LMFDB - Embedded newform 546.2.bm.a.277.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,2,Mod(205,546)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("546.205"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 249x^{12} + 1144x^{10} + 2766x^{8} + 3554x^{6} + 2260x^{4} + 564x^{2} + 9 $ x^16 + 26x^14 + 249x^12 + 1144x^10 + 2766x^8 + 3554x^6 + 2260x^4 + 564*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			277.8
Root			$-1.38609i$ of defining polynomial
Character	$\chi$	$=$	546.277
Dual form			546.2.bm.a.205.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(3.80406 - 2.19627i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.39669 - 1.12066i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.19627 + 3.80406i) q^{10} +(0.849860 - 0.490667i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.727736 + 3.53135i) q^{13} +(1.12066 - 2.39669i) q^{14} +(3.80406 + 2.19627i) q^{15} +1.00000 q^{16} +5.67660 q^{17} +(-0.866025 - 0.500000i) q^{18} +(-0.522121 - 0.301447i) q^{19} +(-3.80406 + 2.19627i) q^{20} +(-0.227820 - 2.63592i) q^{21} +(0.490667 + 0.849860i) q^{22} +4.65372 q^{23} +(0.866025 - 0.500000i) q^{24} +(7.14723 - 12.3794i) q^{25} +(-3.53135 + 0.727736i) q^{26} -1.00000 q^{27} +(2.39669 + 1.12066i) q^{28} +(-1.58902 + 2.75226i) q^{29} +(-2.19627 + 3.80406i) q^{30} +(5.23622 + 3.02313i) q^{31} +1.00000i q^{32} +(0.849860 + 0.490667i) q^{33} +5.67660i q^{34} +(-11.5784 + 1.00071i) q^{35} +(0.500000 - 0.866025i) q^{36} +0.144068i q^{37} +(0.301447 - 0.522121i) q^{38} +(-2.69437 + 2.39591i) q^{39} +(-2.19627 - 3.80406i) q^{40} +(-8.37436 - 4.83494i) q^{41} +(2.63592 - 0.227820i) q^{42} +(-3.17681 - 5.50239i) q^{43} +(-0.849860 + 0.490667i) q^{44} +4.39255i q^{45} +4.65372i q^{46} +(-8.79254 + 5.07637i) q^{47} +(0.500000 + 0.866025i) q^{48} +(4.48822 + 5.37176i) q^{49} +(12.3794 + 7.14723i) q^{50} +(2.83830 + 4.91608i) q^{51} +(-0.727736 - 3.53135i) q^{52} +(2.74644 - 4.75697i) q^{53} -1.00000i q^{54} +(2.15528 - 3.73305i) q^{55} +(-1.12066 + 2.39669i) q^{56} -0.602893i q^{57} +(-2.75226 - 1.58902i) q^{58} +8.81577i q^{59} +(-3.80406 - 2.19627i) q^{60} +(0.812623 - 1.40750i) q^{61} +(-3.02313 + 5.23622i) q^{62} +(2.16887 - 1.51526i) q^{63} -1.00000 q^{64} +(10.5241 + 11.8351i) q^{65} +(-0.490667 + 0.849860i) q^{66} +(-9.45592 + 5.45938i) q^{67} -5.67660 q^{68} +(2.32686 + 4.03024i) q^{69} +(-1.00071 - 11.5784i) q^{70} +(-11.1654 + 6.44637i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-4.77913 - 2.75923i) q^{73} -0.144068 q^{74} +14.2945 q^{75} +(0.522121 + 0.301447i) q^{76} +(-2.58672 + 0.223568i) q^{77} +(-2.39591 - 2.69437i) q^{78} +(-6.75613 - 11.7020i) q^{79} +(3.80406 - 2.19627i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.83494 - 8.37436i) q^{82} -7.90170i q^{83} +(0.227820 + 2.63592i) q^{84} +(21.5941 - 12.4674i) q^{85} +(5.50239 - 3.17681i) q^{86} -3.17804 q^{87} +(-0.490667 - 0.849860i) q^{88} +1.45147i q^{89} -4.39255 q^{90} +(2.21330 - 9.27908i) q^{91} -4.65372 q^{92} +6.04627i q^{93} +(-5.07637 - 8.79254i) q^{94} -2.64824 q^{95} +(-0.866025 + 0.500000i) q^{96} +(-0.165011 + 0.0952691i) q^{97} +(-5.37176 + 4.48822i) q^{98} +0.981333i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29}+ \cdots - 60 q^{98}+O(q^{100}) $ 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.00000			−0.500000
$5$	3.80406	−	2.19627i	1.70123	−	0.982203i	0.756702	−	0.653760i	$-0.226810\pi$
$5$	3.80406	−	2.19627i	1.70123	−	0.982203i	0.944524	−	0.328443i	$-0.106524\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−2.39669	−	1.12066i	−0.905863	−	0.423571i
$7$	−2.39669	−	1.12066i	−0.905863	−	0.423571i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.19627	+	3.80406i	0.694522	+	1.20295i
$11$	0.849860	−	0.490667i	0.256242	−	0.147942i	−0.366377	−	0.930467i	$-0.619402\pi$
$11$	0.849860	−	0.490667i	0.256242	−	0.147942i	0.622619	+	0.782525i	$0.286069\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.727736	+	3.53135i	0.201838	+	0.979419i
$13$	0.727736	+	3.53135i	0.201838	+	0.979419i
$14$	1.12066	−	2.39669i	0.299510	−	0.640542i
$15$	3.80406	+	2.19627i	0.982203	+	0.567075i
$16$	1.00000			0.250000
$17$	5.67660			1.37678			0.688389	−	0.725341i	$-0.258318\pi$
$17$	5.67660			1.37678			0.688389	+	0.725341i	$0.258318\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−0.522121	−	0.301447i	−0.119783	−	0.0691566i	0.438912	−	0.898530i	$-0.355364\pi$
$19$	−0.522121	−	0.301447i	−0.119783	−	0.0691566i	−0.558694	+	0.829374i	$0.688697\pi$
$20$	−3.80406	+	2.19627i	−0.850613	+	0.491102i
$21$	−0.227820	−	2.63592i	−0.0497145	−	0.575206i
$22$	0.490667	+	0.849860i	0.104610	+	0.181191i
$23$	4.65372			0.970368			0.485184	−	0.874412i	$-0.338753\pi$
$23$	4.65372			0.970368			0.485184	+	0.874412i	$0.338753\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	7.14723	−	12.3794i	1.42945	−	2.47587i
$26$	−3.53135	+	0.727736i	−0.692554	+	0.142721i
$27$	−1.00000			−0.192450
$28$	2.39669	+	1.12066i	0.452931	+	0.211786i
$29$	−1.58902	+	2.75226i	−0.295074	+	0.511083i	−0.975002	−	0.222196i	$-0.928678\pi$
$29$	−1.58902	+	2.75226i	−0.295074	+	0.511083i	0.679928	+	0.733279i	$0.262011\pi$
$30$	−2.19627	+	3.80406i	−0.400983	+	0.694522i
$31$	5.23622	+	3.02313i	0.940453	+	0.542971i	0.890102	−	0.455761i	$-0.150633\pi$
$31$	5.23622	+	3.02313i	0.940453	+	0.542971i	0.0503510	+	0.998732i	$0.483966\pi$
$32$			1.00000i			0.176777i
$33$	0.849860	+	0.490667i	0.147942	+	0.0854141i
$34$			5.67660i			0.973529i
$35$	−11.5784	+	1.00071i	−1.95711	+	0.169151i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$			0.144068i			0.0236846i	0.999930	+	0.0118423i	$0.00376961\pi$
$37$			0.144068i			0.0236846i	−0.999930	+	0.0118423i	$0.996230\pi$
$38$	0.301447	−	0.522121i	0.0489011	−	0.0846992i
$39$	−2.69437	+	2.39591i	−0.431444	+	0.383653i
$40$	−2.19627	−	3.80406i	−0.347261	−	0.601474i
$41$	−8.37436	−	4.83494i	−1.30785	−	0.755090i	−0.326117	−	0.945329i	$-0.605740\pi$
$41$	−8.37436	−	4.83494i	−1.30785	−	0.755090i	−0.981738	+	0.190239i	$0.939074\pi$
$42$	2.63592	−	0.227820i	0.406732	−	0.0351534i
$43$	−3.17681	−	5.50239i	−0.484458	−	0.839106i	0.515382	−	0.856960i	$-0.327650\pi$
$43$	−3.17681	−	5.50239i	−0.484458	−	0.839106i	−0.999841	+	0.0178540i	$0.994317\pi$
$44$	−0.849860	+	0.490667i	−0.128121	+	0.0739708i
$45$			4.39255i			0.654802i
$46$			4.65372i			0.686154i
$47$	−8.79254	+	5.07637i	−1.28252	+	0.740465i	−0.977309	−	0.211819i	$-0.932061\pi$
$47$	−8.79254	+	5.07637i	−1.28252	+	0.740465i	−0.305214	+	0.952284i	$0.598728\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	4.48822	+	5.37176i	0.641175	+	0.767395i
$50$	12.3794	+	7.14723i	1.75071	+	1.01077i
$51$	2.83830	+	4.91608i	0.397442	+	0.688389i
$52$	−0.727736	−	3.53135i	−0.100919	−	0.489709i
$53$	2.74644	−	4.75697i	0.377252	−	0.653420i	−0.613409	−	0.789765i	$-0.710202\pi$
$53$	2.74644	−	4.75697i	0.377252	−	0.653420i	0.990661	+	0.136345i	$0.0435356\pi$
$54$		−	1.00000i		−	0.136083i
$55$	2.15528	−	3.73305i	0.290617	−	0.503364i
$56$	−1.12066	+	2.39669i	−0.149755	+	0.320271i
$57$		−	0.602893i		−	0.0798552i
$58$	−2.75226	−	1.58902i	−0.361390	−	0.208649i
$59$			8.81577i			1.14772i	0.818955	+	0.573858i	$0.194554\pi$
$59$			8.81577i			1.14772i	−0.818955	+	0.573858i	$0.805446\pi$
$60$	−3.80406	−	2.19627i	−0.491102	−	0.283538i
$61$	0.812623	−	1.40750i	0.104046	−	0.180212i	−0.809302	−	0.587393i	$-0.800155\pi$
$61$	0.812623	−	1.40750i	0.104046	−	0.180212i	0.913348	+	0.407180i	$0.133488\pi$
$62$	−3.02313	+	5.23622i	−0.383938	+	0.665001i
$63$	2.16887	−	1.51526i	0.273252	−	0.190905i
$64$	−1.00000			−0.125000
$65$	10.5241	+	11.8351i	1.30536	+	1.46797i
$66$	−0.490667	+	0.849860i	−0.0603969	+	0.104610i
$67$	−9.45592	+	5.45938i	−1.15522	+	0.666969i	−0.950155	−	0.311778i	$-0.899075\pi$
$67$	−9.45592	+	5.45938i	−1.15522	+	0.666969i	−0.205070	+	0.978747i	$0.565742\pi$
$68$	−5.67660			−0.688389
$69$	2.32686	+	4.03024i	0.280121	+	0.485184i
$70$	−1.00071	−	11.5784i	−0.119608	−	1.38389i
$71$	−11.1654	+	6.44637i	−1.32509	+	0.765043i	−0.984536	−	0.175181i	$-0.943949\pi$
$71$	−11.1654	+	6.44637i	−1.32509	+	0.765043i	−0.340557	+	0.940224i	$0.610616\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−4.77913	−	2.75923i	−0.559355	−	0.322944i	0.193531	−	0.981094i	$-0.438006\pi$
$73$	−4.77913	−	2.75923i	−0.559355	−	0.322944i	−0.752887	+	0.658150i	$0.771339\pi$
$74$	−0.144068			−0.0167476
$75$	14.2945			1.65058
$76$	0.522121	+	0.301447i	0.0598914	+	0.0345783i
$77$	−2.58672	+	0.223568i	−0.294784	+	0.0254779i
$78$	−2.39591	−	2.69437i	−0.271283	−	0.305077i
$79$	−6.75613	−	11.7020i	−0.760124	−	1.31657i	−0.942786	−	0.333398i	$-0.891805\pi$
$79$	−6.75613	−	11.7020i	−0.760124	−	1.31657i	0.182662	−	0.983176i	$-0.441529\pi$
$80$	3.80406	−	2.19627i	0.425306	−	0.245551i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.83494	−	8.37436i	0.533929	−	0.924793i
$83$		−	7.90170i		−	0.867324i	−0.901076	−	0.433662i	$-0.857221\pi$
$83$		−	7.90170i		−	0.867324i	0.901076	−	0.433662i	$-0.142779\pi$
$84$	0.227820	+	2.63592i	0.0248572	+	0.287603i
$85$	21.5941	−	12.4674i	2.34221	−	1.35228i
$86$	5.50239	−	3.17681i	0.593338	−	0.342564i
$87$	−3.17804			−0.340722
$88$	−0.490667	−	0.849860i	−0.0523052	−	0.0905953i
$89$			1.45147i			0.153855i	0.997037	+	0.0769277i	$0.0245111\pi$
$89$			1.45147i			0.153855i	−0.997037	+	0.0769277i	$0.975489\pi$
$90$	−4.39255			−0.463015
$91$	2.21330	−	9.27908i	0.232016	−	0.972712i
$92$	−4.65372			−0.485184
$93$			6.04627i			0.626969i
$94$	−5.07637	−	8.79254i	−0.523588	−	0.906881i
$95$	−2.64824			−0.271703
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−0.165011	+	0.0952691i	−0.0167543	+	0.00967311i	−0.508354	−	0.861148i	$-0.669746\pi$
$97$	−0.165011	+	0.0952691i	−0.0167543	+	0.00967311i	0.491599	+	0.870821i	$0.336412\pi$
$98$	−5.37176	+	4.48822i	−0.542630	+	0.453379i
$99$			0.981333i			0.0986277i
$100$	−7.14723	+	12.3794i	−0.714723	+	1.23794i
$101$	−5.80131	−	10.0482i	−0.577251	−	0.999829i	−0.995793	−	0.0916312i	$-0.970792\pi$
$101$	−5.80131	−	10.0482i	−0.577251	−	0.999829i	0.418542	−	0.908198i	$-0.362541\pi$
$102$	−4.91608	+	2.83830i	−0.486765	+	0.281034i
$103$	−4.08281	−	7.07164i	−0.402292	−	0.696790i	0.591710	−	0.806151i	$-0.298453\pi$
$103$	−4.08281	−	7.07164i	−0.402292	−	0.696790i	−0.994002	+	0.109361i	$0.965120\pi$
$104$	3.53135	−	0.727736i	0.346277	−	0.0713604i
$105$	−6.65585	−	9.52685i	−0.649544	−	0.929725i
$106$	4.75697	+	2.74644i	0.462038	+	0.266758i
$107$	−11.8639			−1.14693			−0.573466	−	0.819230i	$-0.694401\pi$
$107$	−11.8639			−1.14693			−0.573466	+	0.819230i	$0.694401\pi$
$108$	1.00000			0.0962250
$109$	6.66746	+	3.84946i	0.638627	+	0.368711i	0.784085	−	0.620653i	$-0.213132\pi$
$109$	6.66746	+	3.84946i	0.638627	+	0.368711i	−0.145459	+	0.989364i	$0.546466\pi$
$110$	3.73305	+	2.15528i	0.355932	+	0.205497i
$111$	−0.124767	+	0.0720340i	−0.0118423	+	0.00683716i
$112$	−2.39669	−	1.12066i	−0.226466	−	0.105893i
$113$	8.88358	+	15.3868i	0.835697	+	1.44747i	0.893462	+	0.449139i	$0.148269\pi$
$113$	8.88358	+	15.3868i	0.835697	+	1.44747i	−0.0577654	+	0.998330i	$0.518398\pi$
$114$	0.602893			0.0564661
$115$	17.7030	−	10.2208i	1.65082	−	0.953099i
$116$	1.58902	−	2.75226i	0.147537	−	0.255541i
$117$	−3.42210	−	1.13543i	−0.316374	−	0.104971i
$118$	−8.81577			−0.811558
$119$	−13.6050	−	6.36157i	−1.24717	−	0.583164i
$120$	2.19627	−	3.80406i	0.200491	−	0.347261i
$121$	−5.01849	+	8.69228i	−0.456227	+	0.790208i
$122$	1.40750	+	0.812623i	0.127429	+	0.0735714i
$123$		−	9.66987i		−	0.871903i
$124$	−5.23622	−	3.02313i	−0.470227	−	0.271486i
$125$		−	40.8263i		−	3.65162i
$126$	1.51526	+	2.16887i	0.134990	+	0.193218i
$127$	0.800233	−	1.38604i	0.0710092	−	0.122992i	−0.828335	−	0.560234i	$-0.810711\pi$
$127$	0.800233	−	1.38604i	0.0710092	−	0.122992i	0.899344	+	0.437242i	$0.144045\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.17681	−	5.50239i	0.279702	−	0.484458i
$130$	−11.8351	+	10.5241i	−1.03801	+	0.923029i
$131$	6.92324	+	11.9914i	0.604886	+	1.04769i	0.992070	+	0.125691i	$0.0401146\pi$
$131$	6.92324	+	11.9914i	0.604886	+	1.04769i	−0.387184	+	0.922003i	$0.626552\pi$
$132$	−0.849860	−	0.490667i	−0.0739708	−	0.0427070i
$133$	0.913540	+	1.30760i	0.0792140	+	0.113383i
$134$	−5.45938	−	9.45592i	−0.471619	−	0.816867i
$135$	−3.80406	+	2.19627i	−0.327401	+	0.189025i
$136$		−	5.67660i		−	0.486765i
$137$			5.24850i			0.448410i	0.974542	+	0.224205i	$0.0719785\pi$
$137$			5.24850i			0.448410i	−0.974542	+	0.224205i	$0.928022\pi$
$138$	−4.03024	+	2.32686i	−0.343077	+	0.198076i
$139$	−2.40712	−	4.16925i	−0.204169	−	0.353631i	0.745699	−	0.666283i	$-0.232116\pi$
$139$	−2.40712	−	4.16925i	−0.204169	−	0.353631i	−0.949868	+	0.312652i	$0.898783\pi$
$140$	11.5784	−	1.00071i	0.978555	−	0.0845755i
$141$	−8.79254	−	5.07637i	−0.740465	−	0.427508i
$142$	−6.44637	−	11.1654i	−0.540967	−	0.936983i
$143$	2.35119	+	2.64407i	0.196616	+	0.221108i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$			13.9597i			1.15929i
$146$	2.75923	−	4.77913i	0.228356	−	0.395524i
$147$	−2.40797	+	6.57280i	−0.198606	+	0.542115i
$148$		−	0.144068i		−	0.0118423i
$149$	−4.89051	−	2.82354i	−0.400647	−	0.231313i	0.286116	−	0.958195i	$-0.407636\pi$
$149$	−4.89051	−	2.82354i	−0.400647	−	0.231313i	−0.686763	+	0.726881i	$0.740969\pi$
$150$			14.2945i			1.16714i
$151$	5.61817	+	3.24365i	0.457200	+	0.263964i	0.710866	−	0.703327i	$-0.248303\pi$
$151$	5.61817	+	3.24365i	0.457200	+	0.263964i	−0.253666	+	0.967292i	$0.581636\pi$
$152$	−0.301447	+	0.522121i	−0.0244506	+	0.0423496i
$153$	−2.83830	+	4.91608i	−0.229463	+	0.397442i
$154$	−0.223568	−	2.58672i	−0.0180156	−	0.208444i
$155$	26.5585			2.13323
$156$	2.69437	−	2.39591i	0.215722	−	0.191826i
$157$	−2.90214	+	5.02666i	−0.231616	+	0.401171i	−0.958284	−	0.285818i	$-0.907735\pi$
$157$	−2.90214	+	5.02666i	−0.231616	+	0.401171i	0.726668	+	0.686989i	$0.241068\pi$
$158$	11.7020	−	6.75613i	0.930958	−	0.537489i
$159$	5.49288			0.435613
$160$	2.19627	+	3.80406i	0.173631	+	0.300737i
$161$	−11.1535	−	5.21526i	−0.879021	−	0.411020i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	8.92436	+	5.15248i	0.699010	+	0.403574i	0.806979	−	0.590581i	$-0.201101\pi$
$163$	8.92436	+	5.15248i	0.699010	+	0.403574i	−0.107969	+	0.994154i	$0.534435\pi$
$164$	8.37436	+	4.83494i	0.653927	+	0.377545i
$165$	4.31055			0.335576
$166$	7.90170			0.613291
$167$	−11.3642	−	6.56115i	−0.879391	−	0.507717i	−0.00893375	−	0.999960i	$-0.502844\pi$
$167$	−11.3642	−	6.56115i	−0.879391	−	0.507717i	−0.870458	+	0.492243i	$0.836177\pi$
$168$	−2.63592	+	0.227820i	−0.203366	+	0.0175767i
$169$	−11.9408	+	5.13978i	−0.918523	+	0.395367i
$170$	12.4674	+	21.5941i	0.956204	+	1.65619i
$171$	0.522121	−	0.301447i	0.0399276	−	0.0230522i
$172$	3.17681	+	5.50239i	0.242229	+	0.419553i
$173$	3.90610	−	6.76557i	0.296975	−	0.514376i	−0.678467	−	0.734631i	$-0.737355\pi$
$173$	3.90610	−	6.76557i	0.296975	−	0.514376i	0.975442	+	0.220254i	$0.0706887\pi$
$174$		−	3.17804i		−	0.240927i
$175$	−31.0028	+	21.6598i	−2.34359	+	1.63733i
$176$	0.849860	−	0.490667i	0.0640606	−	0.0369854i
$177$	−7.63468	+	4.40789i	−0.573858	+	0.331317i
$178$	−1.45147			−0.108792
$179$	6.66230	+	11.5394i	0.497963	+	0.862498i	0.999997	−	0.00235008i	$-0.000748055\pi$
$179$	6.66230	+	11.5394i	0.497963	+	0.862498i	−0.502034	+	0.864848i	$0.667415\pi$
$180$		−	4.39255i		−	0.327401i
$181$	22.5285			1.67453			0.837267	−	0.546794i	$-0.184152\pi$
$181$	22.5285			1.67453			0.837267	+	0.546794i	$0.184152\pi$
$182$	9.27908	+	2.21330i	0.687811	+	0.164060i
$183$	1.62525			0.120142
$184$		−	4.65372i		−	0.343077i
$185$	0.316413	+	0.548043i	0.0232631	+	0.0402929i
$186$	−6.04627			−0.443334
$187$	4.82432	−	2.78532i	0.352789	−	0.203683i
$188$	8.79254	−	5.07637i	0.641262	−	0.370233i
$189$	2.39669	+	1.12066i	0.174333	+	0.0815163i
$190$		−	2.64824i		−	0.192123i
$191$	0.855584	−	1.48191i	0.0619079	−	0.107228i	−0.833410	−	0.552655i	$-0.813615\pi$
$191$	0.855584	−	1.48191i	0.0619079	−	0.107228i	0.895318	+	0.445427i	$0.146948\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	4.40350	−	2.54236i	0.316971	−	0.183003i	−0.333071	−	0.942902i	$-0.608085\pi$
$193$	4.40350	−	2.54236i	0.316971	−	0.183003i	0.650042	+	0.759899i	$0.274751\pi$
$194$	−0.0952691	−	0.165011i	−0.00683992	−	0.0118471i
$195$	−4.98745	+	15.0317i	−0.357159	+	1.07645i
$196$	−4.48822	−	5.37176i	−0.320587	−	0.383697i
$197$	−17.1710	−	9.91366i	−1.22338	−	0.706319i	−0.257744	−	0.966213i	$-0.582979\pi$
$197$	−17.1710	−	9.91366i	−1.22338	−	0.706319i	−0.965637	+	0.259894i	$0.916312\pi$
$198$	−0.981333			−0.0697403
$199$	17.7883			1.26098			0.630491	−	0.776197i	$-0.282854\pi$
$199$	17.7883			1.26098			0.630491	+	0.776197i	$0.282854\pi$
$200$	−12.3794	−	7.14723i	−0.875353	−	0.505385i
$201$	−9.45592	−	5.45938i	−0.666969	−	0.385075i
$202$	10.0482	−	5.80131i	0.706986	−	0.408178i
$203$	6.89275	−	4.81556i	0.483776	−	0.337986i
$204$	−2.83830	−	4.91608i	−0.198721	−	0.344195i
$205$	−42.4754			−2.96661
$206$	7.07164	−	4.08281i	0.492705	−	0.284463i
$207$	−2.32686	+	4.03024i	−0.161728	+	0.280121i
$208$	0.727736	+	3.53135i	0.0504594	+	0.244855i
$209$	−0.591639			−0.0409245
$210$	9.52685	−	6.65585i	0.657415	−	0.459297i
$211$	−1.33521	+	2.31265i	−0.0919196	+	0.159209i	−0.908319	−	0.418278i	$-0.862634\pi$
$211$	−1.33521	+	2.31265i	−0.0919196	+	0.159209i	0.816399	+	0.577488i	$0.195967\pi$
$212$	−2.74644	+	4.75697i	−0.188626	+	0.326710i
$213$	−11.1654	−	6.44637i	−0.765043	−	0.441698i
$214$		−	11.8639i		−	0.811003i
$215$	−24.1695	−	13.9543i	−1.64835	−	0.951673i
$216$			1.00000i			0.0680414i
$217$	−9.16167	−	13.1136i	−0.621935	−	0.890206i
$218$	−3.84946	+	6.66746i	−0.260718	+	0.451577i
$219$		−	5.51847i		−	0.372903i
$220$	−2.15528	+	3.73305i	−0.145309	+	0.251682i
$221$	4.13107	+	20.0460i	0.277886	+	1.34844i
$222$	−0.0720340	−	0.124767i	−0.00483460	−	0.00837378i
$223$	−1.18976	−	0.686910i	−0.0796724	−	0.0459989i	0.459635	−	0.888108i	$-0.347980\pi$
$223$	−1.18976	−	0.686910i	−0.0796724	−	0.0459989i	−0.539307	+	0.842109i	$0.681314\pi$
$224$	1.12066	−	2.39669i	0.0748775	−	0.160135i
$225$	7.14723	+	12.3794i	0.476482	+	0.825291i
$226$	−15.3868	+	8.88358i	−1.02352	+	0.590927i
$227$		−	17.6759i		−	1.17319i	−0.809879	−	0.586596i	$-0.800468\pi$
$227$		−	17.6759i		−	1.17319i	0.809879	−	0.586596i	$-0.199532\pi$
$228$			0.602893i			0.0399276i
$229$	−18.7520	+	10.8265i	−1.23917	+	0.715433i	−0.968924	−	0.247359i	$-0.920437\pi$
$229$	−18.7520	+	10.8265i	−1.23917	+	0.715433i	−0.270243	+	0.962792i	$0.587104\pi$
$230$	10.2208	+	17.7030i	0.673943	+	1.16730i
$231$	−1.48698	−	2.12838i	−0.0978358	−	0.140037i
$232$	2.75226	+	1.58902i	0.180695	+	0.104324i
$233$	11.8049	+	20.4467i	0.773364	+	1.33951i	0.935710	+	0.352771i	$0.114761\pi$
$233$	11.8049	+	20.4467i	0.773364	+	1.33951i	−0.162346	+	0.986734i	$0.551906\pi$
$234$	1.13543	−	3.42210i	0.0742257	−	0.223710i
$235$	−22.2982	+	38.6216i	−1.45457	+	2.51940i
$236$		−	8.81577i		−	0.573858i
$237$	6.75613	−	11.7020i	0.438858	−	0.760124i
$238$	6.36157	−	13.6050i	0.412359	−	0.881884i
$239$			8.99248i			0.581675i	0.956772	+	0.290838i	$0.0939340\pi$
$239$			8.99248i			0.581675i	−0.956772	+	0.290838i	$0.906066\pi$
$240$	3.80406	+	2.19627i	0.245551	+	0.141769i
$241$		−	11.7378i		−	0.756096i	−0.925786	−	0.378048i	$-0.876595\pi$
$241$		−	11.7378i		−	0.756096i	0.925786	−	0.378048i	$-0.123405\pi$
$242$	−8.69228	−	5.01849i	−0.558761	−	0.322601i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.812623	+	1.40750i	−0.0520229	+	0.0901062i
$245$	28.8713	+	10.5771i	1.84452	+	0.675748i
$246$	9.66987			0.616529
$247$	0.684546	−	2.06316i	0.0435566	−	0.131276i
$248$	3.02313	−	5.23622i	0.191969	−	0.332500i
$249$	6.84307	−	3.95085i	0.433662	−	0.250375i
$250$	40.8263			2.58208
$251$	1.69099	+	2.92888i	0.106734	+	0.184869i	0.914445	−	0.404709i	$-0.132627\pi$
$251$	1.69099	+	2.92888i	0.106734	+	0.184869i	−0.807711	+	0.589578i	$0.799294\pi$
$252$	−2.16887	+	1.51526i	−0.136626	+	0.0954524i
$253$	3.95501	−	2.28343i	0.248649	−	0.143558i
$254$	1.38604	+	0.800233i	0.0869682	+	0.0502111i
$255$	21.5941	+	12.4674i	1.35228	+	0.780737i
$256$	1.00000			0.0625000
$257$	−20.5007			−1.27880			−0.639401	−	0.768874i	$-0.720818\pi$
$257$	−20.5007			−1.27880			−0.639401	+	0.768874i	$0.720818\pi$
$258$	5.50239	+	3.17681i	0.342564	+	0.197779i
$259$	0.161452	−	0.345286i	0.0100321	−	0.0214550i
$260$	−10.5241	−	11.8351i	−0.652680	−	0.733983i
$261$	−1.58902	−	2.75226i	−0.0983579	−	0.170361i
$262$	−11.9914	+	6.92324i	−0.740831	+	0.427719i
$263$	−5.72768	−	9.92064i	−0.353184	−	0.611733i	0.633621	−	0.773643i	$-0.281568\pi$
$263$	−5.72768	−	9.92064i	−0.353184	−	0.611733i	−0.986805	+	0.161911i	$0.948234\pi$
$264$	0.490667	−	0.849860i	0.0301984	−	0.0523052i
$265$		−	24.1277i		−	1.48215i
$266$	−1.30760	+	0.913540i	−0.0801738	+	0.0560128i
$267$	−1.25701	+	0.725734i	−0.0769277	+	0.0444142i
$268$	9.45592	−	5.45938i	0.577612	−	0.333485i
$269$	9.16355			0.558711			0.279356	−	0.960188i	$-0.409879\pi$
$269$	9.16355			0.558711			0.279356	+	0.960188i	$0.409879\pi$
$270$	−2.19627	−	3.80406i	−0.133661	−	0.231507i
$271$			11.5526i			0.701768i	0.936419	+	0.350884i	$0.114119\pi$
$271$			11.5526i			0.701768i	−0.936419	+	0.350884i	$0.885881\pi$
$272$	5.67660			0.344195
$273$	9.14257	−	2.72277i	0.553333	−	0.164790i
$274$	−5.24850			−0.317073
$275$		−	14.0276i		−	0.845898i
$276$	−2.32686	−	4.03024i	−0.140061	−	0.242592i
$277$	9.23072			0.554620			0.277310	−	0.960780i	$-0.410557\pi$
$277$	9.23072			0.554620			0.277310	+	0.960780i	$0.410557\pi$
$278$	4.16925	−	2.40712i	0.250055	−	0.144369i
$279$	−5.23622	+	3.02313i	−0.313484	+	0.180990i
$280$	1.00071	+	11.5784i	0.0598039	+	0.691943i
$281$			28.4923i			1.69971i	0.527018	+	0.849854i	$0.323310\pi$
$281$			28.4923i			1.69971i	−0.527018	+	0.849854i	$0.676690\pi$
$282$	5.07637	−	8.79254i	0.302294	−	0.523588i
$283$	0.531372	+	0.920363i	0.0315868	+	0.0547099i	0.881387	−	0.472396i	$-0.156611\pi$
$283$	0.531372	+	0.920363i	0.0315868	+	0.0547099i	−0.849800	+	0.527105i	$0.823277\pi$
$284$	11.1654	−	6.44637i	0.662547	−	0.382522i
$285$	−1.32412	−	2.29344i	−0.0784340	−	0.135852i
$286$	−2.64407	+	2.35119i	−0.156347	+	0.139029i
$287$	14.6524	+	20.9727i	0.864902	+	1.23798i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	15.2238			0.895519
$290$	−13.9597			−0.819741
$291$	−0.165011	−	0.0952691i	−0.00967311	−	0.00558477i
$292$	4.77913	+	2.75923i	0.279678	+	0.161472i
$293$	−7.92143	+	4.57344i	−0.462775	+	0.267183i	−0.713210	−	0.700950i	$-0.752760\pi$
$293$	−7.92143	+	4.57344i	−0.462775	+	0.267183i	0.250436	+	0.968133i	$0.419426\pi$
$294$	−6.57280	−	2.40797i	−0.383333	−	0.140436i
$295$	19.3618	+	33.5357i	1.12729	+	1.95252i
$296$	0.144068			0.00837378
$297$	−0.849860	+	0.490667i	−0.0493139	+	0.0284714i
$298$	2.82354	−	4.89051i	0.163563	−	0.283300i
$299$	3.38668	+	16.4339i	0.195857	+	0.950397i
$300$	−14.2945			−0.825291
$301$	1.44748	+	16.7476i	0.0834314	+	0.965318i
$302$	−3.24365	+	5.61817i	−0.186651	+	0.323289i
$303$	5.80131	−	10.0482i	0.333276	−	0.577251i
$304$	−0.522121	−	0.301447i	−0.0299457	−	0.0172892i
$305$		−	7.13897i		−	0.408776i
$306$	−4.91608	−	2.83830i	−0.281034	−	0.162255i
$307$		−	4.67641i		−	0.266897i	−0.991056	−	0.133448i	$-0.957395\pi$
$307$		−	4.67641i		−	0.266897i	0.991056	−	0.133448i	$-0.0426050\pi$
$308$	2.58672	−	0.223568i	0.147392	−	0.0127389i
$309$	4.08281	−	7.07164i	0.232263	−	0.402292i
$310$			26.5585i			1.50842i
$311$	−0.384467	+	0.665917i	−0.0218011	+	0.0377607i	−0.876720	−	0.481001i	$-0.840273\pi$
$311$	−0.384467	+	0.665917i	−0.0218011	+	0.0377607i	0.854919	+	0.518761i	$0.173607\pi$
$312$	2.39591	+	2.69437i	0.135642	+	0.152538i
$313$	4.77117	+	8.26391i	0.269682	+	0.467104i	0.968780	−	0.247923i	$-0.0797479\pi$
$313$	4.77117	+	8.26391i	0.269682	+	0.467104i	−0.699097	+	0.715027i	$0.746415\pi$
$314$	−5.02666	−	2.90214i	−0.283671	−	0.163777i
$315$	4.92257	−	10.5276i	0.277355	−	0.593161i
$316$	6.75613	+	11.7020i	0.380062	+	0.658287i
$317$	−0.258436	+	0.149208i	−0.0145152	+	0.00838036i	−0.507240	−	0.861805i	$-0.669334\pi$
$317$	−0.258436	+	0.149208i	−0.0145152	+	0.00838036i	0.492725	+	0.870185i	$0.336001\pi$
$318$			5.49288i			0.308025i
$319$			3.11872i			0.174615i
$320$	−3.80406	+	2.19627i	−0.212653	+	0.122775i
$321$	−5.93197	−	10.2745i	−0.331090	−	0.573466i
$322$	5.21526	−	11.1535i	0.290635	−	0.621562i
$323$	−2.96387	−	1.71119i	−0.164914	−	0.0952133i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	48.9171	+	16.2304i	2.71343	+	0.900302i
$326$	−5.15248	+	8.92436i	−0.285370	+	0.494275i
$327$			7.69892i			0.425751i
$328$	−4.83494	+	8.37436i	−0.266965	+	0.462396i
$329$	26.7619	−	2.31300i	1.47543	−	0.127520i
$330$			4.31055i			0.237288i
$331$	15.9834	+	9.22804i	0.878529	+	0.507219i	0.870173	−	0.492746i	$-0.164007\pi$
$331$	15.9834	+	9.22804i	0.878529	+	0.507219i	0.00835564	+	0.999965i	$0.497340\pi$
$332$			7.90170i			0.433662i
$333$	−0.124767	−	0.0720340i	−0.00683716	−	0.00394744i
$334$	6.56115	−	11.3642i	0.359010	−	0.621824i
$335$	−23.9806	+	41.5356i	−1.31020	+	2.26933i
$336$	−0.227820	−	2.63592i	−0.0124286	−	0.143801i
$337$	12.4534			0.678378			0.339189	−	0.940718i	$-0.389847\pi$
$337$	12.4534			0.678378			0.339189	+	0.940718i	$0.389847\pi$
$338$	−5.13978	−	11.9408i	−0.279567	−	0.649494i
$339$	−8.88358	+	15.3868i	−0.482490	+	0.835697i
$340$	−21.5941	+	12.4674i	−1.17111	+	0.676138i
$341$	5.93341			0.321312
$342$	0.301447	+	0.522121i	0.0163004	+	0.0282331i
$343$	−4.73693	−	17.9042i	−0.255770	−	0.966738i
$344$	−5.50239	+	3.17681i	−0.296669	+	0.171282i
$345$	17.7030	+	10.2208i	0.953099	+	0.550272i
$346$	6.76557	+	3.90610i	0.363719	+	0.209993i
$347$	−12.6737			−0.680359			−0.340179	−	0.940361i	$-0.610488\pi$
$347$	−12.6737			−0.680359			−0.340179	+	0.940361i	$0.610488\pi$
$348$	3.17804			0.170361
$349$	−21.4958	−	12.4106i	−1.15064	−	0.664324i	−0.201600	−	0.979468i	$-0.564614\pi$
$349$	−21.4958	−	12.4106i	−1.15064	−	0.664324i	−0.949044	+	0.315144i	$0.897947\pi$
$350$	−21.6598	−	31.0028i	−1.15777	−	1.65717i
$351$	−0.727736	−	3.53135i	−0.0388437	−	0.188489i
$352$	0.490667	+	0.849860i	0.0261526	+	0.0452977i
$353$	29.3266	−	16.9317i	1.56090	−	0.901185i	0.563732	−	0.825958i	$-0.309365\pi$
$353$	29.3266	−	16.9317i	1.56090	−	0.901185i	0.997166	−	0.0752268i	$-0.0239681\pi$
$354$	−4.40789	−	7.63468i	−0.234277	−	0.405779i
$355$	−28.3160	+	49.0447i	−1.50286	+	2.60302i
$356$		−	1.45147i		−	0.0769277i
$357$	−1.29325	−	14.9631i	−0.0684458	−	0.791931i
$358$	−11.5394	+	6.66230i	−0.609878	+	0.352113i
$359$	28.4048	−	16.3995i	1.49915	−	0.865533i	0.499148	−	0.866517i	$-0.333646\pi$
$359$	28.4048	−	16.3995i	1.49915	−	0.865533i	1.00000		0.000983725i	$0.000313129\pi$
$360$	4.39255			0.231507
$361$	−9.31826	−	16.1397i	−0.490435	−	0.849458i
$362$			22.5285i			1.18407i
$363$	−10.0370			−0.526805
$364$	−2.21330	+	9.27908i	−0.116008	+	0.486356i
$365$	−24.2401			−1.26879
$366$			1.62525i			0.0849530i
$367$	−14.3081	−	24.7824i	−0.746879	−	1.29363i	−0.949312	−	0.314336i	$-0.898218\pi$
$367$	−14.3081	−	24.7824i	−0.746879	−	1.29363i	0.202433	−	0.979296i	$-0.435115\pi$
$368$	4.65372			0.242592
$369$	8.37436	−	4.83494i	0.435952	−	0.251697i
$370$	−0.548043	+	0.316413i	−0.0284914	+	0.0164495i
$371$	−11.9133	+	8.32314i	−0.618509	+	0.432116i
$372$		−	6.04627i		−	0.313484i
$373$	0.639048	−	1.10686i	0.0330887	−	0.0573112i	−0.849007	−	0.528382i	$-0.822799\pi$
$373$	0.639048	−	1.10686i	0.0330887	−	0.0573112i	0.882096	+	0.471071i	$0.156132\pi$
$374$	2.78532	+	4.82432i	0.144025	+	0.249459i
$375$	35.3566	−	20.4132i	1.82581	−	1.05413i
$376$	5.07637	+	8.79254i	0.261794	+	0.453440i
$377$	−10.8756	−	3.60846i	−0.560121	−	0.185845i
$378$	−1.12066	+	2.39669i	−0.0576407	+	0.123272i
$379$	5.23684	+	3.02349i	0.268999	+	0.155306i	0.628432	−	0.777864i	$-0.283697\pi$
$379$	5.23684	+	3.02349i	0.268999	+	0.155306i	−0.359434	+	0.933171i	$0.617030\pi$
$380$	2.64824			0.135852
$381$	1.60047			0.0819944
$382$	1.48191	+	0.855584i	0.0758213	+	0.0437755i
$383$	−13.0340	−	7.52518i	−0.666006	−	0.384519i	0.128555	−	0.991702i	$-0.458966\pi$
$383$	−13.0340	−	7.52518i	−0.666006	−	0.384519i	−0.794562	+	0.607183i	$0.792299\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	−9.34901	+	6.53161i	−0.476470	+	0.332882i
$386$	2.54236	+	4.40350i	0.129403	+	0.224132i
$387$	6.35361			0.322972
$388$	0.165011	−	0.0952691i	0.00837716	−	0.00483655i
$389$	3.16331	−	5.47902i	0.160386	−	0.277797i	−0.774621	−	0.632426i	$-0.782059\pi$
$389$	3.16331	−	5.47902i	0.160386	−	0.277797i	0.935007	+	0.354628i	$0.115393\pi$
$390$	−15.0317	−	4.98745i	−0.761162	−	0.252549i
$391$	26.4173			1.33598
$392$	5.37176	−	4.48822i	0.271315	−	0.226690i
$393$	−6.92324	+	11.9914i	−0.349231	+	0.604886i
$394$	9.91366	−	17.1710i	0.499443	−	0.865061i
$395$	−51.4014	−	29.6766i	−2.58629	−	1.49319i
$396$		−	0.981333i		−	0.0493139i
$397$	−29.8892	−	17.2565i	−1.50010	−	0.866081i	−1.00000		0.000111505i	$-0.999965\pi$
$397$	−29.8892	−	17.2565i	−1.50010	−	0.866081i	−0.500097	−	0.865970i	$-0.666702\pi$
$398$			17.7883i			0.891648i
$399$	−0.675641	+	1.44495i	−0.0338243	+	0.0723378i
$400$	7.14723	−	12.3794i	0.357361	−	0.618968i
$401$			9.69400i			0.484095i	0.970264	+	0.242048i	$0.0778190\pi$
$401$			9.69400i			0.484095i	−0.970264	+	0.242048i	$0.922181\pi$
$402$	5.45938	−	9.45592i	0.272289	−	0.471619i
$403$	−6.86514	+	20.6910i	−0.341977	+	1.03069i
$404$	5.80131	+	10.0482i	0.288626	+	0.499914i
$405$	−3.80406	−	2.19627i	−0.189025	−	0.109134i
$406$	4.81556	+	6.89275i	0.238992	+	0.342081i
$407$	0.0706894	+	0.122438i	0.00350394	+	0.00606900i
$408$	4.91608	−	2.83830i	0.243382	−	0.140517i
$409$			18.2285i			0.901342i	0.892690	+	0.450671i	$0.148815\pi$
$409$			18.2285i			0.901342i	−0.892690	+	0.450671i	$0.851185\pi$
$410$		−	42.4754i		−	2.09771i
$411$	−4.54533	+	2.62425i	−0.224205	+	0.129445i
$412$	4.08281	+	7.07164i	0.201146	+	0.348395i
$413$	9.87952	−	21.1287i	0.486139	−	1.03967i
$414$	−4.03024	−	2.32686i	−0.198076	−	0.114359i
$415$	−17.3543	−	30.0585i	−0.851889	−	1.47551i
$416$	−3.53135	+	0.727736i	−0.173138	+	0.0356802i
$417$	2.40712	−	4.16925i	0.117877	−	0.204169i
$418$		−	0.591639i		−	0.0289380i
$419$	−11.1427	+	19.2997i	−0.544356	+	0.942853i	0.454291	+	0.890853i	$0.349893\pi$
$419$	−11.1427	+	19.2997i	−0.544356	+	0.942853i	−0.998647	+	0.0519993i	$0.983441\pi$
$420$	6.65585	+	9.52685i	0.324772	+	0.464863i
$421$		−	13.4386i		−	0.654957i	−0.944859	−	0.327479i	$-0.893801\pi$
$421$		−	13.4386i		−	0.654957i	0.944859	−	0.327479i	$-0.106199\pi$
$422$	−2.31265	−	1.33521i	−0.112578	−	0.0649970i
$423$		−	10.1527i		−	0.493643i
$424$	−4.75697	−	2.74644i	−0.231019	−	0.133379i
$425$	40.5720	−	70.2727i	1.96803	−	3.40873i
$426$	6.44637	−	11.1654i	0.312328	−	0.540967i
$427$	−3.52494	+	2.46267i	−0.170584	+	0.119177i
$428$	11.8639			0.573466
$429$	−1.11424	+	3.35822i	−0.0537960	+	0.162137i
$430$	13.9543	−	24.1695i	0.672934	−	1.16556i
$431$	−1.36279	+	0.786807i	−0.0656432	+	0.0378991i	−0.532462	−	0.846454i	$-0.678733\pi$
$431$	−1.36279	+	0.786807i	−0.0656432	+	0.0378991i	0.466819	+	0.884353i	$0.345400\pi$
$432$	−1.00000			−0.0481125
$433$	−11.5299	−	19.9703i	−0.554091	−	0.959713i	−0.997974	−	0.0636284i	$-0.979733\pi$
$433$	−11.5299	−	19.9703i	−0.554091	−	0.959713i	0.443883	−	0.896085i	$-0.353601\pi$
$434$	13.1136	−	9.16167i	0.629471	−	0.439774i
$435$	−12.0894	+	6.97984i	−0.579645	+	0.334658i
$436$	−6.66746	−	3.84946i	−0.319313	−	0.184356i
$437$	−2.42981	−	1.40285i	−0.116233	−	0.0671074i
$438$	5.51847			0.263683
$439$	23.7779			1.13486			0.567429	−	0.823423i	$-0.307938\pi$
$439$	23.7779			1.13486			0.567429	+	0.823423i	$0.307938\pi$
$440$	−3.73305	−	2.15528i	−0.177966	−	0.102749i
$441$	−6.89620	+	1.20103i	−0.328390	+	0.0571921i
$442$	−20.0460	+	4.13107i	−0.953493	+	0.196495i
$443$	11.2447	+	19.4764i	0.534252	+	0.925351i	0.999199	+	0.0400129i	$0.0127399\pi$
$443$	11.2447	+	19.4764i	0.534252	+	0.925351i	−0.464947	+	0.885338i	$0.653927\pi$
$444$	0.124767	−	0.0720340i	0.00592116	−	0.00341858i
$445$	3.18782	+	5.52147i	0.151117	+	0.261743i
$446$	0.686910	−	1.18976i	0.0325261	−	0.0563369i
$447$		−	5.64708i		−	0.267098i
$448$	2.39669	+	1.12066i	0.113233	+	0.0529464i
$449$	−6.93155	+	4.00193i	−0.327120	+	0.188863i	−0.654562	−	0.756008i	$-0.727147\pi$
$449$	−6.93155	+	4.00193i	−0.327120	+	0.188863i	0.327442	+	0.944871i	$0.393814\pi$
$450$	−12.3794	+	7.14723i	−0.583569	+	0.336924i
$451$	−9.48937			−0.446837
$452$	−8.88358	−	15.3868i	−0.417848	−	0.723734i
$453$			6.48730i			0.304800i
$454$	17.6759			0.829573
$455$	−11.9599	−	40.1591i	−0.560688	−	1.88269i
$456$	−0.602893			−0.0282331
$457$			1.56945i			0.0734157i	0.999326	+	0.0367079i	$0.0116871\pi$
$457$			1.56945i			0.0734157i	−0.999326	+	0.0367079i	$0.988313\pi$
$458$	−10.8265	−	18.7520i	−0.505888	−	0.876223i
$459$	−5.67660			−0.264961
$460$	−17.7030	+	10.2208i	−0.825408	+	0.476549i
$461$	−12.7749	+	7.37561i	−0.594988	+	0.343516i	−0.767067	−	0.641567i	$-0.778285\pi$
$461$	−12.7749	+	7.37561i	−0.594988	+	0.343516i	0.172080	+	0.985083i	$0.444951\pi$
$462$	2.12838	−	1.48698i	0.0990213	−	0.0691804i
$463$		−	33.6875i		−	1.56559i	−0.622278	−	0.782797i	$-0.713793\pi$
$463$		−	33.6875i		−	1.56559i	0.622278	−	0.782797i	$-0.286207\pi$
$464$	−1.58902	+	2.75226i	−0.0737684	+	0.127771i
$465$	13.2793	+	23.0003i	0.615811	+	1.06662i
$466$	−20.4467	+	11.8049i	−0.947173	+	0.546851i
$467$	−2.56456	−	4.44196i	−0.118674	−	0.205549i	0.800569	−	0.599241i	$-0.204531\pi$
$467$	−2.56456	−	4.44196i	−0.118674	−	0.205549i	−0.919242	+	0.393692i	$0.871198\pi$
$468$	3.42210	+	1.13543i	0.158187	+	0.0524855i
$469$	28.7810	−	2.48752i	1.32898	−	0.114863i
$470$	−38.6216	−	22.2982i	−1.78148	−	1.02854i
$471$	−5.80428			−0.267447
$472$	8.81577			0.405779
$473$	−5.39968	−	3.11750i	−0.248277	−	0.143343i
$474$	11.7020	+	6.75613i	0.537489	+	0.310319i
$475$	−7.46343	+	4.30902i	−0.342446	+	0.197711i
$476$	13.6050	+	6.36157i	0.623586	+	0.291582i
$477$	2.74644	+	4.75697i	0.125751	+	0.217807i
$478$	−8.99248			−0.411307
$479$	9.22289	−	5.32484i	0.421404	−	0.243298i	−0.274274	−	0.961652i	$-0.588437\pi$
$479$	9.22289	−	5.32484i	0.421404	−	0.243298i	0.695678	+	0.718354i	$0.255104\pi$
$480$	−2.19627	+	3.80406i	−0.100246	+	0.173631i
$481$	−0.508754	+	0.104843i	−0.0231972	+	0.00478045i
$482$	11.7378			0.534640
$483$	−1.06021	−	12.2669i	−0.0482413	−	0.558162i
$484$	5.01849	−	8.69228i	0.228113	−	0.395104i
$485$	−0.418474	+	0.724818i	−0.0190019	+	0.0329123i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$			14.9196i			0.676072i	0.941133	+	0.338036i	$0.109763\pi$
$487$			14.9196i			0.676072i	−0.941133	+	0.338036i	$0.890237\pi$
$488$	−1.40750	−	0.812623i	−0.0637147	−	0.0367857i
$489$			10.3050i			0.466007i
$490$	−10.5771	+	28.8713i	−0.477826	+	1.30427i
$491$	−14.2618	+	24.7022i	−0.643628	+	1.11480i	0.340989	+	0.940067i	$0.389238\pi$
$491$	−14.2618	+	24.7022i	−0.643628	+	1.11480i	−0.984617	+	0.174728i	$0.944095\pi$
$492$			9.66987i			0.435952i
$493$	−9.02024	+	15.6235i	−0.406251	+	0.703648i
$494$	2.06316	+	0.684546i	0.0928261	+	0.0307992i
$495$	2.15528	+	3.73305i	0.0968724	+	0.167788i
$496$	5.23622	+	3.02313i	0.235113	+	0.135743i
$497$	33.9843	−	2.93723i	1.52440	−	0.131753i
$498$	3.95085	+	6.84307i	0.177042	+	0.306645i
$499$	30.5466	−	17.6361i	1.36745	−	0.789500i	0.376851	−	0.926274i	$-0.377007\pi$
$499$	30.5466	−	17.6361i	1.36745	−	0.789500i	0.990602	+	0.136774i	$0.0436735\pi$
$500$			40.8263i			1.82581i
$501$		−	13.1223i		−	0.586261i
$502$	−2.92888	+	1.69099i	−0.130722	+	0.0754725i
$503$	−3.66511	−	6.34815i	−0.163419	−	0.283050i	0.772674	−	0.634803i	$-0.218919\pi$
$503$	−3.66511	−	6.34815i	−0.163419	−	0.283050i	−0.936093	+	0.351753i	$0.885586\pi$
$504$	−1.51526	−	2.16887i	−0.0674951	−	0.0966090i
$505$	−44.1370	−	25.4825i	−1.96407	−	1.13396i
$506$	2.28343	+	3.95501i	0.101511	+	0.175822i
$507$	−10.4216	−	7.77115i	−0.462838	−	0.345129i
$508$	−0.800233	+	1.38604i	−0.0355046	+	0.0614958i
$509$			15.1378i			0.670971i	0.942045	+	0.335486i	$0.108900\pi$
$509$			15.1378i			0.670971i	−0.942045	+	0.335486i	$0.891100\pi$
$510$	−12.4674	+	21.5941i	−0.552064	+	0.956204i
$511$	8.36191	+	11.9688i	0.369909	+	0.529470i
$512$			1.00000i			0.0441942i
$513$	0.522121	+	0.301447i	0.0230522	+	0.0133092i
$514$		−	20.5007i		−	0.904249i
$515$	−31.0625	−	17.9340i	−1.36878	−	0.790264i
$516$	−3.17681	+	5.50239i	−0.139851	+	0.242229i
$517$	−4.98161	+	8.62841i	−0.219091	+	0.379477i
$518$	0.345286	+	0.161452i	0.0151710	+	0.00709379i
$519$	7.81220			0.342918
$520$	11.8351	−	10.5241i	0.519005	−	0.461514i
$521$	−4.32817	+	7.49661i	−0.189620	+	0.328432i	−0.945124	−	0.326713i	$-0.894059\pi$
$521$	−4.32817	+	7.49661i	−0.189620	+	0.328432i	0.755503	+	0.655145i	$0.227392\pi$
$522$	2.75226	−	1.58902i	0.120463	−	0.0695495i
$523$	−0.0416624			−0.00182177			−0.000910886	−	1.00000i	$-0.500290\pi$
$523$	−0.0416624			−0.00182177			−0.000910886		1.00000i	$0.500290\pi$
$524$	−6.92324	−	11.9914i	−0.302443	−	0.523847i
$525$	−34.2593	−	16.0193i	−1.49520	−	0.699139i
$526$	9.92064	−	5.72768i	0.432560	−	0.249739i
$527$	29.7240	+	17.1611i	1.29480	+	0.747551i
$528$	0.849860	+	0.490667i	0.0369854	+	0.0213535i
$529$	−1.34286			−0.0583850
$530$	24.1277			1.04804
$531$	−7.63468	−	4.40789i	−0.331317	−	0.191286i
$532$	−0.913540	−	1.30760i	−0.0396070	−	0.0566915i
$533$	10.9795	−	33.0913i	0.475575	−	1.43334i
$534$	−0.725734	−	1.25701i	−0.0314056	−	0.0543961i
$535$	−45.1311	+	26.0565i	−1.95119	+	1.12652i
$536$	5.45938	+	9.45592i	0.235809	+	0.408434i
$537$	−6.66230	+	11.5394i	−0.287499	+	0.497963i
$538$			9.16355i			0.395069i
$539$	6.45011	+	2.36302i	0.277826	+	0.101783i
$540$	3.80406	−	2.19627i	0.163701	−	0.0945125i
$541$	−3.82785	+	2.21001i	−0.164572	+	0.0950157i	−0.580024	−	0.814599i	$-0.696957\pi$
$541$	−3.82785	+	2.21001i	−0.164572	+	0.0950157i	0.415452	+	0.909615i	$0.363623\pi$
$542$	−11.5526			−0.496225
$543$	11.2643	+	19.5103i	0.483396	+	0.837267i
$544$			5.67660i			0.243382i
$545$	33.8179			1.44860
$546$	2.72277	+	9.14257i	0.116524	+	0.391266i
$547$	−11.5643			−0.494453			−0.247227	−	0.968958i	$-0.579519\pi$
$547$	−11.5643			−0.494453			−0.247227	+	0.968958i	$0.579519\pi$
$548$		−	5.24850i		−	0.224205i
$549$	0.812623	+	1.40750i	0.0346819	+	0.0600708i
$550$	14.0276			0.598140
$551$	1.65932	−	0.958010i	0.0706895	−	0.0408126i
$552$	4.03024	−	2.32686i	0.171539	−	0.0990378i
$553$	3.07837	+	35.6173i	0.130906	+	1.51460i
$554$			9.23072i			0.392176i
$555$	−0.316413	+	0.548043i	−0.0134310	+	0.0232631i
$556$	2.40712	+	4.16925i	0.102085	+	0.176816i
$557$	−8.66947	+	5.00532i	−0.367337	+	0.212082i	−0.672295	−	0.740284i	$-0.734691\pi$
$557$	−8.66947	+	5.00532i	−0.367337	+	0.212082i	0.304957	+	0.952366i	$0.401358\pi$
$558$	−3.02313	−	5.23622i	−0.127979	−	0.221667i
$559$	17.1190	−	15.2227i	0.724055	−	0.643851i
$560$	−11.5784	+	1.00071i	−0.489277	+	0.0422878i
$561$	4.82432	+	2.78532i	0.203683	+	0.117596i
$562$	−28.4923			−1.20188
$563$	19.2033			0.809324			0.404662	−	0.914466i	$-0.367389\pi$
$563$	19.2033			0.809324			0.404662	+	0.914466i	$0.367389\pi$
$564$	8.79254	+	5.07637i	0.370233	+	0.213754i
$565$	67.5872	+	39.0215i	2.84342	+	1.64165i
$566$	−0.920363	+	0.531372i	−0.0386857	+	0.0223352i
$567$	0.227820	+	2.63592i	0.00956755	+	0.110698i
$568$	6.44637	+	11.1654i	0.270484	+	0.468491i
$569$	9.02535			0.378362			0.189181	−	0.981942i	$-0.439417\pi$
$569$	9.02535			0.378362			0.189181	+	0.981942i	$0.439417\pi$
$570$	2.29344	−	1.32412i	0.0960616	−	0.0554612i
$571$	7.99270	−	13.8438i	0.334484	−	0.579343i	−0.648901	−	0.760872i	$-0.724771\pi$
$571$	7.99270	−	13.8438i	0.334484	−	0.579343i	0.983386	+	0.181529i	$0.0581046\pi$
$572$	−2.35119	−	2.64407i	−0.0983081	−	0.110554i
$573$	1.71117			0.0714850
$574$	−20.9727	+	14.6524i	−0.875382	+	0.611578i
$575$	33.2612	−	57.6101i	1.38709	−	2.40251i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−37.5246	−	21.6648i	−1.56217	−	0.901919i	−0.997037	−	0.0769186i	$-0.975492\pi$
$577$	−37.5246	−	21.6648i	−1.56217	−	0.901919i	−0.565132	−	0.825000i	$-0.691175\pi$
$578$			15.2238i			0.633228i
$579$	4.40350	+	2.54236i	0.183003	+	0.105657i
$580$		−	13.9597i		−	0.579645i
$581$	−8.85515	+	18.9379i	−0.367374	+	0.785677i
$582$	0.0952691	−	0.165011i	0.00394903	−	0.00683992i
$583$		−	5.39034i		−	0.223245i
$584$	−2.75923	+	4.77913i	−0.114178	+	0.197762i
$585$	−15.5116	+	3.19661i	−0.641326	+	0.132164i
$586$	−4.57344	−	7.92143i	−0.188927	−	0.327231i
$587$	2.71747	+	1.56893i	0.112162	+	0.0647567i	0.555032	−	0.831829i	$-0.312706\pi$
$587$	2.71747	+	1.56893i	0.112162	+	0.0647567i	−0.442870	+	0.896586i	$0.646040\pi$
$588$	2.40797	−	6.57280i	0.0993031	−	0.271058i
$589$	−1.82263	−	3.15688i	−0.0751001	−	0.130077i
$590$	−33.5357	+	19.3618i	−1.38064	+	0.797115i
$591$		−	19.8273i		−	0.815587i
$592$			0.144068i			0.00592116i
$593$	−28.1879	+	16.2743i	−1.15754	+	0.668304i	−0.950713	−	0.310074i	$-0.899646\pi$
$593$	−28.1879	+	16.2743i	−1.15754	+	0.668304i	−0.206825	+	0.978378i	$0.566313\pi$
$594$	−0.490667	−	0.849860i	−0.0201323	−	0.0348702i
$595$	−65.7261	+	5.68064i	−2.69451	+	0.232884i
$596$	4.89051	+	2.82354i	0.200323	+	0.115657i
$597$	8.89416	+	15.4051i	0.364014	+	0.630491i
$598$	−16.4339	+	3.38668i	−0.672032	+	0.138492i
$599$	11.2690	−	19.5185i	0.460440	−	0.797505i	−0.538543	−	0.842598i	$-0.681025\pi$
$599$	11.2690	−	19.5185i	0.460440	−	0.797505i	0.998983	+	0.0450931i	$0.0143584\pi$
$600$		−	14.2945i		−	0.583569i
$601$	0.165055	−	0.285884i	0.00673275	−	0.0116615i	−0.862639	−	0.505819i	$-0.831190\pi$
$601$	0.165055	−	0.285884i	0.00673275	−	0.0116615i	0.869372	+	0.494158i	$0.164524\pi$
$602$	−16.7476	+	1.44748i	−0.682583	+	0.0589949i
$603$		−	10.9188i		−	0.444646i
$604$	−5.61817	−	3.24365i	−0.228600	−	0.131982i
$605$			44.0879i			1.79243i
$606$	10.0482	+	5.80131i	0.408178	+	0.235662i
$607$	3.06129	−	5.30232i	0.124254	−	0.215214i	−0.797187	−	0.603732i	$-0.793680\pi$
$607$	3.06129	−	5.30232i	0.124254	−	0.215214i	0.921441	+	0.388518i	$0.127013\pi$
$608$	0.301447	−	0.522121i	0.0122253	−	0.0211748i
$609$	7.61677	+	3.56152i	0.308647	+	0.144320i
$610$	7.13897			0.289048
$611$	−24.3251	−	27.3552i	−0.984087	−	1.10667i
$612$	2.83830	−	4.91608i	0.114732	−	0.198721i
$613$	24.9334	−	14.3953i	1.00705	−	0.581422i	0.0967249	−	0.995311i	$-0.469163\pi$
$613$	24.9334	−	14.3953i	1.00705	−	0.581422i	0.910327	+	0.413889i	$0.135830\pi$
$614$	4.67641			0.188725
$615$	−21.2377	−	36.7847i	−0.856386	−	1.48330i
$616$	0.223568	+	2.58672i	0.00900780	+	0.104222i
$617$	13.7454	−	7.93589i	0.553368	−	0.319487i	−0.197112	−	0.980381i	$-0.563156\pi$
$617$	13.7454	−	7.93589i	0.553368	−	0.319487i	0.750479	+	0.660894i	$0.229823\pi$
$618$	7.07164	+	4.08281i	0.284463	+	0.164235i
$619$	26.6026	+	15.3590i	1.06925	+	0.617330i	0.927976	−	0.372641i	$-0.121548\pi$
$619$	26.6026	+	15.3590i	1.06925	+	0.617330i	0.141271	+	0.989971i	$0.454881\pi$
$620$	−26.5585			−1.06662
$621$	−4.65372			−0.186747
$622$	−0.665917	−	0.384467i	−0.0267008	−	0.0154157i
$623$	1.62661	−	3.47872i	0.0651687	−	0.139372i
$624$	−2.69437	+	2.39591i	−0.107861	+	0.0959132i
$625$	−53.9296	−	93.4088i	−2.15718	−	3.73635i
$626$	−8.26391	+	4.77117i	−0.330292	+	0.190694i
$627$	−0.295820	−	0.512375i	−0.0118139	−	0.0204623i
$628$	2.90214	−	5.02666i	0.115808	−	0.200585i
$629$			0.817817i			0.0326085i
$630$	10.5276	+	4.92257i	0.419428	+	0.196120i
$631$	33.3375	−	19.2474i	1.32715	−	0.766228i	0.342288	−	0.939595i	$-0.388798\pi$
$631$	33.3375	−	19.2474i	1.32715	−	0.766228i	0.984857	+	0.173367i	$0.0554648\pi$
$632$	−11.7020	+	6.75613i	−0.465479	+	0.268745i
$633$	−2.67042			−0.106140
$634$	−0.149208	−	0.258436i	−0.00592581	−	0.0102638i
$635$		−	7.03012i		−	0.278982i
$636$	−5.49288			−0.217807
$637$	−15.7033	+	19.7587i	−0.622188	+	0.782868i
$638$	−3.11872			−0.123471
$639$		−	12.8927i		−	0.510029i
$640$	−2.19627	−	3.80406i	−0.0868153	−	0.150369i
$641$	20.8081			0.821872			0.410936	−	0.911664i	$-0.365202\pi$
$641$	20.8081			0.821872			0.410936	+	0.911664i	$0.365202\pi$
$642$	10.2745	−	5.93197i	0.405501	−	0.234116i
$643$	33.7170	−	19.4665i	1.32967	−	0.767684i	0.344420	−	0.938816i	$-0.388076\pi$
$643$	33.7170	−	19.4665i	1.32967	−	0.767684i	0.985248	+	0.171132i	$0.0547423\pi$
$644$	11.1535	+	5.21526i	0.439510	+	0.205510i
$645$		−	27.9085i		−	1.09890i
$646$	1.71119	−	2.96387i	0.0673260	−	0.116612i
$647$	6.31559	+	10.9389i	0.248291	+	0.430053i	0.963052	−	0.269316i	$-0.0867976\pi$
$647$	6.31559	+	10.9389i	0.248291	+	0.430053i	−0.714761	+	0.699369i	$0.753464\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	4.32561	+	7.49217i	0.169795	+	0.294093i
$650$	−16.2304	+	48.9171i	−0.636609	+	1.91869i
$651$	6.77584	−	14.4910i	0.265566	−	0.567948i
$652$	−8.92436	−	5.15248i	−0.349505	−	0.201787i
$653$	−46.9287			−1.83646			−0.918232	−	0.396044i	$-0.870383\pi$
$653$	−46.9287			−1.83646			−0.918232	+	0.396044i	$0.870383\pi$
$654$	−7.69892			−0.301052
$655$	52.6728	+	30.4106i	2.05809	+	1.18824i
$656$	−8.37436	−	4.83494i	−0.326964	−	0.188773i
$657$	4.77913	−	2.75923i	0.186452	−	0.107648i
$658$	2.31300	+	26.7619i	0.0901702	+	1.04329i
$659$	−2.74654	−	4.75715i	−0.106990	−	0.185312i	0.807559	−	0.589786i	$-0.200788\pi$
$659$	−2.74654	−	4.75715i	−0.106990	−	0.185312i	−0.914550	+	0.404474i	$0.867455\pi$
$660$	−4.31055			−0.167788
$661$	22.8173	−	13.1736i	0.887489	−	0.512392i	0.0143685	−	0.999897i	$-0.495426\pi$
$661$	22.8173	−	13.1736i	0.887489	−	0.512392i	0.873120	+	0.487505i	$0.162093\pi$
$662$	−9.22804	+	15.9834i	−0.358658	+	0.621214i
$663$	−15.2949	+	13.6006i	−0.594003	+	0.528205i
$664$	−7.90170			−0.306645
$665$	6.34700	+	2.96778i	0.246126	+	0.115086i
$666$	0.0720340	−	0.124767i	0.00279126	−	0.00483460i
$667$	−7.39486	+	12.8083i	−0.286330	+	0.495938i
$668$	11.3642	+	6.56115i	0.439696	+	0.253858i
$669$		−	1.37382i		−	0.0531150i
$670$	−41.5356	−	23.9806i	−1.60466	−	0.926450i
$671$		−	1.59491i		−	0.0615708i
$672$	2.63592	−	0.227820i	0.101683	−	0.00878836i
$673$	−10.3282	+	17.8890i	−0.398123	+	0.689570i	−0.993494	−	0.113881i	$-0.963672\pi$
$673$	−10.3282	+	17.8890i	−0.398123	+	0.689570i	0.595371	+	0.803451i	$0.297005\pi$
$674$			12.4534i			0.479686i
$675$	−7.14723	+	12.3794i	−0.275097	+	0.476482i
$676$	11.9408	−	5.13978i	0.459262	−	0.197684i
$677$	−18.4908	−	32.0270i	−0.710659	−	1.23090i	−0.964610	−	0.263681i	$-0.915063\pi$
$677$	−18.4908	−	32.0270i	−0.710659	−	1.23090i	0.253951	−	0.967217i	$-0.418270\pi$
$678$	−15.3868	−	8.88358i	−0.590927	−	0.341172i
$679$	0.502244	−	0.0434085i	0.0192744	−	0.00166586i
$680$	−12.4674	−	21.5941i	−0.478102	−	0.828097i
$681$	15.3078	−	8.83797i	0.586596	−	0.338672i
$682$			5.93341i			0.227202i
$683$			4.58653i			0.175499i	0.996143	+	0.0877494i	$0.0279675\pi$
$683$			4.58653i			0.175499i	−0.996143	+	0.0877494i	$0.972033\pi$
$684$	−0.522121	+	0.301447i	−0.0199638	+	0.0115261i
$685$	11.5271	+	19.9656i	0.440429	+	0.762846i
$686$	17.9042	−	4.73693i	0.683587	−	0.180857i
$687$	−18.7520	−	10.8265i	−0.715433	−	0.413056i
$688$	−3.17681	−	5.50239i	−0.121115	−	0.209777i
$689$	18.7972	+	6.23680i	0.716116	+	0.237603i
$690$	−10.2208	+	17.7030i	−0.389101	+	0.673943i
$691$			21.2181i			0.807176i	0.914941	+	0.403588i	$0.132237\pi$
$691$			21.2181i			0.807176i	−0.914941	+	0.403588i	$0.867763\pi$
$692$	−3.90610	+	6.76557i	−0.148488	+	0.257188i
$693$	1.09974	−	2.35195i	0.0417759	−	0.0893432i
$694$		−	12.6737i		−	0.481086i
$695$	−18.3136	−	10.5734i	−0.694676	−	0.401071i
$696$			3.17804i			0.120463i
$697$	−47.5379	−	27.4460i	−1.80063	−	1.03959i
$698$	12.4106	−	21.4958i	0.469748	−	0.813628i
$699$	−11.8049	+	20.4467i	−0.446502	+	0.773364i
$700$	31.0028	−	21.6598i	1.17179	−	0.818664i
$701$	−2.29081			−0.0865226			−0.0432613	−	0.999064i	$-0.513775\pi$
$701$	−2.29081			−0.0865226			−0.0432613	+	0.999064i	$0.513775\pi$
$702$	3.53135	−	0.727736i	0.133282	−	0.0274666i
$703$	0.0434288	−	0.0752209i	0.00163795	−	0.00283701i
$704$	−0.849860	+	0.490667i	−0.0320303	+	0.0184927i
$705$	−44.5964			−1.67960
$706$	16.9317	+	29.3266i	0.637234	+	1.10372i
$707$	2.64331	+	30.5836i	0.0994119	+	1.15021i
$708$	7.63468	−	4.40789i	0.286929	−	0.165659i
$709$	−24.0517	−	13.8863i	−0.903282	−	0.521510i	−0.0250182	−	0.999687i	$-0.507964\pi$
$709$	−24.0517	−	13.8863i	−0.903282	−	0.521510i	−0.878263	+	0.478177i	$0.841298\pi$
$710$	−49.0447	−	28.3160i	−1.84061	−	1.06268i
$711$	13.5123			0.506750
$712$	1.45147			0.0543961
$713$	24.3679	+	14.0688i	0.912586	+	0.526882i
$714$	14.9631	−	1.29325i	0.559980	−	0.0483985i
$715$	14.7511	+	4.89435i	0.551662	+	0.183038i
$716$	−6.66230	−	11.5394i	−0.248982	−	0.431249i
$717$	−7.78772	+	4.49624i	−0.290838	+	0.167915i
$718$	16.3995	+	28.4048i	0.612024	+	1.06006i
$719$	−2.81631	+	4.87799i	−0.105031	+	0.181918i	−0.913751	−	0.406275i	$-0.866827\pi$
$719$	−2.81631	+	4.87799i	−0.105031	+	0.181918i	0.808720	+	0.588194i	$0.200161\pi$
$720$			4.39255i			0.163701i
$721$	1.86030	+	21.5240i	0.0692811	+	0.801595i
$722$	16.1397	−	9.31826i	0.600657	−	0.346790i
$723$	10.1652	−	5.86888i	0.378048	−	0.218266i
$724$	−22.5285			−0.837267
$725$	22.7142	+	39.3421i	0.843584	+	1.46113i
$726$		−	10.0370i		−	0.372507i
$727$	39.3859			1.46074			0.730372	−	0.683050i	$-0.239347\pi$
$727$	39.3859			1.46074			0.730372	+	0.683050i	$0.239347\pi$
$728$	−9.27908	−	2.21330i	−0.343906	−	0.0820302i
$729$	1.00000			0.0370370
$730$		−	24.2401i		−	0.897167i
$731$	−18.0335	−	31.2349i	−0.666992	−	1.15526i
$732$	−1.62525			−0.0600708
$733$	28.6445	−	16.5379i	1.05801	−	0.610842i	0.133128	−	0.991099i	$-0.457498\pi$
$733$	28.6445	−	16.5379i	1.05801	−	0.610842i	0.924881	+	0.380257i	$0.124165\pi$
$734$	24.7824	−	14.3081i	0.914736	−	0.528123i
$735$	5.27560	+	30.2919i	0.194593	+	1.11733i
$736$			4.65372i			0.171539i
$737$	−5.35747	+	9.27941i	−0.197345	+	0.341812i
$738$	4.83494	+	8.37436i	0.177976	+	0.308264i
$739$	28.2785	−	16.3266i	1.04024	−	0.600583i	0.120339	−	0.992733i	$-0.461602\pi$
$739$	28.2785	−	16.3266i	1.04024	−	0.600583i	0.919901	+	0.392150i	$0.128269\pi$
$740$	−0.316413	−	0.548043i	−0.0116316	−	0.0201464i
$741$	2.12902	−	0.438747i	0.0782117	−	0.0161178i
$742$	−8.32314	−	11.9133i	−0.305552	−	0.437352i
$743$	16.9528	+	9.78772i	0.621939	+	0.359077i	0.777624	−	0.628730i	$-0.216425\pi$
$743$	16.9528	+	9.78772i	0.621939	+	0.359077i	−0.155684	+	0.987807i	$0.549758\pi$
$744$	6.04627			0.221667
$745$	−24.8051			−0.908787
$746$	1.10686	+	0.639048i	0.0405252	+	0.0233972i
$747$	6.84307	+	3.95085i	0.250375	+	0.144554i
$748$	−4.82432	+	2.78532i	−0.176394	+	0.101841i
$749$	28.4342	+	13.2955i	1.03896	+	0.485807i
$750$	20.4132	+	35.3566i	0.745383	+	1.29104i
$751$	45.5768			1.66312			0.831560	−	0.555434i	$-0.187448\pi$
$751$	45.5768			1.66312			0.831560	+	0.555434i	$0.187448\pi$
$752$	−8.79254	+	5.07637i	−0.320631	+	0.185116i
$753$	−1.69099	+	2.92888i	−0.0616230	+	0.106734i
$754$	3.60846	−	10.8756i	0.131412	−	0.396065i
$755$	28.4958			1.03707
$756$	−2.39669	−	1.12066i	−0.0871667	−	0.0407582i
$757$	−21.5003	+	37.2396i	−0.781441	+	1.35350i	0.149661	+	0.988737i	$0.452182\pi$
$757$	−21.5003	+	37.2396i	−0.781441	+	1.35350i	−0.931102	+	0.364759i	$0.881151\pi$
$758$	−3.02349	+	5.23684i	−0.109818	+	0.190211i
$759$	3.95501	+	2.28343i	0.143558	+	0.0828831i
$760$			2.64824i			0.0960616i
$761$	37.3769	+	21.5796i	1.35491	+	0.782258i	0.988933	−	0.148365i	$-0.0474010\pi$
$761$	37.3769	+	21.5796i	1.35491	+	0.782258i	0.365979	+	0.930623i	$0.380734\pi$
$762$			1.60047i			0.0579788i
$763$	−11.6659	−	16.6979i	−0.422333	−	0.604506i
$764$	−0.855584	+	1.48191i	−0.0309539	+	0.0536138i
$765$			24.9347i			0.901517i
$766$	7.52518	−	13.0340i	0.271896	−	0.470937i
$767$	−31.1315	+	6.41556i	−1.12409	+	0.231652i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−11.5961	−	6.69499i	−0.418165	−	0.241428i	0.276127	−	0.961121i	$-0.410949\pi$
$769$	−11.5961	−	6.69499i	−0.418165	−	0.241428i	−0.694292	+	0.719694i	$0.744282\pi$
$770$	−6.53161	−	9.34901i	−0.235383	−	0.336915i
$771$	−10.2504	−	17.7542i	−0.369158	−	0.639401i
$772$	−4.40350	+	2.54236i	−0.158486	+	0.0915016i
$773$			22.2139i			0.798979i	0.916738	+	0.399489i	$0.130813\pi$
$773$			22.2139i			0.798979i	−0.916738	+	0.399489i	$0.869187\pi$
$774$			6.35361i			0.228376i
$775$	74.8490	−	43.2141i	2.68865	−	1.55229i
$776$	0.0952691	+	0.165011i	0.00341996	+	0.00592355i
$777$	0.379752	−	0.0328216i	0.0136235	−	0.00117747i
$778$	5.47902	+	3.16331i	0.196432	+	0.113410i
$779$	2.91495	+	5.04884i	0.104439	+	0.180894i
$780$	4.98745	−	15.0317i	0.178579	−	0.538223i
$781$	−6.32604	+	10.9570i	−0.226363	+	0.392073i
$782$			26.4173i			0.944682i
$783$	1.58902	−	2.75226i	0.0567870	−	0.0983579i
$784$	4.48822	+	5.37176i	0.160294	+	0.191849i
$785$			25.4956i			0.909976i
$786$	−11.9914	−	6.92324i	−0.427719	−	0.246944i
$787$		−	3.47716i		−	0.123947i	−0.998078	−	0.0619737i	$-0.980261\pi$
$787$		−	3.47716i		−	0.123947i	0.998078	−	0.0619737i	$-0.0197395\pi$
$788$	17.1710	+	9.91366i	0.611690	+	0.353160i
$789$	5.72768	−	9.92064i	0.203911	−	0.353184i
$790$	29.6766	−	51.4014i	1.05585	−	1.82878i
$791$	−4.04772	−	46.8329i	−0.143920	−	1.66519i
$792$	0.981333			0.0348702
$793$	5.56176	+	1.84536i	0.197504	+	0.0655307i
$794$	17.2565	−	29.8892i	0.612412	−	1.06073i
$795$	20.8952	−	12.0639i	0.741077	−	0.427861i
$796$	−17.7883			−0.630491
$797$	16.2271	+	28.1062i	0.574794	+	0.995573i	0.996064	+	0.0886373i	$0.0282512\pi$
$797$	16.2271	+	28.1062i	0.574794	+	0.995573i	−0.421270	+	0.906935i	$0.638415\pi$
$798$	−1.44495	−	0.675641i	−0.0511506	−	0.0239174i
$799$	−49.9117	+	28.8166i	−1.76575	+	1.01946i
$800$	12.3794	+	7.14723i	0.437677	+	0.252693i
$801$	−1.25701	−	0.725734i	−0.0444142	−	0.0256426i
$802$	−9.69400			−0.342307
$803$	−5.41546			−0.191107
$804$	9.45592	+	5.45938i	0.333485	+	0.192537i
$805$	−53.8828	+	4.65703i	−1.89912	+	0.164139i
$806$	−20.6910	−	6.86514i	−0.728808	−	0.241814i
$807$	4.58177	+	7.93587i	0.161286	+	0.279356i
$808$	−10.0482	+	5.80131i	−0.353493	+	0.204089i
$809$	7.24246	+	12.5443i	0.254631	+	0.441035i	0.964795	−	0.263002i	$-0.0847125\pi$
$809$	7.24246	+	12.5443i	0.254631	+	0.441035i	−0.710164	+	0.704036i	$0.751379\pi$
$810$	2.19627	−	3.80406i	0.0771692	−	0.133661i
$811$			0.508283i			0.0178482i	0.999960	+	0.00892411i	$0.00284067\pi$
$811$			0.508283i			0.0178482i	−0.999960	+	0.00892411i	$0.997159\pi$
$812$	−6.89275	+	4.81556i	−0.241888	+	0.168993i
$813$	−10.0048	+	5.77628i	−0.350884	+	0.202583i
$814$	−0.122438	+	0.0706894i	−0.00429143	+	0.00247766i
$815$	45.2650			1.58556
$816$	2.83830	+	4.91608i	0.0993604	+	0.172097i
$817$			3.83055i			0.134014i
$818$	−18.2285			−0.637345
$819$	6.92927	+	6.55631i	0.242128	+	0.229096i
$820$	42.4754			1.48330
$821$			34.5648i			1.20632i	0.797620	+	0.603160i	$0.206092\pi$
$821$			34.5648i			1.20632i	−0.797620	+	0.603160i	$0.793908\pi$
$822$	−2.62425	−	4.54533i	−0.0915312	−	0.158537i
$823$	43.1552			1.50430			0.752149	−	0.658993i	$-0.229018\pi$
$823$	43.1552			1.50430			0.752149	+	0.658993i	$0.229018\pi$
$824$	−7.07164	+	4.08281i	−0.246352	+	0.142232i
$825$	12.1483	−	7.01381i	0.422949	−	0.244190i
$826$	21.1287	+	9.87952i	0.735160	+	0.343753i
$827$			45.8647i			1.59487i	0.603404	+	0.797435i	$0.293810\pi$
$827$			45.8647i			1.59487i	−0.603404	+	0.797435i	$0.706190\pi$
$828$	2.32686	−	4.03024i	0.0808640	−	0.140061i
$829$	−25.1800	−	43.6130i	−0.874536	−	1.51474i	−0.857256	−	0.514891i	$-0.827833\pi$
$829$	−25.1800	−	43.6130i	−0.874536	−	1.51474i	−0.0172803	−	0.999851i	$-0.505501\pi$
$830$	30.0585	−	17.3543i	1.04335	−	0.602376i
$831$	4.61536	+	7.99404i	0.160105	+	0.277310i
$832$	−0.727736	−	3.53135i	−0.0252297	−	0.122427i
$833$	25.4779	+	30.4934i	0.882756	+	1.05653i
$834$	4.16925	+	2.40712i	0.144369	+	0.0833517i
$835$	−57.6403			−1.99472
$836$	0.591639			0.0204623
$837$	−5.23622	−	3.02313i	−0.180990	−	0.104495i
$838$	−19.2997	−	11.1427i	−0.666698	−	0.384918i
$839$	−15.4290	+	8.90791i	−0.532667	+	0.307535i	−0.742102	−	0.670287i	$-0.766171\pi$
$839$	−15.4290	+	8.90791i	−0.532667	+	0.307535i	0.209435	+	0.977823i	$0.432838\pi$
$840$	−9.52685	+	6.65585i	−0.328708	+	0.229649i
$841$	9.45003	+	16.3679i	0.325863	+	0.564411i
$842$	13.4386			0.463125
$843$	−24.6751	+	14.2461i	−0.849854	+	0.490663i
$844$	1.33521	−	2.31265i	0.0459598	−	0.0796047i
$845$	−34.1351	+	45.7773i	−1.17428	+	1.57479i
$846$	10.1527			0.349059
$847$	21.7689	−	15.2086i	0.747988	−	0.522575i
$848$	2.74644	−	4.75697i	0.0943131	−	0.163355i
$849$	−0.531372	+	0.920363i	−0.0182366	+	0.0315868i
$850$	70.2727	+	40.5720i	2.41033	+	1.39161i
$851$			0.670453i			0.0229828i
$852$	11.1654	+	6.44637i	0.382522	+	0.220849i
$853$		−	0.0212438i		−	0.000727374i	−1.00000		0.000363687i	$-0.999884\pi$
$853$		−	0.0212438i		−	0.000727374i	1.00000		0.000363687i	$-0.000115765\pi$
$854$	−2.46267	−	3.52494i	−0.0842709	−	0.120621i
$855$	1.32412	−	2.29344i	0.0452839	−	0.0784340i
$856$			11.8639i			0.405501i
$857$	−24.1424	+	41.8159i	−0.824690	+	1.42841i	0.0774656	+	0.996995i	$0.475317\pi$
$857$	−24.1424	+	41.8159i	−0.824690	+	1.42841i	−0.902156	+	0.431410i	$0.858016\pi$
$858$	−3.35822	−	1.11424i	−0.114648	−	0.0380395i
$859$	−20.1110	−	34.8334i	−0.686180	−	1.18850i	−0.973064	−	0.230534i	$-0.925953\pi$
$859$	−20.1110	−	34.8334i	−0.686180	−	1.18850i	0.286884	−	0.957965i	$-0.407381\pi$
$860$	24.1695	+	13.9543i	0.824173	+	0.475836i
$861$	−10.8367	+	23.1757i	−0.369313	+	0.789825i
$862$	−0.786807	−	1.36279i	−0.0267987	−	0.0464168i
$863$	34.8461	−	20.1184i	1.18617	−	0.684838i	0.228739	−	0.973488i	$-0.426540\pi$
$863$	34.8461	−	20.1184i	1.18617	−	0.684838i	0.957435	+	0.288650i	$0.0932064\pi$
$864$		−	1.00000i		−	0.0340207i
$865$		−	34.3155i		−	1.16676i
$866$	19.9703	−	11.5299i	0.678620	−	0.391801i
$867$	7.61191	+	13.1842i	0.258514	+	0.447760i
$868$	9.16167	+	13.1136i	0.310967	+	0.445103i
$869$	−11.4835	−	6.63002i	−0.389552	−	0.224908i
$870$	−6.97984	−	12.0894i	−0.236639	−	0.409871i
$871$	−26.1604	−	29.4191i	−0.886410	−	0.996830i
$872$	3.84946	−	6.66746i	0.130359	−	0.225789i
$873$		−	0.190538i		−	0.00644874i
$874$	1.40285	−	2.42981i	0.0474521	−	0.0821894i
$875$	−45.7526	+	97.8479i	−1.54672	+	3.30786i
$876$			5.51847i			0.186452i
$877$	0.0334779	+	0.0193285i	0.00113047	+	0.000652676i	0.500565	−	0.865699i	$-0.333126\pi$
$877$	0.0334779	+	0.0193285i	0.00113047	+	0.000652676i	−0.499435	+	0.866352i	$0.666459\pi$
$878$			23.7779i			0.802465i
$879$	−7.92143	−	4.57344i	−0.267183	−	0.154258i
$880$	2.15528	−	3.73305i	0.0726543	−	0.125841i
$881$	9.26662	−	16.0503i	0.312200	−	0.540747i	−0.666638	−	0.745382i	$-0.732267\pi$
$881$	9.26662	−	16.0503i	0.312200	−	0.540747i	0.978838	+	0.204635i	$0.0656007\pi$
$882$	−1.20103	−	6.89620i	−0.0404409	−	0.232207i
$883$	−17.2118			−0.579224			−0.289612	−	0.957144i	$-0.593526\pi$
$883$	−17.2118			−0.579224			−0.289612	+	0.957144i	$0.593526\pi$
$884$	−4.13107	−	20.0460i	−0.138943	−	0.674221i
$885$	−19.3618	+	33.5357i	−0.650841	+	1.12729i
$886$	−19.4764	+	11.2447i	−0.654322	+	0.377773i
$887$	33.1790			1.11404			0.557021	−	0.830498i	$-0.311944\pi$
$887$	33.1790			1.11404			0.557021	+	0.830498i	$0.311944\pi$
$888$	0.0720340	+	0.124767i	0.00241730	+	0.00418689i
$889$	−3.47120	+	2.42512i	−0.116420	+	0.0813360i
$890$	−5.52147	+	3.18782i	−0.185080	+	0.106856i
$891$	−0.849860	−	0.490667i	−0.0284714	−	0.0164380i
$892$	1.18976	+	0.686910i	0.0398362	+	0.0229995i
$893$	6.12102			0.204832
$894$	5.64708			0.188867
$895$	50.6875	+	29.2644i	1.69430	+	0.978202i
$896$	−1.12066	+	2.39669i	−0.0374388	+	0.0800677i
$897$	−12.5388	+	11.1499i	−0.418660	+	0.372285i
$898$	−4.00193	−	6.93155i	−0.133546	−	0.231309i
$899$	−16.6409	+	9.60765i	−0.555006	+	0.320433i
$900$	−7.14723	−	12.3794i	−0.238241	−	0.412645i
$901$	15.5904	−	27.0034i	0.519393	−	0.899615i
$902$		−	9.48937i		−	0.315961i
$903$	−13.7801	+	9.62737i	−0.458574	+	0.320379i
$904$	15.3868	−	8.88358i	0.511758	−	0.295463i
$905$	85.6999	−	49.4788i	2.84876	−	1.64473i
$906$	−6.48730			−0.215526
$907$	−0.887026	−	1.53637i	−0.0294532	−	0.0510144i	0.850923	−	0.525290i	$-0.176043\pi$
$907$	−0.887026	−	1.53637i	−0.0294532	−	0.0510144i	−0.880376	+	0.474276i	$0.842710\pi$
$908$			17.6759i			0.586596i
$909$	11.6026			0.384834
$910$	40.1591	−	11.9599i	1.33126	−	0.396467i
$911$	−4.41204			−0.146177			−0.0730887	−	0.997325i	$-0.523286\pi$
$911$	−4.41204			−0.146177			−0.0730887	+	0.997325i	$0.523286\pi$
$912$		−	0.602893i		−	0.0199638i
$913$	−3.87710	−	6.71534i	−0.128313	−	0.222245i
$914$	−1.56945			−0.0519128
$915$	6.18253	−	3.56948i	0.204388	−	0.118004i
$916$	18.7520	−	10.8265i	0.619583	−	0.357717i
$917$	−3.15451	−	36.4983i	−0.104171	−	1.20528i
$918$		−	5.67660i		−	0.187356i
$919$	10.3701	−	17.9615i	0.342078	−	0.592496i	−0.642740	−	0.766084i	$-0.722203\pi$
$919$	10.3701	−	17.9615i	0.342078	−	0.592496i	0.984818	+	0.173588i	$0.0555360\pi$
$920$	−10.2208	−	17.7030i	−0.336971	−	0.583651i
$921$	4.04989	−	2.33820i	0.133448	−	0.0770465i
$922$	−7.37561	−	12.7749i	−0.242903	−	0.420720i
$923$	−30.8898	−	34.7378i	−1.01675	−	1.14341i
$924$	1.48698	+	2.12838i	0.0489179	+	0.0700186i
$925$	1.78347	+	1.02969i	0.0586401	+	0.0338559i
$926$	33.6875			1.10704
$927$	8.16563			0.268194
$928$	−2.75226	−	1.58902i	−0.0903475	−	0.0521622i
$929$	−10.7762	−	6.22163i	−0.353555	−	0.204125i	0.312695	−	0.949854i	$-0.398768\pi$
$929$	−10.7762	−	6.22163i	−0.353555	−	0.204125i	−0.666250	+	0.745729i	$0.732102\pi$
$930$	−23.0003	+	13.2793i	−0.754211	+	0.435444i
$931$	−0.724095	−	4.15767i	−0.0237313	−	0.136262i
$932$	−11.8049	−	20.4467i	−0.386682	−	0.669753i
$933$	−0.768934			−0.0251738
$934$	4.44196	−	2.56456i	0.145345	−	0.0839151i
$935$	12.2346	−	21.1910i	0.400116	−	0.693021i
$936$	−1.13543	+	3.42210i	−0.0371128	+	0.111855i
$937$	−11.3834			−0.371879			−0.185939	−	0.982561i	$-0.559533\pi$
$937$	−11.3834			−0.371879			−0.185939	+	0.982561i	$0.559533\pi$
$938$	2.48752	+	28.7810i	0.0812202	+	0.939734i
$939$	−4.77117	+	8.26391i	−0.155701	+	0.269682i
$940$	22.2982	−	38.6216i	0.727287	−	1.25970i
$941$	24.5840	+	14.1936i	0.801415	+	0.462697i	0.843966	−	0.536397i	$-0.180215\pi$
$941$	24.5840	+	14.1936i	0.801415	+	0.462697i	−0.0425509	+	0.999094i	$0.513548\pi$
$942$		−	5.80428i		−	0.189114i
$943$	−38.9719	−	22.5005i	−1.26910	−	0.732716i
$944$			8.81577i			0.286929i
$945$	11.5784	−	1.00071i	0.376646	−	0.0325531i
$946$	3.11750	−	5.39968i	0.101359	−	0.175559i
$947$		−	19.0286i		−	0.618347i	−0.951006	−	0.309174i	$-0.899948\pi$
$947$		−	19.0286i		−	0.618347i	0.951006	−	0.309174i	$-0.100052\pi$
$948$	−6.75613	+	11.7020i	−0.219429	+	0.380062i
$949$	6.26586	−	18.8848i	0.203398	−	0.613025i
$950$	−4.30902	−	7.46343i	−0.139803	−	0.242146i
$951$	−0.258436	−	0.149208i	−0.00838036	−	0.00483840i
$952$	−6.36157	+	13.6050i	−0.206180	+	0.440942i
$953$	0.195153	+	0.338014i	0.00632162	+	0.0109494i	0.869169	−	0.494515i	$-0.164654\pi$
$953$	0.195153	+	0.338014i	0.00632162	+	0.0109494i	−0.862847	+	0.505465i	$0.831321\pi$
$954$	−4.75697	+	2.74644i	−0.154013	+	0.0889192i
$955$		−	7.51638i		−	0.243224i
$956$		−	8.99248i		−	0.290838i
$957$	−2.70089	+	1.55936i	−0.0873073	+	0.0504069i
$958$	5.32484	+	9.22289i	0.172038	+	0.297978i
$959$	5.88181	−	12.5790i	0.189933	−	0.406198i
$960$	−3.80406	−	2.19627i	−0.122775	−	0.0708844i
$961$	2.77869	+	4.81282i	0.0896350	+	0.155252i
$962$	−0.104843	−	0.508754i	−0.00338029	−	0.0164029i
$963$	5.93197	−	10.2745i	0.191155	−	0.331090i
$964$			11.7378i			0.378048i
$965$	11.1674	−	19.3426i	0.359493	−	0.622660i
$966$	12.2669	−	1.06021i	0.394680	−	0.0341118i
$967$		−	15.1319i		−	0.486608i	−0.969950	−	0.243304i	$-0.921769\pi$
$967$		−	15.1319i		−	0.486608i	0.969950	−	0.243304i	$-0.0782313\pi$
$968$	8.69228	+	5.01849i	0.279381	+	0.161300i
$969$		−	3.42239i		−	0.109943i
$970$	−0.724818	−	0.418474i	−0.0232725	−	0.0134364i
$971$	22.2571	−	38.5504i	0.714264	−	1.23714i	−0.248979	−	0.968509i	$-0.580095\pi$
$971$	22.2571	−	38.5504i	0.714264	−	1.23714i	0.963243	−	0.268632i	$-0.0865717\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	1.09678	+	12.6900i	0.0351612	+	0.406822i
$974$	−14.9196			−0.478055
$975$	10.4026	+	50.4787i	0.333150	+	1.61661i
$976$	0.812623	−	1.40750i	0.0260114	−	0.0450531i
$977$	44.7625	−	25.8437i	1.43208	−	0.826812i	0.434801	−	0.900527i	$-0.356819\pi$
$977$	44.7625	−	25.8437i	1.43208	−	0.826812i	0.997279	+	0.0737151i	$0.0234856\pi$
$978$	−10.3050			−0.329516
$979$	0.712187	+	1.23354i	0.0227616	+	0.0394242i
$980$	−28.8713	−	10.5771i	−0.922260	−	0.337874i
$981$	−6.66746	+	3.84946i	−0.212876	+	0.122904i
$982$	−24.7022	−	14.2618i	−0.788280	−	0.455113i
$983$	−22.3994	−	12.9323i	−0.714431	−	0.412477i	0.0982685	−	0.995160i	$-0.468670\pi$
$983$	−22.3994	−	12.9323i	−0.714431	−	0.412477i	−0.812700	+	0.582683i	$0.802003\pi$
$984$	−9.66987			−0.308264
$985$	−87.0924			−2.77500
$986$	−15.6235	−	9.02024i	−0.497554	−	0.287263i
$987$	15.3841	+	22.0200i	0.489680	+	0.700903i
$988$	−0.684546	+	2.06316i	−0.0217783	+	0.0656380i
$989$	−14.7840	−	25.6066i	−0.470103	−	0.814242i
$990$	−3.73305	+	2.15528i	−0.118644	+	0.0684992i
$991$	9.85802	+	17.0746i	0.313150	+	0.542392i	0.979043	−	0.203656i	$-0.0652823\pi$
$991$	9.85802	+	17.0746i	0.313150	+	0.542392i	−0.665892	+	0.746048i	$0.731949\pi$
$992$	−3.02313	+	5.23622i	−0.0959846	+	0.166250i
$993$			18.4561i			0.585686i
$994$	2.93723	+	33.9843i	0.0931632	+	1.07792i
$995$	67.6678	−	39.0680i	2.14521	−	1.23854i
$996$	−6.84307	+	3.95085i	−0.216831	+	0.125187i
$997$	5.68358			0.180001			0.0900004	−	0.995942i	$-0.471313\pi$
$997$	5.68358			0.180001			0.0900004	+	0.995942i	$0.471313\pi$
$998$	17.6361	+	30.5466i	0.558261	+	0.966936i
$999$		−	0.144068i		−	0.00455811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.a.277.8	yes	16
3.2	odd	2		1638.2.dt.a.1369.1		16
7.2	even	3		546.2.bd.a.121.5	✓	16
13.10	even	6		546.2.bd.a.361.5	yes	16
21.2	odd	6		1638.2.cr.a.667.4		16
39.23	odd	6		1638.2.cr.a.361.4		16
91.23	even	6	inner	546.2.bm.a.205.4	yes	16
273.23	odd	6		1638.2.dt.a.1297.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.5	✓	16	7.2	even	3
546.2.bd.a.361.5	yes	16	13.10	even	6
546.2.bm.a.205.4	yes	16	91.23	even	6	inner
546.2.bm.a.277.8	yes	16	1.1	even	1	trivial
1638.2.cr.a.361.4		16	39.23	odd	6
1638.2.cr.a.667.4		16	21.2	odd	6
1638.2.dt.a.1297.5		16	273.23	odd	6
1638.2.dt.a.1369.1		16	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(3.80406 - 2.19627i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.39669 - 1.12066i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.19627 + 3.80406i) q^{10} +(0.849860 - 0.490667i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.727736 + 3.53135i) q^{13} +(1.12066 - 2.39669i) q^{14} +(3.80406 + 2.19627i) q^{15} +1.00000 q^{16} +5.67660 q^{17} +(-0.866025 - 0.500000i) q^{18} +(-0.522121 - 0.301447i) q^{19} +(-3.80406 + 2.19627i) q^{20} +(-0.227820 - 2.63592i) q^{21} +(0.490667 + 0.849860i) q^{22} +4.65372 q^{23} +(0.866025 - 0.500000i) q^{24} +(7.14723 - 12.3794i) q^{25} +(-3.53135 + 0.727736i) q^{26} -1.00000 q^{27} +(2.39669 + 1.12066i) q^{28} +(-1.58902 + 2.75226i) q^{29} +(-2.19627 + 3.80406i) q^{30} +(5.23622 + 3.02313i) q^{31} +1.00000i q^{32} +(0.849860 + 0.490667i) q^{33} +5.67660i q^{34} +(-11.5784 + 1.00071i) q^{35} +(0.500000 - 0.866025i) q^{36} +0.144068i q^{37} +(0.301447 - 0.522121i) q^{38} +(-2.69437 + 2.39591i) q^{39} +(-2.19627 - 3.80406i) q^{40} +(-8.37436 - 4.83494i) q^{41} +(2.63592 - 0.227820i) q^{42} +(-3.17681 - 5.50239i) q^{43} +(-0.849860 + 0.490667i) q^{44} +4.39255i q^{45} +4.65372i q^{46} +(-8.79254 + 5.07637i) q^{47} +(0.500000 + 0.866025i) q^{48} +(4.48822 + 5.37176i) q^{49} +(12.3794 + 7.14723i) q^{50} +(2.83830 + 4.91608i) q^{51} +(-0.727736 - 3.53135i) q^{52} +(2.74644 - 4.75697i) q^{53} -1.00000i q^{54} +(2.15528 - 3.73305i) q^{55} +(-1.12066 + 2.39669i) q^{56} -0.602893i q^{57} +(-2.75226 - 1.58902i) q^{58} +8.81577i q^{59} +(-3.80406 - 2.19627i) q^{60} +(0.812623 - 1.40750i) q^{61} +(-3.02313 + 5.23622i) q^{62} +(2.16887 - 1.51526i) q^{63} -1.00000 q^{64} +(10.5241 + 11.8351i) q^{65} +(-0.490667 + 0.849860i) q^{66} +(-9.45592 + 5.45938i) q^{67} -5.67660 q^{68} +(2.32686 + 4.03024i) q^{69} +(-1.00071 - 11.5784i) q^{70} +(-11.1654 + 6.44637i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-4.77913 - 2.75923i) q^{73} -0.144068 q^{74} +14.2945 q^{75} +(0.522121 + 0.301447i) q^{76} +(-2.58672 + 0.223568i) q^{77} +(-2.39591 - 2.69437i) q^{78} +(-6.75613 - 11.7020i) q^{79} +(3.80406 - 2.19627i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.83494 - 8.37436i) q^{82} -7.90170i q^{83} +(0.227820 + 2.63592i) q^{84} +(21.5941 - 12.4674i) q^{85} +(5.50239 - 3.17681i) q^{86} -3.17804 q^{87} +(-0.490667 - 0.849860i) q^{88} +1.45147i q^{89} -4.39255 q^{90} +(2.21330 - 9.27908i) q^{91} -4.65372 q^{92} +6.04627i q^{93} +(-5.07637 - 8.79254i) q^{94} -2.64824 q^{95} +(-0.866025 + 0.500000i) q^{96} +(-0.165011 + 0.0952691i) q^{97} +(-5.37176 + 4.48822i) q^{98} +0.981333i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29}+ \cdots - 60 q^{98}+O(q^{100}) \) 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

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