LMFDB - Embedded newform 966.2.k.b.229.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(229,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.12
Character	$\chi$	$=$	966.229
Dual form			966.2.k.b.367.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.814185 + 1.41021i) q^{5} -1.00000i q^{6} +(-0.285113 + 2.63034i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.814185 + 1.41021i) q^{5} -1.00000i q^{6} +(-0.285113 + 2.63034i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.814185 + 1.41021i) q^{10} +(-2.94746 + 1.70172i) q^{11} +(-0.866025 - 0.500000i) q^{12} +2.17675i q^{13} +(2.13539 + 1.56209i) q^{14} +1.62837i q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.88244 + 3.26048i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.718786 - 1.24497i) q^{19} +1.62837 q^{20} +(1.06826 + 2.42050i) q^{21} +3.40343i q^{22} +(-2.48956 + 4.09904i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.17421 + 2.03378i) q^{25} +(1.88512 + 1.08837i) q^{26} -1.00000i q^{27} +(2.42050 - 1.06826i) q^{28} +0.885961 q^{29} +(1.41021 + 0.814185i) q^{30} +(2.73108 - 1.57679i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.70172 + 2.94746i) q^{33} +3.76488 q^{34} +(-3.47720 - 2.54366i) q^{35} -1.00000 q^{36} +(1.94506 + 1.12298i) q^{37} +(-0.718786 - 1.24497i) q^{38} +(1.08837 + 1.88512i) q^{39} +(0.814185 - 1.41021i) q^{40} +2.77788i q^{41} +(2.63034 + 0.285113i) q^{42} +4.13821i q^{43} +(2.94746 + 1.70172i) q^{44} +(0.814185 + 1.41021i) q^{45} +(2.30509 + 4.20554i) q^{46} +(-4.01919 - 2.32048i) q^{47} +1.00000i q^{48} +(-6.83742 - 1.49989i) q^{49} +2.34841 q^{50} +(3.26048 + 1.88244i) q^{51} +(1.88512 - 1.08837i) q^{52} +(-2.58766 + 1.49399i) q^{53} +(-0.866025 - 0.500000i) q^{54} -5.54204i q^{55} +(0.285113 - 2.63034i) q^{56} -1.43757i q^{57} +(0.442980 - 0.767265i) q^{58} +(-0.365310 + 0.210912i) q^{59} +(1.41021 - 0.814185i) q^{60} +(2.94126 - 5.09440i) q^{61} -3.15357i q^{62} +(2.13539 + 1.56209i) q^{63} +1.00000 q^{64} +(-3.06967 - 1.77227i) q^{65} +(1.70172 + 2.94746i) q^{66} +(1.86042 - 1.07411i) q^{67} +(1.88244 - 3.26048i) q^{68} +(-0.106502 + 4.79465i) q^{69} +(-3.94147 + 1.73952i) q^{70} +14.3009 q^{71} +(-0.500000 + 0.866025i) q^{72} +(0.284998 - 0.164544i) q^{73} +(1.94506 - 1.12298i) q^{74} +(2.03378 + 1.17421i) q^{75} -1.43757 q^{76} +(-3.63574 - 8.23801i) q^{77} +2.17675 q^{78} +(-0.901973 - 0.520755i) q^{79} +(-0.814185 - 1.41021i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.40571 + 1.38894i) q^{82} -13.8526 q^{83} +(1.56209 - 2.13539i) q^{84} -6.13062 q^{85} +(3.58380 + 2.06911i) q^{86} +(0.767265 - 0.442980i) q^{87} +(2.94746 - 1.70172i) q^{88} +(-2.18696 + 3.78793i) q^{89} +1.62837 q^{90} +(-5.72559 - 0.620619i) q^{91} +(4.79465 + 0.106502i) q^{92} +(1.57679 - 2.73108i) q^{93} +(-4.01919 + 2.32048i) q^{94} +(1.17045 + 2.02728i) q^{95} +(0.866025 + 0.500000i) q^{96} +0.917714 q^{97} +(-4.71765 + 5.17144i) q^{98} +3.40343i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.814185	+	1.41021i	−0.364115	+	0.630665i	−0.988634	−	0.150345i	$-0.951962\pi$
$5$	−0.814185	+	1.41021i	−0.364115	+	0.630665i	0.624519	+	0.781010i	$0.285295\pi$
$6$		−	1.00000i		−	0.408248i
$7$	−0.285113	+	2.63034i	−0.107763	+	0.994177i
$7$	−0.285113	+	2.63034i	−0.107763	+	0.994177i
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.814185	+	1.41021i	0.257468	+	0.445947i
$11$	−2.94746	+	1.70172i	−0.888692	+	0.513086i	−0.873514	−	0.486798i	$-0.838165\pi$
$11$	−2.94746	+	1.70172i	−0.888692	+	0.513086i	−0.0151774	+	0.999885i	$0.504831\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$			2.17675i			0.603721i	0.953352	+	0.301861i	$0.0976077\pi$
$13$			2.17675i			0.603721i	−0.953352	+	0.301861i	$0.902392\pi$
$14$	2.13539	+	1.56209i	0.570707	+	0.417485i
$15$			1.62837i			0.420443i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.88244	+	3.26048i	0.456559	+	0.790784i	0.998776	−	0.0494546i	$-0.0157483\pi$
$17$	1.88244	+	3.26048i	0.456559	+	0.790784i	−0.542217	+	0.840238i	$0.682415\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	0.718786	−	1.24497i	0.164901	−	0.285617i	−0.771719	−	0.635963i	$-0.780603\pi$
$19$	0.718786	−	1.24497i	0.164901	−	0.285617i	0.936620	+	0.350347i	$0.113936\pi$
$20$	1.62837			0.364115
$21$	1.06826	+	2.42050i	0.233113	+	0.528197i
$22$			3.40343i			0.725614i
$23$	−2.48956	+	4.09904i	−0.519109	+	0.854708i
$23$	−2.48956	+	4.09904i	−0.519109	+	0.854708i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	1.17421	+	2.03378i	0.234841	+	0.406757i
$26$	1.88512	+	1.08837i	0.369702	+	0.213448i
$27$		−	1.00000i		−	0.192450i
$28$	2.42050	−	1.06826i	0.457432	−	0.201882i
$29$	0.885961			0.164519			0.0822594	−	0.996611i	$-0.473786\pi$
$29$	0.885961			0.164519			0.0822594	+	0.996611i	$0.473786\pi$
$30$	1.41021	+	0.814185i	0.257468	+	0.148649i
$31$	2.73108	−	1.57679i	0.490516	−	0.283199i	−0.234273	−	0.972171i	$-0.575271\pi$
$31$	2.73108	−	1.57679i	0.490516	−	0.283199i	0.724788	+	0.688972i	$0.241938\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.70172	+	2.94746i	−0.296231	+	0.513086i
$34$	3.76488			0.645672
$35$	−3.47720	−	2.54366i	−0.587754	−	0.429956i
$36$	−1.00000			−0.166667
$37$	1.94506	+	1.12298i	0.319766	+	0.184617i	0.651288	−	0.758831i	$-0.274229\pi$
$37$	1.94506	+	1.12298i	0.319766	+	0.184617i	−0.331522	+	0.943447i	$0.607562\pi$
$38$	−0.718786	−	1.24497i	−0.116603	−	0.201961i
$39$	1.08837	+	1.88512i	0.174279	+	0.301861i
$40$	0.814185	−	1.41021i	0.128734	−	0.222974i
$41$			2.77788i			0.433831i	0.976190	+	0.216916i	$0.0695997\pi$
$41$			2.77788i			0.433831i	−0.976190	+	0.216916i	$0.930400\pi$
$42$	2.63034	+	0.285113i	0.405871	+	0.0439939i
$43$			4.13821i			0.631071i	0.948914	+	0.315536i	$0.102184\pi$
$43$			4.13821i			0.631071i	−0.948914	+	0.315536i	$0.897816\pi$
$44$	2.94746	+	1.70172i	0.444346	+	0.256543i
$45$	0.814185	+	1.41021i	0.121372	+	0.210222i
$46$	2.30509	+	4.20554i	0.339867	+	0.620073i
$47$	−4.01919	−	2.32048i	−0.586260	−	0.338477i	0.177358	−	0.984146i	$-0.443245\pi$
$47$	−4.01919	−	2.32048i	−0.586260	−	0.338477i	−0.763617	+	0.645669i	$0.776578\pi$
$48$			1.00000i			0.144338i
$49$	−6.83742	−	1.49989i	−0.976774	−	0.214270i
$50$	2.34841			0.332116
$51$	3.26048	+	1.88244i	0.456559	+	0.263595i
$52$	1.88512	−	1.08837i	0.261419	−	0.150930i
$53$	−2.58766	+	1.49399i	−0.355443	+	0.205215i	−0.667080	−	0.744986i	$-0.732456\pi$
$53$	−2.58766	+	1.49399i	−0.355443	+	0.205215i	0.311637	+	0.950201i	$0.399123\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		−	5.54204i		−	0.747289i
$56$	0.285113	−	2.63034i	0.0380998	−	0.351495i
$57$		−	1.43757i		−	0.190411i
$58$	0.442980	−	0.767265i	0.0581662	−	0.100747i
$59$	−0.365310	+	0.210912i	−0.0475593	+	0.0274584i	−0.523591	−	0.851970i	$-0.675408\pi$
$59$	−0.365310	+	0.210912i	−0.0475593	+	0.0274584i	0.476032	+	0.879428i	$0.342075\pi$
$60$	1.41021	−	0.814185i	0.182057	−	0.105111i
$61$	2.94126	−	5.09440i	0.376589	−	0.652272i	−0.613974	−	0.789326i	$-0.710430\pi$
$61$	2.94126	−	5.09440i	0.376589	−	0.652272i	0.990564	+	0.137054i	$0.0437635\pi$
$62$		−	3.15357i		−	0.400504i
$63$	2.13539	+	1.56209i	0.269034	+	0.196804i
$64$	1.00000			0.125000
$65$	−3.06967	−	1.77227i	−0.380746	−	0.219824i
$66$	1.70172	+	2.94746i	0.209467	+	0.362807i
$67$	1.86042	−	1.07411i	0.227286	−	0.131224i	−0.382033	−	0.924149i	$-0.624776\pi$
$67$	1.86042	−	1.07411i	0.227286	−	0.131224i	0.609320	+	0.792925i	$0.291443\pi$
$68$	1.88244	−	3.26048i	0.228280	−	0.395392i
$69$	−0.106502	+	4.79465i	−0.0128214	+	0.577208i
$70$	−3.94147	+	1.73952i	−0.471096	+	0.207912i
$71$	14.3009			1.69721			0.848603	−	0.529030i	$-0.177444\pi$
$71$	14.3009			1.69721			0.848603	+	0.529030i	$0.177444\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	0.284998	−	0.164544i	0.0333565	−	0.0192584i	−0.483229	−	0.875494i	$-0.660536\pi$
$73$	0.284998	−	0.164544i	0.0333565	−	0.0192584i	0.516586	+	0.856236i	$0.327203\pi$
$74$	1.94506	−	1.12298i	0.226109	−	0.130544i
$75$	2.03378	+	1.17421i	0.234841	+	0.135586i
$76$	−1.43757			−0.164901
$77$	−3.63574	−	8.23801i	−0.414331	−	0.938808i
$78$	2.17675			0.246468
$79$	−0.901973	−	0.520755i	−0.101480	−	0.0585895i	0.448401	−	0.893832i	$-0.351994\pi$
$79$	−0.901973	−	0.520755i	−0.101480	−	0.0585895i	−0.549881	+	0.835243i	$0.685327\pi$
$80$	−0.814185	−	1.41021i	−0.0910286	−	0.157666i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.40571	+	1.38894i	0.265666	+	0.153383i
$83$	−13.8526			−1.52052			−0.760261	−	0.649618i	$-0.774929\pi$
$83$	−13.8526			−1.52052			−0.760261	+	0.649618i	$0.774929\pi$
$84$	1.56209	−	2.13539i	0.170438	−	0.232990i
$85$	−6.13062			−0.664959
$86$	3.58380	+	2.06911i	0.386451	+	0.223117i
$87$	0.767265	−	0.442980i	0.0822594	−	0.0474925i
$88$	2.94746	−	1.70172i	0.314200	−	0.181403i
$89$	−2.18696	+	3.78793i	−0.231817	+	0.401519i	−0.958343	−	0.285620i	$-0.907801\pi$
$89$	−2.18696	+	3.78793i	−0.231817	+	0.401519i	0.726526	+	0.687139i	$0.241134\pi$
$90$	1.62837			0.171645
$91$	−5.72559	−	0.620619i	−0.600205	−	0.0650585i
$92$	4.79465	+	0.106502i	0.499877	+	0.0111036i
$93$	1.57679	−	2.73108i	0.163505	−	0.283199i
$94$	−4.01919	+	2.32048i	−0.414548	+	0.239339i
$95$	1.17045	+	2.02728i	0.120086	+	0.207994i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	0.917714			0.0931798			0.0465899	−	0.998914i	$-0.485165\pi$
$97$	0.917714			0.0931798			0.0465899	+	0.998914i	$0.485165\pi$
$98$	−4.71765	+	5.17144i	−0.476555	+	0.522394i
$99$			3.40343i			0.342058i
$100$	1.17421	−	2.03378i	0.117421	−	0.203378i
$101$	11.2127	−	6.47363i	1.11570	−	0.644150i	0.175401	−	0.984497i	$-0.443878\pi$
$101$	11.2127	−	6.47363i	1.11570	−	0.644150i	0.940300	+	0.340347i	$0.110544\pi$
$102$	3.26048	−	1.88244i	0.322836	−	0.186390i
$103$	4.94223	−	8.56019i	0.486972	−	0.843460i	−0.512916	−	0.858439i	$-0.671435\pi$
$103$	4.94223	−	8.56019i	0.486972	−	0.843460i	0.999888	+	0.0149785i	$0.00476800\pi$
$104$		−	2.17675i		−	0.213448i
$105$	−4.28317	−	0.464269i	−0.417995	−	0.0453080i
$106$			2.98798i			0.290218i
$107$	−4.91902	−	2.84000i	−0.475539	−	0.274553i	0.243016	−	0.970022i	$-0.421863\pi$
$107$	−4.91902	−	2.84000i	−0.475539	−	0.274553i	−0.718556	+	0.695469i	$0.755196\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	16.2120	−	9.35999i	1.55283	−	0.896524i	0.554916	−	0.831907i	$-0.312750\pi$
$109$	16.2120	−	9.35999i	1.55283	−	0.896524i	0.997910	−	0.0646179i	$-0.0205829\pi$
$110$	−4.79955	−	2.77102i	−0.457619	−	0.264207i
$111$	2.24596			0.213177
$112$	−2.13539	−	1.56209i	−0.201775	−	0.147603i
$113$			1.43982i			0.135447i	0.997704	+	0.0677236i	$0.0215736\pi$
$113$			1.43982i			0.135447i	−0.997704	+	0.0677236i	$0.978426\pi$
$114$	−1.24497	−	0.718786i	−0.116603	−	0.0673205i
$115$	−3.75354	−	6.84817i	−0.350019	−	0.638595i
$116$	−0.442980	−	0.767265i	−0.0411297	−	0.0712387i
$117$	1.88512	+	1.08837i	0.174279	+	0.100620i
$118$			0.421824i			0.0388320i
$119$	−9.11291	+	4.02186i	−0.835379	+	0.368684i
$120$		−	1.62837i		−	0.148649i
$121$	0.291669	−	0.505186i	0.0265154	−	0.0459260i
$122$	−2.94126	−	5.09440i	−0.266289	−	0.461226i
$123$	1.38894	+	2.40571i	0.125236	+	0.216916i
$124$	−2.73108	−	1.57679i	−0.245258	−	0.141600i
$125$	−11.9659			−1.07027
$126$	2.42050	−	1.06826i	0.215635	−	0.0951679i
$127$	−1.95231			−0.173239			−0.0866196	−	0.996241i	$-0.527606\pi$
$127$	−1.95231			−0.173239			−0.0866196	+	0.996241i	$0.527606\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.06911	+	3.58380i	0.182175	+	0.315536i
$130$	−3.06967	+	1.77227i	−0.269228	+	0.155439i
$131$	−10.2308	−	5.90676i	−0.893870	−	0.516076i	−0.0186635	−	0.999826i	$-0.505941\pi$
$131$	−10.2308	−	5.90676i	−0.893870	−	0.516076i	−0.875206	+	0.483750i	$0.839274\pi$
$132$	3.40343			0.296231
$133$	3.06978	+	2.24561i	0.266183	+	0.194719i
$134$		−	2.14823i		−	0.185579i
$135$	1.41021	+	0.814185i	0.121372	+	0.0700739i
$136$	−1.88244	−	3.26048i	−0.161418	−	0.279584i
$137$	−9.20884	+	5.31673i	−0.786764	+	0.454239i	−0.838822	−	0.544405i	$-0.816755\pi$
$137$	−9.20884	+	5.31673i	−0.786764	+	0.454239i	0.0520579	+	0.998644i	$0.483422\pi$
$138$	4.09904	+	2.48956i	0.348933	+	0.211925i
$139$		−	3.58139i		−	0.303769i	−0.988398	−	0.151885i	$-0.951466\pi$
$139$		−	3.58139i		−	0.303769i	0.988398	−	0.151885i	$-0.0485342\pi$
$140$	−0.464269	+	4.28317i	−0.0392379	+	0.361994i
$141$	−4.64096			−0.390840
$142$	7.15046	−	12.3850i	0.600053	−	1.03932i
$143$	−3.70420	−	6.41587i	−0.309761	−	0.536522i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−0.721336	+	1.24939i	−0.0599037	+	0.103756i
$146$		−	0.329087i		−	0.0272355i
$147$	−6.67133	+	2.11977i	−0.550242	+	0.174835i
$148$		−	2.24596i		−	0.184617i
$149$	−6.59332	−	3.80665i	−0.540145	−	0.311853i	0.204992	−	0.978764i	$-0.434283\pi$
$149$	−6.59332	−	3.80665i	−0.540145	−	0.311853i	−0.745138	+	0.666910i	$0.767616\pi$
$150$	2.03378	−	1.17421i	0.166058	−	0.0958735i
$151$	11.3261	+	19.6173i	0.921702	+	1.59643i	0.796782	+	0.604267i	$0.206534\pi$
$151$	11.3261	+	19.6173i	0.921702	+	1.59643i	0.124920	+	0.992167i	$0.460133\pi$
$152$	−0.718786	+	1.24497i	−0.0583013	+	0.100981i
$153$	3.76488			0.304373
$154$	−8.95219	−	0.970362i	−0.721388	−	0.0781940i
$155$			5.13519i			0.412468i
$156$	1.08837	−	1.88512i	0.0871396	−	0.150930i
$157$	3.54987	+	6.14856i	0.283311	+	0.490709i	0.972198	−	0.234160i	$-0.0752339\pi$
$157$	3.54987	+	6.14856i	0.283311	+	0.490709i	−0.688887	+	0.724868i	$0.741901\pi$
$158$	−0.901973	+	0.520755i	−0.0717571	+	0.0414290i
$159$	−1.49399	+	2.58766i	−0.118481	+	0.205215i
$160$	−1.62837			−0.128734
$161$	−10.0721	−	7.71708i	−0.793790	−	0.608191i
$162$	−1.00000			−0.0785674
$163$	2.78875	−	4.83025i	0.218432	−	0.378335i	−0.735897	−	0.677093i	$-0.763239\pi$
$163$	2.78875	−	4.83025i	0.218432	−	0.378335i	0.954329	+	0.298759i	$0.0965726\pi$
$164$	2.40571	−	1.38894i	0.187854	−	0.108458i
$165$	−2.77102	−	4.79955i	−0.215724	−	0.373644i
$166$	−6.92630	+	11.9967i	−0.537586	+	0.931125i
$167$			23.1602i			1.79219i	0.443859	+	0.896097i	$0.353609\pi$
$167$			23.1602i			1.79219i	−0.443859	+	0.896097i	$0.646391\pi$
$168$	−1.06826	−	2.42050i	−0.0824178	−	0.186746i
$169$	8.26177			0.635521
$170$	−3.06531	+	5.30927i	−0.235099	+	0.407203i
$171$	−0.718786	−	1.24497i	−0.0549670	−	0.0952056i
$172$	3.58380	−	2.06911i	0.273262	−	0.157768i
$173$	−6.22488	−	3.59393i	−0.473269	−	0.273242i	0.244338	−	0.969690i	$-0.421429\pi$
$173$	−6.22488	−	3.59393i	−0.473269	−	0.273242i	−0.717607	+	0.696448i	$0.754763\pi$
$174$		−	0.885961i		−	0.0671645i
$175$	−5.68434	+	2.50871i	−0.429695	+	0.189641i
$176$		−	3.40343i		−	0.256543i
$177$	−0.210912	+	0.365310i	−0.0158531	+	0.0274584i
$178$	2.18696	+	3.78793i	0.163920	+	0.283917i
$179$	5.38836	+	9.33292i	0.402745	+	0.697575i	0.994056	−	0.108869i	$-0.0347228\pi$
$179$	5.38836	+	9.33292i	0.402745	+	0.697575i	−0.591311	+	0.806444i	$0.701389\pi$
$180$	0.814185	−	1.41021i	0.0606858	−	0.105111i
$181$	19.3687			1.43967			0.719834	−	0.694146i	$-0.244218\pi$
$181$	19.3687			1.43967			0.719834	+	0.694146i	$0.244218\pi$
$182$	−3.40027	+	4.64820i	−0.252045	+	0.344548i
$183$		−	5.88251i		−	0.434848i
$184$	2.48956	−	4.09904i	0.183533	−	0.302185i
$185$	−3.16728	+	1.82863i	−0.232863	+	0.134443i
$186$	−1.57679	−	2.73108i	−0.115616	−	0.200252i
$187$	−11.0968	−	6.40676i	−0.811481	−	0.468509i
$188$			4.64096i			0.338477i
$189$	2.63034	+	0.285113i	0.191329	+	0.0207389i
$190$	2.34090			0.169827
$191$	−12.4113	−	7.16569i	−0.898053	−	0.518491i	−0.0214848	−	0.999769i	$-0.506839\pi$
$191$	−12.4113	−	7.16569i	−0.898053	−	0.518491i	−0.876568	+	0.481278i	$0.840173\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	1.25178	+	2.16814i	0.0901050	+	0.156066i	0.907555	−	0.419933i	$-0.137946\pi$
$193$	1.25178	+	2.16814i	0.0901050	+	0.156066i	−0.817450	+	0.575999i	$0.804613\pi$
$194$	0.458857	−	0.794764i	0.0329440	−	0.0570607i
$195$	−3.54455			−0.253830
$196$	2.11977	+	6.67133i	0.151412	+	0.476523i
$197$	11.3703			0.810098			0.405049	−	0.914295i	$-0.367254\pi$
$197$	11.3703			0.810098			0.405049	+	0.914295i	$0.367254\pi$
$198$	2.94746	+	1.70172i	0.209467	+	0.120936i
$199$	−8.83361	−	15.3003i	−0.626198	−	1.08461i	−0.988308	−	0.152471i	$-0.951277\pi$
$199$	−8.83361	−	15.3003i	−0.626198	−	1.08461i	0.362110	−	0.932135i	$-0.382056\pi$
$200$	−1.17421	−	2.03378i	−0.0830289	−	0.143810i
$201$	1.07411	−	1.86042i	0.0757622	−	0.131224i
$202$		−	12.9473i		−	0.910966i
$203$	−0.252599	+	2.33038i	−0.0177290	+	0.163561i
$204$		−	3.76488i		−	0.263595i
$205$	−3.91739	−	2.26170i	−0.273602	−	0.157964i
$206$	−4.94223	−	8.56019i	−0.344341	−	0.596417i
$207$	2.30509	+	4.20554i	0.160215	+	0.292305i
$208$	−1.88512	−	1.08837i	−0.130709	−	0.0754651i
$209$			4.89268i			0.338434i
$210$	−2.54366	+	3.47720i	−0.175529	+	0.239950i
$211$	4.15632			0.286133			0.143066	−	0.989713i	$-0.454304\pi$
$211$	4.15632			0.286133			0.143066	+	0.989713i	$0.454304\pi$
$212$	2.58766	+	1.49399i	0.177721	+	0.102608i
$213$	12.3850	−	7.15046i	0.848603	−	0.489941i
$214$	−4.91902	+	2.84000i	−0.336257	+	0.194138i
$215$	−5.83575	−	3.36927i	−0.397995	−	0.229782i
$216$			1.00000i			0.0680414i
$217$	3.36883	+	7.63323i	0.228691	+	0.518178i
$218$		−	18.7200i		−	1.26788i
$219$	0.164544	−	0.284998i	0.0111188	−	0.0192584i
$220$	−4.79955	+	2.77102i	−0.323586	+	0.186822i
$221$	−7.09725	+	4.09760i	−0.477413	+	0.275634i
$222$	1.12298	−	1.94506i	0.0753695	−	0.130544i
$223$		−	13.1437i		−	0.880167i	−0.897957	−	0.440084i	$-0.854949\pi$
$223$		−	13.1437i		−	0.880167i	0.897957	−	0.440084i	$-0.145051\pi$
$224$	−2.42050	+	1.06826i	−0.161727	+	0.0713759i
$225$	2.34841			0.156561
$226$	1.24692	+	0.719912i	0.0829441	+	0.0478878i
$227$	1.12273	+	1.94463i	0.0745183	+	0.129069i	0.900877	−	0.434075i	$-0.142925\pi$
$227$	1.12273	+	1.94463i	0.0745183	+	0.129069i	−0.826358	+	0.563145i	$0.809591\pi$
$228$	−1.24497	+	0.718786i	−0.0824504	+	0.0476028i
$229$	−3.07827	+	5.33172i	−0.203418	+	0.352330i	−0.949628	−	0.313381i	$-0.898538\pi$
$229$	−3.07827	+	5.33172i	−0.203418	+	0.352330i	0.746210	+	0.665711i	$0.231872\pi$
$230$	−7.80746	−	0.173425i	−0.514809	−	0.0114353i
$231$	−7.26765	−	5.31645i	−0.478176	−	0.349797i
$232$	−0.885961			−0.0581662
$233$	−0.0803609	+	0.139189i	−0.00526462	+	0.00911858i	−0.868646	−	0.495434i	$-0.835009\pi$
$233$	−0.0803609	+	0.139189i	−0.00526462	+	0.00911858i	0.863381	+	0.504552i	$0.168342\pi$
$234$	1.88512	−	1.08837i	0.123234	−	0.0711492i
$235$	6.54473	−	3.77860i	0.426931	−	0.246489i
$236$	0.365310	+	0.210912i	0.0237797	+	0.0137292i
$237$	−1.04151			−0.0676533
$238$	−1.07342	+	9.90294i	−0.0695793	+	0.641912i
$239$	18.2735			1.18202			0.591008	−	0.806666i	$-0.298730\pi$
$239$	18.2735			1.18202			0.591008	+	0.806666i	$0.298730\pi$
$240$	−1.41021	−	0.814185i	−0.0910286	−	0.0525554i
$241$	11.6187	+	20.1242i	0.748426	+	1.29631i	0.948577	+	0.316546i	$0.102523\pi$
$241$	11.6187	+	20.1242i	0.748426	+	1.29631i	−0.200151	+	0.979765i	$0.564143\pi$
$242$	−0.291669	−	0.505186i	−0.0187492	−	0.0324746i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−5.88251			−0.376589
$245$	7.68208	−	8.42101i	0.490790	−	0.537998i
$246$	2.77788			0.177111
$247$	2.70999	+	1.56462i	0.172433	+	0.0995541i
$248$	−2.73108	+	1.57679i	−0.173423	+	0.100126i
$249$	−11.9967	+	6.92630i	−0.760261	+	0.438937i
$250$	−5.98297	+	10.3628i	−0.378396	+	0.655401i
$251$	−5.40607			−0.341228			−0.170614	−	0.985338i	$-0.554575\pi$
$251$	−5.40607			−0.341228			−0.170614	+	0.985338i	$0.554575\pi$
$252$	0.285113	−	2.63034i	0.0179604	−	0.165696i
$253$	0.362473	−	16.3183i	0.0227885	−	1.02592i
$254$	−0.976153	+	1.69075i	−0.0612493	+	0.106087i
$255$	−5.30927	+	3.06531i	−0.332480	+	0.191957i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−23.3982	−	13.5089i	−1.45954	−	0.842664i	−0.460549	−	0.887634i	$-0.652347\pi$
$257$	−23.3982	−	13.5089i	−1.45954	−	0.842664i	−0.998988	+	0.0449699i	$0.985681\pi$
$258$	4.13821			0.257634
$259$	−3.50839	+	4.79600i	−0.218001	+	0.298009i
$260$			3.54455i			0.219824i
$261$	0.442980	−	0.767265i	0.0274198	−	0.0474925i
$262$	−10.2308	+	5.90676i	−0.632061	+	0.364921i
$263$	−8.65870	+	4.99910i	−0.533918	+	0.308258i	−0.742611	−	0.669723i	$-0.766413\pi$
$263$	−8.65870	+	4.99910i	−0.533918	+	0.308258i	0.208692	+	0.977981i	$0.433079\pi$
$264$	1.70172	−	2.94746i	0.104733	−	0.181403i
$265$		−	4.86553i		−	0.298887i
$266$	3.47965	−	1.53570i	0.213351	−	0.0941596i
$267$			4.37392i			0.267680i
$268$	−1.86042	−	1.07411i	−0.113643	−	0.0656120i
$269$	14.9303	−	8.62000i	0.910315	−	0.525570i	0.0297823	−	0.999556i	$-0.490519\pi$
$269$	14.9303	−	8.62000i	0.910315	−	0.525570i	0.880532	+	0.473986i	$0.157185\pi$
$270$	1.41021	−	0.814185i	0.0858226	−	0.0495497i
$271$	−18.2708	−	10.5487i	−1.10987	−	0.640787i	−0.171078	−	0.985258i	$-0.554725\pi$
$271$	−18.2708	−	10.5487i	−1.10987	−	0.640787i	−0.938797	+	0.344471i	$0.888058\pi$
$272$	−3.76488			−0.228280
$273$	−5.26882	+	2.32533i	−0.318883	+	0.140735i
$274$			10.6335i			0.642390i
$275$	−6.92185	−	3.99633i	−0.417403	−	0.240988i
$276$	4.20554	−	2.30509i	0.253144	−	0.138750i
$277$	13.6853	+	23.7036i	0.822270	+	1.42421i	0.903988	+	0.427558i	$0.140626\pi$
$277$	13.6853	+	23.7036i	0.822270	+	1.42421i	−0.0817181	+	0.996655i	$0.526041\pi$
$278$	−3.10157	−	1.79069i	−0.186020	−	0.107399i
$279$		−	3.15357i		−	0.188800i
$280$	3.47720	+	2.54366i	0.207803	+	0.152012i
$281$		−	6.74214i		−	0.402202i	−0.979570	−	0.201101i	$-0.935548\pi$
$281$		−	6.74214i		−	0.402202i	0.979570	−	0.201101i	$-0.0644520\pi$
$282$	−2.32048	+	4.01919i	−0.138183	+	0.239339i
$283$	−11.2706	−	19.5212i	−0.669967	−	1.16042i	−0.977913	−	0.209013i	$-0.932975\pi$
$283$	−11.2706	−	19.5212i	−0.669967	−	1.16042i	0.307946	−	0.951404i	$-0.400359\pi$
$284$	−7.15046	−	12.3850i	−0.424302	−	0.734912i
$285$	2.02728	+	1.17045i	0.120086	+	0.0693314i
$286$	−7.40841			−0.438068
$287$	−7.30677	−	0.792008i	−0.431305	−	0.0467508i
$288$	1.00000			0.0589256
$289$	1.41283	−	2.44709i	0.0831074	−	0.143946i
$290$	0.721336	+	1.24939i	0.0423583	+	0.0733667i
$291$	0.794764	−	0.458857i	0.0465899	−	0.0268987i
$292$	−0.284998	−	0.164544i	−0.0166783	−	0.00962919i
$293$	22.2834			1.30181			0.650904	−	0.759160i	$-0.274390\pi$
$293$	22.2834			1.30181			0.650904	+	0.759160i	$0.274390\pi$
$294$	−1.49989	+	6.83742i	−0.0874754	+	0.398767i
$295$		−	0.686885i		−	0.0399920i
$296$	−1.94506	−	1.12298i	−0.113054	−	0.0652719i
$297$	1.70172	+	2.94746i	0.0987435	+	0.171029i
$298$	−6.59332	+	3.80665i	−0.381941	+	0.220513i
$299$	−8.92257	−	5.41914i	−0.516005	−	0.313397i
$300$		−	2.34841i		−	0.135586i
$301$	−10.8849	−	1.17986i	−0.627396	−	0.0680059i
$302$	22.6521			1.30348
$303$	6.47363	−	11.2127i	0.371900	−	0.644150i
$304$	0.718786	+	1.24497i	0.0412252	+	0.0714042i
$305$	4.78945	+	8.29557i	0.274243	+	0.475003i
$306$	1.88244	−	3.26048i	0.107612	−	0.186390i
$307$		−	5.50484i		−	0.314178i	−0.987584	−	0.157089i	$-0.949789\pi$
$307$		−	5.50484i		−	0.314178i	0.987584	−	0.157089i	$-0.0502110\pi$
$308$	−5.31645	+	7.26765i	−0.302933	+	0.414113i
$309$		−	9.88445i		−	0.562307i
$310$	4.44720	+	2.56759i	0.252584	+	0.145829i
$311$	11.1980	−	6.46519i	0.634982	−	0.366607i	−0.147697	−	0.989033i	$-0.547186\pi$
$311$	11.1980	−	6.46519i	0.634982	−	0.366607i	0.782679	+	0.622426i	$0.213853\pi$
$312$	−1.08837	−	1.88512i	−0.0616170	−	0.106724i
$313$	1.79557	−	3.11002i	0.101492	−	0.175788i	−0.810808	−	0.585312i	$-0.800972\pi$
$313$	1.79557	−	3.11002i	0.101492	−	0.175788i	0.912299	+	0.409524i	$0.134305\pi$
$314$	7.09975			0.400662
$315$	−3.94147	+	1.73952i	−0.222077	+	0.0980107i
$316$			1.04151i			0.0585895i
$317$	3.36520	−	5.82870i	0.189008	−	0.327372i	−0.755911	−	0.654674i	$-0.772806\pi$
$317$	3.36520	−	5.82870i	0.189008	−	0.327372i	0.944920	+	0.327302i	$0.106139\pi$
$318$	1.49399	+	2.58766i	0.0837787	+	0.145109i
$319$	−2.61133	+	1.50765i	−0.146206	+	0.0844124i
$320$	−0.814185	+	1.41021i	−0.0455143	+	0.0788331i
$321$	−5.67999			−0.317026
$322$	−11.7192	+	4.86413i	−0.653087	+	0.271067i
$323$	5.41229			0.301148
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−4.42704	+	2.55595i	−0.245568	+	0.141779i
$326$	−2.78875	−	4.83025i	−0.154454	−	0.267523i
$327$	9.35999	−	16.2120i	0.517609	−	0.896524i
$328$		−	2.77788i		−	0.153383i
$329$	7.24959	−	9.91026i	0.399683	−	0.546370i
$330$	−5.54204			−0.305079
$331$	−2.36392	+	4.09443i	−0.129933	+	0.225050i	−0.923650	−	0.383236i	$-0.874810\pi$
$331$	−2.36392	+	4.09443i	−0.129933	+	0.225050i	0.793717	+	0.608287i	$0.208143\pi$
$332$	6.92630	+	11.9967i	0.380130	+	0.658405i
$333$	1.94506	−	1.12298i	0.106589	−	0.0615389i
$334$	20.0574	+	11.5801i	1.09749	+	0.633636i
$335$			3.49811i			0.191122i
$336$	−2.63034	−	0.285113i	−0.143497	−	0.0155542i
$337$			7.56201i			0.411929i	0.978559	+	0.205964i	$0.0660331\pi$
$337$			7.56201i			0.411929i	−0.978559	+	0.205964i	$0.933967\pi$
$338$	4.13089	−	7.15490i	0.224691	−	0.389176i
$339$	0.719912	+	1.24692i	0.0391002	+	0.0677236i
$340$	3.06531	+	5.30927i	0.166240	+	0.287936i
$341$	−5.36649	+	9.29503i	−0.290612	+	0.503354i
$342$	−1.43757			−0.0777350
$343$	5.89466	−	17.5571i	0.318282	−	0.947996i
$344$		−	4.13821i		−	0.223117i
$345$	−6.67475	−	4.05392i	−0.359356	−	0.218256i
$346$	−6.22488	+	3.59393i	−0.334651	+	0.193211i
$347$	0.901089	+	1.56073i	0.0483730	+	0.0837845i	0.889198	−	0.457522i	$-0.151263\pi$
$347$	0.901089	+	1.56073i	0.0483730	+	0.0837845i	−0.840825	+	0.541307i	$0.817930\pi$
$348$	−0.767265	−	0.442980i	−0.0411297	−	0.0237462i
$349$			6.96125i			0.372627i	0.982490	+	0.186313i	$0.0596540\pi$
$349$			6.96125i			0.372627i	−0.982490	+	0.186313i	$0.940346\pi$
$350$	−0.669563	+	6.17713i	−0.0357896	+	0.330182i
$351$	2.17675			0.116186
$352$	−2.94746	−	1.70172i	−0.157100	−	0.0907017i
$353$	−25.2883	+	14.6002i	−1.34596	+	0.777091i	−0.987675	−	0.156521i	$-0.949972\pi$
$353$	−25.2883	+	14.6002i	−1.34596	+	0.777091i	−0.358286	+	0.933612i	$0.616639\pi$
$354$	0.210912	+	0.365310i	0.0112098	+	0.0194160i
$355$	−11.6436	+	20.1673i	−0.617978	+	1.07037i
$356$	4.37392			0.231817
$357$	−5.88108	+	8.03949i	−0.311260	+	0.425495i
$358$	10.7767			0.569568
$359$	−14.1302	−	8.15805i	−0.745761	−	0.430565i	0.0783993	−	0.996922i	$-0.475019\pi$
$359$	−14.1302	−	8.15805i	−0.745761	−	0.430565i	−0.824160	+	0.566357i	$0.808352\pi$
$360$	−0.814185	−	1.41021i	−0.0429113	−	0.0743246i
$361$	8.46669	+	14.6647i	0.445615	+	0.771829i
$362$	9.68437	−	16.7738i	0.508999	−	0.881613i
$363$		−	0.583338i		−	0.0306173i
$364$	2.32533	+	5.26882i	0.121880	+	0.276161i
$365$			0.535876i			0.0280490i
$366$	−5.09440	−	2.94126i	−0.266289	−	0.153742i
$367$	8.15000	+	14.1162i	0.425427	+	0.736861i	0.996460	−	0.0840660i	$-0.0267907\pi$
$367$	8.15000	+	14.1162i	0.425427	+	0.736861i	−0.571033	+	0.820927i	$0.693457\pi$
$368$	−2.30509	−	4.20554i	−0.120161	−	0.219229i
$369$	2.40571	+	1.38894i	0.125236	+	0.0723052i
$370$			3.65725i			0.190132i
$371$	−3.19193	−	7.23240i	−0.165717	−	0.375488i
$372$	−3.15357			−0.163505
$373$	25.1039	+	14.4937i	1.29983	+	0.750457i	0.980375	−	0.197144i	$-0.0631666\pi$
$373$	25.1039	+	14.4937i	1.29983	+	0.750457i	0.319456	+	0.947601i	$0.396500\pi$
$374$	−11.0968	+	6.40676i	−0.573804	+	0.331286i
$375$	−10.3628	+	5.98297i	−0.535133	+	0.308959i
$376$	4.01919	+	2.32048i	0.207274	+	0.119670i
$377$			1.92851i			0.0993234i
$378$	1.56209	−	2.13539i	0.0803451	−	0.109833i
$379$		−	26.1894i		−	1.34526i	−0.739979	−	0.672630i	$-0.765165\pi$
$379$		−	26.1894i		−	1.34526i	0.739979	−	0.672630i	$-0.234835\pi$
$380$	1.17045	−	2.02728i	0.0600428	−	0.103997i
$381$	−1.69075	+	0.976153i	−0.0866196	+	0.0500098i
$382$	−12.4113	+	7.16569i	−0.635019	+	0.366628i
$383$	10.8737	−	18.8339i	0.555623	−	0.962366i	−0.442232	−	0.896901i	$-0.645813\pi$
$383$	10.8737	−	18.8339i	0.555623	−	0.962366i	0.997855	−	0.0654659i	$-0.0208534\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	14.5775	+	1.58011i	0.742937	+	0.0805298i
$386$	2.50356			0.127428
$387$	3.58380	+	2.06911i	0.182175	+	0.105179i
$388$	−0.458857	−	0.794764i	−0.0232949	−	0.0403480i
$389$	5.36748	−	3.09892i	0.272142	−	0.157121i	−0.357719	−	0.933829i	$-0.616445\pi$
$389$	5.36748	−	3.09892i	0.272142	−	0.157121i	0.629861	+	0.776708i	$0.283112\pi$
$390$	−1.77227	+	3.06967i	−0.0897426	+	0.155439i
$391$	−18.0513	−	0.400969i	−0.912893	−	0.0202779i
$392$	6.83742	+	1.49989i	0.345342	+	0.0757559i
$393$	−11.8135			−0.595913
$394$	5.68514	−	9.84695i	0.286413	−	0.496082i
$395$	1.46875	−	0.847981i	0.0739006	−	0.0426665i
$396$	2.94746	−	1.70172i	0.148115	−	0.0855144i
$397$	−14.2638	−	8.23518i	−0.715877	−	0.413312i	0.0973562	−	0.995250i	$-0.468961\pi$
$397$	−14.2638	−	8.23518i	−0.715877	−	0.413312i	−0.813233	+	0.581938i	$0.802295\pi$
$398$	−17.6672			−0.885577
$399$	3.78131	+	0.409870i	0.189302	+	0.0205192i
$400$	−2.34841			−0.117421
$401$	31.6782	+	18.2894i	1.58193	+	0.913329i	0.994577	+	0.103999i	$0.0331640\pi$
$401$	31.6782	+	18.2894i	1.58193	+	0.913329i	0.587355	+	0.809330i	$0.300169\pi$
$402$	−1.07411	−	1.86042i	−0.0535719	−	0.0927893i
$403$	3.43227	+	5.94486i	0.170973	+	0.296135i
$404$	−11.2127	−	6.47363i	−0.557851	−	0.322075i
$405$	1.62837			0.0809143
$406$	1.89187	+	1.38395i	0.0938920	+	0.0686842i
$407$	−7.64397			−0.378898
$408$	−3.26048	−	1.88244i	−0.161418	−	0.0931948i
$409$	8.14265	−	4.70116i	0.402628	−	0.232457i	−0.284989	−	0.958531i	$-0.591990\pi$
$409$	8.14265	−	4.70116i	0.402628	−	0.232457i	0.687617	+	0.726073i	$0.258657\pi$
$410$	−3.91739	+	2.26170i	−0.193466	+	0.111698i
$411$	−5.31673	+	9.20884i	−0.262255	+	0.454239i
$412$	−9.88445			−0.486972
$413$	−0.450616	−	1.02103i	−0.0221734	−	0.0502414i
$414$	4.79465	+	0.106502i	0.235644	+	0.00523430i
$415$	11.2786	−	19.5351i	0.553644	−	0.958939i
$416$	−1.88512	+	1.08837i	−0.0924255	+	0.0533619i
$417$	−1.79069	−	3.10157i	−0.0876907	−	0.151885i
$418$	4.23718	+	2.44634i	0.207247	+	0.119654i
$419$	27.1703			1.32736			0.663678	−	0.748018i	$-0.268995\pi$
$419$	27.1703			1.32736			0.663678	+	0.748018i	$0.268995\pi$
$420$	1.73952	+	3.94147i	0.0848798	+	0.192324i
$421$			10.2823i			0.501127i	0.968100	+	0.250563i	$0.0806158\pi$
$421$			10.2823i			0.501127i	−0.968100	+	0.250563i	$0.919384\pi$
$422$	2.07816	−	3.59948i	0.101163	−	0.175220i
$423$	−4.01919	+	2.32048i	−0.195420	+	0.112826i
$424$	2.58766	−	1.49399i	0.125668	−	0.0725545i
$425$	−4.42075	+	7.65696i	−0.214438	+	0.371417i
$426$		−	14.3009i		−	0.692882i
$427$	12.5614	+	9.18900i	0.607891	+	0.444687i
$428$			5.67999i			0.274553i
$429$	−6.41587	−	3.70420i	−0.309761	−	0.178841i
$430$	−5.83575	+	3.36927i	−0.281425	+	0.162481i
$431$	35.1132	−	20.2726i	1.69135	−	0.976499i	0.737911	−	0.674898i	$-0.235812\pi$
$431$	35.1132	−	20.2726i	1.69135	−	0.976499i	0.953434	−	0.301601i	$-0.0975210\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	25.8240			1.24102			0.620511	−	0.784198i	$-0.286925\pi$
$433$	25.8240			1.24102			0.620511	+	0.784198i	$0.286925\pi$
$434$	8.29499	+	0.899125i	0.398172	+	0.0431594i
$435$			1.44267i			0.0691708i
$436$	−16.2120	−	9.35999i	−0.776413	−	0.448262i
$437$	3.31373	+	6.04577i	0.158517	+	0.289208i
$438$	−0.164544	−	0.284998i	−0.00786220	−	0.0136177i
$439$	−17.4144	−	10.0542i	−0.831142	−	0.479860i	0.0231016	−	0.999733i	$-0.492646\pi$
$439$	−17.4144	−	10.0542i	−0.831142	−	0.479860i	−0.854244	+	0.519873i	$0.825979\pi$
$440$			5.54204i			0.264207i
$441$	−4.71765	+	5.17144i	−0.224650	+	0.246259i
$442$			8.19520i			0.389806i
$443$	9.93991	−	17.2164i	0.472259	−	0.817977i	−0.527237	−	0.849718i	$-0.676772\pi$
$443$	9.93991	−	17.2164i	0.472259	−	0.817977i	0.999496	+	0.0317414i	$0.0101053\pi$
$444$	−1.12298	−	1.94506i	−0.0532943	−	0.0923084i
$445$	−3.56118	−	6.16815i	−0.168816	−	0.292398i
$446$	−11.3828	−	6.57185i	−0.538990	−	0.311186i
$447$	−7.61331			−0.360097
$448$	−0.285113	+	2.63034i	−0.0134703	+	0.124272i
$449$	6.85403			0.323462			0.161731	−	0.986835i	$-0.448292\pi$
$449$	6.85403			0.323462			0.161731	+	0.986835i	$0.448292\pi$
$450$	1.17421	−	2.03378i	0.0553526	−	0.0958735i
$451$	−4.72715	−	8.18767i	−0.222593	−	0.385542i
$452$	1.24692	−	0.719912i	0.0586504	−	0.0338618i
$453$	19.6173	+	11.3261i	0.921702	+	0.532145i
$454$	2.24546			0.105385
$455$	5.53689	−	7.56899i	0.259574	−	0.354840i
$456$			1.43757i			0.0673205i
$457$	24.1446	+	13.9399i	1.12944	+	0.652080i	0.943793	−	0.330537i	$-0.107230\pi$
$457$	24.1446	+	13.9399i	1.12944	+	0.652080i	0.185643	+	0.982617i	$0.440563\pi$
$458$	3.07827	+	5.33172i	0.143838	+	0.249135i
$459$	3.26048	−	1.88244i	0.152186	−	0.0878649i
$460$	−4.05392	+	6.67475i	−0.189015	+	0.311212i
$461$			9.09892i			0.423779i	0.977294	+	0.211890i	$0.0679617\pi$
$461$			9.09892i			0.423779i	−0.977294	+	0.211890i	$0.932038\pi$
$462$	−8.23801	+	3.63574i	−0.383267	+	0.169150i
$463$	−6.71090			−0.311882			−0.155941	−	0.987766i	$-0.549841\pi$
$463$	−6.71090			−0.311882			−0.155941	+	0.987766i	$0.549841\pi$
$464$	−0.442980	+	0.767265i	−0.0205648	+	0.0356194i
$465$	2.56759	+	4.44720i	0.119069	+	0.206234i
$466$	0.0803609	+	0.139189i	0.00372265	+	0.00644781i
$467$	−7.70978	+	13.3537i	−0.356766	+	0.617937i	−0.987419	−	0.158128i	$-0.949454\pi$
$467$	−7.70978	+	13.3537i	−0.356766	+	0.617937i	0.630652	+	0.776065i	$0.282787\pi$
$468$		−	2.17675i		−	0.100620i
$469$	2.29486	+	5.19979i	0.105967	+	0.240104i
$470$		−	7.55720i		−	0.348588i
$471$	6.14856	+	3.54987i	0.283311	+	0.163570i
$472$	0.365310	−	0.210912i	0.0168148	−	0.00970801i
$473$	−7.04206	−	12.1972i	−0.323794	−	0.560828i
$474$	−0.520755	+	0.901973i	−0.0239190	+	0.0414290i
$475$	3.37601			0.154902
$476$	8.03949	+	5.88108i	0.368489	+	0.269559i
$477$			2.98798i			0.136810i
$478$	9.13675	−	15.8253i	0.417905	−	0.723833i
$479$	3.92661	+	6.80109i	0.179411	+	0.310750i	0.941679	−	0.336512i	$-0.109247\pi$
$479$	3.92661	+	6.80109i	0.179411	+	0.310750i	−0.762268	+	0.647262i	$0.775914\pi$
$480$	−1.41021	+	0.814185i	−0.0643670	+	0.0371623i
$481$	−2.44444	+	4.23390i	−0.111457	+	0.193049i
$482$	23.2374			1.05843
$483$	−12.5812	−	1.64715i	−0.572465	−	0.0749481i
$484$	−0.583338			−0.0265154
$485$	−0.747189	+	1.29417i	−0.0339281	+	0.0587652i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	16.1556	+	27.9823i	0.732079	+	1.26800i	0.955993	+	0.293389i	$0.0947831\pi$
$487$	16.1556	+	27.9823i	0.732079	+	1.26800i	−0.223914	+	0.974609i	$0.571884\pi$
$488$	−2.94126	+	5.09440i	−0.133144	+	0.230613i
$489$		−	5.57750i		−	0.252223i
$490$	−3.45177	−	10.8634i	−0.155935	−	0.490758i
$491$	10.3039			0.465008			0.232504	−	0.972595i	$-0.425308\pi$
$491$	10.3039			0.465008			0.232504	+	0.972595i	$0.425308\pi$
$492$	1.38894	−	2.40571i	0.0626182	−	0.108458i
$493$	1.66777	+	2.88866i	0.0751126	+	0.130099i
$494$	2.70999	−	1.56462i	0.121928	−	0.0703954i
$495$	−4.79955	−	2.77102i	−0.215724	−	0.124548i
$496$			3.15357i			0.141600i
$497$	−4.07738	+	37.6163i	−0.182895	+	1.68732i
$498$			13.8526i			0.620750i
$499$	5.87997	−	10.1844i	0.263224	−	0.455917i	−0.703873	−	0.710326i	$-0.748548\pi$
$499$	5.87997	−	10.1844i	0.263224	−	0.455917i	0.967097	+	0.254409i	$0.0818809\pi$
$500$	5.98297	+	10.3628i	0.267566	+	0.463439i
$501$	11.5801	+	20.0574i	0.517362	+	0.896097i
$502$	−2.70304	+	4.68179i	−0.120642	+	0.208959i
$503$	37.1243			1.65529			0.827645	−	0.561252i	$-0.189680\pi$
$503$	37.1243			1.65529			0.827645	+	0.561252i	$0.189680\pi$
$504$	−2.13539	−	1.56209i	−0.0951178	−	0.0695809i
$505$			21.0829i			0.938178i
$506$	−13.9508	−	8.47304i	−0.620188	−	0.376672i
$507$	7.15490	−	4.13089i	0.317760	−	0.183459i
$508$	0.976153	+	1.69075i	0.0433098	+	0.0750147i
$509$	1.20344	+	0.694809i	0.0533417	+	0.0307969i	0.526434	−	0.850216i	$-0.323529\pi$
$509$	1.20344	+	0.694809i	0.0533417	+	0.0307969i	−0.473092	+	0.881013i	$0.656862\pi$
$510$			6.13062i			0.271469i
$511$	0.351550	+	0.796557i	0.0155517	+	0.0352376i
$512$	−1.00000			−0.0441942
$513$	−1.24497	−	0.718786i	−0.0549670	−	0.0317352i
$514$	−23.3982	+	13.5089i	−1.03205	+	0.595854i
$515$	8.04777	+	13.9392i	0.354627	+	0.614232i
$516$	2.06911	−	3.58380i	0.0910873	−	0.157768i
$517$	15.7952			0.694672
$518$	2.39926	+	5.43635i	0.105418	+	0.238860i
$519$	−7.18787			−0.315512
$520$	3.06967	+	1.77227i	0.134614	+	0.0777194i
$521$	6.21027	+	10.7565i	0.272077	+	0.471251i	0.969393	−	0.245512i	$-0.0789562\pi$
$521$	6.21027	+	10.7565i	0.272077	+	0.471251i	−0.697317	+	0.716763i	$0.745623\pi$
$522$	−0.442980	−	0.767265i	−0.0193887	−	0.0335823i
$523$	16.4338	−	28.4642i	0.718600	−	1.24465i	−0.242954	−	0.970038i	$-0.578117\pi$
$523$	16.4338	−	28.4642i	0.718600	−	1.24465i	0.961554	−	0.274614i	$-0.0885502\pi$
$524$			11.8135i			0.516076i
$525$	−3.66842	+	5.01477i	−0.160103	+	0.218863i
$526$			9.99821i			0.435942i
$527$	10.2822	+	5.93642i	0.447899	+	0.258595i
$528$	−1.70172	−	2.94746i	−0.0740576	−	0.128272i
$529$	−10.6042	−	20.4096i	−0.461052	−	0.887373i
$530$	−4.21367	−	2.43277i	−0.183030	−	0.105673i
$531$			0.421824i			0.0183056i
$532$	0.409870	−	3.78131i	0.0177701	−	0.163941i
$533$	−6.04673			−0.261913
$534$	3.78793	+	2.18696i	0.163920	+	0.0946390i
$535$	8.00998	−	4.62456i	0.346301	−	0.199937i
$536$	−1.86042	+	1.07411i	−0.0803579	+	0.0463947i
$537$	9.33292	+	5.38836i	0.402745	+	0.232525i
$538$		−	17.2400i		−	0.743269i
$539$	22.7054	−	7.21448i	0.977990	−	0.310750i
$540$		−	1.62837i		−	0.0700739i
$541$	−10.1900	+	17.6496i	−0.438102	+	0.758815i	−0.997543	−	0.0700551i	$-0.977682\pi$
$541$	−10.1900	+	17.6496i	−0.438102	+	0.758815i	0.559441	+	0.828870i	$0.311016\pi$
$542$	−18.2708	+	10.5487i	−0.784800	+	0.453104i
$543$	16.7738	−	9.68437i	0.719834	−	0.415596i
$544$	−1.88244	+	3.26048i	−0.0807090	+	0.139792i
$545$			30.4830i			1.30575i
$546$	−0.620619	+	5.72559i	−0.0265600	+	0.245033i
$547$	−44.5112			−1.90316			−0.951581	−	0.307399i	$-0.900541\pi$
$547$	−44.5112			−1.90316			−0.951581	+	0.307399i	$0.900541\pi$
$548$	9.20884	+	5.31673i	0.393382	+	0.227119i
$549$	−2.94126	−	5.09440i	−0.125530	−	0.217424i
$550$	−6.92185	+	3.99633i	−0.295148	+	0.170404i
$551$	0.636816	−	1.10300i	0.0271293	−	0.0469893i
$552$	0.106502	−	4.79465i	0.00453304	−	0.204074i
$553$	1.62693	−	2.22403i	0.0691840	−	0.0945752i
$554$	27.3706			1.16287
$555$	−1.82863	+	3.16728i	−0.0776209	+	0.134443i
$556$	−3.10157	+	1.79069i	−0.131536	+	0.0759423i
$557$	30.4890	−	17.6028i	1.29186	−	0.745857i	0.312877	−	0.949794i	$-0.398707\pi$
$557$	30.4890	−	17.6028i	1.29186	−	0.745857i	0.978984	+	0.203937i	$0.0653738\pi$
$558$	−2.73108	−	1.57679i	−0.115616	−	0.0667507i
$559$	−9.00784			−0.380991
$560$	3.94147	−	1.73952i	0.166558	−	0.0735080i
$561$	−12.8135			−0.540987
$562$	−5.83886	−	3.37107i	−0.246298	−	0.142200i
$563$	−1.02938	−	1.78293i	−0.0433831	−	0.0751417i	0.843518	−	0.537100i	$-0.180480\pi$
$563$	−1.02938	−	1.78293i	−0.0433831	−	0.0751417i	−0.886902	+	0.461958i	$0.847147\pi$
$564$	2.32048	+	4.01919i	0.0977099	+	0.169239i
$565$	−2.03045	−	1.17228i	−0.0854218	−	0.0493183i
$566$	−22.5412			−0.947477
$567$	2.42050	−	1.06826i	0.101652	−	0.0448626i
$568$	−14.3009			−0.600053
$569$	33.4262	+	19.2986i	1.40130	+	0.809041i	0.994526	−	0.104489i	$-0.0333206\pi$
$569$	33.4262	+	19.2986i	1.40130	+	0.809041i	0.406773	+	0.913529i	$0.366654\pi$
$570$	2.02728	−	1.17045i	0.0849133	−	0.0490247i
$571$	−24.0280	+	13.8725i	−1.00554	+	0.580548i	−0.909882	−	0.414866i	$-0.863828\pi$
$571$	−24.0280	+	13.8725i	−1.00554	+	0.580548i	−0.0956563	+	0.995414i	$0.530495\pi$
$572$	−3.70420	+	6.41587i	−0.154881	+	0.268261i
$573$	−14.3314			−0.598702
$574$	−4.33928	+	5.93184i	−0.181118	+	0.247590i
$575$	−11.2598	−	0.250111i	−0.469567	−	0.0104304i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	14.7349	−	8.50719i	0.613421	−	0.354159i	−0.160882	−	0.986974i	$-0.551434\pi$
$577$	14.7349	−	8.50719i	0.613421	−	0.354159i	0.774303	+	0.632815i	$0.218101\pi$
$578$	−1.41283	−	2.44709i	−0.0587658	−	0.101785i
$579$	2.16814	+	1.25178i	0.0901050	+	0.0520221i
$580$	1.44267			0.0599037
$581$	3.94956	−	36.4371i	0.163855	−	1.51167i
$582$		−	0.917714i		−	0.0380405i
$583$	5.08469	−	8.80693i	0.210586	−	0.364746i
$584$	−0.284998	+	0.164544i	−0.0117933	+	0.00680887i
$585$	−3.06967	+	1.77227i	−0.126915	+	0.0732745i
$586$	11.1417	−	19.2980i	0.460259	−	0.797192i
$587$			21.4804i			0.886591i	0.896376	+	0.443295i	$0.146191\pi$
$587$			21.4804i			0.886591i	−0.896376	+	0.443295i	$0.853809\pi$
$588$	5.17144	+	4.71765i	0.213266	+	0.194553i
$589$		−	4.53349i		−	0.186799i
$590$	−0.594860	−	0.343443i	−0.0244900	−	0.0141393i
$591$	9.84695	−	5.68514i	0.405049	−	0.233855i
$592$	−1.94506	+	1.12298i	−0.0799414	+	0.0461542i
$593$	0.419117	+	0.241977i	0.0172111	+	0.00993682i	0.508581	−	0.861014i	$-0.330170\pi$
$593$	0.419117	+	0.241977i	0.0172111	+	0.00993682i	−0.491370	+	0.870951i	$0.663504\pi$
$594$	3.40343			0.139644
$595$	1.74792	−	16.1256i	0.0716577	−	0.661087i
$596$			7.61331i			0.311853i
$597$	−15.3003	−	8.83361i	−0.626198	−	0.361535i
$598$	−9.15439	+	5.01760i	−0.374351	+	0.205185i
$599$	6.62025	+	11.4666i	0.270496	+	0.468513i	0.968989	−	0.247104i	$-0.0794790\pi$
$599$	6.62025	+	11.4666i	0.270496	+	0.468513i	−0.698493	+	0.715617i	$0.746146\pi$
$600$	−2.03378	−	1.17421i	−0.0830289	−	0.0479368i
$601$		−	24.5617i		−	1.00189i	−0.865479	−	0.500946i	$-0.832986\pi$
$601$		−	24.5617i		−	1.00189i	0.865479	−	0.500946i	$-0.167014\pi$
$602$	−6.46425	+	8.83669i	−0.263463	+	0.360157i
$603$		−	2.14823i		−	0.0874826i
$604$	11.3261	−	19.6173i	0.460851	−	0.798217i
$605$	0.474945	+	0.822629i	0.0193093	+	0.0334446i
$606$	−6.47363	−	11.2127i	−0.262973	−	0.455483i
$607$	9.92650	+	5.73107i	0.402904	+	0.232617i	0.687736	−	0.725960i	$-0.258604\pi$
$607$	9.92650	+	5.73107i	0.402904	+	0.232617i	−0.284832	+	0.958577i	$0.591938\pi$
$608$	1.43757			0.0583013
$609$	0.946434	+	2.14447i	0.0383514	+	0.0868983i
$610$	9.57890			0.387838
$611$	5.05110	−	8.74877i	0.204346	−	0.353937i
$612$	−1.88244	−	3.26048i	−0.0760932	−	0.131797i
$613$	28.9729	−	16.7275i	1.17020	−	0.675618i	0.216476	−	0.976288i	$-0.430544\pi$
$613$	28.9729	−	16.7275i	1.17020	−	0.675618i	0.953728	+	0.300670i	$0.0972102\pi$
$614$	−4.76734	−	2.75242i	−0.192394	−	0.111079i
$615$	−4.52341			−0.182401
$616$	3.63574	+	8.23801i	0.146488	+	0.331919i
$617$			43.1152i			1.73575i	0.496782	+	0.867876i	$0.334515\pi$
$617$			43.1152i			1.73575i	−0.496782	+	0.867876i	$0.665485\pi$
$618$	−8.56019	−	4.94223i	−0.344341	−	0.198806i
$619$	−13.2191	−	22.8961i	−0.531319	−	0.920271i	−0.999332	−	0.0365493i	$-0.988363\pi$
$619$	−13.2191	−	22.8961i	−0.531319	−	0.920271i	0.468013	−	0.883721i	$-0.344970\pi$
$620$	4.44720	−	2.56759i	0.178604	−	0.103117i
$621$	4.09904	+	2.48956i	0.164489	+	0.0999025i
$622$		−	12.9304i		−	0.518461i
$623$	−9.34002	−	6.83245i	−0.374200	−	0.273736i
$624$	−2.17675			−0.0871396
$625$	3.87145	−	6.70554i	0.154858	−	0.268222i
$626$	−1.79557	−	3.11002i	−0.0717653	−	0.124301i
$627$	2.44634	+	4.23718i	0.0976974	+	0.169217i
$628$	3.54987	−	6.14856i	0.141655	−	0.245354i
$629$			8.45578i			0.337154i
$630$	−0.464269	+	4.28317i	−0.0184969	+	0.170646i
$631$			13.9906i			0.556958i	0.960442	+	0.278479i	$0.0898303\pi$
$631$			13.9906i			0.556958i	−0.960442	+	0.278479i	$0.910170\pi$
$632$	0.901973	+	0.520755i	0.0358786	+	0.0207145i
$633$	3.59948	−	2.07816i	0.143066	−	0.0825994i
$634$	−3.36520	−	5.82870i	−0.133649	−	0.231487i
$635$	1.58954	−	2.75316i	0.0630789	−	0.109256i
$636$	2.98798			0.118481
$637$	3.26488	−	14.8833i	0.129359	−	0.589699i
$638$			3.01531i			0.119377i
$639$	7.15046	−	12.3850i	0.282868	−	0.489941i
$640$	0.814185	+	1.41021i	0.0321835	+	0.0557434i
$641$	−22.0974	+	12.7580i	−0.872796	+	0.503909i	−0.868276	−	0.496081i	$-0.834772\pi$
$641$	−22.0974	+	12.7580i	−0.872796	+	0.503909i	−0.00451976	+	0.999990i	$0.501439\pi$
$642$	−2.84000	+	4.91902i	−0.112086	+	0.194138i
$643$	−42.9950			−1.69556			−0.847778	−	0.530352i	$-0.822060\pi$
$643$	−42.9950			−1.69556			−0.847778	+	0.530352i	$0.822060\pi$
$644$	−1.64715	+	12.5812i	−0.0649070	+	0.495769i
$645$	−6.73854			−0.265330
$646$	2.70615	−	4.68718i	0.106472	−	0.184415i
$647$	5.92501	−	3.42081i	0.232936	−	0.134486i	−0.378990	−	0.925401i	$-0.623728\pi$
$647$	5.92501	−	3.42081i	0.232936	−	0.134486i	0.611926	+	0.790915i	$0.290395\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	0.717824	−	1.24331i	0.0281771	−	0.0488041i
$650$			5.11190i			0.200505i
$651$	6.73411	+	4.92616i	0.263930	+	0.193071i
$652$	−5.57750			−0.218432
$653$	3.33555	−	5.77734i	0.130530	−	0.226085i	−0.793351	−	0.608765i	$-0.791665\pi$
$653$	3.33555	−	5.77734i	0.130530	−	0.226085i	0.923881	+	0.382680i	$0.124999\pi$
$654$	−9.35999	−	16.2120i	−0.366005	−	0.633939i
$655$	16.6595	−	9.61839i	0.650942	−	0.375822i
$656$	−2.40571	−	1.38894i	−0.0939272	−	0.0542289i
$657$		−	0.329087i		−	0.0128389i
$658$	−4.95774	−	11.2335i	−0.193273	−	0.437926i
$659$		−	9.83396i		−	0.383077i	−0.981485	−	0.191538i	$-0.938652\pi$
$659$		−	9.83396i		−	0.383077i	0.981485	−	0.191538i	$-0.0613476\pi$
$660$	−2.77102	+	4.79955i	−0.107862	+	0.186822i
$661$	6.83545	+	11.8393i	0.265868	+	0.460497i	0.967791	−	0.251756i	$-0.0810081\pi$
$661$	6.83545	+	11.8393i	0.265868	+	0.460497i	−0.701923	+	0.712253i	$0.747675\pi$
$662$	2.36392	+	4.09443i	0.0918764	+	0.159135i
$663$	−4.09760	+	7.09725i	−0.159138	+	0.275634i
$664$	13.8526			0.537586
$665$	−5.66615	+	2.50068i	−0.219724	+	0.0969723i
$666$		−	2.24596i		−	0.0870292i
$667$	−2.20565	+	3.63159i	−0.0854031	+	0.140616i
$668$	20.0574	−	11.5801i	0.776043	−	0.448048i
$669$	−6.57185	−	11.3828i	−0.254082	−	0.440084i
$670$	3.02945	+	1.74905i	0.117038	+	0.0675719i
$671$			20.0207i			0.772891i
$672$	−1.56209	+	2.13539i	−0.0602588	+	0.0823744i
$673$	−10.4906			−0.404385			−0.202192	−	0.979346i	$-0.564807\pi$
$673$	−10.4906			−0.404385			−0.202192	+	0.979346i	$0.564807\pi$
$674$	6.54889	+	3.78101i	0.252254	+	0.145639i
$675$	2.03378	−	1.17421i	0.0782804	−	0.0451952i
$676$	−4.13089	−	7.15490i	−0.158880	−	0.275189i
$677$	0.421250	−	0.729626i	0.0161899	−	0.0280418i	−0.857817	−	0.513955i	$-0.828180\pi$
$677$	0.421250	−	0.729626i	0.0161899	−	0.0280418i	0.874007	+	0.485914i	$0.161513\pi$
$678$	1.43982			0.0552961
$679$	−0.261652	+	2.41390i	−0.0100413	+	0.0926371i
$680$	6.13062			0.235099
$681$	1.94463	+	1.12273i	0.0745183	+	0.0430231i
$682$	5.36649	+	9.29503i	0.205493	+	0.355925i
$683$	−2.24887	−	3.89516i	−0.0860506	−	0.149044i	0.819788	−	0.572667i	$-0.194091\pi$
$683$	−2.24887	−	3.89516i	−0.0860506	−	0.149044i	−0.905838	+	0.423623i	$0.860758\pi$
$684$	−0.718786	+	1.24497i	−0.0274835	+	0.0476028i
$685$		−	17.3152i		−	0.661579i
$686$	−12.2576	−	13.8835i	−0.467997	−	0.530074i
$687$			6.15654i			0.234887i
$688$	−3.58380	−	2.06911i	−0.136631	−	0.0788839i
$689$	−3.25203	−	5.63269i	−0.123893	−	0.214588i
$690$	−6.84817	+	3.75354i	−0.260705	+	0.142895i
$691$	−27.9698	−	16.1484i	−1.06402	−	0.614314i	−0.137480	−	0.990504i	$-0.543900\pi$
$691$	−27.9698	−	16.1484i	−1.06402	−	0.614314i	−0.926542	+	0.376191i	$0.877234\pi$
$692$			7.18787i			0.273242i
$693$	−8.95219	−	0.970362i	−0.340066	−	0.0368610i
$694$	1.80218			0.0684098
$695$	5.05051	+	2.91591i	0.191577	+	0.110607i
$696$	−0.767265	+	0.442980i	−0.0290831	+	0.0167911i
$697$	−9.05722	+	5.22919i	−0.343067	+	0.198070i
$698$	6.02862	+	3.48062i	0.228186	+	0.131744i
$699$			0.160722i			0.00607906i
$700$	5.01477	+	3.66842i	0.189541	+	0.138653i
$701$		−	5.36860i		−	0.202769i	−0.994847	−	0.101385i	$-0.967673\pi$
$701$		−	5.36860i		−	0.202769i	0.994847	−	0.101385i	$-0.0323272\pi$
$702$	1.08837	−	1.88512i	0.0410780	−	0.0711492i
$703$	2.79616	−	1.61437i	0.105459	−	0.0608870i
$704$	−2.94746	+	1.70172i	−0.111086	+	0.0641358i
$705$	3.77860	−	6.54473i	0.142310	−	0.246489i
$706$			29.2004i			1.09897i
$707$	13.8310	+	31.3389i	0.520169	+	1.17862i
$708$	0.421824			0.0158531
$709$	−26.6720	−	15.3991i	−1.00169	−	0.578324i	−0.0929402	−	0.995672i	$-0.529627\pi$
$709$	−26.6720	−	15.3991i	−1.00169	−	0.578324i	−0.908747	+	0.417347i	$0.862960\pi$
$710$	11.6436	+	20.1673i	0.436976	+	0.756865i
$711$	−0.901973	+	0.520755i	−0.0338266	+	0.0195298i
$712$	2.18696	−	3.78793i	0.0819598	−	0.141959i
$713$	−0.335863	+	15.1203i	−0.0125782	+	0.566259i
$714$	4.02186	+	9.11291i	0.150514	+	0.341042i
$715$	12.0636			0.451154
$716$	5.38836	−	9.33292i	0.201373	−	0.348788i
$717$	15.8253	−	9.13675i	0.591008	−	0.341218i
$718$	−14.1302	+	8.15805i	−0.527333	+	0.304456i
$719$	−30.3376	−	17.5154i	−1.13140	−	0.653215i	−0.187115	−	0.982338i	$-0.559914\pi$
$719$	−30.3376	−	17.5154i	−1.13140	−	0.653215i	−0.944287	+	0.329123i	$0.893247\pi$
$720$	−1.62837			−0.0606858
$721$	21.1071	+	15.4404i	0.786071	+	0.575030i
$722$	16.9334			0.630195
$723$	20.1242	+	11.6187i	0.748426	+	0.432104i
$724$	−9.68437	−	16.7738i	−0.359917	−	0.623394i
$725$	1.04030	+	1.80185i	0.0386358	+	0.0669192i
$726$	−0.505186	−	0.291669i	−0.0187492	−	0.0108249i
$727$	−38.0498			−1.41119			−0.705595	−	0.708616i	$-0.749320\pi$
$727$	−38.0498			−1.41119			−0.705595	+	0.708616i	$0.749320\pi$
$728$	5.72559	+	0.620619i	0.212205	+	0.0230017i
$729$	−1.00000			−0.0370370
$730$	0.464082	+	0.267938i	0.0171765	+	0.00991683i
$731$	−13.4926	+	7.78994i	−0.499041	+	0.288121i
$732$	−5.09440	+	2.94126i	−0.188295	+	0.108712i
$733$	3.33831	−	5.78212i	0.123303	−	0.213567i	−0.797765	−	0.602968i	$-0.793985\pi$
$733$	3.33831	−	5.78212i	0.123303	−	0.213567i	0.921068	+	0.389401i	$0.127318\pi$
$734$	16.3000			0.601644
$735$	2.44238	−	11.1338i	0.0900884	−	0.410678i
$736$	−4.79465	−	0.106502i	−0.176733	−	0.00392573i
$737$	−3.65567	+	6.33181i	−0.134658	+	0.233235i
$738$	2.40571	−	1.38894i	0.0885554	−	0.0511275i
$739$	23.7020	+	41.0530i	0.871892	+	1.51016i	0.860038	+	0.510231i	$0.170440\pi$
$739$	23.7020	+	41.0530i	0.871892	+	1.51016i	0.0118541	+	0.999930i	$0.496227\pi$
$740$	3.16728	+	1.82863i	0.116431	+	0.0672217i
$741$	3.12923			0.114955
$742$	−7.85941	−	0.851911i	−0.288528	−	0.0312746i
$743$			12.6347i			0.463522i	0.972773	+	0.231761i	$0.0744488\pi$
$743$			12.6347i			0.463522i	−0.972773	+	0.231761i	$0.925551\pi$
$744$	−1.57679	+	2.73108i	−0.0578078	+	0.100126i
$745$	10.7364	−	6.19864i	0.393350	−	0.227101i
$746$	25.1039	−	14.4937i	0.919119	−	0.530654i
$747$	−6.92630	+	11.9967i	−0.253420	+	0.438937i
$748$			12.8135i			0.468509i
$749$	8.87264	−	12.1290i	0.324199	−	0.443184i
$750$			11.9659i			0.436934i
$751$	−24.1667	−	13.9526i	−0.881855	−	0.509139i	−0.0105855	−	0.999944i	$-0.503370\pi$
$751$	−24.1667	−	13.9526i	−0.881855	−	0.509139i	−0.871270	+	0.490805i	$0.836703\pi$
$752$	4.01919	−	2.32048i	0.146565	−	0.0846193i
$753$	−4.68179	+	2.70304i	−0.170614	+	0.0985041i
$754$	1.67014	+	0.964256i	0.0608229	+	0.0351161i
$755$	−36.8860			−1.34242
$756$	−1.06826	−	2.42050i	−0.0388521	−	0.0880328i
$757$		−	39.1304i		−	1.42222i	−0.703081	−	0.711110i	$-0.748193\pi$
$757$		−	39.1304i		−	1.42222i	0.703081	−	0.711110i	$-0.251807\pi$
$758$	−22.6807	−	13.0947i	−0.823800	−	0.475621i
$759$	−7.84522	−	14.3133i	−0.284763	−	0.519538i
$760$	−1.17045	−	2.02728i	−0.0424567	−	0.0735371i
$761$	1.47276	+	0.850297i	0.0533874	+	0.0308233i	0.526456	−	0.850202i	$-0.323520\pi$
$761$	1.47276	+	0.850297i	0.0533874	+	0.0308233i	−0.473069	+	0.881026i	$0.656854\pi$
$762$			1.95231i			0.0707246i
$763$	19.9978	+	45.3117i	0.723967	+	1.64040i
$764$			14.3314i			0.518491i
$765$	−3.06531	+	5.30927i	−0.110827	+	0.191957i
$766$	−10.8737	−	18.8339i	−0.392884	−	0.680496i
$767$	−0.459102	−	0.795188i	−0.0165772	−	0.0287126i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−32.4459			−1.17003			−0.585014	−	0.811023i	$-0.698911\pi$
$769$	−32.4459			−1.17003			−0.585014	+	0.811023i	$0.698911\pi$
$770$	8.65715	−	11.8344i	0.311982	−	0.426483i
$771$	−27.0179			−0.973025
$772$	1.25178	−	2.16814i	0.0450525	−	0.0780332i
$773$	−14.8820	−	25.7764i	−0.535270	−	0.927114i	−0.999150	−	0.0412166i	$-0.986877\pi$
$773$	−14.8820	−	25.7764i	−0.535270	−	0.927114i	0.463881	−	0.885898i	$-0.346457\pi$
$774$	3.58380	−	2.06911i	0.128817	−	0.0743725i
$775$	6.41369	+	3.70295i	0.230387	+	0.133014i
$776$	−0.917714			−0.0329440
$777$	−0.640352	+	5.90765i	−0.0229725	+	0.211936i
$778$		−	6.19783i		−	0.222203i
$779$	3.45838	+	1.99670i	0.123909	+	0.0715392i
$780$	1.77227	+	3.06967i	0.0634576	+	0.109912i
$781$	−42.1513	+	24.3361i	−1.50829	+	0.870814i
$782$	−9.37290	+	15.4324i	−0.335174	+	0.551861i
$783$		−	0.885961i		−	0.0316617i
$784$	4.71765	−	5.17144i	0.168488	−	0.184694i
$785$	−11.5610			−0.412630
$786$	−5.90676	+	10.2308i	−0.210687	+	0.364921i
$787$	10.0256	+	17.3649i	0.357375	+	0.618992i	0.987522	−	0.157484i	$-0.0503383\pi$
$787$	10.0256	+	17.3649i	0.357375	+	0.618992i	−0.630146	+	0.776477i	$0.717005\pi$
$788$	−5.68514	−	9.84695i	−0.202525	−	0.350783i
$789$	−4.99910	+	8.65870i	−0.177973	+	0.308258i
$790$		−	1.69596i		−	0.0603396i
$791$	−3.78723	−	0.410512i	−0.134658	−	0.0145961i
$792$		−	3.40343i		−	0.120936i
$793$	11.0892	+	6.40237i	0.393790	+	0.227355i
$794$	−14.2638	+	8.23518i	−0.506202	+	0.292256i
$795$	−2.43277	−	4.21367i	−0.0862813	−	0.149444i
$796$	−8.83361	+	15.3003i	−0.313099	+	0.542303i
$797$	39.9018			1.41340			0.706698	−	0.707516i	$-0.250184\pi$
$797$	39.9018			1.41340			0.706698	+	0.707516i	$0.250184\pi$
$798$	2.24561	−	3.06978i	0.0794939	−	0.108669i
$799$		−	17.4727i		−	0.618139i
$800$	−1.17421	+	2.03378i	−0.0415145	+	0.0719052i
$801$	2.18696	+	3.78793i	0.0772725	+	0.133840i
$802$	31.6782	−	18.2894i	1.11859	−	0.645821i
$803$	−0.560013	+	0.969971i	−0.0197624	+	0.0342295i
$804$	−2.14823			−0.0757622
$805$	19.0832	−	7.92060i	0.672596	−	0.279164i
$806$	6.86453			0.241793
$807$	8.62000	−	14.9303i	0.303438	−	0.525570i
$808$	−11.2127	+	6.47363i	−0.394460	+	0.227742i
$809$	−18.5716	−	32.1670i	−0.652943	−	1.13093i	−0.982405	−	0.186762i	$-0.940201\pi$
$809$	−18.5716	−	32.1670i	−0.652943	−	1.13093i	0.329462	−	0.944169i	$-0.393133\pi$
$810$	0.814185	−	1.41021i	0.0286075	−	0.0495497i
$811$			5.15343i			0.180961i	0.995898	+	0.0904807i	$0.0288403\pi$
$811$			5.15343i			0.180961i	−0.995898	+	0.0904807i	$0.971160\pi$
$812$	2.14447	−	0.946434i	0.0752561	−	0.0332133i
$813$	−21.0974			−0.739917
$814$	−3.82199	+	6.61987i	−0.133961	+	0.232026i
$815$	4.54111	+	7.86544i	0.159068	+	0.275514i
$816$	−3.26048	+	1.88244i	−0.114140	+	0.0658986i
$817$	5.15197	+	2.97449i	0.180245	+	0.104064i
$818$		−	9.40232i		−	0.328744i
$819$	−3.40027	+	4.64820i	−0.118815	+	0.162421i
$820$			4.52341i			0.157964i
$821$	−14.6198	+	25.3222i	−0.510235	+	0.883752i	0.489695	+	0.871894i	$0.337108\pi$
$821$	−14.6198	+	25.3222i	−0.510235	+	0.883752i	−0.999930	+	0.0118585i	$0.996225\pi$
$822$	5.31673	+	9.20884i	0.185442	+	0.321195i
$823$	18.8600	+	32.6664i	0.657417	+	1.13868i	0.981282	+	0.192576i	$0.0616842\pi$
$823$	18.8600	+	32.6664i	0.657417	+	1.13868i	−0.323865	+	0.946103i	$0.604983\pi$
$824$	−4.94223	+	8.56019i	−0.172171	+	0.298208i
$825$	−7.99266			−0.278269
$826$	−1.10954	−	0.120267i	−0.0386059	−	0.00418464i
$827$			41.6936i			1.44983i	0.688840	+	0.724914i	$0.258120\pi$
$827$			41.6936i			1.44983i	−0.688840	+	0.724914i	$0.741880\pi$
$828$	2.48956	−	4.09904i	0.0865181	−	0.142451i
$829$	−30.8759	+	17.8262i	−1.07236	+	0.619130i	−0.928827	−	0.370515i	$-0.879181\pi$
$829$	−30.8759	+	17.8262i	−1.07236	+	0.619130i	−0.143538	+	0.989645i	$0.545848\pi$
$830$	−11.2786	−	19.5351i	−0.391485	−	0.678073i
$831$	23.7036	+	13.6853i	0.822270	+	0.474738i
$832$			2.17675i			0.0754651i
$833$	−7.98068	−	25.1168i	−0.276514	−	0.870244i
$834$	−3.58139			−0.124013
$835$	−32.6608	−	18.8567i	−1.13027	−	0.652564i
$836$	4.23718	−	2.44634i	0.146546	−	0.0846084i
$837$	−1.57679	−	2.73108i	−0.0545017	−	0.0943998i
$838$	13.5851	−	23.5302i	0.469291	−	0.812836i
$839$	−7.69354			−0.265611			−0.132805	−	0.991142i	$-0.542398\pi$
$839$	−7.69354			−0.265611			−0.132805	+	0.991142i	$0.542398\pi$
$840$	4.28317	+	0.464269i	0.147783	+	0.0160188i
$841$	−28.2151			−0.972934
$842$	8.90470	+	5.14113i	0.306876	+	0.177175i
$843$	−3.37107	−	5.83886i	−0.116106	−	0.201101i
$844$	−2.07816	−	3.59948i	−0.0715332	−	0.123899i
$845$	−6.72661	+	11.6508i	−0.231402	+	0.400801i
$846$			4.64096i			0.159560i
$847$	1.24565	+	0.911225i	0.0428012	+	0.0313101i
$848$		−	2.98798i		−	0.102608i
$849$	−19.5212	−	11.2706i	−0.669967	−	0.386806i
$850$	4.42075	+	7.65696i	0.151630	+	0.262632i
$851$	−9.44548	+	5.17714i	−0.323787	+	0.177470i
$852$	−12.3850	−	7.15046i	−0.424302	−	0.244971i
$853$			12.9650i			0.443915i	0.975056	+	0.221957i	$0.0712446\pi$
$853$			12.9650i			0.443915i	−0.975056	+	0.221957i	$0.928755\pi$
$854$	14.2386	−	6.28403i	0.487236	−	0.215035i
$855$	2.34090			0.0800571
$856$	4.91902	+	2.84000i	0.168129	+	0.0970690i
$857$	33.6775	−	19.4437i	1.15040	−	0.664184i	0.201416	−	0.979506i	$-0.435446\pi$
$857$	33.6775	−	19.4437i	1.15040	−	0.664184i	0.948985	+	0.315321i	$0.102112\pi$
$858$	−6.41587	+	3.70420i	−0.219034	+	0.126459i
$859$	22.2732	+	12.8594i	0.759950	+	0.438757i	0.829278	−	0.558837i	$-0.188752\pi$
$859$	22.2732	+	12.8594i	0.759950	+	0.438757i	−0.0693277	+	0.997594i	$0.522085\pi$
$860$			6.73854i			0.229782i
$861$	−6.72385	+	2.96749i	−0.229148	+	0.101132i
$862$		−	40.5453i		−	1.38098i
$863$	−4.53454	+	7.85406i	−0.154358	+	0.267355i	−0.932825	−	0.360330i	$-0.882664\pi$
$863$	−4.53454	+	7.85406i	−0.154358	+	0.267355i	0.778467	+	0.627685i	$0.215997\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	10.1364	−	5.85225i	0.344648	−	0.198983i
$866$	12.9120	−	22.3642i	0.438767	−	0.759967i
$867$		−	2.82565i		−	0.0959641i
$868$	4.92616	−	6.73411i	0.167205	−	0.228570i
$869$	3.54470			0.120246
$870$	1.24939	+	0.721336i	0.0423583	+	0.0244556i
$871$	2.33807	+	4.04966i	0.0792226	+	0.137218i
$872$	−16.2120	+	9.35999i	−0.549007	+	0.316969i
$873$	0.458857	−	0.794764i	0.0155300	−	0.0268987i
$874$	6.89265	+	0.153105i	0.233148	+	0.00517885i
$875$	3.41164	−	31.4745i	0.115335	−	1.06403i
$876$	−0.329087			−0.0111188
$877$	−8.71014	+	15.0864i	−0.294121	+	0.509432i	−0.974780	−	0.223168i	$-0.928360\pi$
$877$	−8.71014	+	15.0864i	−0.294121	+	0.509432i	0.680659	+	0.732600i	$0.261693\pi$
$878$	−17.4144	+	10.0542i	−0.587706	+	0.339312i
$879$	19.2980	−	11.1417i	0.650904	−	0.375800i
$880$	4.79955	+	2.77102i	0.161793	+	0.0934111i
$881$	−39.1430			−1.31876			−0.659381	−	0.751809i	$-0.729182\pi$
$881$	−39.1430			−1.31876			−0.659381	+	0.751809i	$0.729182\pi$
$882$	2.11977	+	6.67133i	0.0713763	+	0.224635i
$883$	−39.2833			−1.32199			−0.660994	−	0.750391i	$-0.729865\pi$
$883$	−39.2833			−1.32199			−0.660994	+	0.750391i	$0.729865\pi$
$884$	7.09725	+	4.09760i	0.238706	+	0.137817i
$885$	−0.343443	−	0.594860i	−0.0115447	−	0.0199960i
$886$	−9.93991	−	17.2164i	−0.333938	−	0.578397i
$887$	−44.4507	−	25.6636i	−1.49251	−	0.861701i	−0.492546	−	0.870286i	$-0.663934\pi$
$887$	−44.4507	−	25.6636i	−1.49251	−	0.861701i	−0.999963	+	0.00858562i	$0.997267\pi$
$888$	−2.24596			−0.0753695
$889$	0.556628	−	5.13524i	0.0186687	−	0.172230i
$890$	−7.12236			−0.238742
$891$	2.94746	+	1.70172i	0.0987435	+	0.0570096i
$892$	−11.3828	+	6.57185i	−0.381124	+	0.220042i
$893$	−5.77788	+	3.33586i	−0.193349	+	0.111630i
$894$	−3.80665	+	6.59332i	−0.127314	+	0.220513i
$895$	−17.5485			−0.586581
$896$	2.13539	+	1.56209i	0.0713383	+	0.0521857i
$897$	−10.4367	−	0.231829i	−0.348473	−	0.00774053i
$898$	3.42701	−	5.93576i	0.114361	−	0.198079i
$899$	2.41963	−	1.39697i	0.0806990	−	0.0465916i
$900$	−1.17421	−	2.03378i	−0.0391402	−	0.0677928i
$901$	−9.74225	−	5.62469i	−0.324562	−	0.187386i
$902$	−9.45431			−0.314794
$903$	−10.0165	+	4.42067i	−0.333330	+	0.147111i
$904$		−	1.43982i		−	0.0478878i
$905$	−15.7697	+	27.3140i	−0.524204	+	0.907948i
$906$	19.6173	−	11.3261i	0.651741	−	0.376283i
$907$	−39.9463	+	23.0630i	−1.32640	+	0.765795i	−0.984740	−	0.174031i	$-0.944321\pi$
$907$	−39.9463	+	23.0630i	−1.32640	+	0.765795i	−0.341655	+	0.939825i	$0.610987\pi$
$908$	1.12273	−	1.94463i	0.0372591	−	0.0645347i
$909$		−	12.9473i		−	0.429434i
$910$	−3.78649	−	8.57958i	−0.125521	−	0.284410i
$911$		−	34.4890i		−	1.14267i	−0.820717	−	0.571335i	$-0.806426\pi$
$911$		−	34.4890i		−	1.14267i	0.820717	−	0.571335i	$-0.193574\pi$
$912$	1.24497	+	0.718786i	0.0412252	+	0.0238014i
$913$	40.8300	−	23.5732i	1.35127	−	0.780159i
$914$	24.1446	−	13.9399i	0.798632	−	0.461090i
$915$	8.29557	+	4.78945i	0.274243	+	0.158334i
$916$	6.15654			0.203418
$917$	18.4537	−	25.2265i	0.609396	−	0.833051i
$918$		−	3.76488i		−	0.124260i
$919$	−44.2444	−	25.5445i	−1.45949	−	0.842636i	−0.460502	−	0.887659i	$-0.652331\pi$
$919$	−44.2444	−	25.5445i	−1.45949	−	0.842636i	−0.998986	+	0.0450231i	$0.985664\pi$
$920$	3.75354	+	6.84817i	0.123751	+	0.225778i
$921$	−2.75242	−	4.76734i	−0.0906954	−	0.157089i
$922$	7.87990	+	4.54946i	0.259511	+	0.149829i
$923$			31.1295i			1.02464i
$924$	−0.970362	+	8.95219i	−0.0319226	+	0.294506i
$925$			5.27444i			0.173423i
$926$	−3.35545	+	5.81181i	−0.110267	+	0.190988i
$927$	−4.94223	−	8.56019i	−0.162324	−	0.281153i
$928$	0.442980	+	0.767265i	0.0145415	+	0.0251867i
$929$	26.7035	+	15.4173i	0.876114	+	0.505825i	0.869375	−	0.494153i	$-0.164522\pi$
$929$	26.7035	+	15.4173i	0.876114	+	0.505825i	0.00673898	+	0.999977i	$0.497855\pi$
$930$	5.13519			0.168389
$931$	−6.78197	+	7.43431i	−0.222270	+	0.243650i
$932$	0.160722			0.00526462
$933$	6.46519	−	11.1980i	0.211661	−	0.366607i
$934$	7.70978	+	13.3537i	0.252272	+	0.436948i
$935$	18.0697	−	10.4326i	0.590944	−	0.341182i
$936$	−1.88512	−	1.08837i	−0.0616170	−	0.0355746i
$937$	30.6206			1.00033			0.500166	−	0.865930i	$-0.333272\pi$
$937$	30.6206			1.00033			0.500166	+	0.865930i	$0.333272\pi$
$938$	5.65058	+	0.612488i	0.184498	+	0.0199984i
$939$		−	3.59114i		−	0.117192i
$940$	−6.54473	−	3.77860i	−0.213466	−	0.123244i
$941$	−29.8035	−	51.6211i	−0.971566	−	1.68280i	−0.690832	−	0.723015i	$-0.742756\pi$
$941$	−29.8035	−	51.6211i	−0.971566	−	1.68280i	−0.280733	−	0.959786i	$-0.590578\pi$
$942$	6.14856	−	3.54987i	0.200331	−	0.115661i
$943$	−11.3866	−	6.91568i	−0.370799	−	0.225206i
$944$		−	0.421824i		−	0.0137292i
$945$	−2.54366	+	3.47720i	−0.0827451	+	0.113113i
$946$	−14.0841			−0.457914
$947$	26.0670	−	45.1494i	0.847064	−	1.46716i	−0.0367527	−	0.999324i	$-0.511701\pi$
$947$	26.0670	−	45.1494i	0.847064	−	1.46716i	0.883817	−	0.467833i	$-0.154965\pi$
$948$	0.520755	+	0.901973i	0.0169133	+	0.0292947i
$949$	0.358170	+	0.620369i	0.0116267	+	0.0201380i
$950$	1.68801	−	2.92371i	0.0547662	−	0.0948578i
$951$		−	6.73040i		−	0.218248i
$952$	9.11291	−	4.02186i	0.295351	−	0.130349i
$953$		−	17.4615i		−	0.565635i	−0.959174	−	0.282817i	$-0.908731\pi$
$953$		−	17.4615i		−	0.565635i	0.959174	−	0.282817i	$-0.0912690\pi$
$954$	2.58766	+	1.49399i	0.0837787	+	0.0483697i
$955$	20.2102	−	11.6684i	0.653988	−	0.377580i
$956$	−9.13675	−	15.8253i	−0.295504	−	0.511828i
$957$	−1.50765	+	2.61133i	−0.0487355	+	0.0844124i
$958$	7.85322			0.253726
$959$	−11.3593	−	25.7383i	−0.366810	−	0.831133i
$960$			1.62837i			0.0525554i
$961$	−10.5275	+	18.2341i	−0.339596	+	0.588198i
$962$	2.44444	+	4.23390i	0.0788120	+	0.136506i
$963$	−4.91902	+	2.84000i	−0.158513	+	0.0915176i
$964$	11.6187	−	20.1242i	0.374213	−	0.648156i
$965$	−4.07672			−0.131234
$966$	−7.71708	+	10.0721i	−0.248293	+	0.324064i
$967$	2.14205			0.0688838			0.0344419	−	0.999407i	$-0.489035\pi$
$967$	2.14205			0.0688838			0.0344419	+	0.999407i	$0.489035\pi$
$968$	−0.291669	+	0.505186i	−0.00937460	+	0.0162373i
$969$	4.68718	−	2.70615i	0.150574	−	0.0869339i
$970$	0.747189	+	1.29417i	0.0239908	+	0.0415533i
$971$	27.7546	−	48.0723i	0.890686	−	1.54271i	0.0516314	−	0.998666i	$-0.483558\pi$
$971$	27.7546	−	48.0723i	0.890686	−	1.54271i	0.839055	−	0.544047i	$-0.183109\pi$
$972$			1.00000i			0.0320750i
$973$	9.42028	+	1.02110i	0.302000	+	0.0327350i
$974$	32.3111			1.03532
$975$	−2.55595	+	4.42704i	−0.0818559	+	0.141779i
$976$	2.94126	+	5.09440i	0.0941473	+	0.163068i
$977$	−21.6556	+	12.5029i	−0.692825	+	0.400003i	−0.804670	−	0.593723i	$-0.797658\pi$
$977$	−21.6556	+	12.5029i	−0.692825	+	0.400003i	0.111844	+	0.993726i	$0.464324\pi$
$978$	−4.83025	−	2.78875i	−0.154454	−	0.0891743i
$979$		−	14.8863i		−	0.475769i
$980$	−11.1338	−	2.44238i	−0.355658	−	0.0780188i
$981$		−	18.7200i		−	0.597683i
$982$	5.15195	−	8.92343i	0.164405	−	0.284758i
$983$	20.2030	+	34.9926i	0.644376	+	1.11609i	0.984445	+	0.175691i	$0.0562161\pi$
$983$	20.2030	+	34.9926i	0.644376	+	1.11609i	−0.340069	+	0.940400i	$0.610451\pi$
$984$	−1.38894	−	2.40571i	−0.0442777	−	0.0766913i
$985$	−9.25750	+	16.0345i	−0.294969	+	0.510901i
$986$	3.33554			0.106225
$987$	1.32320	−	12.2073i	0.0421179	−	0.388564i
$988$		−	3.12923i		−	0.0995541i
$989$	−16.9627	−	10.3023i	−0.539382	−	0.327595i
$990$	−4.79955	+	2.77102i	−0.152540	+	0.0880688i
$991$	−11.3756	−	19.7032i	−0.361359	−	0.625892i	0.626826	−	0.779159i	$-0.284354\pi$
$991$	−11.3756	−	19.7032i	−0.361359	−	0.625892i	−0.988185	+	0.153268i	$0.951020\pi$
$992$	2.73108	+	1.57679i	0.0867117	+	0.0500630i
$993$			4.72784i			0.150034i
$994$	30.5380	+	22.3393i	0.968607	+	0.708559i
$995$	28.7688			0.912031
$996$	11.9967	+	6.92630i	0.380130	+	0.219468i
$997$	35.0793	−	20.2530i	1.11097	−	0.641420i	0.171891	−	0.985116i	$-0.445012\pi$
$997$	35.0793	−	20.2530i	1.11097	−	0.641420i	0.939081	+	0.343696i	$0.111679\pi$
$998$	−5.87997	−	10.1844i	−0.186127	−	0.322382i
$999$	1.12298	−	1.94506i	0.0355295	−	0.0615389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.b.229.12	✓	32
7.3	odd	6	inner	966.2.k.b.367.13	yes	32
23.22	odd	2	inner	966.2.k.b.229.13	yes	32
161.45	even	6	inner	966.2.k.b.367.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.b.229.12	✓	32	1.1	even	1	trivial
966.2.k.b.229.13	yes	32	23.22	odd	2	inner
966.2.k.b.367.12	yes	32	161.45	even	6	inner
966.2.k.b.367.13	yes	32	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.814185 + 1.41021i) q^{5} -1.00000i q^{6} +(-0.285113 + 2.63034i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.814185 + 1.41021i) q^{5} -1.00000i q^{6} +(-0.285113 + 2.63034i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.814185 + 1.41021i) q^{10} +(-2.94746 + 1.70172i) q^{11} +(-0.866025 - 0.500000i) q^{12} +2.17675i q^{13} +(2.13539 + 1.56209i) q^{14} +1.62837i q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.88244 + 3.26048i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.718786 - 1.24497i) q^{19} +1.62837 q^{20} +(1.06826 + 2.42050i) q^{21} +3.40343i q^{22} +(-2.48956 + 4.09904i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.17421 + 2.03378i) q^{25} +(1.88512 + 1.08837i) q^{26} -1.00000i q^{27} +(2.42050 - 1.06826i) q^{28} +0.885961 q^{29} +(1.41021 + 0.814185i) q^{30} +(2.73108 - 1.57679i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.70172 + 2.94746i) q^{33} +3.76488 q^{34} +(-3.47720 - 2.54366i) q^{35} -1.00000 q^{36} +(1.94506 + 1.12298i) q^{37} +(-0.718786 - 1.24497i) q^{38} +(1.08837 + 1.88512i) q^{39} +(0.814185 - 1.41021i) q^{40} +2.77788i q^{41} +(2.63034 + 0.285113i) q^{42} +4.13821i q^{43} +(2.94746 + 1.70172i) q^{44} +(0.814185 + 1.41021i) q^{45} +(2.30509 + 4.20554i) q^{46} +(-4.01919 - 2.32048i) q^{47} +1.00000i q^{48} +(-6.83742 - 1.49989i) q^{49} +2.34841 q^{50} +(3.26048 + 1.88244i) q^{51} +(1.88512 - 1.08837i) q^{52} +(-2.58766 + 1.49399i) q^{53} +(-0.866025 - 0.500000i) q^{54} -5.54204i q^{55} +(0.285113 - 2.63034i) q^{56} -1.43757i q^{57} +(0.442980 - 0.767265i) q^{58} +(-0.365310 + 0.210912i) q^{59} +(1.41021 - 0.814185i) q^{60} +(2.94126 - 5.09440i) q^{61} -3.15357i q^{62} +(2.13539 + 1.56209i) q^{63} +1.00000 q^{64} +(-3.06967 - 1.77227i) q^{65} +(1.70172 + 2.94746i) q^{66} +(1.86042 - 1.07411i) q^{67} +(1.88244 - 3.26048i) q^{68} +(-0.106502 + 4.79465i) q^{69} +(-3.94147 + 1.73952i) q^{70} +14.3009 q^{71} +(-0.500000 + 0.866025i) q^{72} +(0.284998 - 0.164544i) q^{73} +(1.94506 - 1.12298i) q^{74} +(2.03378 + 1.17421i) q^{75} -1.43757 q^{76} +(-3.63574 - 8.23801i) q^{77} +2.17675 q^{78} +(-0.901973 - 0.520755i) q^{79} +(-0.814185 - 1.41021i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.40571 + 1.38894i) q^{82} -13.8526 q^{83} +(1.56209 - 2.13539i) q^{84} -6.13062 q^{85} +(3.58380 + 2.06911i) q^{86} +(0.767265 - 0.442980i) q^{87} +(2.94746 - 1.70172i) q^{88} +(-2.18696 + 3.78793i) q^{89} +1.62837 q^{90} +(-5.72559 - 0.620619i) q^{91} +(4.79465 + 0.106502i) q^{92} +(1.57679 - 2.73108i) q^{93} +(-4.01919 + 2.32048i) q^{94} +(1.17045 + 2.02728i) q^{95} +(0.866025 + 0.500000i) q^{96} +0.917714 q^{97} +(-4.71765 + 5.17144i) q^{98} +3.40343i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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