0.0390311i
$811$	−14.2538	+	14.2538i	−0.500520	+	0.500520i	−0.911599	−	0.411080i	$-0.865152\pi$
$811$	−14.2538	+	14.2538i	−0.500520	+	0.500520i	0.411080	+	0.911599i	$0.365152\pi$
$812$	−6.70014	+	2.32302i	−0.235129	+	0.0815221i
$813$	−9.29494	+	9.29494i	−0.325988	+	0.325988i
$814$	1.84837	+	2.95100i	0.0647852	+	0.103433i
$815$	−38.5920			−1.35182
$816$	7.10578	+	0.841761i	0.248752	+	0.0294675i
$817$	17.3643			0.607500
$818$	9.33016	−	5.84396i	0.326221	−	0.204329i
$819$	−18.3756	+	18.3756i	−0.642096	+	0.642096i
$820$	−17.4650	+	6.05533i	−0.609904	+	0.211461i
$821$	−18.9753	−	18.9753i	−0.662241	−	0.662241i	0.293667	−	0.955908i	$-0.405124\pi$
$821$	−18.9753	−	18.9753i	−0.662241	−	0.662241i	−0.955908	+	0.293667i	$0.905124\pi$
$822$	3.95811	−	17.2281i	0.138055	−	0.600901i
$823$	41.2601			1.43824			0.719118	−	0.694888i	$-0.244546\pi$
$823$	41.2601			1.43824			0.719118	+	0.694888i	$0.244546\pi$
$824$	1.53025	+	14.1250i	0.0533088	+	0.492068i
$825$	3.56007			0.123946
$826$	−5.93628	+	25.8384i	−0.206550	+	0.899033i
$827$	15.2544	+	15.2544i	0.530446	+	0.530446i	0.920705	−	0.390259i	$-0.127615\pi$
$827$	15.2544	+	15.2544i	0.530446	+	0.530446i	−0.390259	+	0.920705i	$0.627615\pi$
$828$	−8.03160	+	18.4740i	−0.279117	+	0.642015i
$829$	−36.9713	+	36.9713i	−1.28407	+	1.28407i	−0.345735	+	0.938332i	$0.612371\pi$
$829$	−36.9713	+	36.9713i	−1.28407	+	1.28407i	−0.938332	+	0.345735i	$0.887629\pi$
$830$	16.6825	−	10.4491i	0.579060	−	0.362695i
$831$			25.0733i			0.869783i
$832$	−23.4534	+	36.6255i	−0.813102	+	1.26976i
$833$			3.43127i			0.118886i
$834$	−0.433831	−	0.692632i	−0.0150224	−	0.0239839i
$835$	−14.3616	+	14.3616i	−0.497002	+	0.497002i
$836$	−30.1913	+	62.2375i	−1.04419	+	2.15253i
$837$	−13.8946	−	13.8946i	−0.480268	−	0.480268i
$838$	1.83387	+	0.421324i	0.0633498	+	0.0145544i
$839$		−	7.19889i		−	0.248533i	−0.992249	−	0.124267i	$-0.960342\pi$
$839$		−	7.19889i		−	0.248533i	0.992249	−	0.124267i	$-0.0396578\pi$
$840$	−1.34821	−	12.4447i	−0.0465178	−	0.429383i
$841$			26.5732i			0.916317i
$842$	−44.6424	−	10.2564i	−1.53848	−	0.353460i
$843$	−1.95458	−	1.95458i	−0.0673194	−	0.0673194i
$844$	21.5404	−	7.46831i	0.741450	−	0.257070i
$845$	23.9947	+	23.9947i	0.825443	+	0.825443i
$846$	−20.4178	−	32.5980i	−0.701979	−	1.12074i
$847$	−25.2693			−0.868264
$848$	−51.6696	−	6.12085i	−1.77434	−	0.210191i
$849$			13.8197i			0.474291i
$850$	1.13014	+	1.80433i	0.0387636	+	0.0618879i
$851$	1.84830	+	1.70074i	0.0633588	+	0.0583005i
$852$	3.31662	−	1.14991i	0.113625	−	0.0393954i
$853$	17.9050	+	17.9050i	0.613056	+	0.613056i	0.943741	−	0.330685i	$-0.107280\pi$
$853$	17.9050	+	17.9050i	0.613056	+	0.613056i	−0.330685	+	0.943741i	$0.607280\pi$
$854$	1.22108	+	0.280539i	0.0417846	+	0.00959985i
$855$	−31.6713			−1.08314
$856$	−19.4528	−	15.6499i	−0.664883	−	0.534902i
$857$		−	35.8217i		−	1.22364i	−0.790995	−	0.611822i	$-0.790437\pi$
$857$		−	35.8217i		−	1.22364i	0.790995	−	0.611822i	$-0.209563\pi$
$858$	7.67713	−	33.4157i	0.262093	−	1.14079i
$859$	21.8167	−	21.8167i	0.744376	−	0.744376i	−0.229041	−	0.973417i	$-0.573559\pi$
$859$	21.8167	−	21.8167i	0.744376	−	0.744376i	0.973417	+	0.229041i	$0.0735589\pi$
$860$	−4.22324	+	8.70594i	−0.144011	+	0.296870i
$861$	6.88369	+	6.88369i	0.234596	+	0.234596i
$862$	21.8367	+	34.8634i	0.743762	+	1.18745i
$863$		−	4.79857i		−	0.163345i	−0.996659	−	0.0816726i	$-0.973974\pi$
$863$		−	4.79857i		−	0.163345i	0.996659	−	0.0816726i	$-0.0260262\pi$
$864$	11.6980	+	24.7415i	0.397974	+	0.841723i
$865$		−	8.47793i		−	0.288258i
$866$	24.1941	−	15.1540i	0.822149	−	0.514954i
$867$	9.01731	+	9.01731i	0.306244	+	0.306244i
$868$	−8.06966	+	16.6351i	−0.273902	+	0.564632i
$869$	−9.25175	−	9.25175i	−0.313844	−	0.313844i
$870$	4.17495	+	0.959179i	0.141544	+	0.0325192i
$871$		−	70.4842i		−	2.38827i
$872$	22.6992	+	18.2616i	0.768692	+	0.618417i
$873$	−36.2749			−1.22772
$874$	−9.14276	+	49.0521i	−0.309258	+	1.65921i
$875$	19.1286	−	19.1286i	0.646666	−	0.646666i
$876$	−7.13247	−	20.5717i	−0.240984	−	0.695053i
$877$	1.69273	−	1.69273i	0.0571594	−	0.0571594i	−0.677949	−	0.735109i	$-0.737131\pi$
$877$	1.69273	−	1.69273i	0.0571594	−	0.0571594i	0.735109	+	0.677949i	$0.237131\pi$
$878$	−7.32976	−	11.7023i	−0.247367	−	0.394934i
$879$	−17.4847			−0.589743
$880$	−23.8611	−	30.2740i	−0.804357	−	1.02054i
$881$		−	22.9786i		−	0.774168i	−0.922044	−	0.387084i	$-0.873482\pi$
$881$		−	22.9786i		−	0.774168i	0.922044	−	0.387084i	$-0.126518\pi$
$882$	−4.57991	+	2.86864i	−0.154214	+	0.0965920i
$883$	−33.9764	−	33.9764i	−1.14340	−	1.14340i	−0.987824	−	0.155574i	$-0.950277\pi$
$883$	−33.9764	−	33.9764i	−1.14340	−	1.14340i	−0.155574	−	0.987824i	$-0.549723\pi$
$884$	19.3729	−	6.71684i	0.651582	−	0.225912i
$885$	11.3242	−	11.3242i	0.380658	−	0.380658i
$886$	33.7238	+	7.74793i	1.13297	+	0.260297i
$887$	22.2082			0.745677			0.372839	−	0.927896i	$-0.378384\pi$
$887$	22.2082			0.745677			0.372839	+	0.927896i	$0.378384\pi$
$888$	1.39699	−	0.151345i	0.0468798	−	0.00507880i
$889$	1.04208			0.0349504
$890$	42.9410	+	9.86554i	1.43939	+	0.330694i
$891$	5.68917	+	5.68917i	0.190594	+	0.190594i
$892$	−13.6214	−	6.60772i	−0.456079	−	0.221243i
$893$	−67.3698	−	67.3698i	−2.25444	−	2.25444i
$894$	8.76478	+	13.9934i	0.293138	+	0.468009i
$895$	−19.6929			−0.658263
$896$	18.3897	−	18.0256i	0.614356	−	0.602194i
$897$	−1.02738	−	24.7102i	−0.0343034	−	0.825050i
$898$	4.22103	+	6.73908i	0.140858	+	0.224886i
$899$	−4.47407	−	4.47407i	−0.149218	−	0.149218i
$900$	−1.46351	+	3.01693i	−0.0487836	+	0.100564i
$901$	17.3456	+	17.3456i	0.577864	+	0.577864i
$902$	29.2172	+	6.71254i	0.972826	+	0.223503i
$903$	5.09594			0.169582
$904$	−3.25717	−	30.0653i	−0.108332	−	0.999958i
$905$		−	36.3239i		−	1.20745i
$906$	−5.17969	+	22.5452i	−0.172084	+	0.749015i
$907$	10.1920	+	10.1920i	0.338421	+	0.338421i	0.855773	−	0.517352i	$-0.173082\pi$
$907$	10.1920	+	10.1920i	0.338421	+	0.338421i	−0.517352	+	0.855773i	$0.673082\pi$
$908$	−2.71553	−	7.83222i	−0.0901180	−	0.259921i
$909$	5.48217	−	5.48217i	0.181832	−	0.181832i
$910$	−19.0403	−	30.3988i	−0.631181	−	1.00771i
$911$	−0.410402			−0.0135972			−0.00679862	−	0.999977i	$-0.502164\pi$
$911$	−0.410402			−0.0135972			−0.00679862	+	0.999977i	$0.502164\pi$
$912$	17.2794	+	21.9235i	0.572179	+	0.725959i
$913$	−31.9243			−1.05654
$914$	2.26320	+	3.61330i	0.0748599	+	0.119517i
$915$	−0.535163	−	0.535163i	−0.0176919	−	0.0176919i
$916$	−0.557738	−	1.60865i	−0.0184282	−	0.0531512i
$917$	−15.9375	+	15.9375i	−0.526304	+	0.526304i
$918$	2.88907	−	12.5750i	0.0953536	−	0.415038i
$919$		−	6.62347i		−	0.218488i	−0.994015	−	0.109244i	$-0.965157\pi$
$919$		−	6.62347i		−	0.218488i	0.994015	−	0.109244i	$-0.0348430\pi$
$920$	−22.3696	−	16.5140i	−0.737504	−	0.544452i
$921$		−	27.3136i		−	0.900013i
$922$	−7.58006	−	1.74149i	−0.249636	−	0.0573530i
$923$	7.11275	−	7.11275i	0.234119	−	0.234119i
$924$	−8.86029	+	18.2649i	−0.291482	+	0.600873i
$925$	0.295637	+	0.295637i	0.00972047	+	0.00972047i
$926$	−11.6471	+	7.29516i	−0.382747	+	0.239734i
$927$	10.5496			0.346494
$928$	3.76676	+	7.96677i	0.123650	+	0.261522i
$929$	−29.0178			−0.952045			−0.476022	−	0.879433i	$-0.657922\pi$
$929$	−29.0178			−0.952045			−0.476022	+	0.879433i	$0.657922\pi$
$930$	9.46527	−	5.92859i	0.310378	−	0.194406i
$931$	−9.46524	+	9.46524i	−0.310211	+	0.310211i
$932$	24.7215	+	11.9923i	0.809778	+	0.392822i
$933$	−2.78441	−	2.78441i	−0.0911576	−	0.0911576i
$934$	−45.6290	−	10.4831i	−1.49303	−	0.343018i
$935$			18.1732i			0.594329i
$936$	25.1617	+	20.2427i	0.822434	+	0.661654i
$937$	29.9983			0.980002			0.490001	−	0.871722i	$-0.336996\pi$
$937$	29.9983			0.980002			0.490001	+	0.871722i	$0.336996\pi$
$938$	−9.34457	+	40.6734i	−0.305111	+	1.32803i
$939$	2.19037	+	2.19037i	0.0714800	+	0.0714800i
$940$	50.1624	−	17.3919i	1.63612	−	0.567263i
$941$	2.67705	+	2.67705i	0.0872693	+	0.0872693i	0.749394	−	0.662125i	$-0.230345\pi$
$941$	2.67705	+	2.67705i	0.0872693	+	0.0872693i	−0.662125	+	0.749394i	$0.730345\pi$
$942$	15.4296	−	9.66435i	0.502723	−	0.314882i
$943$	21.6055	−	0.898299i	0.703572	−	0.0292526i
$944$	32.7166	+	3.87566i	1.06483	+	0.126142i
$945$	−22.5715			−0.734250
$946$	13.2992	−	8.33000i	0.432395	−	0.270832i
$947$	29.3730	+	29.3730i	0.954493	+	0.954493i	0.999009	−	0.0445156i	$-0.0141745\pi$
$947$	29.3730	+	29.3730i	0.954493	+	0.954493i	−0.0445156	+	0.999009i	$0.514174\pi$
$948$	−4.98858	+	1.72960i	−0.162022	+	0.0561749i
$949$	−44.1176	−	44.1176i	−1.43212	−	1.43212i
$950$	−1.85975	+	8.09481i	−0.0603384	+	0.262630i
$951$	−25.4312			−0.824664
$952$	−12.0698	+	1.30760i	−0.391184	+	0.0423795i
$953$	37.4763			1.21398			0.606989	−	0.794710i	$-0.292377\pi$
$953$	37.4763			1.21398			0.606989	+	0.794710i	$0.292377\pi$
$954$	−8.65075	+	37.6535i	−0.280079	+	1.21908i
$955$	23.5725	−	23.5725i	0.762789	−	0.762789i
$956$	−3.80146	−	1.84408i	−0.122948	−	0.0596419i
$957$	−4.91242	−	4.91242i	−0.158796	−	0.158796i
$958$	8.43681	+	13.4698i	0.272581	+	0.435188i
$959$			29.9919i			0.968489i
$960$	−15.1944	+	3.33131i	−0.490396	+	0.107517i
$961$	14.5032			0.467846
$962$	3.41244	−	2.13739i	0.110021	−	0.0689121i
$963$	−13.1087	+	13.1087i	−0.422420	+	0.422420i
$964$	−34.7539	−	16.8590i	−1.11935	−	0.542993i
$965$	5.98099	−	5.98099i	0.192535	−	0.192535i
$966$	−2.68314	+	14.3954i	−0.0863286	+	0.463165i
$967$	30.8859			0.993224			0.496612	−	0.867973i	$-0.334577\pi$
$967$	30.8859			0.993224			0.496612	+	0.867973i	$0.334577\pi$
$968$	3.38215	+	31.2190i	0.108707	+	1.00342i
$969$		−	13.1605i		−	0.422776i
$970$	11.2112	−	48.7983i	0.359971	−	1.56682i
$971$	16.8735	+	16.8735i	0.541496	+	0.541496i	0.923967	−	0.382471i	$-0.124927\pi$
$971$	16.8735	+	16.8735i	0.541496	+	0.541496i	−0.382471	+	0.923967i	$0.624927\pi$
$972$	30.4937	−	10.5725i	0.978085	−	0.339114i
$973$	0.980511	+	0.980511i	0.0314337	+	0.0314337i
$974$	15.2813	+	24.3973i	0.489644	+	0.781740i
$975$		−	4.11675i		−	0.131841i
$976$	0.183157	−	1.54613i	0.00586273	−	0.0494906i
$977$			17.9666i			0.574802i	0.957810	+	0.287401i	$0.0927912\pi$
$977$			17.9666i			0.574802i	−0.957810	+	0.287401i	$0.907209\pi$
$978$	21.4045	−	13.4068i	0.684442	−	0.428701i
$979$	−50.5262	−	50.5262i	−1.61482	−	1.61482i
$980$	−2.44351	−	7.04766i	−0.0780552	−	0.225129i
$981$	15.2963	−	15.2963i	0.488373	−	0.488373i
$982$	−10.9794	−	2.52247i	−0.350366	−	0.0804953i
$983$			54.0851i			1.72505i	0.506017	+	0.862523i	$0.331117\pi$
$983$			54.0851i			1.72505i	−0.506017	+	0.862523i	$0.668883\pi$
$984$	7.58312	−	9.42580i	0.241741	−	0.300484i
$985$	21.7280			0.692311
$986$	0.930282	−	4.04917i	0.0296262	−	0.128952i
$987$	−19.7711	−	19.7711i	−0.629322	−	0.629322i
$988$	71.9693	+	34.9121i	2.28965	+	1.11070i
$989$	7.66468	−	8.32968i	0.243723	−	0.264869i
$990$	−24.2569	+	15.1933i	−0.770934	+	0.482876i
$991$		−	13.4385i		−	0.426888i	−0.976955	−	0.213444i	$-0.931532\pi$
$991$		−	13.4385i		−	0.426888i	0.976955	−	0.213444i	$-0.0684682\pi$
$992$	21.6319	+	7.74315i	0.686814	+	0.245845i
$993$	25.5941			0.812203
$994$	−5.04745	+	3.16148i	−0.160095	+	0.100276i
$995$	7.40891	+	7.40891i	0.234878	+	0.234878i
$996$	−5.62275	+	11.5910i	−0.178164	+	0.367273i
$997$	21.7461	+	21.7461i	0.688705	+	0.688705i	0.961946	−	0.273241i	$-0.0880957\pi$
$997$	21.7461	+	21.7461i	0.688705	+	0.688705i	−0.273241	+	0.961946i	$0.588096\pi$
$998$	2.65625	−	11.5617i	0.0840822	−	0.365978i
$999$		−	2.53377i		−	0.0801651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.i.b.91.15	✓	80
4.3	odd	2		1472.2.i.b.1103.16		80
16.3	odd	4	inner	368.2.i.b.275.16	yes	80
16.13	even	4		1472.2.i.b.367.15		80
23.22	odd	2	inner	368.2.i.b.91.16	yes	80
92.91	even	2		1472.2.i.b.1103.15		80
368.45	odd	4		1472.2.i.b.367.16		80
368.275	even	4	inner	368.2.i.b.275.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.i.b.91.15	✓	80	1.1	even	1	trivial
368.2.i.b.91.16	yes	80	23.22	odd	2	inner
368.2.i.b.275.15	yes	80	368.275	even	4	inner
368.2.i.b.275.16	yes	80	16.3	odd	4	inner
1472.2.i.b.367.15		80	16.13	even	4
1472.2.i.b.367.16		80	368.45	odd	4
1472.2.i.b.1103.15		80	92.91	even	2
1472.2.i.b.1103.16		80	4.3	odd	2

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.750696 - 1.19852i) q^{2} +(0.670749 + 0.670749i) q^{3} +(-0.872910 + 1.79945i) q^{4} +(-1.44943 + 1.44943i) q^{5} +(0.300379 - 1.30744i) q^{6} +2.27607i q^{7} +(2.81197 - 0.304639i) q^{8} -2.10019i q^{9} +(2.82526 + 0.649093i) q^{10} +(-3.32432 - 3.32432i) q^{11} +(-1.79248 + 0.621477i) q^{12} +(-3.84412 + 3.84412i) q^{13} +(2.72792 - 1.70864i) q^{14} -1.94441 q^{15} +(-2.47605 - 3.14152i) q^{16} +1.88583i q^{17} +(-2.51713 + 1.57661i) q^{18} +(-5.20211 + 5.20211i) q^{19} +(-1.34296 - 3.87340i) q^{20} +(-1.52667 + 1.52667i) q^{21} +(-1.48872 + 6.47982i) q^{22} +(0.199226 + 4.79169i) q^{23} +(2.09046 + 1.68179i) q^{24} +0.798301i q^{25} +(7.49304 + 1.72150i) q^{26} +(3.42095 - 3.42095i) q^{27} +(-4.09568 - 1.98681i) q^{28} +(1.10155 - 1.10155i) q^{29} +(1.45966 + 2.33042i) q^{30} -4.06162i q^{31} +(-1.90642 + 5.32593i) q^{32} -4.45956i q^{33} +(2.26021 - 1.41569i) q^{34} +(-3.29901 - 3.29901i) q^{35} +(3.77919 + 1.83328i) q^{36} +(0.370332 - 0.370332i) q^{37} +(10.1400 + 2.32964i) q^{38} -5.15688 q^{39} +(-3.63421 + 4.51731i) q^{40} -4.50895i q^{41} +(2.97582 + 0.683683i) q^{42} +(-1.66897 - 1.66897i) q^{43} +(8.88378 - 3.08012i) q^{44} +(3.04408 + 3.04408i) q^{45} +(5.59339 - 3.83588i) q^{46} +12.9505i q^{47} +(0.446361 - 3.76798i) q^{48} +1.81950 q^{49} +(0.956781 - 0.599282i) q^{50} +(-1.26492 + 1.26492i) q^{51} +(-3.56174 - 10.2729i) q^{52} +(9.19784 - 9.19784i) q^{53} +(-6.66818 - 1.53199i) q^{54} +9.63673 q^{55} +(0.693380 + 6.40025i) q^{56} -6.97862 q^{57} +(-2.14716 - 0.493301i) q^{58} +(-5.82397 + 5.82397i) q^{59} +(1.69729 - 3.49887i) q^{60} +(0.275232 + 0.275232i) q^{61} +(-4.86794 + 3.04904i) q^{62} +4.78019 q^{63} +(7.81439 - 1.71327i) q^{64} -11.1436i q^{65} +(-5.34489 + 3.34778i) q^{66} +(-9.16779 + 9.16779i) q^{67} +(-3.39346 - 1.64616i) q^{68} +(-3.08039 + 3.34765i) q^{69} +(-1.47738 + 6.43049i) q^{70} -1.85029 q^{71} +(-0.639801 - 5.90568i) q^{72} +11.4766i q^{73} +(-0.721858 - 0.165844i) q^{74} +(-0.535460 + 0.535460i) q^{75} +(-4.81997 - 13.9019i) q^{76} +(7.56638 - 7.56638i) q^{77} +(3.87125 + 6.18064i) q^{78} +2.78305 q^{79} +(8.14229 + 0.964547i) q^{80} -1.71138 q^{81} +(-5.40408 + 3.38485i) q^{82} +(4.80163 - 4.80163i) q^{83} +(-1.41453 - 4.07982i) q^{84} +(-2.73338 - 2.73338i) q^{85} +(-0.747407 + 3.25318i) q^{86} +1.47772 q^{87} +(-10.3606 - 8.33517i) q^{88} +15.1990 q^{89} +(1.36322 - 5.93358i) q^{90} +(-8.74950 - 8.74950i) q^{91} +(-8.79633 - 3.82422i) q^{92} +(2.72433 - 2.72433i) q^{93} +(15.5214 - 9.72188i) q^{94} -15.0802i q^{95} +(-4.85109 + 2.29364i) q^{96} -17.2722i q^{97} +(-1.36589 - 2.18071i) q^{98} +(-6.98170 + 6.98170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} - 4 q^{3} - 16 q^{6} - 4 q^{8} + 20 q^{12} - 4 q^{13} - 16 q^{16} + 24 q^{18} + 4 q^{23} + 4 q^{24} - 24 q^{26} + 44 q^{27} - 20 q^{29} - 24 q^{32} + 16 q^{35} + 104 q^{36} - 128 q^{39} - 16 q^{46}+ \cdots - 88 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 - 4 * q^3 - 16 * q^6 - 4 * q^8 + 20 * q^12 - 4 * q^13 - 16 * q^16 + 24 * q^18 + 4 * q^23 + 4 * q^24 - 24 * q^26 + 44 * q^27 - 20 * q^29 - 24 * q^32 + 16 * q^35 + 104 * q^36 - 128 * q^39 - 16 * q^46 + 56 * q^48 - 160 * q^49 + 8 * q^50 - 72 * q^52 + 52 * q^54 - 8 * q^55 - 44 * q^58 + 80 * q^59 - 92 * q^62 - 24 * q^69 - 12 * q^70 - 8 * q^71 - 120 * q^72 - 12 * q^75 + 40 * q^77 + 136 * q^78 + 40 * q^81 + 132 * q^82 - 16 * q^85 - 8 * q^87 + 4 * q^92 - 28 * q^93 - 60 * q^94 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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