LMFDB - Embedded newform 847.2.f.t.372.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [847,2,Mod(148,847)] 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("847.148"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(847, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-2,1,-8,-1,-12,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 $ x^12 - x^11 + 7x^10 - 15x^9 + 59x^8 + 118x^7 + 266x^6 + 324x^5 + 1036x^4 + 376x^3 + 136x^2 + 48x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.3
Root			$-1.42513 - 1.03542i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.t.148.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.853368 - 2.62640i) q^{2} +(-1.42513 + 1.03542i) q^{3} +(-4.55169 - 3.30700i) q^{4} +(-0.811540 - 2.49766i) q^{5} +(1.50326 + 4.62655i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-8.10146 + 5.88605i) q^{8} +(0.0318546 - 0.0980384i) q^{9} -7.25240 q^{10} +9.91087 q^{12} +(-0.737857 + 2.27089i) q^{13} +(-2.23415 + 1.62320i) q^{14} +(3.74267 + 2.71921i) q^{15} +(5.06841 + 15.5990i) q^{16} +(-0.737857 - 2.27089i) q^{17} +(-0.230304 - 0.167326i) q^{18} +(1.39902 - 1.01645i) q^{19} +(-4.56588 + 14.0523i) q^{20} +1.76156 q^{21} -0.626198 q^{23} +(5.45111 - 16.7768i) q^{24} +(-1.53464 + 1.11498i) q^{25} +(5.33460 + 3.87581i) q^{26} +(-1.57694 - 4.85332i) q^{27} +(1.73859 + 5.35083i) q^{28} +(-1.39902 - 1.01645i) q^{29} +(10.3356 - 7.50926i) q^{30} +(-0.691717 + 2.12889i) q^{31} +25.2663 q^{32} -6.59392 q^{34} +(-0.811540 + 2.49766i) q^{35} +(-0.469205 + 0.340897i) q^{36} +(5.57972 + 4.05391i) q^{37} +(-1.47571 - 4.54178i) q^{38} +(-1.29978 - 4.00030i) q^{39} +(21.2760 + 15.4579i) q^{40} +(-8.40387 + 6.10577i) q^{41} +(1.50326 - 4.62655i) q^{42} +7.25240 q^{43} -0.270718 q^{45} +(-0.534377 + 1.64464i) q^{46} +(-5.16780 + 3.75463i) q^{47} +(-23.3746 - 16.9826i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.61877 + 4.98206i) q^{50} +(3.40286 + 2.47232i) q^{51} +(10.8683 - 7.89630i) q^{52} +(-2.85915 + 8.79955i) q^{53} -14.0925 q^{54} +10.0140 q^{56} +(-0.941336 + 2.89714i) q^{57} +(-3.86347 + 2.80697i) q^{58} +(1.42513 + 1.03542i) q^{59} +(-8.04307 - 24.7540i) q^{60} +(-3.20999 - 9.87934i) q^{61} +(5.00101 + 3.63345i) q^{62} +(-0.0833965 + 0.0605911i) q^{63} +(11.4247 - 35.1616i) q^{64} +6.27072 q^{65} -6.42003 q^{67} +(-4.15133 + 12.7765i) q^{68} +(0.892413 - 0.648376i) q^{69} +(5.86731 + 4.26285i) q^{70} +(2.49833 + 7.68907i) q^{71} +(0.318991 + 0.981752i) q^{72} +(-8.40387 - 6.10577i) q^{73} +(15.4087 - 11.1951i) q^{74} +(1.03259 - 3.17798i) q^{75} -9.72928 q^{76} -11.6156 q^{78} +(4.71325 - 14.5059i) q^{79} +(34.8477 - 25.3183i) q^{80} +(7.52275 + 5.46559i) q^{81} +(8.86458 + 27.2824i) q^{82} +(3.94785 + 12.1502i) q^{83} +(-8.01806 - 5.82546i) q^{84} +(-5.07312 + 3.68584i) q^{85} +(6.18896 - 19.0477i) q^{86} +3.04623 q^{87} -14.1493 q^{89} +(-0.231022 + 0.711014i) q^{90} +(1.93173 - 1.40349i) q^{91} +(2.85026 + 2.07083i) q^{92} +(-1.21850 - 3.75015i) q^{93} +(5.45111 + 16.7768i) q^{94} +(-3.67410 - 2.66939i) q^{95} +(-36.0078 + 26.1612i) q^{96} +(-2.58199 + 7.94653i) q^{97} +2.76156 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + q^{3} - 8 q^{4} - q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} - 4 q^{9} - 16 q^{10} + 8 q^{12} - 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} - 8 q^{17} + 18 q^{18} + 14 q^{20} - 4 q^{21} + 28 q^{23}+ \cdots + 8 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + q^3 - 8 * q^4 - q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 - 4 * q^9 - 16 * q^10 + 8 * q^12 - 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 - 8 * q^17 + 18 * q^18 + 14 * q^20 - 4 * q^21 + 28 * q^23 - 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 - 8 * q^28 + 8 * q^30 + 13 * q^31 + 136 * q^32 - 48 * q^34 - q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 + 20 * q^39 + 36 * q^40 - 16 * q^41 - 12 * q^42 + 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 - 22 * q^50 + 20 * q^51 + 10 * q^53 + 32 * q^54 + 24 * q^56 - 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 + 16 * q^61 - 4 * q^62 - 4 * q^63 - 34 * q^64 + 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 - 2 * q^72 - 16 * q^73 + 32 * q^74 - 20 * q^75 - 96 * q^76 + 112 * q^78 - 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 84 * q^89 + 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 - 20 * q^94 - 24 * q^95 - 20 * q^96 + 11 * q^97 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.853368	−	2.62640i	0.603422	−	1.85714i	0.0961306	−	0.995369i	$-0.469353\pi$
$2$	0.853368	−	2.62640i	0.603422	−	1.85714i	0.507292	−	0.861774i	$-0.330647\pi$
$3$	−1.42513	+	1.03542i	−0.822799	+	0.597798i	−0.917513	−	0.397706i	$-0.869806\pi$
$3$	−1.42513	+	1.03542i	−0.822799	+	0.597798i	0.0947139	+	0.995505i	$0.469806\pi$
$4$	−4.55169	−	3.30700i	−2.27584	−	1.65350i
$5$	−0.811540	−	2.49766i	−0.362932	−	1.11699i	−0.951266	−	0.308371i	$-0.900216\pi$
$5$	−0.811540	−	2.49766i	−0.362932	−	1.11699i	0.588334	−	0.808618i	$-0.299784\pi$
$6$	1.50326	+	4.62655i	0.613702	+	1.88878i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−8.10146	+	5.88605i	−2.86430	+	2.08103i
$9$	0.0318546	−	0.0980384i	0.0106182	−	0.0326795i
$10$	−7.25240			−2.29341
$11$		0			0
$11$		0			0
$12$	9.91087			2.86102
$13$	−0.737857	+	2.27089i	−0.204645	+	0.629832i	0.795083	+	0.606501i	$0.207427\pi$
$13$	−0.737857	+	2.27089i	−0.204645	+	0.629832i	−0.999728	+	0.0233311i	$0.992573\pi$
$14$	−2.23415	+	1.62320i	−0.597101	+	0.433819i
$15$	3.74267	+	2.71921i	0.966354	+	0.702097i
$16$	5.06841	+	15.5990i	1.26710	+	3.89974i
$17$	−0.737857	−	2.27089i	−0.178957	−	0.550772i	0.820835	−	0.571165i	$-0.193508\pi$
$17$	−0.737857	−	2.27089i	−0.178957	−	0.550772i	−0.999792	+	0.0203930i	$0.993508\pi$
$18$	−0.230304	−	0.167326i	−0.0542832	−	0.0394391i
$19$	1.39902	−	1.01645i	0.320957	−	0.233189i	−0.415627	−	0.909535i	$-0.636438\pi$
$19$	1.39902	−	1.01645i	0.320957	−	0.233189i	0.736584	+	0.676346i	$0.236438\pi$
$20$	−4.56588	+	14.0523i	−1.02096	+	3.14220i
$21$	1.76156			0.384403
$22$		0			0
$23$	−0.626198			−0.130571			−0.0652857	−	0.997867i	$-0.520796\pi$
$23$	−0.626198			−0.130571			−0.0652857	+	0.997867i	$0.520796\pi$
$24$	5.45111	−	16.7768i	1.11270	−	3.42455i
$25$	−1.53464	+	1.11498i	−0.306928	+	0.222996i
$26$	5.33460	+	3.87581i	1.04620	+	0.760109i
$27$	−1.57694	−	4.85332i	−0.303482	−	0.934022i
$28$	1.73859	+	5.35083i	0.328563	+	1.01121i
$29$	−1.39902	−	1.01645i	−0.259791	−	0.188749i	0.450264	−	0.892896i	$-0.351330\pi$
$29$	−1.39902	−	1.01645i	−0.259791	−	0.188749i	−0.710055	+	0.704146i	$0.751330\pi$
$30$	10.3356	−	7.50926i	1.88701	−	1.37100i
$31$	−0.691717	+	2.12889i	−0.124236	+	0.382359i	−0.993761	−	0.111530i	$-0.964425\pi$
$31$	−0.691717	+	2.12889i	−0.124236	+	0.382359i	0.869525	+	0.493889i	$0.164425\pi$
$32$	25.2663			4.46650
$33$		0			0
$34$	−6.59392			−1.13085
$35$	−0.811540	+	2.49766i	−0.137175	+	0.422182i
$36$	−0.469205	+	0.340897i	−0.0782008	+	0.0568162i
$37$	5.57972	+	4.05391i	0.917301	+	0.666458i	0.942851	−	0.333216i	$-0.108134\pi$
$37$	5.57972	+	4.05391i	0.917301	+	0.666458i	−0.0255499	+	0.999674i	$0.508134\pi$
$38$	−1.47571	−	4.54178i	−0.239392	−	0.736774i
$39$	−1.29978	−	4.00030i	−0.208131	−	0.640561i
$40$	21.2760	+	15.4579i	3.36404	+	2.44412i
$41$	−8.40387	+	6.10577i	−1.31246	+	0.953561i	−0.312471	+	0.949927i	$0.601157\pi$
$41$	−8.40387	+	6.10577i	−1.31246	+	0.953561i	−0.999993	+	0.00363356i	$0.998843\pi$
$42$	1.50326	−	4.62655i	0.231958	−	0.713892i
$43$	7.25240			1.10598			0.552990	−	0.833188i	$-0.313487\pi$
$43$	7.25240			1.10598			0.552990	+	0.833188i	$0.313487\pi$
$44$		0			0
$45$	−0.270718			−0.0403563
$46$	−0.534377	+	1.64464i	−0.0787897	+	0.242490i
$47$	−5.16780	+	3.75463i	−0.753801	+	0.547669i	−0.897003	−	0.442025i	$-0.854260\pi$
$47$	−5.16780	+	3.75463i	−0.753801	+	0.547669i	0.143201	+	0.989694i	$0.454260\pi$
$48$	−23.3746	−	16.9826i	−3.37383	−	2.45123i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	1.61877	+	4.98206i	0.228928	+	0.704569i
$51$	3.40286	+	2.47232i	0.476496	+	0.346194i
$52$	10.8683	−	7.89630i	1.50716	−	1.09502i
$53$	−2.85915	+	8.79955i	−0.392734	+	1.20871i	0.537978	+	0.842959i	$0.319188\pi$
$53$	−2.85915	+	8.79955i	−0.392734	+	1.20871i	−0.930712	+	0.365753i	$0.880812\pi$
$54$	−14.0925			−1.91774
$55$		0			0
$56$	10.0140			1.33817
$57$	−0.941336	+	2.89714i	−0.124683	+	0.383735i
$58$	−3.86347	+	2.80697i	−0.507298	+	0.368574i
$59$	1.42513	+	1.03542i	0.185536	+	0.134800i	0.676676	−	0.736281i	$-0.263420\pi$
$59$	1.42513	+	1.03542i	0.185536	+	0.134800i	−0.491140	+	0.871081i	$0.663420\pi$
$60$	−8.04307	−	24.7540i	−1.03836	−	3.19573i
$61$	−3.20999	−	9.87934i	−0.410997	−	1.26492i	−0.915782	−	0.401675i	$-0.868428\pi$
$61$	−3.20999	−	9.87934i	−0.410997	−	1.26492i	0.504785	−	0.863245i	$-0.331572\pi$
$62$	5.00101	+	3.63345i	0.635129	+	0.461448i
$63$	−0.0833965	+	0.0605911i	−0.0105070	+	0.00763376i
$64$	11.4247	−	35.1616i	1.42809	−	4.39519i
$65$	6.27072			0.777787
$66$		0			0
$67$	−6.42003			−0.784332			−0.392166	−	0.919895i	$-0.628274\pi$
$67$	−6.42003			−0.784332			−0.392166	+	0.919895i	$0.628274\pi$
$68$	−4.15133	+	12.7765i	−0.503423	+	1.54938i
$69$	0.892413	−	0.648376i	0.107434	−	0.0780553i
$70$	5.86731	+	4.26285i	0.701278	+	0.509508i
$71$	2.49833	+	7.68907i	0.296497	+	0.912524i	0.982714	+	0.185128i	$0.0592699\pi$
$71$	2.49833	+	7.68907i	0.296497	+	0.912524i	−0.686217	+	0.727396i	$0.740730\pi$
$72$	0.318991	+	0.981752i	0.0375934	+	0.115701i
$73$	−8.40387	−	6.10577i	−0.983599	−	0.714626i	−0.0250887	−	0.999685i	$-0.507987\pi$
$73$	−8.40387	−	6.10577i	−0.983599	−	0.714626i	−0.958510	+	0.285059i	$0.907987\pi$
$74$	15.4087	−	11.1951i	1.79123	−	1.30140i
$75$	1.03259	−	3.17798i	0.119233	−	0.366962i
$76$	−9.72928			−1.11603
$77$		0			0
$78$	−11.6156			−1.31520
$79$	4.71325	−	14.5059i	0.530282	−	1.63204i	−0.223346	−	0.974739i	$-0.571698\pi$
$79$	4.71325	−	14.5059i	0.530282	−	1.63204i	0.753628	−	0.657301i	$-0.228302\pi$
$80$	34.8477	−	25.3183i	3.89609	−	2.83068i
$81$	7.52275	+	5.46559i	0.835861	+	0.607288i
$82$	8.86458	+	27.2824i	0.978929	+	3.01283i
$83$	3.94785	+	12.1502i	0.433333	+	1.33366i	0.894785	+	0.446496i	$0.147328\pi$
$83$	3.94785	+	12.1502i	0.433333	+	1.33366i	−0.461453	+	0.887165i	$0.652672\pi$
$84$	−8.01806	−	5.82546i	−0.874842	−	0.635610i
$85$	−5.07312	+	3.68584i	−0.550257	+	0.399785i
$86$	6.18896	−	19.0477i	0.667373	−	2.05396i
$87$	3.04623			0.326590
$88$		0			0
$89$	−14.1493			−1.49982			−0.749912	−	0.661538i	$-0.769904\pi$
$89$	−14.1493			−1.49982			−0.749912	+	0.661538i	$0.769904\pi$
$90$	−0.231022	+	0.711014i	−0.0243519	+	0.0749474i
$91$	1.93173	−	1.40349i	0.202501	−	0.147125i
$92$	2.85026	+	2.07083i	0.297160	+	0.215899i
$93$	−1.21850	−	3.75015i	−0.126352	−	0.388873i
$94$	5.45111	+	16.7768i	0.562239	+	1.73039i
$95$	−3.67410	−	2.66939i	−0.376955	−	0.273874i
$96$	−36.0078	+	26.1612i	−3.67503	+	2.67007i
$97$	−2.58199	+	7.94653i	−0.262161	+	0.806848i	0.730173	+	0.683262i	$0.239439\pi$
$97$	−2.58199	+	7.94653i	−0.262161	+	0.806848i	−0.992334	+	0.123586i	$0.960561\pi$
$98$	2.76156			0.278959
$99$		0			0
$100$	10.6724			1.06724
$101$	−4.27875	+	13.1686i	−0.425751	+	1.31033i	0.476522	+	0.879163i	$0.341897\pi$
$101$	−4.27875	+	13.1686i	−0.425751	+	1.31033i	−0.902273	+	0.431165i	$0.858103\pi$
$102$	9.39720	−	6.82746i	0.930461	−	0.676019i
$103$	2.36977	+	1.72174i	0.233500	+	0.169648i	0.698383	−	0.715725i	$-0.253903\pi$
$103$	2.36977	+	1.72174i	0.233500	+	0.169648i	−0.464883	+	0.885372i	$0.653903\pi$
$104$	−7.38887	−	22.7406i	−0.724538	−	2.22990i
$105$	−1.42957	−	4.39978i	−0.139512	−	0.429374i
$106$	20.6712	+	15.0185i	2.00777	+	1.45873i
$107$	−2.79804	+	2.03289i	−0.270496	+	0.196527i	−0.714762	−	0.699368i	$-0.753465\pi$
$107$	−2.79804	+	2.03289i	−0.270496	+	0.196527i	0.444265	+	0.895895i	$0.353465\pi$
$108$	−8.87217	+	27.3057i	−0.853725	+	2.62750i
$109$	−16.2341			−1.55494			−0.777471	−	0.628919i	$-0.783498\pi$
$109$	−16.2341			−1.55494			−0.777471	+	0.628919i	$0.783498\pi$
$110$		0			0
$111$	−12.1493			−1.15316
$112$	5.06841	−	15.5990i	0.478919	−	1.47396i
$113$	−5.74652	+	4.17509i	−0.540587	+	0.392759i	−0.824303	−	0.566149i	$-0.808433\pi$
$113$	−5.74652	+	4.17509i	−0.540587	+	0.392759i	0.283716	+	0.958908i	$0.408433\pi$
$114$	6.80572	+	4.94465i	0.637414	+	0.463109i
$115$	0.508185	+	1.56403i	0.0473885	+	0.145847i
$116$	3.00651	+	9.25310i	0.279148	+	0.859128i
$117$	0.199130	+	0.144677i	0.0184096	+	0.0133754i
$118$	3.93558	−	2.85936i	0.362299	−	0.263226i
$119$	−0.737857	+	2.27089i	−0.0676392	+	0.208172i
$120$	−46.3265			−4.22901
$121$		0			0
$122$	−28.6864			−2.59714
$123$	5.65459	−	17.4030i	0.509857	−	1.56918i
$124$	10.1887	−	7.40252i	0.914972	−	0.664766i
$125$	−6.59293	−	4.79005i	−0.589690	−	0.428435i
$126$	0.0879683	+	0.270739i	0.00783684	+	0.0241193i
$127$	−1.40338	−	4.31916i	−0.124530	−	0.383264i	0.869285	−	0.494311i	$-0.164580\pi$
$127$	−1.40338	−	4.31916i	−0.124530	−	0.383264i	−0.993815	+	0.111047i	$0.964580\pi$
$128$	−41.7169	−	30.3091i	−3.68729	−	2.67897i
$129$	−10.3356	+	7.50926i	−0.909999	+	0.661153i
$130$	5.35123	−	16.4694i	0.469334	−	1.44446i
$131$	−6.27072			−0.547875			−0.273938	−	0.961747i	$-0.588326\pi$
$131$	−6.27072			−0.547875			−0.273938	+	0.961747i	$0.588326\pi$
$132$		0			0
$133$	−1.72928			−0.149948
$134$	−5.47865	+	16.8615i	−0.473283	+	1.45662i
$135$	−10.8422	+	7.87733i	−0.933149	+	0.677972i
$136$	19.3443	+	14.0545i	1.65876	+	1.20516i
$137$	2.90529	+	8.94156i	0.248215	+	0.763929i	0.995091	+	0.0989648i	$0.0315531\pi$
$137$	2.90529	+	8.94156i	0.248215	+	0.763929i	−0.746875	+	0.664964i	$0.768447\pi$
$138$	−0.941336	−	2.89714i	−0.0801319	−	0.246621i
$139$	−12.8001	−	9.29978i	−1.08569	−	0.788797i	−0.107021	−	0.994257i	$-0.534131\pi$
$139$	−12.8001	−	9.29978i	−1.08569	−	0.788797i	−0.978666	+	0.205459i	$0.934131\pi$
$140$	11.9536	−	8.68483i	1.01027	−	0.734002i
$141$	3.47718	−	10.7017i	0.292832	−	0.901243i
$142$	22.3265			1.87360
$143$		0			0
$144$	1.69075			0.140896
$145$	−1.40338	+	4.31916i	−0.116544	+	0.358687i
$146$	−23.2078	+	16.8614i	−1.92069	+	1.39546i
$147$	−1.42513	−	1.03542i	−0.117543	−	0.0853998i
$148$	−11.9909	−	36.9042i	−0.985647	−	3.03351i
$149$	1.06875	+	3.28929i	0.0875558	+	0.269469i	0.985242	−	0.171166i	$-0.0547534\pi$
$149$	1.06875	+	3.28929i	0.0875558	+	0.269469i	−0.897686	+	0.440635i	$0.854753\pi$
$150$	−7.46546	−	5.42397i	−0.609552	−	0.442866i
$151$	8.33176	−	6.05338i	0.678029	−	0.492617i	−0.194674	−	0.980868i	$-0.562365\pi$
$151$	8.33176	−	6.05338i	0.678029	−	0.492617i	0.872703	+	0.488251i	$0.162365\pi$
$152$	−5.35123	+	16.4694i	−0.434042	+	1.33584i
$153$	−0.246139			−0.0198991
$154$		0			0
$155$	5.87859			0.472180
$156$	−7.31280	+	22.5065i	−0.585493	+	1.80196i
$157$	−9.17195	+	6.66381i	−0.732002	+	0.531830i	−0.890196	−	0.455578i	$-0.849433\pi$
$157$	−9.17195	+	6.66381i	−0.732002	+	0.531830i	0.158194	+	0.987408i	$0.449433\pi$
$158$	−34.0761	−	24.7577i	−2.71095	−	1.96962i
$159$	−5.03655	−	15.5009i	−0.399425	−	1.22930i
$160$	−20.5046	−	63.1068i	−1.62103	−	4.98903i
$161$	0.506605	+	0.368070i	0.0399261	+	0.0290080i
$162$	20.7745	−	15.0936i	1.63220	−	1.18586i
$163$	−3.00651	+	9.25310i	−0.235488	+	0.724758i	0.761568	+	0.648085i	$0.224430\pi$
$163$	−3.00651	+	9.25310i	−0.235488	+	0.724758i	−0.997056	+	0.0766734i	$0.975570\pi$
$164$	58.4436			4.56368
$165$		0			0
$166$	35.2803			2.73828
$167$	6.95436	−	21.4033i	0.538145	−	1.65624i	−0.198609	−	0.980079i	$-0.563643\pi$
$167$	6.95436	−	21.4033i	0.538145	−	1.65624i	0.736754	−	0.676161i	$-0.236357\pi$
$168$	−14.2712	+	10.3686i	−1.10105	+	0.799956i
$169$	5.90471	+	4.29002i	0.454209	+	0.330002i
$170$	5.35123	+	16.4694i	0.410421	+	1.26314i
$171$	−0.0550856	−	0.169536i	−0.00421250	−	0.0129647i
$172$	−33.0107	−	23.9836i	−2.51704	−	1.82874i
$173$	−5.60583	+	4.07288i	−0.426204	+	0.309655i	−0.780129	−	0.625619i	$-0.784847\pi$
$173$	−5.60583	+	4.07288i	−0.426204	+	0.309655i	0.353925	+	0.935274i	$0.384847\pi$
$174$	2.59955	−	8.00061i	0.197072	−	0.606524i
$175$	1.89692			0.143393
$176$		0			0
$177$	−3.10308			−0.233242
$178$	−12.0746	+	37.1617i	−0.905027	+	2.78539i
$179$	−11.2802	+	8.19558i	−0.843125	+	0.612566i	−0.923242	−	0.384219i	$-0.874471\pi$
$179$	−11.2802	+	8.19558i	−0.843125	+	0.612566i	0.0801170	+	0.996785i	$0.474471\pi$
$180$	1.23223	+	0.895264i	0.0918447	+	0.0667291i
$181$	0.978853	+	3.01260i	0.0727576	+	0.223925i	0.980822	−	0.194906i	$-0.0624401\pi$
$181$	0.978853	+	3.01260i	0.0727576	+	0.223925i	−0.908064	+	0.418831i	$0.862440\pi$
$182$	−2.03763	−	6.27119i	−0.151039	−	0.464852i
$183$	14.8039	+	10.7557i	1.09434	+	0.795081i
$184$	5.07312	−	3.68584i	0.373995	−	0.271723i
$185$	5.59712	−	17.2262i	0.411509	−	1.26649i
$186$	−10.8892			−0.798436
$187$		0			0
$188$	35.9388			2.62110
$189$	−1.57694	+	4.85332i	−0.114705	+	0.353027i
$190$	−10.1462	+	7.37167i	−0.736085	+	0.534797i
$191$	−14.8499	−	10.7891i	−1.07450	−	0.780670i	−0.0977849	−	0.995208i	$-0.531176\pi$
$191$	−14.8499	−	10.7891i	−1.07450	−	0.780670i	−0.976716	+	0.214537i	$0.931176\pi$
$192$	20.1252	+	61.9391i	1.45241	+	4.47007i
$193$	−0.941336	−	2.89714i	−0.0677589	−	0.208540i	0.911444	−	0.411424i	$-0.134969\pi$
$193$	−0.941336	−	2.89714i	−0.0677589	−	0.208540i	−0.979203	+	0.202884i	$0.934969\pi$
$194$	18.6674	+	13.5626i	1.34024	+	0.973741i
$195$	−8.93659	+	6.49281i	−0.639962	+	0.464960i
$196$	1.73859	−	5.35083i	0.124185	−	0.382202i
$197$	4.95377			0.352942			0.176471	−	0.984306i	$-0.443532\pi$
$197$	4.95377			0.352942			0.176471	+	0.984306i	$0.443532\pi$
$198$		0			0
$199$	15.7047			1.11328			0.556638	−	0.830755i	$-0.312091\pi$
$199$	15.7047			1.11328			0.556638	+	0.830755i	$0.312091\pi$
$200$	5.86997	−	18.0659i	0.415070	−	1.27745i
$201$	9.14938	−	6.64741i	0.645347	−	0.468872i
$202$	30.9347	+	22.4754i	2.17656	+	1.58136i
$203$	0.534377	+	1.64464i	0.0375059	+	0.115431i
$204$	−7.31280	−	22.5065i	−0.511999	−	1.57577i
$205$	22.0702	+	16.0350i	1.54145	+	1.11993i
$206$	6.54424	−	4.75467i	0.455959	−	0.331274i
$207$	−0.0199473	+	0.0613915i	−0.00138643	+	0.00426700i
$208$	−39.1633			−2.71548
$209$		0			0
$210$	−12.7755			−0.881594
$211$	5.42356	−	16.6920i	0.373374	−	1.14913i	−0.571196	−	0.820814i	$-0.693520\pi$
$211$	5.42356	−	16.6920i	0.373374	−	1.14913i	0.944569	−	0.328312i	$-0.106480\pi$
$212$	42.1140	−	30.5976i	2.89240	−	2.10145i
$213$	−11.5218	−	8.37110i	−0.789463	−	0.573578i
$214$	2.95143	+	9.08356i	0.201755	+	0.620939i
$215$	−5.88561	−	18.1140i	−0.401395	−	1.23537i
$216$	41.3424	+	30.0370i	2.81300	+	2.04376i
$217$	1.81094	−	1.31572i	0.122935	−	0.0893171i
$218$	−13.8536	+	42.6371i	−0.938287	+	2.88775i
$219$	18.2986			1.23651
$220$		0			0
$221$	5.70138			0.383516
$222$	−10.3678	+	31.9089i	−0.695844	+	2.14159i
$223$	18.0364	−	13.1042i	1.20781	−	0.877524i	0.212779	−	0.977100i	$-0.431749\pi$
$223$	18.0364	−	13.1042i	1.20781	−	0.877524i	0.995030	+	0.0995759i	$0.0317486\pi$
$224$	−20.4409	−	14.8512i	−1.36577	−	0.992287i
$225$	0.0604255	+	0.185971i	0.00402837	+	0.0123980i
$226$	6.06155	+	18.6555i	0.403208	+	1.24095i
$227$	−11.5453	−	8.38812i	−0.766285	−	0.556739i	0.134546	−	0.990907i	$-0.457042\pi$
$227$	−11.5453	−	8.38812i	−0.766285	−	0.556739i	−0.900832	+	0.434168i	$0.857042\pi$
$228$	13.8655	−	10.0739i	0.918264	−	0.667158i
$229$	−1.19855	+	3.68876i	−0.0792025	+	0.243760i	−0.982816	−	0.184589i	$-0.940905\pi$
$229$	−1.19855	+	3.68876i	−0.0792025	+	0.243760i	0.903613	+	0.428349i	$0.140905\pi$
$230$	4.54144			0.299453
$231$		0			0
$232$	17.3169			1.13691
$233$	2.06518	−	6.35596i	0.135294	−	0.416393i	−0.860341	−	0.509718i	$-0.829750\pi$
$233$	2.06518	−	6.35596i	0.135294	−	0.416393i	0.995636	+	0.0933253i	$0.0297497\pi$
$234$	0.549910	−	0.399533i	0.0359487	−	0.0261183i
$235$	13.5717	+	9.86040i	0.885318	+	0.643221i
$236$	−3.06263	−	9.42580i	−0.199360	−	0.613567i
$237$	8.30266	+	25.5530i	0.539316	+	1.65984i
$238$	5.33460	+	3.87581i	0.345790	+	0.251231i
$239$	3.67410	−	2.66939i	0.237658	−	0.172668i	−0.462581	−	0.886577i	$-0.653077\pi$
$239$	3.67410	−	2.66939i	0.237658	−	0.172668i	0.700239	+	0.713908i	$0.253077\pi$
$240$	−23.4475	+	72.1638i	−1.51353	+	4.65816i
$241$	−3.70470			−0.238641			−0.119320	−	0.992856i	$-0.538072\pi$
$241$	−3.70470			−0.238641			−0.119320	+	0.992856i	$0.538072\pi$
$242$		0			0
$243$	−1.07081			−0.0686924
$244$	−18.0601	+	55.5831i	−1.15618	+	3.55835i
$245$	2.12464	−	1.54364i	0.135738	−	0.0986196i
$246$	−40.8818	−	29.7024i	−2.60653	−	1.89375i
$247$	1.27596	+	3.92701i	0.0811876	+	0.249870i
$248$	−6.92682	−	21.3186i	−0.439854	−	1.35373i
$249$	−18.2068	−	13.2280i	−1.15381	−	0.838289i
$250$	−18.2068	+	13.2280i	−1.15150	+	0.836611i
$251$	2.62948	−	8.09269i	0.165971	−	0.510806i	−0.833136	−	0.553069i	$-0.813457\pi$
$251$	2.62948	−	8.09269i	0.165971	−	0.510806i	0.999107	+	0.0422626i	$0.0134566\pi$
$252$	0.579969			0.0365346
$253$		0			0
$254$	−12.5414			−0.786920
$255$	3.41347	−	10.5056i	0.213760	−	0.657885i
$256$	−55.3833	+	40.2383i	−3.46146	+	2.51490i
$257$	2.38965	+	1.73618i	0.149062	+	0.108300i	0.659817	−	0.751426i	$-0.270634\pi$
$257$	2.38965	+	1.73618i	0.149062	+	0.108300i	−0.510754	+	0.859727i	$0.670634\pi$
$258$	10.9022	+	33.5536i	0.678742	+	2.08895i
$259$	−2.13126	−	6.55936i	−0.132430	−	0.407579i
$260$	−28.5424	−	20.7372i	−1.77012	−	1.28607i
$261$	−0.144216	+	0.104779i	−0.00892675	+	0.00648566i
$262$	−5.35123	+	16.4694i	−0.330600	+	1.01748i
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$		0			0
$265$	24.2986			1.49265
$266$	−1.47571	+	4.54178i	−0.0904818	+	0.278474i
$267$	20.1646	−	14.6504i	1.23405	−	0.896593i
$268$	29.2220	+	21.2310i	1.78502	+	1.29689i
$269$	−2.09375	−	6.44389i	−0.127658	−	0.392891i	0.866718	−	0.498799i	$-0.166225\pi$
$269$	−2.09375	−	6.44389i	−0.127658	−	0.392891i	−0.994376	+	0.105907i	$0.966225\pi$
$270$	11.4366	+	35.1982i	0.696009	+	2.14209i
$271$	−2.79804	−	2.03289i	−0.169969	−	0.123489i	0.499549	−	0.866286i	$-0.333499\pi$
$271$	−2.79804	−	2.03289i	−0.169969	−	0.123489i	−0.669518	+	0.742796i	$0.733499\pi$
$272$	31.6837	−	23.0196i	1.92111	−	1.39577i
$273$	−1.29978	+	4.00030i	−0.0786661	+	0.242109i
$274$	25.9634			1.56850
$275$		0			0
$276$	−6.20617			−0.373567
$277$	−3.54089	+	10.8977i	−0.212752	+	0.654782i	0.786554	+	0.617521i	$0.211863\pi$
$277$	−3.54089	+	10.8977i	−0.212752	+	0.654782i	−0.999306	+	0.0372604i	$0.988137\pi$
$278$	−35.3481	+	25.6819i	−2.12004	+	1.54030i
$279$	0.186678	+	0.135630i	0.0111761	+	0.00811994i
$280$	−8.12672	−	25.0115i	−0.485665	−	1.49472i
$281$	−6.89928	−	21.2338i	−0.411576	−	1.26670i	−0.915277	−	0.402824i	$-0.868029\pi$
$281$	−6.89928	−	21.2338i	−0.411576	−	1.26670i	0.503701	−	0.863878i	$-0.331971\pi$
$282$	−25.1395	−	18.2649i	−1.49704	−	1.08766i
$283$	10.0020	−	7.26689i	0.594558	−	0.431972i	−0.249385	−	0.968404i	$-0.580228\pi$
$283$	10.0020	−	7.26689i	0.594558	−	0.431972i	0.843943	+	0.536433i	$0.180228\pi$
$284$	14.0561	−	43.2602i	0.834076	−	2.56702i
$285$	8.00000			0.473879
$286$		0			0
$287$	10.3878			0.613170
$288$	0.804850	−	2.47707i	0.0474262	−	0.145963i
$289$	9.14078	−	6.64117i	0.537693	−	0.390657i
$290$	10.1462	+	7.37167i	0.595807	+	0.432879i
$291$	−4.54831	−	13.9983i	−0.266627	−	0.820593i
$292$	18.0601	+	55.5831i	1.05688	+	3.25276i
$293$	−1.74236	−	1.26590i	−0.101790	−	0.0739548i	0.535726	−	0.844392i	$-0.320038\pi$
$293$	−1.74236	−	1.26590i	−0.101790	−	0.0739548i	−0.637516	+	0.770437i	$0.720038\pi$
$294$	−3.93558	+	2.85936i	−0.229528	+	0.166762i
$295$	1.42957	−	4.39978i	0.0832330	−	0.256165i
$296$	−69.0654			−4.01434
$297$		0			0
$298$	9.55102			0.553276
$299$	0.462045	−	1.42203i	0.0267207	−	0.0822379i
$300$	−15.2096	+	11.0504i	−0.878126	+	0.637996i
$301$	−5.86731	−	4.26285i	−0.338186	−	0.245707i
$302$	−8.78852	−	27.0483i	−0.505722	−	1.55645i
$303$	−7.53726	−	23.1973i	−0.433004	−	1.33265i
$304$	22.9463	+	16.6715i	1.31606	+	0.956174i
$305$	−22.0702	+	16.0350i	−1.26374	+	0.918159i
$306$	−0.210047	+	0.646458i	−0.0120076	+	0.0369555i
$307$	−31.8217			−1.81616			−0.908081	−	0.418794i	$-0.862453\pi$
$307$	−31.8217			−1.81616			−0.908081	+	0.418794i	$0.862453\pi$
$308$		0			0
$309$	−5.15994			−0.293539
$310$	5.01660	−	15.4395i	0.284924	−	0.876906i
$311$	8.84190	−	6.42402i	0.501378	−	0.364273i	−0.308165	−	0.951333i	$-0.599715\pi$
$311$	8.84190	−	6.42402i	0.501378	−	0.364273i	0.809543	+	0.587060i	$0.199715\pi$
$312$	34.0761	+	24.7577i	1.92918	+	1.40163i
$313$	2.28725	+	7.03944i	0.129283	+	0.397893i	0.994657	−	0.103234i	$-0.0329190\pi$
$313$	2.28725	+	7.03944i	0.129283	+	0.397893i	−0.865374	+	0.501127i	$0.832919\pi$
$314$	9.67477	+	29.7759i	0.545979	+	1.68035i
$315$	0.219016	+	0.159124i	0.0123401	+	0.00896563i
$316$	−69.4242	+	50.4396i	−3.90542	+	2.83745i
$317$	−2.74930	+	8.46147i	−0.154416	+	0.475244i	−0.998101	−	0.0615946i	$-0.980381\pi$
$317$	−2.74930	+	8.46147i	−0.154416	+	0.475244i	0.843685	+	0.536838i	$0.180381\pi$
$318$	−45.0096			−2.52401
$319$		0			0
$320$	−97.0933			−5.42768
$321$	1.88267	−	5.79427i	0.105081	−	0.323405i
$322$	1.39902	−	1.01645i	0.0779642	−	0.0566443i
$323$	−3.34051	−	2.42703i	−0.185871	−	0.135043i
$324$	−16.1665	−	49.7554i	−0.898139	−	2.76419i
$325$	−1.39965	−	4.30769i	−0.0776388	−	0.238948i
$326$	21.7366	+	15.7926i	1.20388	+	0.874671i
$327$	23.1357	−	16.8090i	1.27940	−	0.929542i
$328$	32.1447	−	98.9313i	1.77490	−	5.46257i
$329$	6.38776			0.352168
$330$		0			0
$331$	8.56165			0.470591			0.235295	−	0.971924i	$-0.424394\pi$
$331$	8.56165			0.470591			0.235295	+	0.971924i	$0.424394\pi$
$332$	22.2114	−	68.3596i	1.21901	−	3.75172i
$333$	0.575178	−	0.417892i	0.0315196	−	0.0229003i
$334$	−50.2790	−	36.5298i	−2.75114	−	1.99882i
$335$	5.21011	+	16.0351i	0.284659	+	0.876090i
$336$	8.92829	+	27.4784i	0.487078	+	1.49907i
$337$	7.87115	+	5.71873i	0.428769	+	0.311519i	0.781157	−	0.624335i	$-0.214630\pi$
$337$	7.87115	+	5.71873i	0.428769	+	0.311519i	−0.352387	+	0.935854i	$0.614630\pi$
$338$	16.3062	−	11.8471i	0.886940	−	0.644400i
$339$	3.86657	−	11.9001i	0.210003	−	0.646324i
$340$	35.2803			1.91334
$341$		0			0
$342$	−0.492277			−0.0266193
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	−58.7550	+	42.6880i	−3.16786	+	2.30158i
$345$	−2.34365	−	1.70276i	−0.126178	−	0.0916738i
$346$	5.91315	+	18.1988i	0.317893	+	0.978374i
$347$	4.58583	+	14.1137i	0.246180	+	0.757665i	0.995440	+	0.0953889i	$0.0304095\pi$
$347$	4.58583	+	14.1137i	0.246180	+	0.757665i	−0.749260	+	0.662276i	$0.769591\pi$
$348$	−13.8655	−	10.0739i	−0.743268	−	0.540016i
$349$	−13.1434	+	9.54924i	−0.703550	+	0.511159i	−0.881087	−	0.472955i	$-0.843187\pi$
$349$	−13.1434	+	9.54924i	−0.703550	+	0.511159i	0.177536	+	0.984114i	$0.443187\pi$
$350$	1.61877	−	4.98206i	0.0865268	−	0.266302i
$351$	12.1849			0.650383
$352$		0			0
$353$	30.8603			1.64253			0.821263	−	0.570549i	$-0.193270\pi$
$353$	30.8603			1.64253			0.821263	+	0.570549i	$0.193270\pi$
$354$	−2.64807	+	8.14993i	−0.140743	+	0.433164i
$355$	17.1772	−	12.4800i	0.911671	−	0.662368i
$356$	64.4033	+	46.7917i	3.41337	+	2.47996i
$357$	−1.29978	−	4.00030i	−0.0687915	−	0.211718i
$358$	11.8986	+	36.6202i	0.628862	+	1.93544i
$359$	9.54141	+	6.93224i	0.503576	+	0.365870i	0.810381	−	0.585903i	$-0.199260\pi$
$359$	9.54141	+	6.93224i	0.503576	+	0.365870i	−0.306805	+	0.951772i	$0.599260\pi$
$360$	2.19321	−	1.59346i	0.115592	−	0.0839828i
$361$	−4.94723	+	15.2260i	−0.260381	+	0.801369i
$362$	8.74760			0.459764
$363$		0			0
$364$	−13.4340			−0.704132
$365$	−8.43008	+	25.9451i	−0.441250	+	1.35803i
$366$	40.8818	−	29.7024i	2.13693	−	1.55257i
$367$	2.87637	+	2.08981i	0.150145	+	0.109087i	0.660322	−	0.750983i	$-0.270420\pi$
$367$	2.87637	+	2.08981i	0.150145	+	0.109087i	−0.510176	+	0.860070i	$0.670420\pi$
$368$	−3.17383	−	9.76803i	−0.165447	−	0.509194i
$369$	0.330898	+	1.01840i	0.0172259	+	0.0530157i
$370$	−40.4664	−	29.4005i	−2.10375	−	1.52846i
$371$	7.48535	−	5.43842i	0.388620	−	0.282349i
$372$	−6.85552	+	21.0991i	−0.355442	+	1.09394i
$373$	22.5048			1.16525			0.582627	−	0.812740i	$-0.302025\pi$
$373$	22.5048			1.16525			0.582627	+	0.812740i	$0.302025\pi$
$374$		0			0
$375$	14.3555			0.741314
$376$	19.7668	−	60.8359i	1.01939	−	3.13737i
$377$	3.34051	−	2.42703i	0.172045	−	0.124998i
$378$	11.4010	+	8.28334i	0.586406	+	0.426049i
$379$	7.24015	+	22.2829i	0.371901	+	1.14460i	0.945545	+	0.325490i	$0.105529\pi$
$379$	7.24015	+	22.2829i	0.371901	+	1.14460i	−0.573644	+	0.819105i	$0.694471\pi$
$380$	7.89570	+	24.3005i	0.405041	+	1.24659i
$381$	6.47214	+	4.70228i	0.331578	+	0.240905i
$382$	−41.0088	+	29.7947i	−2.09819	+	1.52443i
$383$	−1.05878	+	3.25859i	−0.0541012	+	0.166506i	−0.974456	−	0.224578i	$-0.927900\pi$
$383$	−1.05878	+	3.25859i	−0.0541012	+	0.166506i	0.920355	+	0.391084i	$0.127900\pi$
$384$	90.8347			4.63539
$385$		0			0
$386$	−8.41233			−0.428177
$387$	0.231022	−	0.711014i	0.0117435	−	0.0361428i
$388$	38.0316	−	27.6315i	1.93076	−	1.40278i
$389$	−6.51813	−	4.73570i	−0.330482	−	0.240110i	0.410153	−	0.912017i	$-0.365475\pi$
$389$	−6.51813	−	4.73570i	−0.330482	−	0.240110i	−0.740635	+	0.671907i	$0.765475\pi$
$390$	9.42650	+	29.0118i	0.477329	+	1.46907i
$391$	0.462045	+	1.42203i	0.0233666	+	0.0719150i
$392$	−8.10146	−	5.88605i	−0.409185	−	0.297291i
$393$	8.93659	−	6.49281i	0.450791	−	0.327519i
$394$	4.22739	−	13.0106i	0.212973	−	0.655463i
$395$	−40.0558			−2.01543
$396$		0			0
$397$	−26.3632			−1.32313			−0.661565	−	0.749888i	$-0.730107\pi$
$397$	−26.3632			−1.32313			−0.661565	+	0.749888i	$0.730107\pi$
$398$	13.4019	−	41.2468i	0.671776	−	2.06751i
$399$	2.46445	−	1.79053i	0.123377	−	0.0896385i
$400$	−25.1707	−	18.2876i	−1.25853	−	0.914378i
$401$	−6.98293	−	21.4913i	−0.348711	−	1.07322i	−0.959567	−	0.281481i	$-0.909175\pi$
$401$	−6.98293	−	21.4913i	−0.348711	−	1.07322i	0.610856	−	0.791742i	$-0.290825\pi$
$402$	−9.65095	−	29.7026i	−0.481346	−	1.48143i
$403$	−4.32408	−	3.14163i	−0.215398	−	0.156496i
$404$	63.0241	−	45.7897i	3.13557	−	2.27812i
$405$	7.54620	−	23.2248i	0.374974	−	1.15405i
$406$	4.77551			0.237005
$407$		0			0
$408$	−42.1204			−2.08527
$409$	2.87537	−	8.84947i	0.142178	−	0.437578i	−0.854460	−	0.519518i	$-0.826112\pi$
$409$	2.87537	−	8.84947i	0.142178	−	0.437578i	0.996637	+	0.0819399i	$0.0261115\pi$
$410$	60.9482	−	44.2815i	3.01002	−	2.18691i
$411$	−13.3987	−	9.73469i	−0.660907	−	0.480177i
$412$	−5.09267	−	15.6736i	−0.250898	−	0.772184i
$413$	−0.544351	−	1.67534i	−0.0267858	−	0.0824381i
$414$	0.144216	+	0.104779i	0.00708783	+	0.00514961i
$415$	27.1433	−	19.7208i	1.33241	−	0.968056i
$416$	−18.6430	+	57.3771i	−0.914046	+	2.81314i
$417$	27.8709			1.36484
$418$		0			0
$419$	−13.8463			−0.676437			−0.338218	−	0.941068i	$-0.609824\pi$
$419$	−13.8463			−0.676437			−0.338218	+	0.941068i	$0.609824\pi$
$420$	−8.04307	+	24.7540i	−0.392461	+	1.20787i
$421$	28.9282	−	21.0175i	1.40987	−	1.02433i	0.416532	−	0.909121i	$-0.363245\pi$
$421$	28.9282	−	21.0175i	1.40987	−	1.02433i	0.993341	−	0.115212i	$-0.0367546\pi$
$422$	−39.2116	−	28.4889i	−1.90879	−	1.38682i
$423$	0.203479	+	0.626245i	0.00989351	+	0.0304491i
$424$	−28.6314	−	88.1183i	−1.39046	−	4.27940i
$425$	3.66434	+	2.66230i	0.177747	+	0.129140i
$426$	−31.8182	+	23.1173i	−1.54160	+	1.12004i
$427$	−3.20999	+	9.87934i	−0.155342	+	0.478095i
$428$	19.4586			0.940565
$429$		0			0
$430$	−52.5972			−2.53646
$431$	−9.67477	+	29.7759i	−0.466017	+	1.43425i	0.391681	+	0.920101i	$0.371894\pi$
$431$	−9.67477	+	29.7759i	−0.466017	+	1.43425i	−0.857699	+	0.514153i	$0.828106\pi$
$432$	67.7141	−	49.1972i	3.25790	−	2.36700i
$433$	−17.4811	−	12.7008i	−0.840090	−	0.610361i	0.0823059	−	0.996607i	$-0.473772\pi$
$433$	−17.4811	−	12.7008i	−0.840090	−	0.610361i	−0.922396	+	0.386246i	$0.873772\pi$
$434$	−1.91022	−	5.87904i	−0.0916933	−	0.282203i
$435$	−2.47214	−	7.60845i	−0.118530	−	0.364797i
$436$	73.8925	+	53.6860i	3.53881	+	2.57109i
$437$	−0.876063	+	0.636497i	−0.0419078	+	0.0304478i
$438$	15.6155	−	48.0595i	0.746136	−	2.29637i
$439$	15.5877			0.743959			0.371979	−	0.928241i	$-0.378679\pi$
$439$	15.5877			0.743959			0.371979	+	0.928241i	$0.378679\pi$
$440$		0			0
$441$	0.103084			0.00490875
$442$	4.86537	−	14.9741i	0.231422	−	0.712244i
$443$	−19.0072	+	13.8095i	−0.903058	+	0.656110i	−0.939250	−	0.343235i	$-0.888477\pi$
$443$	−19.0072	+	13.8095i	−0.903058	+	0.656110i	0.0361914	+	0.999345i	$0.488477\pi$
$444$	55.2999	+	40.1777i	2.62442	+	1.90675i
$445$	11.4827	+	35.3402i	0.544334	+	1.67529i
$446$	−19.0252	−	58.5536i	−0.900870	−	2.77259i
$447$	−4.92890	−	3.58106i	−0.233129	−	0.169378i
$448$	−29.9102	+	21.7310i	−1.41312	+	1.02670i
$449$	7.04040	−	21.6681i	0.332257	−	1.02258i	−0.635801	−	0.771853i	$-0.719330\pi$
$449$	7.04040	−	21.6681i	0.332257	−	1.02258i	0.968058	−	0.250728i	$-0.0806701\pi$
$450$	0.539998			0.0254558
$451$		0			0
$452$	39.9634			1.87972
$453$	−5.60607	+	17.2537i	−0.263396	+	0.810650i
$454$	−31.8829	+	23.1643i	−1.49634	+	1.08715i
$455$	−5.07312	−	3.68584i	−0.237831	−	0.172795i
$456$	−9.42650	−	29.0118i	−0.441436	−	1.35860i
$457$	−4.48223	−	13.7949i	−0.209670	−	0.645297i	−0.999489	−	0.0319578i	$-0.989826\pi$
$457$	−4.48223	−	13.7949i	−0.209670	−	0.645297i	0.789819	−	0.613339i	$-0.210174\pi$
$458$	8.66535	+	6.29574i	0.404905	+	0.294181i
$459$	−9.85780	+	7.16211i	−0.460123	+	0.334299i
$460$	2.85915	−	8.79955i	0.133308	−	0.410281i
$461$	−31.1633			−1.45142			−0.725709	−	0.688002i	$-0.758488\pi$
$461$	−31.1633			−1.45142			−0.725709	+	0.688002i	$0.758488\pi$
$462$		0			0
$463$	−5.87859			−0.273201			−0.136601	−	0.990626i	$-0.543618\pi$
$463$	−5.87859			−0.273201			−0.136601	+	0.990626i	$0.543618\pi$
$464$	8.76470	−	26.9750i	0.406891	−	1.25228i
$465$	−8.37776	+	6.08680i	−0.388509	+	0.282269i
$466$	−14.9309	−	10.8479i	−0.691662	−	0.502522i
$467$	−7.33140	−	22.5637i	−0.339257	−	1.04413i	−0.964587	−	0.263765i	$-0.915036\pi$
$467$	−7.33140	−	22.5637i	−0.339257	−	1.04413i	0.625330	−	0.780360i	$-0.284964\pi$
$468$	−0.427934	−	1.31705i	−0.0197813	−	0.0608805i
$469$	5.19391	+	3.77360i	0.239833	+	0.174249i
$470$	37.4790	−	27.2301i	1.72878	−	1.25603i
$471$	6.17139	−	18.9936i	0.284363	−	0.875179i
$472$	−17.6402			−0.811954
$473$		0			0
$474$	74.1974			3.40800
$475$	−1.01367	+	3.11975i	−0.0465103	+	0.143144i
$476$	10.8683	−	7.89630i	0.498149	−	0.361926i
$477$	0.771617	+	0.560613i	0.0353299	+	0.0256687i
$478$	−3.87552	−	11.9276i	−0.177262	−	0.545556i
$479$	2.59955	+	8.00061i	0.118777	+	0.365557i	0.992716	−	0.120478i	$-0.0384427\pi$
$479$	2.59955	+	8.00061i	0.118777	+	0.365557i	−0.873939	+	0.486035i	$0.838443\pi$
$480$	94.5637	+	68.7045i	4.31622	+	3.13592i
$481$	−13.3230	+	9.67973i	−0.607477	+	0.441358i
$482$	−3.16147	+	9.73002i	−0.144001	+	0.443190i
$483$	−1.10308			−0.0501920
$484$		0			0
$485$	21.9431			0.996387
$486$	−0.913794	+	2.81237i	−0.0414505	+	0.127572i
$487$	−20.0602	+	14.5746i	−0.909013	+	0.660436i	−0.940765	−	0.339059i	$-0.889891\pi$
$487$	−20.0602	+	14.5746i	−0.909013	+	0.660436i	0.0317523	+	0.999496i	$0.489891\pi$
$488$	84.1560	+	61.1429i	3.80956	+	2.76781i
$489$	−5.29615	−	16.2999i	−0.239500	−	0.737105i
$490$	−2.24111	−	6.89744i	−0.101243	−	0.311595i
$491$	−9.87500	−	7.17461i	−0.445652	−	0.323785i	0.342224	−	0.939618i	$-0.388820\pi$
$491$	−9.87500	−	7.17461i	−0.445652	−	0.323785i	−0.787877	+	0.615833i	$0.788820\pi$
$492$	−83.2897	+	60.5135i	−3.75499	+	2.72816i
$493$	−1.27596	+	3.92701i	−0.0574665	+	0.176864i
$494$	11.4028			0.513034
$495$		0			0
$496$	−36.7143			−1.64852
$497$	2.49833	−	7.68907i	0.112065	−	0.344902i
$498$	−50.2790	+	36.5298i	−2.25306	+	1.63694i
$499$	−18.0625	−	13.1232i	−0.808590	−	0.587475i	0.104831	−	0.994490i	$-0.466570\pi$
$499$	−18.0625	−	13.1232i	−0.808590	−	0.587475i	−0.913422	+	0.407015i	$0.866570\pi$
$500$	14.1683	+	43.6056i	0.633627	+	1.95010i
$501$	12.2505	+	37.7032i	0.547312	+	1.68445i
$502$	−19.0107	−	13.8121i	−0.848490	−	0.616464i
$503$	3.67410	−	2.66939i	0.163820	−	0.119022i	−0.502855	−	0.864371i	$-0.667717\pi$
$503$	3.67410	−	2.66939i	0.163820	−	0.119022i	0.666675	+	0.745349i	$0.267717\pi$
$504$	0.318991	−	0.981752i	0.0142090	−	0.0437307i
$505$	36.3632			1.61814
$506$		0			0
$507$	−12.8569			−0.570997
$508$	−7.89570	+	24.3005i	−0.350315	+	1.07816i
$509$	−3.33429	+	2.42250i	−0.147790	+	0.107375i	−0.659223	−	0.751947i	$-0.729115\pi$
$509$	−3.33429	+	2.42250i	−0.147790	+	0.107375i	0.511433	+	0.859323i	$0.329115\pi$
$510$	−24.6789	−	17.9303i	−1.09280	−	0.793966i
$511$	3.20999	+	9.87934i	0.142002	+	0.437036i
$512$	26.5506	+	81.7142i	1.17338	+	3.61129i
$513$	−7.13931	−	5.18701i	−0.315208	−	0.229012i
$514$	6.59916	−	4.79457i	0.291076	−	0.211479i
$515$	2.37716	−	7.31613i	0.104750	−	0.322387i
$516$	71.8776			3.16423
$517$		0			0
$518$	−19.0462			−0.836843
$519$	3.77191	−	11.6088i	0.165569	−	0.509568i
$520$	−50.8020	+	36.9098i	−2.22781	+	1.61860i
$521$	−31.7847	−	23.0929i	−1.39251	−	1.01172i	−0.995585	−	0.0938682i	$-0.970077\pi$
$521$	−31.7847	−	23.0929i	−1.39251	−	1.01172i	−0.396927	−	0.917850i	$-0.629923\pi$
$522$	0.152122	+	0.468184i	0.00665820	+	0.0204918i
$523$	−0.661796	−	2.03680i	−0.0289383	−	0.0890630i	0.935544	−	0.353210i	$-0.114910\pi$
$523$	−0.661796	−	2.03680i	−0.0289383	−	0.0890630i	−0.964483	+	0.264147i	$0.914910\pi$
$524$	28.5424	+	20.7372i	1.24688	+	0.905911i
$525$	−2.70335	+	1.96410i	−0.117984	+	0.0857204i
$526$	−13.6539	+	42.0224i	−0.595338	+	1.83226i
$527$	5.34485			0.232825
$528$		0			0
$529$	−22.6079			−0.982951
$530$	20.7357	−	63.8178i	0.900700	−	2.77207i
$531$	0.146908	−	0.106735i	0.00637525	−	0.00463189i
$532$	7.87115	+	5.71873i	0.341258	+	0.247938i
$533$	−7.66468	−	23.5895i	−0.331994	−	1.02177i
$534$	−21.2700	−	65.4625i	−0.920445	−	2.83284i
$535$	7.34820	+	5.33878i	0.317690	+	0.230816i
$536$	52.0116	−	37.7886i	2.24656	−	1.63222i
$537$	7.58997	−	23.3595i	0.327531	−	1.00804i
$538$	−18.7110			−0.806687
$539$		0			0
$540$	75.4007			3.24473
$541$	−13.3020	+	40.9394i	−0.571898	+	1.76012i	0.0746074	+	0.997213i	$0.476230\pi$
$541$	−13.3020	+	40.9394i	−0.571898	+	1.76012i	−0.646506	+	0.762909i	$0.723770\pi$
$542$	−7.72694	+	5.61395i	−0.331900	+	0.241140i
$543$	−4.51429	−	3.27982i	−0.193727	−	0.140751i
$544$	−18.6430	−	57.3771i	−0.799310	−	2.46002i
$545$	13.1746	+	40.5472i	0.564338	+	1.73685i
$546$	9.39720	+	6.82746i	0.402163	+	0.292188i
$547$	23.4692	−	17.0514i	1.00347	−	0.729065i	0.0406426	−	0.999174i	$-0.487060\pi$
$547$	23.4692	−	17.0514i	1.00347	−	0.729065i	0.962830	+	0.270108i	$0.0870595\pi$
$548$	16.3457	−	50.3070i	0.698255	−	2.14901i
$549$	−1.07081			−0.0457010
$550$		0			0
$551$	−2.99042			−0.127396
$552$	−3.41347	+	10.5056i	−0.145287	+	0.447148i
$553$	−12.3394	+	8.96513i	−0.524727	+	0.381236i
$554$	25.6001	+	18.5996i	1.08764	+	0.790220i
$555$	9.85965	+	30.3449i	0.418519	+	1.28807i
$556$	27.5075	+	84.6595i	1.16658	+	3.59036i
$557$	1.20965	+	0.878861i	0.0512545	+	0.0372385i	0.613118	−	0.789992i	$-0.289915\pi$
$557$	1.20965	+	0.878861i	0.0512545	+	0.0372385i	−0.561863	+	0.827230i	$0.689915\pi$
$558$	0.515523	−	0.374549i	0.0218238	−	0.0158559i
$559$	−5.35123	+	16.4694i	−0.226333	+	0.696581i
$560$	−43.0741			−1.82021
$561$		0			0
$562$	−61.6560			−2.60080
$563$	1.93776	−	5.96381i	0.0816668	−	0.251345i	−0.901883	−	0.431980i	$-0.857815\pi$
$563$	1.93776	−	5.96381i	0.0816668	−	0.251345i	0.983550	+	0.180635i	$0.0578153\pi$
$564$	−51.2174	+	37.2116i	−2.15664	+	1.56689i
$565$	15.0915	+	10.9646i	0.634904	+	0.461285i
$566$	−10.5503	−	32.4706i	−0.443464	−	1.36484i
$567$	−2.87343	−	8.84352i	−0.120673	−	0.371393i
$568$	−65.4984	−	47.5873i	−2.74825	−	1.99672i
$569$	−6.32792	+	4.59750i	−0.265280	+	0.192737i	−0.712472	−	0.701701i	$-0.752424\pi$
$569$	−6.32792	+	4.59750i	−0.265280	+	0.192737i	0.447191	+	0.894438i	$0.352424\pi$
$570$	6.82694	−	21.0112i	0.285949	−	0.880061i
$571$	−15.1753			−0.635068			−0.317534	−	0.948247i	$-0.602855\pi$
$571$	−15.1753			−0.635068			−0.317534	+	0.948247i	$0.602855\pi$
$572$		0			0
$573$	32.3342			1.35078
$574$	8.86458	−	27.2824i	0.370000	−	1.13874i
$575$	0.960987	−	0.698198i	0.0400759	−	0.0291169i
$576$	−3.08326	−	2.24012i	−0.128469	−	0.0933382i
$577$	7.30656	+	22.4873i	0.304176	+	0.936158i	0.979983	+	0.199079i	$0.0637951\pi$
$577$	7.30656	+	22.4873i	0.304176	+	0.936158i	−0.675807	+	0.737078i	$0.736205\pi$
$578$	−9.64189	−	29.6747i	−0.401050	−	1.23430i
$579$	4.34127	+	3.15412i	0.180417	+	0.131081i
$580$	20.6712	−	15.0185i	0.858325	−	0.623610i
$581$	3.94785	−	12.1502i	0.163784	−	0.504077i
$582$	−40.6464			−1.68485
$583$		0			0
$584$	104.022			4.30448
$585$	0.199751	−	0.614771i	0.00825870	−	0.0254177i
$586$	−4.81164	+	3.49586i	−0.198767	+	0.144413i
$587$	8.21450	+	5.96818i	0.339049	+	0.246333i	0.744260	−	0.667890i	$-0.232802\pi$
$587$	8.21450	+	5.96818i	0.339049	+	0.246333i	−0.405212	+	0.914223i	$0.632802\pi$
$588$	3.06263	+	9.42580i	0.126301	+	0.388713i
$589$	1.19617	+	3.68144i	0.0492875	+	0.151691i
$590$	−10.3356	−	7.50926i	−0.425510	−	0.309151i
$591$	−7.05977	+	5.12922i	−0.290400	+	0.210988i
$592$	−34.9564	+	107.585i	−1.43670	+	4.42170i
$593$	33.7972			1.38788			0.693942	−	0.720031i	$-0.255873\pi$
$593$	33.7972			1.38788			0.693942	+	0.720031i	$0.255873\pi$
$594$		0			0
$595$	6.27072			0.257074
$596$	6.01303	−	18.5062i	0.246303	−	0.758043i
$597$	−22.3812	+	16.2609i	−0.916003	+	0.665515i
$598$	−3.34051	−	2.42703i	−0.136604	−	0.0992484i
$599$	−5.66321	−	17.4296i	−0.231392	−	0.712153i	−0.997580	−	0.0695352i	$-0.977848\pi$
$599$	−5.66321	−	17.4296i	−0.231392	−	0.712153i	0.766187	−	0.642618i	$-0.222152\pi$
$600$	10.3403	+	31.8241i	0.422141	+	1.29922i
$601$	−39.2213	−	28.4960i	−1.59987	−	1.16237i	−0.887759	−	0.460308i	$-0.847739\pi$
$601$	−39.2213	−	28.4960i	−1.59987	−	1.16237i	−0.712111	−	0.702066i	$-0.752261\pi$
$602$	−16.2029	+	11.7721i	−0.660382	+	0.479795i
$603$	−0.204508	+	0.629410i	−0.00832819	+	0.0256315i
$604$	−57.9421			−2.35763
$605$		0			0
$606$	−67.3574			−2.73621
$607$	−6.36490	+	19.5891i	−0.258343	+	0.795099i	0.734809	+	0.678274i	$0.237272\pi$
$607$	−6.36490	+	19.5891i	−0.258343	+	0.795099i	−0.993153	+	0.116825i	$0.962728\pi$
$608$	35.3481	−	25.6819i	1.43355	−	1.04154i
$609$	−2.46445	−	1.79053i	−0.0998646	−	0.0725559i
$610$	23.2801	+	71.6489i	0.942585	+	2.90098i
$611$	−4.71325	−	14.5059i	−0.190678	−	0.586846i
$612$	1.12035	+	0.813980i	0.0452873	+	0.0329032i
$613$	−15.2194	+	11.0575i	−0.614704	+	0.446609i	−0.851068	−	0.525056i	$-0.824044\pi$
$613$	−15.2194	+	11.0575i	−0.614704	+	0.446609i	0.236364	+	0.971665i	$0.424044\pi$
$614$	−27.1557	+	83.5765i	−1.09591	+	3.37287i
$615$	−48.0558			−1.93780
$616$		0			0
$617$	−14.2062			−0.571919			−0.285959	−	0.958242i	$-0.592312\pi$
$617$	−14.2062			−0.571919			−0.285959	+	0.958242i	$0.592312\pi$
$618$	−4.40333	+	13.5520i	−0.177128	+	0.545143i
$619$	12.9633	−	9.41840i	0.521040	−	0.378557i	−0.295956	−	0.955202i	$-0.595638\pi$
$619$	12.9633	−	9.41840i	0.521040	−	0.378557i	0.816995	+	0.576644i	$0.195638\pi$
$620$	−26.7575	−	19.4405i	−1.07461	−	0.780749i
$621$	0.987477	+	3.03914i	0.0396261	+	0.121956i
$622$	−9.32662	−	28.7044i	−0.373964	−	1.15094i
$623$	11.4470	+	8.31676i	0.458616	+	0.333204i
$624$	55.8127	−	40.5503i	2.23430	−	1.62331i
$625$	−9.54439	+	29.3746i	−0.381776	+	1.17498i
$626$	20.4402			0.816956
$627$		0			0
$628$	63.7851			2.54530
$629$	5.08894	−	15.6621i	0.202909	−	0.624490i
$630$	0.604824	−	0.439431i	0.0240968	−	0.0175073i
$631$	−12.2935	−	8.93171i	−0.489395	−	0.355566i	0.315557	−	0.948907i	$-0.397809\pi$
$631$	−12.2935	−	8.93171i	−0.489395	−	0.355566i	−0.804951	+	0.593341i	$0.797809\pi$
$632$	47.1983	+	145.261i	1.87745	+	5.77818i
$633$	9.55392	+	29.4039i	0.379734	+	1.16870i
$634$	19.8770	+	14.4415i	0.789417	+	0.573545i
$635$	−9.64891	+	7.01035i	−0.382905	+	0.278197i
$636$	−28.3366	+	87.2112i	−1.12362	+	3.45815i
$637$	−2.38776			−0.0946063
$638$		0			0
$639$	0.833407			0.0329691
$640$	−41.8470	+	128.792i	−1.65415	+	5.09095i
$641$	8.27331	−	6.01091i	0.326776	−	0.237417i	−0.412285	−	0.911055i	$-0.635269\pi$
$641$	8.27331	−	6.01091i	0.326776	−	0.237417i	0.739061	+	0.673638i	$0.235269\pi$
$642$	−13.6114	−	9.88929i	−0.537201	−	0.390299i
$643$	6.35493	+	19.5585i	0.250614	+	0.771310i	0.994662	+	0.103184i	$0.0329032\pi$
$643$	6.35493	+	19.5585i	0.250614	+	0.771310i	−0.744048	+	0.668126i	$0.767097\pi$
$644$	−1.08870	−	3.35068i	−0.0429009	−	0.132035i
$645$	27.1433	+	19.7208i	1.06877	+	0.776506i
$646$	−9.22502	+	6.70237i	−0.362954	+	0.263701i
$647$	−7.86578	+	24.2084i	−0.309236	+	0.951730i	0.668827	+	0.743418i	$0.266797\pi$
$647$	−7.86578	+	24.2084i	−0.309236	+	0.951730i	−0.978063	+	0.208311i	$0.933203\pi$
$648$	−93.1160			−3.65794
$649$		0			0
$650$	−12.5081			−0.490609
$651$	−1.21850	+	3.75015i	−0.0477567	+	0.146980i
$652$	44.2847	−	32.1747i	1.73432	−	1.26006i
$653$	36.6091	+	26.5981i	1.43263	+	1.04086i	0.989520	+	0.144394i	$0.0461231\pi$
$653$	36.6091	+	26.5981i	1.43263	+	1.04086i	0.443105	+	0.896470i	$0.353877\pi$
$654$	−24.4040	−	75.1077i	−0.954271	−	2.93694i
$655$	5.08894	+	15.6621i	0.198841	+	0.611970i
$656$	−137.838	−	100.145i	−5.38166	−	3.91001i
$657$	−0.866302	+	0.629405i	−0.0337977	+	0.0245554i
$658$	5.45111	−	16.7768i	0.212506	−	0.654027i
$659$	−50.3544			−1.96153			−0.980765	−	0.195191i	$-0.937467\pi$
$659$	−50.3544			−1.96153			−0.980765	+	0.195191i	$0.937467\pi$
$660$		0			0
$661$	−23.2234			−0.903287			−0.451644	−	0.892198i	$-0.649162\pi$
$661$	−23.2234			−0.903287			−0.451644	+	0.892198i	$0.649162\pi$
$662$	7.30624	−	22.4863i	0.283965	−	0.873954i
$663$	−8.12520	+	5.90330i	−0.315557	+	0.229265i
$664$	−103.500	−	75.1973i	−4.01659	−	2.91822i
$665$	1.40338	+	4.31916i	0.0544208	+	0.167490i
$666$	−0.606710	−	1.86726i	−0.0235095	−	0.0723549i
$667$	0.876063	+	0.636497i	0.0339213	+	0.0246453i
$668$	−102.435	+	74.4233i	−3.96332	+	2.87952i
$669$	−12.1359	+	37.3505i	−0.469201	+	1.44405i
$670$	46.5606			1.79879
$671$		0			0
$672$	44.5081			1.71694
$673$	−0.996422	+	3.06667i	−0.0384092	+	0.118212i	−0.968423	−	0.249314i	$-0.919795\pi$
$673$	−0.996422	+	3.06667i	−0.0384092	+	0.118212i	0.930013	+	0.367525i	$0.119795\pi$
$674$	21.7366	−	15.7926i	0.837264	−	0.608308i
$675$	7.83138	+	5.68983i	0.301430	+	0.219002i
$676$	−12.6893	−	39.0537i	−0.488051	−	1.50207i
$677$	13.1709	+	40.5358i	0.506198	+	1.55792i	0.798748	+	0.601666i	$0.205496\pi$
$677$	13.1709	+	40.5358i	0.506198	+	1.55792i	−0.292550	+	0.956250i	$0.594504\pi$
$678$	−27.9547	−	20.3103i	−1.07360	−	0.780012i
$679$	6.75973	−	4.91123i	0.259414	−	0.188476i
$680$	19.4046	−	59.7213i	0.744133	−	2.29021i
$681$	25.1387			0.963317
$682$		0			0
$683$	15.5877			0.596445			0.298223	−	0.954496i	$-0.403606\pi$
$683$	15.5877			0.596445			0.298223	+	0.954496i	$0.403606\pi$
$684$	−0.309923	+	0.953844i	−0.0118502	+	0.0364711i
$685$	19.9752	−	14.5129i	0.763215	−	0.554508i
$686$	−2.23415	−	1.62320i	−0.0853001	−	0.0619742i
$687$	−2.11132	−	6.49797i	−0.0805518	−	0.247913i
$688$	36.7581	+	113.130i	1.40139	+	4.31303i
$689$	−17.8732	−	12.9856i	−0.680914	−	0.494713i
$690$	−6.47214	+	4.70228i	−0.246390	+	0.179013i
$691$	12.9574	−	39.8788i	0.492923	−	1.51706i	−0.327245	−	0.944940i	$-0.606120\pi$
$691$	12.9574	−	39.8788i	0.492923	−	1.51706i	0.820168	−	0.572122i	$-0.193880\pi$
$692$	38.9850			1.48199
$693$		0			0
$694$	40.9817			1.55564
$695$	−12.8400	+	39.5174i	−0.487048	+	1.49898i
$696$	−24.6789	+	17.9303i	−0.935451	+	0.679645i
$697$	20.0664	+	14.5791i	0.760069	+	0.552222i
$698$	13.8639	+	42.6688i	0.524758	+	1.61504i
$699$	3.63793	+	11.1964i	0.137599	+	0.423486i
$700$	−8.63417	−	6.27310i	−0.326341	−	0.237101i
$701$	12.4665	−	9.05742i	0.470852	−	0.342094i	−0.326921	−	0.945052i	$-0.606011\pi$
$701$	12.4665	−	9.05742i	0.470852	−	0.342094i	0.797773	+	0.602958i	$0.206011\pi$
$702$	10.3982	−	32.0024i	0.392455	−	1.20785i
$703$	11.9267			0.449824
$704$		0			0
$705$	−29.5510			−1.11296
$706$	26.3352	−	81.0513i	0.991137	−	3.05041i
$707$	11.2019	−	8.13866i	0.421291	−	0.306086i
$708$	14.1243	+	10.2619i	0.530823	+	0.385665i
$709$	0.883873	+	2.72028i	0.0331945	+	0.102162i	0.966281	−	0.257490i	$-0.0828954\pi$
$709$	0.883873	+	2.72028i	0.0331945	+	0.102162i	−0.933086	+	0.359652i	$0.882895\pi$
$710$	−18.1189	−	55.7641i	−0.679989	−	2.09279i
$711$	−1.27200	−	0.924159i	−0.0477036	−	0.0346587i
$712$	114.630	−	83.2836i	4.29594	−	3.12119i
$713$	0.433152	−	1.33310i	0.0162217	−	0.0499251i
$714$	−11.6156			−0.434702
$715$		0			0
$716$	78.4469			2.93170
$717$	−2.47214	+	7.60845i	−0.0923236	+	0.284143i
$718$	26.3492	−	19.1438i	0.983342	−	0.714440i
$719$	27.8889	+	20.2624i	1.04008	+	0.755661i	0.970301	−	0.241901i	$-0.0777710\pi$
$719$	27.8889	+	20.2624i	1.04008	+	0.755661i	0.0697778	+	0.997563i	$0.477771\pi$
$720$	−1.37211	−	4.22292i	−0.0511355	−	0.157379i
$721$	−0.905170	−	2.78583i	−0.0337103	−	0.103750i
$722$	35.7678	+	25.9868i	1.33114	+	0.967129i
$723$	5.27968	−	3.83591i	0.196353	−	0.142659i
$724$	5.50722	−	16.9495i	0.204674	−	0.629923i
$725$	3.28030			0.121827
$726$		0			0
$727$	−40.3309			−1.49579			−0.747895	−	0.663817i	$-0.768935\pi$
$727$	−40.3309			−1.49579			−0.747895	+	0.663817i	$0.768935\pi$
$728$	−7.38887	+	22.7406i	−0.273850	+	0.842822i
$729$	−21.0422	+	15.2881i	−0.779341	+	0.566224i
$730$	60.9482	+	44.2815i	2.25579	+	1.63893i
$731$	−5.35123	−	16.4694i	−0.197922	−	0.609143i
$732$	−31.8138	−	97.9129i	−1.17587	−	3.61896i
$733$	23.2701	+	16.9067i	0.859501	+	0.624464i	0.927749	−	0.373204i	$-0.121741\pi$
$733$	23.2701	+	16.9067i	0.859501	+	0.624464i	−0.0682479	+	0.997668i	$0.521741\pi$
$734$	7.94326	−	5.77112i	0.293191	−	0.213016i
$735$	−1.42957	+	4.39978i	−0.0527306	+	0.162288i
$736$	−15.8217			−0.583197
$737$		0			0
$738$	2.95710			0.108852
$739$	10.8471	−	33.3840i	0.399018	−	1.22805i	−0.526770	−	0.850008i	$-0.676597\pi$
$739$	10.8471	−	33.3840i	0.399018	−	1.22805i	0.925788	−	0.378043i	$-0.123403\pi$
$740$	−82.4432	+	59.8985i	−3.03067	+	2.20191i
$741$	−5.88451	−	4.27534i	−0.216173	−	0.157059i
$742$	−7.89570	−	24.3005i	−0.289860	−	0.892098i
$743$	−10.0332	−	30.8790i	−0.368083	−	1.13284i	−0.948028	−	0.318187i	$-0.896926\pi$
$743$	−10.0332	−	30.8790i	−0.368083	−	1.13284i	0.579945	−	0.814655i	$-0.303074\pi$
$744$	31.9452	+	23.2096i	1.17117	+	0.850904i
$745$	7.34820	−	5.33878i	0.269217	−	0.195598i
$746$	19.2049	−	59.1065i	0.703140	−	2.16404i
$747$	1.31695			0.0481846
$748$		0			0
$749$	3.45856			0.126373
$750$	12.2505	−	37.7032i	0.447325	−	1.37673i
$751$	22.9626	−	16.6833i	0.837919	−	0.608784i	−0.0838698	−	0.996477i	$-0.526728\pi$
$751$	22.9626	−	16.6833i	0.837919	−	0.608784i	0.921788	+	0.387693i	$0.126728\pi$
$752$	−84.7608	−	61.5823i	−3.09091	−	2.24568i
$753$	4.63197	+	14.2557i	0.168798	+	0.519508i
$754$	−3.52364	−	10.8447i	−0.128324	−	0.394939i
$755$	−21.8809	−	15.8974i	−0.796326	−	0.578565i
$756$	23.2277	−	16.8759i	0.844782	−	0.613770i
$757$	−5.26757	+	16.2119i	−0.191453	+	0.589233i	0.808546	+	0.588432i	$0.200255\pi$
$757$	−5.26757	+	16.2119i	−0.191453	+	0.589233i	−1.00000		0.000800126i	$0.999745\pi$
$758$	64.7022			2.35009
$759$		0			0
$760$	45.4777			1.64965
$761$	8.63356	−	26.5714i	0.312966	−	0.963211i	−0.663617	−	0.748072i	$-0.730980\pi$
$761$	8.63356	−	26.5714i	0.312966	−	0.963211i	0.976584	−	0.215139i	$-0.0690203\pi$
$762$	17.8732	−	12.9856i	0.647477	−	0.470419i
$763$	13.1336	+	9.54215i	0.475470	+	0.345449i
$764$	31.9127	+	98.2171i	1.15456	+	3.55337i
$765$	0.199751	+	0.614771i	0.00722202	+	0.0222271i
$766$	7.65483	+	5.56156i	0.276580	+	0.200947i
$767$	−3.40286	+	2.47232i	−0.122870	+	0.0892704i
$768$	37.2649	−	114.690i	1.34468	−	4.13851i
$769$	6.69512			0.241432			0.120716	−	0.992687i	$-0.461481\pi$
$769$	6.69512			0.241432			0.120716	+	0.992687i	$0.461481\pi$
$770$		0			0
$771$	−5.20324			−0.187390
$772$	−5.29615	+	16.2999i	−0.190612	+	0.586645i
$773$	−22.5831	+	16.4076i	−0.812256	+	0.590139i	−0.914484	−	0.404622i	$-0.867403\pi$
$773$	−22.5831	+	16.4076i	−0.812256	+	0.590139i	0.102228	+	0.994761i	$0.467403\pi$
$774$	−1.67026	−	1.21351i	−0.0600361	−	0.0436188i
$775$	−1.31213	−	4.03832i	−0.0471331	−	0.145061i
$776$	−25.8559	−	79.5762i	−0.928172	−	2.85662i
$777$	9.82900	+	7.14119i	0.352613	+	0.256189i
$778$	−18.0002	+	13.0779i	−0.645338	+	0.468866i
$779$	−5.55098	+	17.0842i	−0.198885	+	0.612104i
$780$	62.1483			2.22527
$781$		0			0
$782$	4.12910			0.147656
$783$	−2.72697	+	8.39276i	−0.0974541	+	0.299933i
$784$	−13.2693	+	9.64068i	−0.473902	+	0.344310i
$785$	24.0874	+	17.5005i	0.859715	+	0.624619i
$786$	−9.42650	−	29.0118i	−0.336232	−	1.03482i
$787$	6.75461	+	20.7886i	0.240776	+	0.741032i	0.996303	+	0.0859141i	$0.0273811\pi$
$787$	6.75461	+	20.7886i	0.240776	+	0.741032i	−0.755527	+	0.655118i	$0.772619\pi$
$788$	−22.5480	−	16.3821i	−0.803240	−	0.583588i
$789$	22.8021	−	16.5667i	0.811775	−	0.589789i
$790$	−34.1824	+	105.202i	−1.21615	+	3.74294i
$791$	7.10308			0.252557
$792$		0			0
$793$	24.8034			0.880795
$794$	−22.4975	+	69.2402i	−0.798406	+	2.45724i
$795$	−34.6287	+	25.1592i	−1.22815	+	0.892305i
$796$	−71.4829	−	51.9354i	−2.53365	−	1.84080i
$797$	−10.7001	−	32.9315i	−0.379016	−	1.16649i	−0.940729	−	0.339160i	$-0.889857\pi$
$797$	−10.7001	−	32.9315i	−0.379016	−	1.16649i	0.561712	−	0.827333i	$-0.310143\pi$
$798$	−2.59955	−	8.00061i	−0.0920232	−	0.283218i
$799$	12.3394	+	8.96513i	0.436538	+	0.317164i
$800$	−38.7747	+	28.1715i	−1.37089	+	0.996012i
$801$	−0.450721	+	1.38718i	−0.0159254	+	0.0490135i
$802$	−62.4036			−2.20355
$803$		0			0
$804$	−63.6281			−2.24399
$805$	0.508185	−	1.56403i	0.0179112	−	0.0551249i
$806$	−11.9412	+	8.67578i	−0.420610	+	0.305591i
$807$	9.65598	+	7.01548i	0.339907	+	0.246957i
$808$	−42.8472	−	131.870i	−1.50736	−	4.63917i
$809$	10.8299	+	33.3309i	0.380758	+	1.17185i	0.939511	+	0.342519i	$0.111280\pi$
$809$	10.8299	+	33.3309i	0.380758	+	1.17185i	−0.558753	+	0.829334i	$0.688720\pi$
$810$	−54.5579	−	39.6387i	−1.91697	−	1.39276i
$811$	14.6769	−	10.6634i	0.515375	−	0.374442i	−0.299484	−	0.954101i	$-0.596814\pi$
$811$	14.6769	−	10.6634i	0.515375	−	0.374442i	0.814859	+	0.579660i	$0.196814\pi$
$812$	3.00651	−	9.25310i	0.105508	−	0.324720i
$813$	6.09246			0.213672
$814$		0			0
$815$	25.5510			0.895013
$816$	−21.3186	+	65.6118i	−0.746299	+	2.29687i
$817$	10.1462	−	7.37167i	0.354972	−	0.257902i
$818$	−20.7885	−	15.1037i	−0.726852	−	0.528089i
$819$	−0.0760610	−	0.234092i	−0.00265779	−	0.00817983i
$820$	−47.4293	−	145.972i	−1.65630	−	5.09757i
$821$	2.79804	+	2.03289i	0.0976522	+	0.0709484i	0.635540	−	0.772068i	$-0.280778\pi$
$821$	2.79804	+	2.03289i	0.0976522	+	0.0709484i	−0.537888	+	0.843016i	$0.680778\pi$
$822$	−37.0011	+	26.8829i	−1.29056	+	0.937649i
$823$	−10.3616	+	31.8897i	−0.361182	+	1.11160i	0.591155	+	0.806558i	$0.298672\pi$
$823$	−10.3616	+	31.8897i	−0.361182	+	1.11160i	−0.952337	+	0.305047i	$0.901328\pi$
$824$	−29.3328			−1.02186
$825$		0			0
$826$	−4.86464			−0.169263
$827$	−8.12672	+	25.0115i	−0.282594	+	0.869734i	0.704516	+	0.709688i	$0.251164\pi$
$827$	−8.12672	+	25.0115i	−0.282594	+	0.869734i	−0.987110	+	0.160046i	$0.948836\pi$
$828$	0.293815	−	0.213469i	0.0102108	−	0.00741857i
$829$	23.4630	+	17.0469i	0.814904	+	0.592063i	0.915248	−	0.402890i	$-0.131994\pi$
$829$	23.4630	+	17.0469i	0.814904	+	0.592063i	−0.100344	+	0.994953i	$0.531994\pi$
$830$	−28.6314	−	88.1183i	−0.993809	−	3.05863i
$831$	−6.23748	−	19.1970i	−0.216376	−	0.665936i
$832$	71.4183	+	51.8884i	2.47598	+	1.79891i
$833$	1.93173	−	1.40349i	0.0669306	−	0.0486280i
$834$	23.7841	−	73.2000i	0.823577	−	2.53471i
$835$	−59.1020			−2.04531
$836$		0			0
$837$	11.4230			0.394835
$838$	−11.8160	+	36.3659i	−0.408177	+	1.25624i
$839$	−23.5998	+	17.1463i	−0.814756	+	0.591955i	−0.915206	−	0.402987i	$-0.867972\pi$
$839$	−23.5998	+	17.1463i	−0.814756	+	0.591955i	0.100450	+	0.994942i	$0.467972\pi$
$840$	37.4790	+	27.2301i	1.29315	+	0.939526i
$841$	−8.03740	−	24.7366i	−0.277152	−	0.852986i
$842$	−30.5140	−	93.9126i	−1.05158	−	3.23644i
$843$	31.8182	+	23.1173i	1.09588	+	0.796201i
$844$	−79.8868	+	58.0412i	−2.74982	+	1.99786i
$845$	5.92312	−	18.2295i	0.203762	−	0.627114i
$846$	1.81841			0.0625183
$847$		0			0
$848$	−151.755			−5.21129
$849$	−6.72991	+	20.7125i	−0.230970	+	0.710852i
$850$	10.1193	−	7.35209i	0.347088	−	0.252175i
$851$	−3.49401	−	2.53855i	−0.119773	−	0.0870203i
$852$	24.7606	+	76.2053i	0.848285	+	2.61075i
$853$	3.28233	+	10.1020i	0.112385	+	0.345885i	0.991393	−	0.130923i	$-0.0417940\pi$
$853$	3.28233	+	10.1020i	0.112385	+	0.345885i	−0.879008	+	0.476807i	$0.841794\pi$
$854$	23.2078	+	16.8614i	0.794154	+	0.576986i
$855$	−0.378740	+	0.275171i	−0.0129526	+	0.00941063i
$856$	10.7025	−	32.9388i	0.365803	−	1.12582i
$857$	37.8463			1.29281			0.646403	−	0.762996i	$-0.276273\pi$
$857$	37.8463			1.29281			0.646403	+	0.762996i	$0.276273\pi$
$858$		0			0
$859$	−19.0785			−0.650950			−0.325475	−	0.945551i	$-0.605524\pi$
$859$	−19.0785			−0.650950			−0.325475	+	0.945551i	$0.605524\pi$
$860$	−33.1136	+	101.913i	−1.12916	+	3.47521i
$861$	−14.8039	+	10.7557i	−0.504516	+	0.366552i
$862$	69.9471	+	50.8196i	2.38241	+	1.73092i
$863$	3.45337	+	10.6284i	0.117554	+	0.361794i	0.992471	−	0.122479i	$-0.0390843\pi$
$863$	3.45337	+	10.6284i	0.117554	+	0.361794i	−0.874917	+	0.484273i	$0.839084\pi$
$864$	−39.8435	−	122.626i	−1.35550	−	4.17181i
$865$	14.7220	+	10.6962i	0.500564	+	0.363681i
$866$	−48.2752	+	35.0740i	−1.64046	+	1.19186i
$867$	−6.15042	+	18.9290i	−0.208879	+	0.642864i
$868$	−12.5939			−0.427466
$869$		0			0
$870$	−22.0925			−0.749004
$871$	4.73706	−	14.5792i	0.160509	−	0.493997i
$872$	131.520	−	95.5546i	4.45382	−	3.23589i
$873$	0.696818	+	0.506268i	0.0235837	+	0.0171346i
$874$	0.924089	+	2.84405i	0.0312578	+	0.0962016i
$875$	2.51828	+	7.75046i	0.0851333	+	0.262013i
$876$	−83.2897	−	60.5135i	−2.81410	−	2.04456i
$877$	4.73953	−	3.44347i	0.160043	−	0.116278i	−0.504882	−	0.863189i	$-0.668464\pi$
$877$	4.73953	−	3.44347i	0.160043	−	0.116278i	0.664924	+	0.746911i	$0.268464\pi$
$878$	13.3020	−	40.9394i	0.448921	−	1.38164i
$879$	3.79383			0.127963
$880$		0			0
$881$	−25.9065			−0.872812			−0.436406	−	0.899750i	$-0.643749\pi$
$881$	−25.9065			−0.872812			−0.436406	+	0.899750i	$0.643749\pi$
$882$	0.0879683	−	0.270739i	0.00296205	−	0.00911625i
$883$	−10.8586	+	7.88921i	−0.365420	+	0.265493i	−0.755309	−	0.655369i	$-0.772513\pi$
$883$	−10.8586	+	7.88921i	−0.365420	+	0.265493i	0.389889	+	0.920862i	$0.372513\pi$
$884$	−25.9509	−	18.8544i	−0.872823	−	0.634143i
$885$	2.51828	+	7.75046i	0.0846509	+	0.260529i
$886$	20.0492	+	61.7050i	0.673565	+	2.07302i
$887$	40.1328	+	29.1582i	1.34753	+	0.979035i	0.999131	+	0.0416879i	$0.0132735\pi$
$887$	40.1328	+	29.1582i	1.34753	+	0.979035i	0.348396	+	0.937347i	$0.386726\pi$
$888$	98.4271	−	71.5115i	3.30300	−	2.39977i
$889$	−1.40338	+	4.31916i	−0.0470679	+	0.144860i
$890$	102.616			3.43971
$891$		0			0
$892$	−125.432			−4.19977
$893$	−3.41347	+	10.5056i	−0.114227	+	0.351556i
$894$	−13.6114	+	9.88929i	−0.455235	+	0.330747i
$895$	29.6241	+	21.5232i	0.990226	+	0.719441i
$896$	15.9345	+	49.0412i	0.532333	+	1.63835i
$897$	0.813918	+	2.50498i	0.0271759	+	0.0836389i
$898$	−50.9010	−	36.9818i	−1.69859	−	1.23410i
$899$	3.13162	−	2.27526i	0.104445	−	0.0758841i
$900$	0.339966	−	1.04631i	0.0113322	−	0.0348769i
$901$	22.0925			0.736006
$902$		0			0
$903$	12.7755			0.425142
$904$	21.9804	−	67.6486i	0.731056	−	2.24996i
$905$	6.73008	−	4.88969i	0.223715	−	0.162539i
$906$	40.5310	+	29.4475i	1.34655	+	0.978328i
$907$	−14.7950	−	45.5343i	−0.491259	−	1.51194i	−0.822706	−	0.568466i	$-0.807537\pi$
$907$	−14.7950	−	45.5343i	−0.491259	−	1.51194i	0.331447	−	0.943474i	$-0.392463\pi$
$908$	24.8109	+	76.3602i	0.823380	+	2.53410i
$909$	1.15473	+	0.838963i	0.0383001	+	0.0278267i
$910$	−14.0097	+	10.1786i	−0.464417	+	0.337419i
$911$	7.04934	−	21.6956i	0.233555	−	0.718809i	−0.763755	−	0.645507i	$-0.776646\pi$
$911$	7.04934	−	21.6956i	0.233555	−	0.718809i	0.997310	−	0.0733022i	$-0.0233538\pi$
$912$	−49.9634			−1.65445
$913$		0			0
$914$	−40.0558			−1.32493
$915$	14.8501	−	45.7038i	0.490928	−	1.51092i
$916$	17.6542	−	12.8265i	0.583310	−	0.423799i
$917$	5.07312	+	3.68584i	0.167529	+	0.121717i
$918$	10.3982	+	32.0024i	0.343192	+	1.05624i
$919$	−12.3607	−	38.0423i	−0.407741	−	1.25490i	−0.918585	−	0.395225i	$-0.870667\pi$
$919$	−12.3607	−	38.0423i	−0.407741	−	1.25490i	0.510843	−	0.859674i	$-0.329333\pi$
$920$	−13.3230	−	9.67973i	−0.439247	−	0.319131i
$921$	45.3501	−	32.9488i	1.49434	−	1.08570i
$922$	−26.5937	+	81.8471i	−0.875818	+	2.69549i
$923$	−19.3044			−0.635413
$924$		0			0
$925$	−13.0829			−0.430162
$926$	−5.01660	+	15.4395i	−0.164856	+	0.507374i
$927$	0.244284	−	0.177483i	0.00802335	−	0.00582930i
$928$	−35.3481	−	25.6819i	−1.16036	−	0.843049i
$929$	−4.95560	−	15.2518i	−0.162588	−	0.500394i	0.836263	−	0.548329i	$-0.184736\pi$
$929$	−4.95560	−	15.2518i	−0.162588	−	0.500394i	−0.998850	+	0.0479353i	$0.984736\pi$
$930$	8.83704	+	27.1976i	0.289778	+	0.891844i
$931$	1.39902	+	1.01645i	0.0458510	+	0.0333127i
$932$	−30.4192	+	22.1008i	−0.996414	+	0.723937i
$933$	−5.94932	+	18.3101i	−0.194772	+	0.599446i
$934$	−65.5177			−2.14380
$935$		0			0
$936$	−2.46482			−0.0805652
$937$	−7.81964	+	24.0664i	−0.255456	+	0.786214i	0.738283	+	0.674491i	$0.235637\pi$
$937$	−7.81964	+	24.0664i	−0.255456	+	0.786214i	−0.993739	+	0.111723i	$0.964363\pi$
$938$	14.3433	−	10.4210i	0.468325	−	0.340258i
$939$	−10.5484	−	7.66386i	−0.344234	−	0.250101i
$940$	−29.1657	−	89.7629i	−0.951282	−	2.92774i
$941$	6.34392	+	19.5246i	0.206806	+	0.636484i	0.999634	+	0.0270385i	$0.00860768\pi$
$941$	6.34392	+	19.5246i	0.206806	+	0.636484i	−0.792828	+	0.609445i	$0.791392\pi$
$942$	−44.6183	−	32.4171i	−1.45374	−	1.05620i
$943$	5.26249	−	3.82342i	0.171370	−	0.124508i
$944$	−8.92829	+	27.4784i	−0.290591	+	0.894347i
$945$	13.4017			0.435958
$946$		0			0
$947$	−16.6907			−0.542376			−0.271188	−	0.962526i	$-0.587417\pi$
$947$	−16.6907			−0.542376			−0.271188	+	0.962526i	$0.587417\pi$
$948$	46.7124	−	143.766i	1.51715	−	4.66930i
$949$	20.0664	−	14.5791i	0.651382	−	0.473257i
$950$	7.32868	+	5.32460i	0.237774	+	0.172753i
$951$	−4.84305	−	14.9054i	−0.157047	−	0.483340i
$952$	−7.38887	−	22.7406i	−0.239474	−	0.737027i
$953$	−45.6837	−	33.1911i	−1.47984	−	1.07517i	−0.977608	−	0.210434i	$-0.932512\pi$
$953$	−45.6837	−	33.1911i	−1.47984	−	1.07517i	−0.502232	−	0.864733i	$-0.667488\pi$
$954$	2.13086	−	1.54816i	0.0689893	−	0.0501237i
$955$	−14.8962	+	45.8458i	−0.482030	+	1.48354i
$956$	−25.5510			−0.826379
$957$		0			0
$958$	23.2311			0.750564
$959$	2.90529	−	8.94156i	0.0938166	−	0.288738i
$960$	138.371	−	100.532i	4.46589	−	3.24466i
$961$	21.0258	+	15.2762i	0.678253	+	0.492780i
$962$	14.0534	+	43.2519i	0.453100	+	1.39450i
$963$	0.110171	+	0.339072i	0.00355022	+	0.0109264i
$964$	16.8627	+	12.2514i	0.543110	+	0.394592i
$965$	−6.47214	+	4.70228i	−0.208345	+	0.151372i
$966$	−0.941336	+	2.89714i	−0.0302870	+	0.0932138i
$967$	47.3082			1.52133			0.760665	−	0.649145i	$-0.224873\pi$
$967$	47.3082			1.52133			0.760665	+	0.649145i	$0.224873\pi$
$968$		0			0
$969$	7.27365			0.233663
$970$	18.7256	−	57.6314i	0.601242	−	1.85043i
$971$	20.4160	−	14.8331i	0.655179	−	0.476016i	−0.209852	−	0.977733i	$-0.567298\pi$
$971$	20.4160	−	14.8331i	0.655179	−	0.476016i	0.865032	+	0.501717i	$0.167298\pi$
$972$	4.87399	+	3.54116i	0.156333	+	0.113583i
$973$	4.88919	+	15.0474i	0.156740	+	0.482396i
$974$	21.1599	+	65.1234i	0.678006	+	2.08669i
$975$	6.45494	+	4.68979i	0.206724	+	0.150193i
$976$	137.838	−	100.145i	4.41208	−	3.20556i
$977$	2.19497	−	6.75543i	0.0702234	−	0.216125i	−0.909786	−	0.415078i	$-0.863754\pi$
$977$	2.19497	−	6.75543i	0.0702234	−	0.216125i	0.980009	+	0.198953i	$0.0637541\pi$
$978$	−47.3295			−1.51343
$979$		0			0
$980$	−14.7755			−0.471986
$981$	−0.517130	+	1.59156i	−0.0165107	+	0.0508147i
$982$	−27.2704	+	19.8131i	−0.870232	+	0.632261i
$983$	11.4794	+	8.34025i	0.366135	+	0.266013i	0.755606	−	0.655026i	$-0.227342\pi$
$983$	11.4794	+	8.34025i	0.366135	+	0.266013i	−0.389471	+	0.921039i	$0.627342\pi$
$984$	56.6248	+	174.273i	1.80513	+	5.55562i
$985$	−4.02018	−	12.3729i	−0.128094	−	0.394232i
$986$	9.22502	+	6.70237i	0.293784	+	0.213447i
$987$	−9.10338	+	6.61399i	−0.289764	+	0.210526i
$988$	7.17882	−	22.0941i	0.228389	−	0.702908i
$989$	−4.54144			−0.144409
$990$		0			0
$991$	4.23407			0.134500			0.0672499	−	0.997736i	$-0.478578\pi$
$991$	4.23407			0.134500			0.0672499	+	0.997736i	$0.478578\pi$
$992$	−17.4772	+	53.7892i	−0.554900	+	1.70781i
$993$	−12.2015	+	8.86488i	−0.387202	+	0.281318i
$994$	−18.0625	−	13.1232i	−0.572909	−	0.416243i
$995$	−12.7450	−	39.2251i	−0.404043	−	1.24352i
$996$	39.1266	+	120.419i	1.23977	+	3.81563i
$997$	22.4136	+	16.2844i	0.709845	+	0.515733i	0.883124	−	0.469140i	$-0.155436\pi$
$997$	22.4136	+	16.2844i	0.709845	+	0.515733i	−0.173279	+	0.984873i	$0.555436\pi$
$998$	−49.8807	+	36.2405i	−1.57895	+	1.14717i
$999$	10.8760	−	33.4729i	0.344102	−	1.05904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.t.372.3		12
11.2	odd	10		847.2.f.u.729.3		12
11.3	even	5	inner	847.2.f.t.323.1		12
11.4	even	5		847.2.a.j.1.3	yes	3
11.5	even	5	inner	847.2.f.t.148.3		12
11.6	odd	10		847.2.f.u.148.1		12
11.7	odd	10		847.2.a.i.1.1	✓	3
11.8	odd	10		847.2.f.u.323.3		12
11.9	even	5	inner	847.2.f.t.729.1		12
11.10	odd	2		847.2.f.u.372.1		12
33.26	odd	10		7623.2.a.bz.1.1		3
33.29	even	10		7623.2.a.ce.1.3		3
77.48	odd	10		5929.2.a.y.1.3		3
77.62	even	10		5929.2.a.t.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.i.1.1	✓	3	11.7	odd	10
847.2.a.j.1.3	yes	3	11.4	even	5
847.2.f.t.148.3		12	11.5	even	5	inner
847.2.f.t.323.1		12	11.3	even	5	inner
847.2.f.t.372.3		12	1.1	even	1	trivial
847.2.f.t.729.1		12	11.9	even	5	inner
847.2.f.u.148.1		12	11.6	odd	10
847.2.f.u.323.3		12	11.8	odd	10
847.2.f.u.372.1		12	11.10	odd	2
847.2.f.u.729.3		12	11.2	odd	10
5929.2.a.t.1.1		3	77.62	even	10
5929.2.a.y.1.3		3	77.48	odd	10
7623.2.a.bz.1.1		3	33.26	odd	10
7623.2.a.ce.1.3		3	33.29	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.853368 - 2.62640i) q^{2} +(-1.42513 + 1.03542i) q^{3} +(-4.55169 - 3.30700i) q^{4} +(-0.811540 - 2.49766i) q^{5} +(1.50326 + 4.62655i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-8.10146 + 5.88605i) q^{8} +(0.0318546 - 0.0980384i) q^{9} -7.25240 q^{10} +9.91087 q^{12} +(-0.737857 + 2.27089i) q^{13} +(-2.23415 + 1.62320i) q^{14} +(3.74267 + 2.71921i) q^{15} +(5.06841 + 15.5990i) q^{16} +(-0.737857 - 2.27089i) q^{17} +(-0.230304 - 0.167326i) q^{18} +(1.39902 - 1.01645i) q^{19} +(-4.56588 + 14.0523i) q^{20} +1.76156 q^{21} -0.626198 q^{23} +(5.45111 - 16.7768i) q^{24} +(-1.53464 + 1.11498i) q^{25} +(5.33460 + 3.87581i) q^{26} +(-1.57694 - 4.85332i) q^{27} +(1.73859 + 5.35083i) q^{28} +(-1.39902 - 1.01645i) q^{29} +(10.3356 - 7.50926i) q^{30} +(-0.691717 + 2.12889i) q^{31} +25.2663 q^{32} -6.59392 q^{34} +(-0.811540 + 2.49766i) q^{35} +(-0.469205 + 0.340897i) q^{36} +(5.57972 + 4.05391i) q^{37} +(-1.47571 - 4.54178i) q^{38} +(-1.29978 - 4.00030i) q^{39} +(21.2760 + 15.4579i) q^{40} +(-8.40387 + 6.10577i) q^{41} +(1.50326 - 4.62655i) q^{42} +7.25240 q^{43} -0.270718 q^{45} +(-0.534377 + 1.64464i) q^{46} +(-5.16780 + 3.75463i) q^{47} +(-23.3746 - 16.9826i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.61877 + 4.98206i) q^{50} +(3.40286 + 2.47232i) q^{51} +(10.8683 - 7.89630i) q^{52} +(-2.85915 + 8.79955i) q^{53} -14.0925 q^{54} +10.0140 q^{56} +(-0.941336 + 2.89714i) q^{57} +(-3.86347 + 2.80697i) q^{58} +(1.42513 + 1.03542i) q^{59} +(-8.04307 - 24.7540i) q^{60} +(-3.20999 - 9.87934i) q^{61} +(5.00101 + 3.63345i) q^{62} +(-0.0833965 + 0.0605911i) q^{63} +(11.4247 - 35.1616i) q^{64} +6.27072 q^{65} -6.42003 q^{67} +(-4.15133 + 12.7765i) q^{68} +(0.892413 - 0.648376i) q^{69} +(5.86731 + 4.26285i) q^{70} +(2.49833 + 7.68907i) q^{71} +(0.318991 + 0.981752i) q^{72} +(-8.40387 - 6.10577i) q^{73} +(15.4087 - 11.1951i) q^{74} +(1.03259 - 3.17798i) q^{75} -9.72928 q^{76} -11.6156 q^{78} +(4.71325 - 14.5059i) q^{79} +(34.8477 - 25.3183i) q^{80} +(7.52275 + 5.46559i) q^{81} +(8.86458 + 27.2824i) q^{82} +(3.94785 + 12.1502i) q^{83} +(-8.01806 - 5.82546i) q^{84} +(-5.07312 + 3.68584i) q^{85} +(6.18896 - 19.0477i) q^{86} +3.04623 q^{87} -14.1493 q^{89} +(-0.231022 + 0.711014i) q^{90} +(1.93173 - 1.40349i) q^{91} +(2.85026 + 2.07083i) q^{92} +(-1.21850 - 3.75015i) q^{93} +(5.45111 + 16.7768i) q^{94} +(-3.67410 - 2.66939i) q^{95} +(-36.0078 + 26.1612i) q^{96} +(-2.58199 + 7.94653i) q^{97} +2.76156 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + q^{3} - 8 q^{4} - q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} - 4 q^{9} - 16 q^{10} + 8 q^{12} - 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} - 8 q^{17} + 18 q^{18} + 14 q^{20} - 4 q^{21} + 28 q^{23}+ \cdots + 8 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + q^3 - 8 * q^4 - q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 - 4 * q^9 - 16 * q^10 + 8 * q^12 - 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 - 8 * q^17 + 18 * q^18 + 14 * q^20 - 4 * q^21 + 28 * q^23 - 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 - 8 * q^28 + 8 * q^30 + 13 * q^31 + 136 * q^32 - 48 * q^34 - q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 + 20 * q^39 + 36 * q^40 - 16 * q^41 - 12 * q^42 + 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 - 22 * q^50 + 20 * q^51 + 10 * q^53 + 32 * q^54 + 24 * q^56 - 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 + 16 * q^61 - 4 * q^62 - 4 * q^63 - 34 * q^64 + 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 - 2 * q^72 - 16 * q^73 + 32 * q^74 - 20 * q^75 - 96 * q^76 + 112 * q^78 - 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 84 * q^89 + 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 - 20 * q^94 - 24 * q^95 - 20 * q^96 + 11 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more