LMFDB - Embedded newform 1110.2.l.b.43.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.16
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.b.697.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.132937 - 2.23211i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.47899 - 1.47899i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.132937 - 2.23211i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.47899 - 1.47899i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-2.23211 + 0.132937i) q^{10} +1.15189i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.88999i q^{13} +(-1.47899 - 1.47899i) q^{14} +(-1.67234 - 1.48434i) q^{15} +1.00000 q^{16} +5.62089 q^{17} -1.00000 q^{18} +(1.32254 - 1.32254i) q^{19} +(0.132937 + 2.23211i) q^{20} -2.09160i q^{21} +1.15189 q^{22} -2.70557i q^{23} +(0.707107 + 0.707107i) q^{24} +(-4.96466 + 0.593460i) q^{25} -2.88999 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.47899 + 1.47899i) q^{28} +(-6.59907 - 6.59907i) q^{29} +(-1.48434 + 1.67234i) q^{30} +(-0.920380 + 0.920380i) q^{31} -1.00000i q^{32} +(0.814507 + 0.814507i) q^{33} -5.62089i q^{34} +(-3.49787 - 3.10465i) q^{35} +1.00000i q^{36} +(-3.82793 + 4.72726i) q^{37} +(-1.32254 - 1.32254i) q^{38} +(-2.04353 - 2.04353i) q^{39} +(2.23211 - 0.132937i) q^{40} +6.84388i q^{41} -2.09160 q^{42} +8.92633i q^{43} -1.15189i q^{44} +(-2.23211 + 0.132937i) q^{45} -2.70557 q^{46} +(5.84077 - 5.84077i) q^{47} +(0.707107 - 0.707107i) q^{48} +2.62520i q^{49} +(0.593460 + 4.96466i) q^{50} +(3.97457 - 3.97457i) q^{51} +2.88999i q^{52} +(-4.27233 - 4.27233i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(2.57114 - 0.153128i) q^{55} +(1.47899 + 1.47899i) q^{56} -1.87036i q^{57} +(-6.59907 + 6.59907i) q^{58} +(7.37461 - 7.37461i) q^{59} +(1.67234 + 1.48434i) q^{60} +(0.721634 - 0.721634i) q^{61} +(0.920380 + 0.920380i) q^{62} +(-1.47899 - 1.47899i) q^{63} -1.00000 q^{64} +(-6.45079 + 0.384187i) q^{65} +(0.814507 - 0.814507i) q^{66} +(4.32408 + 4.32408i) q^{67} -5.62089 q^{68} +(-1.91313 - 1.91313i) q^{69} +(-3.10465 + 3.49787i) q^{70} -4.66092 q^{71} +1.00000 q^{72} +(-0.815358 + 0.815358i) q^{73} +(4.72726 + 3.82793i) q^{74} +(-3.09090 + 3.93018i) q^{75} +(-1.32254 + 1.32254i) q^{76} +(1.70362 + 1.70362i) q^{77} +(-2.04353 + 2.04353i) q^{78} +(-11.8987 + 11.8987i) q^{79} +(-0.132937 - 2.23211i) q^{80} -1.00000 q^{81} +6.84388 q^{82} +(-5.88898 - 5.88898i) q^{83} +2.09160i q^{84} +(-0.747224 - 12.5465i) q^{85} +8.92633 q^{86} -9.33249 q^{87} -1.15189 q^{88} +(-6.87434 - 6.87434i) q^{89} +(0.132937 + 2.23211i) q^{90} +(-4.27426 - 4.27426i) q^{91} +2.70557i q^{92} +1.30161i q^{93} +(-5.84077 - 5.84077i) q^{94} +(-3.12787 - 2.77625i) q^{95} +(-0.707107 - 0.707107i) q^{96} +14.2915 q^{97} +2.62520 q^{98} +1.15189 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) $ 40 * q - 40 * q^4 - 4 * q^7	$ 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−0.132937	−	2.23211i	−0.0594512	−	0.998231i
$5$	−0.132937	−	2.23211i	−0.0594512	−	0.998231i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	1.47899	−	1.47899i	0.559004	−	0.559004i	−0.370020	−	0.929024i	$-0.620649\pi$
$7$	1.47899	−	1.47899i	0.559004	−	0.559004i	0.929024	+	0.370020i	$0.120649\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−2.23211	+	0.132937i	−0.705856	+	0.0420383i
$11$			1.15189i			0.347307i	0.984807	+	0.173653i	$0.0555572\pi$
$11$			1.15189i			0.347307i	−0.984807	+	0.173653i	$0.944443\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$		−	2.88999i		−	0.801540i	−0.916179	−	0.400770i	$-0.868743\pi$
$13$		−	2.88999i		−	0.801540i	0.916179	−	0.400770i	$-0.131257\pi$
$14$	−1.47899	−	1.47899i	−0.395276	−	0.395276i
$15$	−1.67234	−	1.48434i	−0.431797	−	0.383255i
$16$	1.00000			0.250000
$17$	5.62089			1.36327			0.681633	−	0.731694i	$-0.261270\pi$
$17$	5.62089			1.36327			0.681633	+	0.731694i	$0.261270\pi$
$18$	−1.00000			−0.235702
$19$	1.32254	−	1.32254i	0.303412	−	0.303412i	−0.538935	−	0.842347i	$-0.681173\pi$
$19$	1.32254	−	1.32254i	0.303412	−	0.303412i	0.842347	+	0.538935i	$0.181173\pi$
$20$	0.132937	+	2.23211i	0.0297256	+	0.499116i
$21$		−	2.09160i		−	0.456425i
$22$	1.15189			0.245583
$23$		−	2.70557i		−	0.564151i	−0.959392	−	0.282075i	$-0.908977\pi$
$23$		−	2.70557i		−	0.564151i	0.959392	−	0.282075i	$-0.0910228\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	−4.96466	+	0.593460i	−0.992931	+	0.118692i
$26$	−2.88999			−0.566775
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.47899	+	1.47899i	−0.279502	+	0.279502i
$29$	−6.59907	−	6.59907i	−1.22542	−	1.22542i	−0.965679	−	0.259737i	$-0.916364\pi$
$29$	−6.59907	−	6.59907i	−1.22542	−	1.22542i	−0.259737	−	0.965679i	$-0.583636\pi$
$30$	−1.48434	+	1.67234i	−0.271002	+	0.305327i
$31$	−0.920380	+	0.920380i	−0.165305	+	0.165305i	−0.784912	−	0.619607i	$-0.787292\pi$
$31$	−0.920380	+	0.920380i	−0.165305	+	0.165305i	0.619607	+	0.784912i	$0.287292\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.814507	+	0.814507i	0.141787	+	0.141787i
$34$		−	5.62089i		−	0.963975i
$35$	−3.49787	−	3.10465i	−0.591249	−	0.524782i
$36$			1.00000i			0.166667i
$37$	−3.82793	+	4.72726i	−0.629307	+	0.777157i
$37$	−3.82793	+	4.72726i	−0.629307	+	0.777157i
$38$	−1.32254	−	1.32254i	−0.214544	−	0.214544i
$39$	−2.04353	−	2.04353i	−0.327227	−	0.327227i
$40$	2.23211	−	0.132937i	0.352928	−	0.0210192i
$41$			6.84388i			1.06883i	0.845221	+	0.534417i	$0.179469\pi$
$41$			6.84388i			1.06883i	−0.845221	+	0.534417i	$0.820531\pi$
$42$	−2.09160			−0.322741
$43$			8.92633i			1.36125i	0.732631	+	0.680626i	$0.238292\pi$
$43$			8.92633i			1.36125i	−0.732631	+	0.680626i	$0.761708\pi$
$44$		−	1.15189i		−	0.173653i
$45$	−2.23211	+	0.132937i	−0.332744	+	0.0198171i
$46$	−2.70557			−0.398915
$47$	5.84077	−	5.84077i	0.851963	−	0.851963i	−0.138412	−	0.990375i	$-0.544200\pi$
$47$	5.84077	−	5.84077i	0.851963	−	0.851963i	0.990375	+	0.138412i	$0.0441997\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			2.62520i			0.375029i
$50$	0.593460	+	4.96466i	0.0839279	+	0.702108i
$51$	3.97457	−	3.97457i	0.556551	−	0.556551i
$52$			2.88999i			0.400770i
$53$	−4.27233	−	4.27233i	−0.586850	−	0.586850i	0.349927	−	0.936777i	$-0.386206\pi$
$53$	−4.27233	−	4.27233i	−0.586850	−	0.586850i	−0.936777	+	0.349927i	$0.886206\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	2.57114	−	0.153128i	0.346692	−	0.0206478i
$56$	1.47899	+	1.47899i	0.197638	+	0.197638i
$57$		−	1.87036i		−	0.247735i
$58$	−6.59907	+	6.59907i	−0.866500	+	0.866500i
$59$	7.37461	−	7.37461i	0.960092	−	0.960092i	−0.0391416	−	0.999234i	$-0.512462\pi$
$59$	7.37461	−	7.37461i	0.960092	−	0.960092i	0.999234	+	0.0391416i	$0.0124623\pi$
$60$	1.67234	+	1.48434i	0.215899	+	0.191628i
$61$	0.721634	−	0.721634i	0.0923958	−	0.0923958i	−0.659398	−	0.751794i	$-0.729189\pi$
$61$	0.721634	−	0.721634i	0.0923958	−	0.0923958i	0.751794	+	0.659398i	$0.229189\pi$
$62$	0.920380	+	0.920380i	0.116888	+	0.116888i
$63$	−1.47899	−	1.47899i	−0.186335	−	0.186335i
$64$	−1.00000			−0.125000
$65$	−6.45079	+	0.384187i	−0.800122	+	0.0476525i
$66$	0.814507	−	0.814507i	0.100259	−	0.100259i
$67$	4.32408	+	4.32408i	0.528271	+	0.528271i	0.920057	−	0.391786i	$-0.128143\pi$
$67$	4.32408	+	4.32408i	0.528271	+	0.528271i	−0.391786	+	0.920057i	$0.628143\pi$
$68$	−5.62089			−0.681633
$69$	−1.91313	−	1.91313i	−0.230314	−	0.230314i
$70$	−3.10465	+	3.49787i	−0.371077	+	0.418076i
$71$	−4.66092			−0.553150			−0.276575	−	0.960992i	$-0.589199\pi$
$71$	−4.66092			−0.553150			−0.276575	+	0.960992i	$0.589199\pi$
$72$	1.00000			0.117851
$73$	−0.815358	+	0.815358i	−0.0954304	+	0.0954304i	−0.753210	−	0.657780i	$-0.771496\pi$
$73$	−0.815358	+	0.815358i	−0.0954304	+	0.0954304i	0.657780	+	0.753210i	$0.271496\pi$
$74$	4.72726	+	3.82793i	0.549533	+	0.444987i
$75$	−3.09090	+	3.93018i	−0.356907	+	0.453818i
$76$	−1.32254	+	1.32254i	−0.151706	+	0.151706i
$77$	1.70362	+	1.70362i	0.194146	+	0.194146i
$78$	−2.04353	+	2.04353i	−0.231385	+	0.231385i
$79$	−11.8987	+	11.8987i	−1.33871	+	1.33871i	−0.441403	+	0.897309i	$0.645519\pi$
$79$	−11.8987	+	11.8987i	−1.33871	+	1.33871i	−0.897309	+	0.441403i	$0.854481\pi$
$80$	−0.132937	−	2.23211i	−0.0148628	−	0.249558i
$81$	−1.00000			−0.111111
$82$	6.84388			0.755780
$83$	−5.88898	−	5.88898i	−0.646399	−	0.646399i	0.305722	−	0.952121i	$-0.401102\pi$
$83$	−5.88898	−	5.88898i	−0.646399	−	0.646399i	−0.952121	+	0.305722i	$0.901102\pi$
$84$			2.09160i			0.228212i
$85$	−0.747224	−	12.5465i	−0.0810478	−	1.36086i
$86$	8.92633			0.962551
$87$	−9.33249			−1.00055
$88$	−1.15189			−0.122791
$89$	−6.87434	−	6.87434i	−0.728678	−	0.728678i	0.241678	−	0.970356i	$-0.422302\pi$
$89$	−6.87434	−	6.87434i	−0.728678	−	0.728678i	−0.970356	+	0.241678i	$0.922302\pi$
$90$	0.132937	+	2.23211i	0.0140128	+	0.235285i
$91$	−4.27426	−	4.27426i	−0.448064	−	0.448064i
$92$			2.70557i			0.282075i
$93$			1.30161i			0.134971i
$94$	−5.84077	−	5.84077i	−0.602429	−	0.602429i
$95$	−3.12787	−	2.77625i	−0.320913	−	0.284837i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	14.2915			1.45108			0.725539	−	0.688181i	$-0.241590\pi$
$97$	14.2915			1.45108			0.725539	+	0.688181i	$0.241590\pi$
$98$	2.62520			0.265186
$99$	1.15189			0.115769
$100$	4.96466	−	0.593460i	0.496466	−	0.0593460i
$101$		−	6.54373i		−	0.651125i	−0.945520	−	0.325563i	$-0.894446\pi$
$101$		−	6.54373i		−	0.651125i	0.945520	−	0.325563i	$-0.105554\pi$
$102$	−3.97457	−	3.97457i	−0.393541	−	0.393541i
$103$	2.35550			0.232094			0.116047	−	0.993244i	$-0.462978\pi$
$103$	2.35550			0.232094			0.116047	+	0.993244i	$0.462978\pi$
$104$	2.88999			0.283387
$105$	−4.66869	+	0.278051i	−0.455618	+	0.0271350i
$106$	−4.27233	+	4.27233i	−0.414965	+	0.414965i
$107$	−6.74914	+	6.74914i	−0.652464	+	0.652464i	−0.953586	−	0.301122i	$-0.902639\pi$
$107$	−6.74914	+	6.74914i	−0.652464	+	0.652464i	0.301122	+	0.953586i	$0.402639\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	1.88769	−	1.88769i	0.180808	−	0.180808i	−0.610900	−	0.791708i	$-0.709192\pi$
$109$	1.88769	−	1.88769i	0.180808	−	0.180808i	0.791708	+	0.610900i	$0.209192\pi$
$110$	−0.153128	−	2.57114i	−0.0146002	−	0.245149i
$111$	0.635924	+	6.04943i	0.0603592	+	0.574186i
$112$	1.47899	−	1.47899i	0.139751	−	0.139751i
$113$	17.4956			1.64585			0.822923	−	0.568153i	$-0.192342\pi$
$113$	17.4956			1.64585			0.822923	+	0.568153i	$0.192342\pi$
$114$	−1.87036			−0.175175
$115$	−6.03914	+	0.359670i	−0.563153	+	0.0335394i
$116$	6.59907	+	6.59907i	0.612708	+	0.612708i
$117$	−2.88999			−0.267180
$118$	−7.37461	−	7.37461i	−0.678888	−	0.678888i
$119$	8.31322	−	8.31322i	0.762072	−	0.762072i
$120$	1.48434	−	1.67234i	0.135501	−	0.152663i
$121$	9.67316			0.879378
$122$	−0.721634	−	0.721634i	−0.0653337	−	0.0653337i
$123$	4.83935	+	4.83935i	0.436350	+	0.436350i
$124$	0.920380	−	0.920380i	0.0826526	−	0.0826526i
$125$	1.98466	+	11.0028i	0.177513	+	0.984118i
$126$	−1.47899	+	1.47899i	−0.131759	+	0.131759i
$127$	0.311708	−	0.311708i	0.0276596	−	0.0276596i	−0.693142	−	0.720801i	$-0.743774\pi$
$127$	0.311708	−	0.311708i	0.0276596	−	0.0276596i	0.720801	+	0.693142i	$0.243774\pi$
$128$			1.00000i			0.0883883i
$129$	6.31187	+	6.31187i	0.555729	+	0.555729i
$130$	0.384187	+	6.45079i	0.0336954	+	0.565772i
$131$	12.4801	−	12.4801i	1.09039	−	1.09039i	0.0949069	−	0.995486i	$-0.469745\pi$
$131$	12.4801	−	12.4801i	1.09039	−	1.09039i	0.995486	−	0.0949069i	$-0.0302553\pi$
$132$	−0.814507	−	0.814507i	−0.0708937	−	0.0708937i
$133$		−	3.91204i		−	0.339217i
$134$	4.32408	−	4.32408i	0.373544	−	0.373544i
$135$	−1.48434	+	1.67234i	−0.127752	+	0.143932i
$136$			5.62089i			0.481988i
$137$	−11.8735	+	11.8735i	−1.01442	+	1.01442i	−0.0145281	+	0.999894i	$0.504625\pi$
$137$	−11.8735	+	11.8735i	−1.01442	+	1.01442i	−0.999894	+	0.0145281i	$0.995375\pi$
$138$	−1.91313	+	1.91313i	−0.162856	+	0.162856i
$139$	15.6010			1.32326			0.661629	−	0.749832i	$-0.269866\pi$
$139$	15.6010			1.32326			0.661629	+	0.749832i	$0.269866\pi$
$140$	3.49787	+	3.10465i	0.295624	+	0.262391i
$141$		−	8.26009i		−	0.695625i
$142$			4.66092i			0.391136i
$143$	3.32894			0.278380
$144$		−	1.00000i		−	0.0833333i
$145$	−13.8526	+	15.6071i	−1.15040	+	1.29610i
$146$	0.815358	+	0.815358i	0.0674795	+	0.0674795i
$147$	1.85630	+	1.85630i	0.153105	+	0.153105i
$148$	3.82793	−	4.72726i	0.314654	−	0.388578i
$149$			4.64148i			0.380245i	0.981760	+	0.190122i	$0.0608885\pi$
$149$			4.64148i			0.380245i	−0.981760	+	0.190122i	$0.939111\pi$
$150$	3.93018	+	3.09090i	0.320898	+	0.252371i
$151$		−	14.5106i		−	1.18086i	−0.807090	−	0.590429i	$-0.798959\pi$
$151$		−	14.5106i		−	1.18086i	0.807090	−	0.590429i	$-0.201041\pi$
$152$	1.32254	+	1.32254i	0.107272	+	0.107272i
$153$		−	5.62089i		−	0.454422i
$154$	1.70362	−	1.70362i	0.137282	−	0.137282i
$155$	2.17675	+	1.93204i	0.174840	+	0.155185i
$156$	2.04353	+	2.04353i	0.163614	+	0.163614i
$157$	−13.1125	+	13.1125i	−1.04649	+	1.04649i	−0.0476223	+	0.998865i	$0.515164\pi$
$157$	−13.1125	+	13.1125i	−1.04649	+	1.04649i	−0.998865	+	0.0476223i	$0.984836\pi$
$158$	11.8987	+	11.8987i	0.946612	+	0.946612i
$159$	−6.04199			−0.479161
$160$	−2.23211	+	0.132937i	−0.176464	+	0.0105096i
$161$	−4.00150	−	4.00150i	−0.315363	−	0.315363i
$162$			1.00000i			0.0785674i
$163$	−8.81029			−0.690076			−0.345038	−	0.938589i	$-0.612134\pi$
$163$	−8.81029			−0.690076			−0.345038	+	0.938589i	$0.612134\pi$
$164$		−	6.84388i		−	0.534417i
$165$	1.70979	−	1.92635i	0.133107	−	0.149966i
$166$	−5.88898	+	5.88898i	−0.457073	+	0.457073i
$167$	13.2859			1.02809			0.514046	−	0.857763i	$-0.328146\pi$
$167$	13.2859			1.02809			0.514046	+	0.857763i	$0.328146\pi$
$168$	2.09160			0.161371
$169$	4.64793			0.357533
$170$	−12.5465	+	0.747224i	−0.962270	+	0.0573094i
$171$	−1.32254	−	1.32254i	−0.101137	−	0.101137i
$172$		−	8.92633i		−	0.680626i
$173$	16.3729	−	16.3729i	1.24481	−	1.24481i	0.286822	−	0.957984i	$-0.407401\pi$
$173$	16.3729	−	16.3729i	1.24481	−	1.24481i	0.957984	−	0.286822i	$-0.0925990\pi$
$174$			9.33249i			0.707495i
$175$	−6.46494	+	8.22037i	−0.488703	+	0.621402i
$176$			1.15189i			0.0868267i
$177$		−	10.4293i		−	0.783912i
$178$	−6.87434	+	6.87434i	−0.515253	+	0.515253i
$179$	−6.39446	−	6.39446i	−0.477945	−	0.477945i	0.426529	−	0.904474i	$-0.359736\pi$
$179$	−6.39446	−	6.39446i	−0.477945	−	0.477945i	−0.904474	+	0.426529i	$0.859736\pi$
$180$	2.23211	−	0.132937i	0.166372	−	0.00990853i
$181$	7.94042			0.590206			0.295103	−	0.955465i	$-0.404646\pi$
$181$	7.94042			0.590206			0.295103	+	0.955465i	$0.404646\pi$
$182$	−4.27426	+	4.27426i	−0.316829	+	0.316829i
$183$		−	1.02055i		−	0.0754409i
$184$	2.70557			0.199457
$185$	11.0606	+	7.91594i	0.813195	+	0.581991i
$186$	1.30161			0.0954390
$187$			6.47463i			0.473472i
$188$	−5.84077	+	5.84077i	−0.425982	+	0.425982i
$189$	−2.09160			−0.152142
$190$	−2.77625	+	3.12787i	−0.201410	+	0.226920i
$191$	17.8463	+	17.8463i	1.29131	+	1.29131i	0.933977	+	0.357332i	$0.116314\pi$
$191$	17.8463	+	17.8463i	1.29131	+	1.29131i	0.357332	+	0.933977i	$0.383686\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$			5.07031i			0.364969i	0.983209	+	0.182485i	$0.0584140\pi$
$193$			5.07031i			0.364969i	−0.983209	+	0.182485i	$0.941586\pi$
$194$		−	14.2915i		−	1.02607i
$195$	−4.28974	+	4.83306i	−0.307195	+	0.346103i
$196$		−	2.62520i		−	0.187514i
$197$	−11.3573	+	11.3573i	−0.809177	+	0.809177i	−0.984509	−	0.175332i	$-0.943900\pi$
$197$	−11.3573	+	11.3573i	−0.809177	+	0.809177i	0.175332	+	0.984509i	$0.443900\pi$
$198$		−	1.15189i		−	0.0818610i
$199$	−12.7174	−	12.7174i	−0.901511	−	0.901511i	0.0940562	−	0.995567i	$-0.470017\pi$
$199$	−12.7174	−	12.7174i	−0.901511	−	0.901511i	−0.995567	+	0.0940562i	$0.970017\pi$
$200$	−0.593460	−	4.96466i	−0.0419640	−	0.351054i
$201$	6.11518			0.431331
$202$	−6.54373			−0.460415
$203$	−19.5199			−1.37003
$204$	−3.97457	+	3.97457i	−0.278276	+	0.278276i
$205$	15.2763	−	0.909804i	1.06694	−	0.0635435i
$206$		−	2.35550i		−	0.164116i
$207$	−2.70557			−0.188050
$208$		−	2.88999i		−	0.200385i
$209$	1.52342	+	1.52342i	0.105377	+	0.105377i
$210$	0.278051	+	4.66869i	0.0191873	+	0.322170i
$211$	21.8632			1.50512			0.752562	−	0.658521i	$-0.228818\pi$
$211$	21.8632			1.50512			0.752562	+	0.658521i	$0.228818\pi$
$212$	4.27233	+	4.27233i	0.293425	+	0.293425i
$213$	−3.29577	+	3.29577i	−0.225823	+	0.225823i
$214$	6.74914	+	6.74914i	0.461361	+	0.461361i
$215$	19.9246	−	1.18664i	1.35885	−	0.0809281i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$			2.72246i			0.184813i
$218$	−1.88769	−	1.88769i	−0.127851	−	0.127851i
$219$			1.15309i			0.0779186i
$220$	−2.57114	+	0.153128i	−0.173346	+	0.0103239i
$221$		−	16.2443i		−	1.09271i
$222$	6.04943	−	0.635924i	0.406011	−	0.0426804i
$223$	−9.79908	−	9.79908i	−0.656195	−	0.656195i	0.298283	−	0.954478i	$-0.403586\pi$
$223$	−9.79908	−	9.79908i	−0.656195	−	0.656195i	−0.954478	+	0.298283i	$0.903586\pi$
$224$	−1.47899	−	1.47899i	−0.0988189	−	0.0988189i
$225$	0.593460	+	4.96466i	0.0395640	+	0.330977i
$226$		−	17.4956i		−	1.16379i
$227$	12.4848			0.828645			0.414322	−	0.910130i	$-0.364019\pi$
$227$	12.4848			0.828645			0.414322	+	0.910130i	$0.364019\pi$
$228$			1.87036i			0.123867i
$229$			4.90899i			0.324395i	0.986758	+	0.162197i	$0.0518582\pi$
$229$			4.90899i			0.324395i	−0.986758	+	0.162197i	$0.948142\pi$
$230$	0.359670	+	6.03914i	0.0237160	+	0.398209i
$231$	2.40929			0.158519
$232$	6.59907	−	6.59907i	0.433250	−	0.433250i
$233$	6.62951	−	6.62951i	0.434313	−	0.434313i	−0.455779	−	0.890093i	$-0.650639\pi$
$233$	6.62951	−	6.62951i	0.434313	−	0.434313i	0.890093	+	0.455779i	$0.150639\pi$
$234$			2.88999i			0.188925i
$235$	−13.8137	−	12.2608i	−0.901106	−	0.799806i
$236$	−7.37461	+	7.37461i	−0.480046	+	0.480046i
$237$			16.8273i			1.09305i
$238$	−8.31322	−	8.31322i	−0.538866	−	0.538866i
$239$	14.4055	−	14.4055i	0.931817	−	0.931817i	−0.0660028	−	0.997819i	$-0.521025\pi$
$239$	14.4055	−	14.4055i	0.931817	−	0.931817i	0.997819	+	0.0660028i	$0.0210246\pi$
$240$	−1.67234	−	1.48434i	−0.107949	−	0.0958138i
$241$	−5.83291	−	5.83291i	−0.375731	−	0.375731i	0.493829	−	0.869559i	$-0.335597\pi$
$241$	−5.83291	−	5.83291i	−0.375731	−	0.375731i	−0.869559	+	0.493829i	$0.835597\pi$
$242$		−	9.67316i		−	0.621814i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−0.721634	+	0.721634i	−0.0461979	+	0.0461979i
$245$	5.85975	−	0.348986i	0.374366	−	0.0222959i
$246$	4.83935	−	4.83935i	0.308546	−	0.308546i
$247$	−3.82214	−	3.82214i	−0.243197	−	0.243197i
$248$	−0.920380	−	0.920380i	−0.0584442	−	0.0584442i
$249$	−8.32827			−0.527783
$250$	11.0028	−	1.98466i	0.695877	−	0.125521i
$251$	12.0063	−	12.0063i	0.757830	−	0.757830i	−0.218097	−	0.975927i	$-0.569985\pi$
$251$	12.0063	−	12.0063i	0.757830	−	0.757830i	0.975927	+	0.218097i	$0.0699848\pi$
$252$	1.47899	+	1.47899i	0.0931673	+	0.0931673i
$253$	3.11651			0.195933
$254$	−0.311708	−	0.311708i	−0.0195583	−	0.0195583i
$255$	−9.40006	−	8.34333i	−0.588655	−	0.522479i
$256$	1.00000			0.0625000
$257$	8.79481			0.548605			0.274303	−	0.961643i	$-0.411553\pi$
$257$	8.79481			0.548605			0.274303	+	0.961643i	$0.411553\pi$
$258$	6.31187	−	6.31187i	0.392960	−	0.392960i
$259$	1.33010	+	12.6530i	0.0826483	+	0.786219i
$260$	6.45079	−	0.384187i	0.400061	−	0.0238262i
$261$	−6.59907	+	6.59907i	−0.408472	+	0.408472i
$262$	−12.4801	−	12.4801i	−0.771024	−	0.771024i
$263$	−4.85857	+	4.85857i	−0.299592	+	0.299592i	−0.840854	−	0.541262i	$-0.817947\pi$
$263$	−4.85857	+	4.85857i	−0.299592	+	0.299592i	0.541262	+	0.840854i	$0.317947\pi$
$264$	−0.814507	+	0.814507i	−0.0501294	+	0.0501294i
$265$	−8.96837	+	10.1043i	−0.550923	+	0.620701i
$266$	−3.91204			−0.239862
$267$	−9.72178			−0.594963
$268$	−4.32408	−	4.32408i	−0.264135	−	0.264135i
$269$			10.8073i			0.658933i	0.944167	+	0.329466i	$0.106869\pi$
$269$			10.8073i			0.658933i	−0.944167	+	0.329466i	$0.893131\pi$
$270$	1.67234	+	1.48434i	0.101776	+	0.0903342i
$271$	20.9907			1.27509			0.637547	−	0.770411i	$-0.279949\pi$
$271$	20.9907			1.27509			0.637547	+	0.770411i	$0.279949\pi$
$272$	5.62089			0.340817
$273$	−6.04472			−0.365843
$274$	11.8735	+	11.8735i	0.717305	+	0.717305i
$275$	−0.683599	−	5.71872i	−0.0412225	−	0.344852i
$276$	1.91313	+	1.91313i	0.115157	+	0.115157i
$277$			2.34619i			0.140969i	0.997513	+	0.0704844i	$0.0224545\pi$
$277$			2.34619i			0.140969i	−0.997513	+	0.0704844i	$0.977545\pi$
$278$		−	15.6010i		−	0.935684i
$279$	0.920380	+	0.920380i	0.0551017	+	0.0551017i
$280$	3.10465	−	3.49787i	0.185538	−	0.209038i
$281$	12.4830	+	12.4830i	0.744674	+	0.744674i	0.973474	−	0.228800i	$-0.0734800\pi$
$281$	12.4830	+	12.4830i	0.744674	+	0.744674i	−0.228800	+	0.973474i	$0.573480\pi$
$282$	−8.26009			−0.491881
$283$	4.16867			0.247802			0.123901	−	0.992295i	$-0.460460\pi$
$283$	4.16867			0.247802			0.123901	+	0.992295i	$0.460460\pi$
$284$	4.66092			0.276575
$285$	−4.17484	+	0.248639i	−0.247296	+	0.0147281i
$286$		−	3.32894i		−	0.196845i
$287$	10.1220	+	10.1220i	0.597483	+	0.597483i
$288$	−1.00000			−0.0589256
$289$	14.5944			0.858496
$290$	15.6071	+	13.8526i	0.916482	+	0.813453i
$291$	10.1056	−	10.1056i	0.592400	−	0.592400i
$292$	0.815358	−	0.815358i	0.0477152	−	0.0477152i
$293$	3.92862	+	3.92862i	0.229513	+	0.229513i	0.812489	−	0.582976i	$-0.198112\pi$
$293$	3.92862	+	3.92862i	0.229513	+	0.229513i	−0.582976	+	0.812489i	$0.698112\pi$
$294$	1.85630	−	1.85630i	0.108262	−	0.108262i
$295$	−17.4413	−	15.4806i	−1.01547	−	0.901315i
$296$	−4.72726	−	3.82793i	−0.274766	−	0.222494i
$297$	0.814507	−	0.814507i	0.0472625	−	0.0472625i
$298$	4.64148			0.268874
$299$	−7.81909			−0.452190
$300$	3.09090	−	3.93018i	0.178453	−	0.226909i
$301$	13.2019	+	13.2019i	0.760946	+	0.760946i
$302$	−14.5106			−0.834993
$303$	−4.62711	−	4.62711i	−0.265821	−	0.265821i
$304$	1.32254	−	1.32254i	0.0758529	−	0.0758529i
$305$	−1.70670	−	1.51484i	−0.0977254	−	0.0867394i
$306$	−5.62089			−0.321325
$307$	0.507816	+	0.507816i	0.0289826	+	0.0289826i	0.721450	−	0.692467i	$-0.243476\pi$
$307$	0.507816	+	0.507816i	0.0289826	+	0.0289826i	−0.692467	+	0.721450i	$0.743476\pi$
$308$	−1.70362	−	1.70362i	−0.0970729	−	0.0970729i
$309$	1.66559	−	1.66559i	0.0947522	−	0.0947522i
$310$	1.93204	−	2.17675i	0.109733	−	0.123631i
$311$	−0.433905	+	0.433905i	−0.0246045	+	0.0246045i	−0.719302	−	0.694697i	$-0.755538\pi$
$311$	−0.433905	+	0.433905i	−0.0246045	+	0.0246045i	0.694697	+	0.719302i	$0.255538\pi$
$312$	2.04353	−	2.04353i	0.115692	−	0.115692i
$313$			18.8073i			1.06305i	0.847042	+	0.531526i	$0.178381\pi$
$313$			18.8073i			1.06305i	−0.847042	+	0.531526i	$0.821619\pi$
$314$	13.1125	+	13.1125i	0.739979	+	0.739979i
$315$	−3.10465	+	3.49787i	−0.174927	+	0.197083i
$316$	11.8987	−	11.8987i	0.669356	−	0.669356i
$317$	−11.5222	−	11.5222i	−0.647149	−	0.647149i	0.305154	−	0.952303i	$-0.401292\pi$
$317$	−11.5222	−	11.5222i	−0.647149	−	0.647149i	−0.952303	+	0.305154i	$0.901292\pi$
$318$			6.04199i			0.338818i
$319$	7.60138	−	7.60138i	0.425596	−	0.425596i
$320$	0.132937	+	2.23211i	0.00743140	+	0.124779i
$321$			9.54472i			0.532734i
$322$	−4.00150	+	4.00150i	−0.222995	+	0.222995i
$323$	7.43386	−	7.43386i	0.413631	−	0.413631i
$324$	1.00000			0.0555556
$325$	1.71510	+	14.3478i	0.0951364	+	0.795874i
$326$			8.81029i			0.487957i
$327$		−	2.66960i		−	0.147629i
$328$	−6.84388			−0.377890
$329$		−	17.2768i		−	0.952502i
$330$	−1.92635	−	1.70979i	−0.106042	−	0.0941210i
$331$	−7.39172	−	7.39172i	−0.406286	−	0.406286i	0.474155	−	0.880441i	$-0.342753\pi$
$331$	−7.39172	−	7.39172i	−0.406286	−	0.406286i	−0.880441	+	0.474155i	$0.842753\pi$
$332$	5.88898	+	5.88898i	0.323199	+	0.323199i
$333$	4.72726	+	3.82793i	0.259052	+	0.209769i
$334$		−	13.2859i		−	0.726971i
$335$	9.07701	−	10.2267i	0.495930	−	0.558743i
$336$		−	2.09160i		−	0.114106i
$337$	4.90709	+	4.90709i	0.267306	+	0.267306i	0.828014	−	0.560708i	$-0.189471\pi$
$337$	4.90709	+	4.90709i	0.267306	+	0.267306i	−0.560708	+	0.828014i	$0.689471\pi$
$338$		−	4.64793i		−	0.252814i
$339$	12.3712	−	12.3712i	0.671914	−	0.671914i
$340$	0.747224	+	12.5465i	0.0405239	+	0.680428i
$341$	−1.06017	−	1.06017i	−0.0574116	−	0.0574116i
$342$	−1.32254	+	1.32254i	−0.0715148	+	0.0715148i
$343$	14.2355	+	14.2355i	0.768647	+	0.768647i
$344$	−8.92633			−0.481276
$345$	−4.01599	+	4.52464i	−0.216214	+	0.243599i
$346$	−16.3729	−	16.3729i	−0.880211	−	0.880211i
$347$		−	5.47655i		−	0.293997i	−0.989137	−	0.146998i	$-0.953039\pi$
$347$		−	5.47655i		−	0.293997i	0.989137	−	0.146998i	$-0.0469612\pi$
$348$	9.33249			0.500274
$349$			17.9938i			0.963188i	0.876394	+	0.481594i	$0.159942\pi$
$349$			17.9938i			0.963188i	−0.876394	+	0.481594i	$0.840058\pi$
$350$	8.22037	+	6.46494i	0.439397	+	0.345565i
$351$	−2.04353	+	2.04353i	−0.109076	+	0.109076i
$352$	1.15189			0.0613957
$353$	0.511524			0.0272257			0.0136128	−	0.999907i	$-0.495667\pi$
$353$	0.511524			0.0272257			0.0136128	+	0.999907i	$0.495667\pi$
$354$	−10.4293			−0.554309
$355$	0.619609	+	10.4037i	0.0328854	+	0.552172i
$356$	6.87434	+	6.87434i	0.364339	+	0.364339i
$357$		−	11.7567i		−	0.622229i
$358$	−6.39446	+	6.39446i	−0.337958	+	0.337958i
$359$		−	30.4736i		−	1.60833i	−0.594403	−	0.804167i	$-0.702612\pi$
$359$		−	30.4736i		−	1.60833i	0.594403	−	0.804167i	$-0.297388\pi$
$360$	−0.132937	−	2.23211i	−0.00700639	−	0.117643i
$361$			15.5018i			0.815883i
$362$		−	7.94042i		−	0.417339i
$363$	6.83996	−	6.83996i	0.359005	−	0.359005i
$364$	4.27426	+	4.27426i	0.224032	+	0.224032i
$365$	1.92836	+	1.71158i	0.100935	+	0.0895882i
$366$	−1.02055			−0.0533448
$367$	1.10113	−	1.10113i	0.0574786	−	0.0574786i	−0.677783	−	0.735262i	$-0.737059\pi$
$367$	1.10113	−	1.10113i	0.0574786	−	0.0574786i	0.735262	+	0.677783i	$0.237059\pi$
$368$		−	2.70557i		−	0.141038i
$369$	6.84388			0.356278
$370$	7.91594	−	11.0606i	0.411530	−	0.575016i
$371$	−12.6374			−0.656103
$372$		−	1.30161i		−	0.0674856i
$373$	−13.3085	+	13.3085i	−0.689088	+	0.689088i	−0.962030	−	0.272943i	$-0.912003\pi$
$373$	−13.3085	+	13.3085i	−0.689088	+	0.689088i	0.272943	+	0.962030i	$0.412003\pi$
$374$	6.47463			0.334795
$375$	9.18350	+	6.37678i	0.474234	+	0.329295i
$376$	5.84077	+	5.84077i	0.301214	+	0.301214i
$377$	−19.0713	+	19.0713i	−0.982221	+	0.982221i
$378$			2.09160i			0.107580i
$379$		−	31.3641i		−	1.61107i	−0.592551	−	0.805533i	$-0.701879\pi$
$379$		−	31.3641i		−	1.61107i	0.592551	−	0.805533i	$-0.298121\pi$
$380$	3.12787	+	2.77625i	0.160457	+	0.142418i
$381$		−	0.440822i		−	0.0225840i
$382$	17.8463	−	17.8463i	0.913094	−	0.913094i
$383$			7.04860i			0.360167i	0.983651	+	0.180083i	$0.0576368\pi$
$383$			7.04860i			0.360167i	−0.983651	+	0.180083i	$0.942363\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	3.57621	−	4.02915i	0.182260	−	0.205345i
$386$	5.07031			0.258072
$387$	8.92633			0.453751
$388$	−14.2915			−0.725539
$389$	−18.3786	+	18.3786i	−0.931831	+	0.931831i	−0.997820	−	0.0659891i	$-0.978980\pi$
$389$	−18.3786	+	18.3786i	−0.931831	+	0.931831i	0.0659891	+	0.997820i	$0.478980\pi$
$390$	4.83306	+	4.28974i	0.244732	+	0.217219i
$391$		−	15.2077i		−	0.769088i
$392$	−2.62520			−0.132593
$393$		−	17.6496i		−	0.890302i
$394$	11.3573	+	11.3573i	0.572175	+	0.572175i
$395$	28.1411	+	24.9775i	1.41593	+	1.25676i
$396$	−1.15189			−0.0578845
$397$	−11.4488	−	11.4488i	−0.574601	−	0.574601i	0.358810	−	0.933411i	$-0.383183\pi$
$397$	−11.4488	−	11.4488i	−0.574601	−	0.574601i	−0.933411	+	0.358810i	$0.883183\pi$
$398$	−12.7174	+	12.7174i	−0.637464	+	0.637464i
$399$	−2.76623	−	2.76623i	−0.138485	−	0.138485i
$400$	−4.96466	+	0.593460i	−0.248233	+	0.0296730i
$401$	−14.1357	+	14.1357i	−0.705906	+	0.705906i	−0.965672	−	0.259766i	$-0.916355\pi$
$401$	−14.1357	+	14.1357i	−0.705906	+	0.705906i	0.259766	+	0.965672i	$0.416355\pi$
$402$		−	6.11518i		−	0.304997i
$403$	2.65989	+	2.65989i	0.132499	+	0.132499i
$404$			6.54373i			0.325563i
$405$	0.132937	+	2.23211i	0.00660568	+	0.110915i
$406$			19.5199i			0.968754i
$407$	−5.44526	−	4.40934i	−0.269912	−	0.218563i
$408$	3.97457	+	3.97457i	0.196771	+	0.196771i
$409$	20.4751	+	20.4751i	1.01243	+	1.01243i	0.999922	+	0.0125077i	$0.00398144\pi$
$409$	20.4751	+	20.4751i	1.01243	+	1.01243i	0.0125077	+	0.999922i	$0.496019\pi$
$410$	−0.909804	−	15.2763i	−0.0449320	−	0.754443i
$411$			16.7917i			0.828273i
$412$	−2.35550			−0.116047
$413$		−	21.8139i		−	1.07339i
$414$			2.70557i			0.132972i
$415$	−12.3620	+	13.9277i	−0.606826	+	0.683685i
$416$	−2.88999			−0.141694
$417$	11.0316	−	11.0316i	0.540218	−	0.540218i
$418$	1.52342	−	1.52342i	0.0745127	−	0.0745127i
$419$		−	16.7209i		−	0.816870i	−0.912787	−	0.408435i	$-0.866075\pi$
$419$		−	16.7209i		−	0.816870i	0.912787	−	0.408435i	$-0.133925\pi$
$420$	4.66869	−	0.278051i	0.227809	−	0.0135675i
$421$	22.8919	−	22.8919i	1.11569	−	1.11569i	0.123318	−	0.992367i	$-0.460647\pi$
$421$	22.8919	−	22.8919i	1.11569	−	1.11569i	0.992367	−	0.123318i	$-0.0393535\pi$
$422$		−	21.8632i		−	1.06428i
$423$	−5.84077	−	5.84077i	−0.283988	−	0.283988i
$424$	4.27233	−	4.27233i	0.207483	−	0.207483i
$425$	−27.9058	+	3.33578i	−1.35363	+	0.161809i
$426$	3.29577	+	3.29577i	0.159681	+	0.159681i
$427$		−	2.13457i		−	0.103299i
$428$	6.74914	−	6.74914i	0.326232	−	0.326232i
$429$	2.35392	−	2.35392i	0.113648	−	0.113648i
$430$	−1.18664	−	19.9246i	−0.0572248	−	0.960849i
$431$	−5.61789	+	5.61789i	−0.270604	+	0.270604i	−0.829343	−	0.558739i	$-0.811285\pi$
$431$	−5.61789	+	5.61789i	−0.270604	+	0.270604i	0.558739	+	0.829343i	$0.311285\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	4.80295	+	4.80295i	0.230815	+	0.230815i	0.813033	−	0.582218i	$-0.197815\pi$
$433$	4.80295	+	4.80295i	0.230815	+	0.230815i	−0.582218	+	0.813033i	$0.697815\pi$
$434$	2.72246			0.130682
$435$	1.24063	+	20.8312i	0.0594838	+	0.998779i
$436$	−1.88769	+	1.88769i	−0.0904041	+	0.0904041i
$437$	−3.57823	−	3.57823i	−0.171170	−	0.171170i
$438$	1.15309			0.0550968
$439$	−7.82626	−	7.82626i	−0.373527	−	0.373527i	0.495233	−	0.868760i	$-0.335083\pi$
$439$	−7.82626	−	7.82626i	−0.373527	−	0.373527i	−0.868760	+	0.495233i	$0.835083\pi$
$440$	0.153128	+	2.57114i	0.00730010	+	0.122574i
$441$	2.62520			0.125010
$442$	−16.2443			−0.772665
$443$	−13.6322	+	13.6322i	−0.647683	+	0.647683i	−0.952433	−	0.304749i	$-0.901427\pi$
$443$	−13.6322	+	13.6322i	−0.647683	+	0.647683i	0.304749	+	0.952433i	$0.401427\pi$
$444$	−0.635924	−	6.04943i	−0.0301796	−	0.287093i
$445$	−14.4304	+	16.2582i	−0.684069	+	0.770710i
$446$	−9.79908	+	9.79908i	−0.464000	+	0.464000i
$447$	3.28202	+	3.28202i	0.155234	+	0.155234i
$448$	−1.47899	+	1.47899i	−0.0698755	+	0.0698755i
$449$	−16.5631	+	16.5631i	−0.781661	+	0.781661i	−0.980111	−	0.198450i	$-0.936409\pi$
$449$	−16.5631	+	16.5631i	−0.781661	+	0.781661i	0.198450	+	0.980111i	$0.436409\pi$
$450$	4.96466	−	0.593460i	0.234036	−	0.0279760i
$451$	−7.88337			−0.371214
$452$	−17.4956			−0.822923
$453$	−10.2606	−	10.2606i	−0.482083	−	0.482083i
$454$		−	12.4848i		−	0.585940i
$455$	−8.97242	+	10.1088i	−0.420634	+	0.473910i
$456$	1.87036			0.0875874
$457$	−15.3145			−0.716381			−0.358191	−	0.933649i	$-0.616606\pi$
$457$	−15.3145			−0.716381			−0.358191	+	0.933649i	$0.616606\pi$
$458$	4.90899			0.229382
$459$	−3.97457	−	3.97457i	−0.185517	−	0.185517i
$460$	6.03914	−	0.359670i	0.281576	−	0.0167697i
$461$	25.8489	+	25.8489i	1.20390	+	1.20390i	0.972970	+	0.230933i	$0.0741777\pi$
$461$	25.8489	+	25.8489i	1.20390	+	1.20390i	0.230933	+	0.972970i	$0.425822\pi$
$462$		−	2.40929i		−	0.112090i
$463$			23.9015i			1.11080i	0.831584	+	0.555399i	$0.187435\pi$
$463$			23.9015i			1.11080i	−0.831584	+	0.555399i	$0.812565\pi$
$464$	−6.59907	−	6.59907i	−0.306354	−	0.306354i
$465$	2.90535	−	0.173033i	0.134732	−	0.00802419i
$466$	−6.62951	−	6.62951i	−0.307106	−	0.307106i
$467$	7.54639			0.349205			0.174603	−	0.984639i	$-0.444136\pi$
$467$	7.54639			0.349205			0.174603	+	0.984639i	$0.444136\pi$
$468$	2.88999			0.133590
$469$	12.7905			0.590611
$470$	−12.2608	+	13.8137i	−0.565548	+	0.637179i
$471$			18.5438i			0.854454i
$472$	7.37461	+	7.37461i	0.339444	+	0.339444i
$473$	−10.2821			−0.472772
$474$	16.8273			0.772906
$475$	−5.78108	+	7.35084i	−0.265254	+	0.337279i
$476$	−8.31322	+	8.31322i	−0.381036	+	0.381036i
$477$	−4.27233	+	4.27233i	−0.195617	+	0.195617i
$478$	−14.4055	−	14.4055i	−0.658894	−	0.658894i
$479$	−24.1200	+	24.1200i	−1.10207	+	1.10207i	−0.107912	+	0.994160i	$0.534417\pi$
$479$	−24.1200	+	24.1200i	−1.10207	+	1.10207i	−0.994160	+	0.107912i	$0.965583\pi$
$480$	−1.48434	+	1.67234i	−0.0677506	+	0.0763317i
$481$	13.6618	+	11.0627i	0.622922	+	0.504415i
$482$	−5.83291	+	5.83291i	−0.265682	+	0.265682i
$483$	−5.65898			−0.257492
$484$	−9.67316			−0.439689
$485$	−1.89986	−	31.9002i	−0.0862683	−	1.44851i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−1.74655			−0.0791437			−0.0395719	−	0.999217i	$-0.512599\pi$
$487$	−1.74655			−0.0791437			−0.0395719	+	0.999217i	$0.512599\pi$
$488$	0.721634	+	0.721634i	0.0326669	+	0.0326669i
$489$	−6.22982	+	6.22982i	−0.281722	+	0.281722i
$490$	−0.348986	−	5.85975i	−0.0157656	−	0.264716i
$491$	−6.46050			−0.291558			−0.145779	−	0.989317i	$-0.546569\pi$
$491$	−6.46050			−0.291558			−0.145779	+	0.989317i	$0.546569\pi$
$492$	−4.83935	−	4.83935i	−0.218175	−	0.218175i
$493$	−37.0927	−	37.0927i	−1.67057	−	1.67057i
$494$	−3.82214	+	3.82214i	−0.171966	+	0.171966i
$495$	−0.153128	−	2.57114i	−0.00688260	−	0.115564i
$496$	−0.920380	+	0.920380i	−0.0413263	+	0.0413263i
$497$	−6.89344	+	6.89344i	−0.309213	+	0.309213i
$498$			8.32827i			0.373199i
$499$	−11.4622	−	11.4622i	−0.513120	−	0.513120i	0.402361	−	0.915481i	$-0.368190\pi$
$499$	−11.4622	−	11.4622i	−0.513120	−	0.513120i	−0.915481	+	0.402361i	$0.868190\pi$
$500$	−1.98466	−	11.0028i	−0.0887565	−	0.492059i
$501$	9.39453	−	9.39453i	0.419717	−	0.419717i
$502$	−12.0063	−	12.0063i	−0.535867	−	0.535867i
$503$			14.2394i			0.634904i	0.948274	+	0.317452i	$0.102827\pi$
$503$			14.2394i			0.634904i	−0.948274	+	0.317452i	$0.897173\pi$
$504$	1.47899	−	1.47899i	0.0658793	−	0.0658793i
$505$	−14.6063	+	0.869903i	−0.649974	+	0.0387102i
$506$		−	3.11651i		−	0.138546i
$507$	3.28658	−	3.28658i	0.145962	−	0.145962i
$508$	−0.311708	+	0.311708i	−0.0138298	+	0.0138298i
$509$	−42.1660			−1.86897			−0.934487	−	0.355997i	$-0.884141\pi$
$509$	−42.1660			−1.86897			−0.934487	+	0.355997i	$0.884141\pi$
$510$	−8.34333	+	9.40006i	−0.369449	+	0.416242i
$511$			2.41180i			0.106692i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.87036			−0.0825782
$514$		−	8.79481i		−	0.387923i
$515$	−0.313133	−	5.25775i	−0.0137983	−	0.231684i
$516$	−6.31187	−	6.31187i	−0.277865	−	0.277865i
$517$	6.72790	+	6.72790i	0.295893	+	0.295893i
$518$	12.6530	−	1.33010i	0.555941	−	0.0584412i
$519$		−	23.1547i		−	1.01638i
$520$	−0.384187	−	6.45079i	−0.0168477	−	0.282886i
$521$			8.55702i			0.374890i	0.982275	+	0.187445i	$0.0600206\pi$
$521$			8.55702i			0.374890i	−0.982275	+	0.187445i	$0.939979\pi$
$522$	6.59907	+	6.59907i	0.288833	+	0.288833i
$523$		−	16.9569i		−	0.741473i	−0.928738	−	0.370737i	$-0.879105\pi$
$523$		−	16.9569i		−	0.741473i	0.928738	−	0.370737i	$-0.120895\pi$
$524$	−12.4801	+	12.4801i	−0.545197	+	0.545197i
$525$	1.24128	+	10.3841i	0.0541740	+	0.453198i
$526$	4.85857	+	4.85857i	0.211844	+	0.211844i
$527$	−5.17336	+	5.17336i	−0.225355	+	0.225355i
$528$	0.814507	+	0.814507i	0.0354469	+	0.0354469i
$529$	15.6799			0.681734
$530$	10.1043	+	8.96837i	0.438902	+	0.389561i
$531$	−7.37461	−	7.37461i	−0.320031	−	0.320031i
$532$			3.91204i			0.169608i
$533$	19.7788			0.856714
$534$			9.72178i			0.420703i
$535$	15.9620	+	14.1676i	0.690099	+	0.612520i
$536$	−4.32408	+	4.32408i	−0.186772	+	0.186772i
$537$	−9.04314			−0.390240
$538$	10.8073			0.465936
$539$	−3.02394			−0.130250
$540$	1.48434	−	1.67234i	0.0638759	−	0.0719662i
$541$	0.972918	+	0.972918i	0.0418290	+	0.0418290i	0.727712	−	0.685883i	$-0.240584\pi$
$541$	0.972918	+	0.972918i	0.0418290	+	0.0418290i	−0.685883	+	0.727712i	$0.740584\pi$
$542$		−	20.9907i		−	0.901628i
$543$	5.61472	−	5.61472i	0.240951	−	0.240951i
$544$		−	5.62089i		−	0.240994i
$545$	−4.46449	−	3.96260i	−0.191238	−	0.169739i
$546$			6.04472i			0.258690i
$547$			3.68086i			0.157382i	0.996899	+	0.0786911i	$0.0250741\pi$
$547$			3.68086i			0.157382i	−0.996899	+	0.0786911i	$0.974926\pi$
$548$	11.8735	−	11.8735i	0.507211	−	0.507211i
$549$	−0.721634	−	0.721634i	−0.0307986	−	0.0307986i
$550$	−5.71872	+	0.683599i	−0.243847	+	0.0291487i
$551$	−17.4551			−0.743611
$552$	1.91313	−	1.91313i	0.0814282	−	0.0814282i
$553$			35.1961i			1.49669i
$554$	2.34619			0.0996800
$555$	13.4185	−	2.22365i	0.569582	−	0.0943885i
$556$	−15.6010			−0.661629
$557$			33.5711i			1.42245i	0.702963	+	0.711227i	$0.251860\pi$
$557$			33.5711i			1.42245i	−0.702963	+	0.711227i	$0.748140\pi$
$558$	0.920380	−	0.920380i	0.0389628	−	0.0389628i
$559$	25.7970			1.09110
$560$	−3.49787	−	3.10465i	−0.147812	−	0.131195i
$561$	4.57825	+	4.57825i	0.193294	+	0.193294i
$562$	12.4830	−	12.4830i	0.526564	−	0.526564i
$563$		−	15.1872i		−	0.640063i	−0.947407	−	0.320031i	$-0.896307\pi$
$563$		−	15.1872i		−	0.640063i	0.947407	−	0.320031i	$-0.103693\pi$
$564$			8.26009i			0.347813i
$565$	−2.32581	−	39.0521i	−0.0978475	−	1.64294i
$566$		−	4.16867i		−	0.175222i
$567$	−1.47899	+	1.47899i	−0.0621116	+	0.0621116i
$568$		−	4.66092i		−	0.195568i
$569$	−23.9696	−	23.9696i	−1.00486	−	1.00486i	−0.999988	−	0.00486775i	$-0.998451\pi$
$569$	−23.9696	−	23.9696i	−1.00486	−	1.00486i	−0.00486775	−	0.999988i	$-0.501549\pi$
$570$	0.248639	+	4.17484i	0.0104143	+	0.174865i
$571$	−8.62869			−0.361100			−0.180550	−	0.983566i	$-0.557788\pi$
$571$	−8.62869			−0.361100			−0.180550	+	0.983566i	$0.557788\pi$
$572$	−3.32894			−0.139190
$573$	25.2384			1.05435
$574$	10.1220	−	10.1220i	0.422484	−	0.422484i
$575$	1.60565	+	13.4322i	0.0669602	+	0.560163i
$576$			1.00000i			0.0416667i
$577$	14.2646			0.593842			0.296921	−	0.954902i	$-0.404040\pi$
$577$	14.2646			0.593842			0.296921	+	0.954902i	$0.404040\pi$
$578$		−	14.5944i		−	0.607049i
$579$	3.58525	+	3.58525i	0.148998	+	0.148998i
$580$	13.8526	−	15.6071i	0.575198	−	0.648051i
$581$	−17.4194			−0.722679
$582$	−10.1056	−	10.1056i	−0.418890	−	0.418890i
$583$	4.92124	−	4.92124i	0.203817	−	0.203817i
$584$	−0.815358	−	0.815358i	−0.0337397	−	0.0337397i
$585$	0.384187	+	6.45079i	0.0158842	+	0.266707i
$586$	3.92862	−	3.92862i	0.162290	−	0.162290i
$587$			22.1077i			0.912481i	0.889856	+	0.456241i	$0.150804\pi$
$587$			22.1077i			0.912481i	−0.889856	+	0.456241i	$0.849196\pi$
$588$	−1.85630	−	1.85630i	−0.0765525	−	0.0765525i
$589$			2.43448i			0.100311i
$590$	−15.4806	+	17.4413i	−0.637326	+	0.718047i
$591$			16.0617i			0.660691i
$592$	−3.82793	+	4.72726i	−0.157327	+	0.194289i
$593$	−4.52142	−	4.52142i	−0.185672	−	0.185672i	0.608150	−	0.793822i	$-0.291912\pi$
$593$	−4.52142	−	4.52142i	−0.185672	−	0.185672i	−0.793822	+	0.608150i	$0.791912\pi$
$594$	−0.814507	−	0.814507i	−0.0334196	−	0.0334196i
$595$	−19.6612	−	17.4509i	−0.806030	−	0.715418i
$596$		−	4.64148i		−	0.190122i
$597$	−17.9851			−0.736080
$598$			7.81909i			0.319746i
$599$			2.38790i			0.0975668i	0.998809	+	0.0487834i	$0.0155344\pi$
$599$			2.38790i			0.0975668i	−0.998809	+	0.0487834i	$0.984466\pi$
$600$	−3.93018	−	3.09090i	−0.160449	−	0.126186i
$601$	−25.0314			−1.02105			−0.510526	−	0.859862i	$-0.670549\pi$
$601$	−25.0314			−1.02105			−0.510526	+	0.859862i	$0.670549\pi$
$602$	13.2019	−	13.2019i	0.538070	−	0.538070i
$603$	4.32408	−	4.32408i	0.176090	−	0.176090i
$604$			14.5106i			0.590429i
$605$	−1.28592	−	21.5916i	−0.0522800	−	0.877823i
$606$	−4.62711	+	4.62711i	−0.187964	+	0.187964i
$607$		−	3.19973i		−	0.129873i	−0.997889	−	0.0649365i	$-0.979316\pi$
$607$		−	3.19973i		−	0.129873i	0.997889	−	0.0649365i	$-0.0206845\pi$
$608$	−1.32254	−	1.32254i	−0.0536361	−	0.0536361i
$609$	−13.8026	+	13.8026i	−0.559311	+	0.559311i
$610$	−1.51484	+	1.70670i	−0.0613340	+	0.0691023i
$611$	−16.8798	−	16.8798i	−0.682883	−	0.682883i
$612$			5.62089i			0.227211i
$613$	−4.03461	+	4.03461i	−0.162956	+	0.162956i	−0.783875	−	0.620919i	$-0.786760\pi$
$613$	−4.03461	+	4.03461i	−0.162956	+	0.162956i	0.620919	+	0.783875i	$0.286760\pi$
$614$	0.507816	−	0.507816i	0.0204938	−	0.0204938i
$615$	10.1587	−	11.4453i	0.409637	−	0.461520i
$616$	−1.70362	+	1.70362i	−0.0686409	+	0.0686409i
$617$	−0.467215	−	0.467215i	−0.0188094	−	0.0188094i	0.697640	−	0.716449i	$-0.254234\pi$
$617$	−0.467215	−	0.467215i	−0.0188094	−	0.0188094i	−0.716449	+	0.697640i	$0.754234\pi$
$618$	−1.66559	−	1.66559i	−0.0669999	−	0.0669999i
$619$	−19.5482			−0.785707			−0.392853	−	0.919601i	$-0.628512\pi$
$619$	−19.5482			−0.785707			−0.392853	+	0.919601i	$0.628512\pi$
$620$	−2.17675	−	1.93204i	−0.0874202	−	0.0775926i
$621$	−1.91313	+	1.91313i	−0.0767712	+	0.0767712i
$622$	0.433905	+	0.433905i	0.0173980	+	0.0173980i
$623$	−20.3341			−0.814668
$624$	−2.04353	−	2.04353i	−0.0818069	−	0.0818069i
$625$	24.2956	−	5.89265i	0.971824	−	0.235706i
$626$	18.8073			0.751691
$627$	2.15444			0.0860399
$628$	13.1125	−	13.1125i	0.523244	−	0.523244i
$629$	−21.5164	+	26.5714i	−0.857914	+	1.05947i
$630$	3.49787	+	3.10465i	0.139359	+	0.123692i
$631$	23.3820	−	23.3820i	0.930821	−	0.930821i	−0.0669364	−	0.997757i	$-0.521322\pi$
$631$	23.3820	−	23.3820i	0.930821	−	0.930821i	0.997757	+	0.0669364i	$0.0213224\pi$
$632$	−11.8987	−	11.8987i	−0.473306	−	0.473306i
$633$	15.4596	−	15.4596i	0.614465	−	0.614465i
$634$	−11.5222	+	11.5222i	−0.457603	+	0.457603i
$635$	−0.737205	−	0.654330i	−0.0292551	−	0.0259663i
$636$	6.04199			0.239580
$637$	7.58682			0.300601
$638$	−7.60138	−	7.60138i	−0.300941	−	0.300941i
$639$			4.66092i			0.184383i
$640$	2.23211	−	0.132937i	0.0882320	−	0.00525479i
$641$	22.8783			0.903637			0.451818	−	0.892110i	$-0.350775\pi$
$641$	22.8783			0.903637			0.451818	+	0.892110i	$0.350775\pi$
$642$	9.54472			0.376700
$643$	−20.4157			−0.805118			−0.402559	−	0.915394i	$-0.631879\pi$
$643$	−20.4157			−0.805118			−0.402559	+	0.915394i	$0.631879\pi$
$644$	4.00150	+	4.00150i	0.157681	+	0.157681i
$645$	13.2497	−	14.9279i	0.521707	−	0.587785i
$646$	−7.43386	−	7.43386i	−0.292481	−	0.292481i
$647$			11.4754i			0.451143i	0.974227	+	0.225572i	$0.0724250\pi$
$647$			11.4754i			0.451143i	−0.974227	+	0.225572i	$0.927575\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	8.49471	+	8.49471i	0.333446	+	0.333446i
$650$	14.3478	−	1.71510i	0.562768	−	0.0672716i
$651$	1.92507	+	1.92507i	0.0754494	+	0.0754494i
$652$	8.81029			0.345038
$653$	20.2423			0.792144			0.396072	−	0.918219i	$-0.370373\pi$
$653$	20.2423			0.792144			0.396072	+	0.918219i	$0.370373\pi$
$654$	−2.66960			−0.104390
$655$	−29.5161	−	26.1980i	−1.15329	−	1.02364i
$656$			6.84388i			0.267209i
$657$	0.815358	+	0.815358i	0.0318101	+	0.0318101i
$658$	−17.2768			−0.673520
$659$	−25.5001			−0.993341			−0.496671	−	0.867939i	$-0.665444\pi$
$659$	−25.5001			−0.993341			−0.496671	+	0.867939i	$0.665444\pi$
$660$	−1.70979	+	1.92635i	−0.0665536	+	0.0749830i
$661$	−20.7117	+	20.7117i	−0.805592	+	0.805592i	−0.983963	−	0.178372i	$-0.942917\pi$
$661$	−20.7117	+	20.7117i	−0.805592	+	0.805592i	0.178372	+	0.983963i	$0.442917\pi$
$662$	−7.39172	+	7.39172i	−0.287287	+	0.287287i
$663$	−11.4865	−	11.4865i	−0.446098	−	0.446098i
$664$	5.88898	−	5.88898i	0.228537	−	0.228537i
$665$	−8.73211	+	0.520054i	−0.338617	+	0.0201668i
$666$	3.82793	−	4.72726i	0.148329	−	0.183178i
$667$	−17.8543	+	17.8543i	−0.691320	+	0.691320i
$668$	−13.2859			−0.514046
$669$	−13.8580			−0.535781
$670$	−10.2267	−	9.07701i	−0.395091	−	0.350676i
$671$	0.831241	+	0.831241i	0.0320897	+	0.0320897i
$672$	−2.09160			−0.0806853
$673$	−28.3498	−	28.3498i	−1.09280	−	1.09280i	−0.995228	−	0.0975766i	$-0.968891\pi$
$673$	−28.3498	−	28.3498i	−1.09280	−	1.09280i	−0.0975766	−	0.995228i	$-0.531109\pi$
$674$	4.90709	−	4.90709i	0.189014	−	0.189014i
$675$	3.93018	+	3.09090i	0.151273	+	0.118969i
$676$	−4.64793			−0.178767
$677$	−7.07539	−	7.07539i	−0.271929	−	0.271929i	0.557947	−	0.829876i	$-0.311589\pi$
$677$	−7.07539	−	7.07539i	−0.271929	−	0.271929i	−0.829876	+	0.557947i	$0.811589\pi$
$678$	−12.3712	−	12.3712i	−0.475115	−	0.475115i
$679$	21.1369	−	21.1369i	0.811159	−	0.811159i
$680$	12.5465	−	0.747224i	0.481135	−	0.0286547i
$681$	8.82808	−	8.82808i	0.338293	−	0.338293i
$682$	−1.06017	+	1.06017i	−0.0405961	+	0.0405961i
$683$			27.8779i			1.06672i	0.845889	+	0.533359i	$0.179070\pi$
$683$			27.8779i			1.06672i	−0.845889	+	0.533359i	$0.820930\pi$
$684$	1.32254	+	1.32254i	0.0505686	+	0.0505686i
$685$	28.0814	+	24.9246i	1.07294	+	0.952320i
$686$	14.2355	−	14.2355i	0.543515	−	0.543515i
$687$	3.47118	+	3.47118i	0.132434	+	0.132434i
$688$			8.92633i			0.340313i
$689$	−12.3470	+	12.3470i	−0.470384	+	0.470384i
$690$	4.52464	+	4.01599i	0.172250	+	0.152886i
$691$		−	36.3085i		−	1.38124i	−0.723218	−	0.690619i	$-0.757338\pi$
$691$		−	36.3085i		−	1.38124i	0.723218	−	0.690619i	$-0.242662\pi$
$692$	−16.3729	+	16.3729i	−0.622403	+	0.622403i
$693$	1.70362	−	1.70362i	0.0647153	−	0.0647153i
$694$	−5.47655			−0.207887
$695$	−2.07394	−	34.8231i	−0.0786692	−	1.32092i
$696$		−	9.33249i		−	0.353747i
$697$			38.4687i			1.45711i
$698$	17.9938			0.681077
$699$		−	9.37554i		−	0.354615i
$700$	6.46494	−	8.22037i	0.244352	−	0.310701i
$701$	−26.0059	−	26.0059i	−0.982229	−	0.982229i	0.0176154	−	0.999845i	$-0.494393\pi$
$701$	−26.0059	−	26.0059i	−0.982229	−	0.982229i	−0.999845	+	0.0176154i	$0.994393\pi$
$702$	2.04353	+	2.04353i	0.0771282	+	0.0771282i
$703$	1.18940	+	11.3146i	0.0448592	+	0.426738i
$704$		−	1.15189i		−	0.0434133i
$705$	−18.4375	+	1.09807i	−0.694395	+	0.0413557i
$706$		−	0.511524i		−	0.0192515i
$707$	−9.67808	−	9.67808i	−0.363982	−	0.363982i
$708$			10.4293i			0.391956i
$709$	1.61126	−	1.61126i	0.0605121	−	0.0605121i	−0.676203	−	0.736715i	$-0.736376\pi$
$709$	1.61126	−	1.61126i	0.0605121	−	0.0605121i	0.736715	+	0.676203i	$0.236376\pi$
$710$	10.4037	−	0.619609i	0.390444	−	0.0232535i
$711$	11.8987	+	11.8987i	0.446237	+	0.446237i
$712$	6.87434	−	6.87434i	0.257627	−	0.257627i
$713$	2.49016	+	2.49016i	0.0932571	+	0.0932571i
$714$	−11.7567			−0.439982
$715$	−0.442539	−	7.43058i	−0.0165500	−	0.277888i
$716$	6.39446	+	6.39446i	0.238972	+	0.238972i
$717$		−	20.3725i		−	0.760825i
$718$	−30.4736			−1.13726
$719$		−	13.7328i		−	0.512145i	−0.966658	−	0.256073i	$-0.917571\pi$
$719$		−	13.7328i		−	0.512145i	0.966658	−	0.256073i	$-0.0824286\pi$
$720$	−2.23211	+	0.132937i	−0.0831859	+	0.00495426i
$721$	3.48375	−	3.48375i	0.129742	−	0.129742i
$722$	15.5018			0.576916
$723$	−8.24898			−0.306783
$724$	−7.94042			−0.295103
$725$	36.6784	+	28.8458i	1.36220	+	1.07131i
$726$	−6.83996	−	6.83996i	−0.253855	−	0.253855i
$727$			30.8968i			1.14590i	0.819591	+	0.572949i	$0.194201\pi$
$727$			30.8968i			1.14590i	−0.819591	+	0.572949i	$0.805799\pi$
$728$	4.27426	−	4.27426i	0.158415	−	0.158415i
$729$			1.00000i			0.0370370i
$730$	1.71158	−	1.92836i	0.0633484	−	0.0713719i
$731$			50.1740i			1.85575i
$732$			1.02055i			0.0377204i
$733$	−33.6973	+	33.6973i	−1.24464	+	1.24464i	−0.286581	+	0.958056i	$0.592519\pi$
$733$	−33.6973	+	33.6973i	−1.24464	+	1.24464i	−0.958056	+	0.286581i	$0.907481\pi$
$734$	−1.10113	−	1.10113i	−0.0406435	−	0.0406435i
$735$	3.89670	−	4.39024i	0.143732	−	0.161936i
$736$	−2.70557			−0.0997287
$737$	−4.98085	+	4.98085i	−0.183472	+	0.183472i
$738$		−	6.84388i		−	0.251927i
$739$	−8.47618			−0.311801			−0.155901	−	0.987773i	$-0.549828\pi$
$739$	−8.47618			−0.311801			−0.155901	+	0.987773i	$0.549828\pi$
$740$	−11.0606	−	7.91594i	−0.406597	−	0.290996i
$741$	−5.40532			−0.198569
$742$			12.6374i			0.463935i
$743$	25.8387	−	25.8387i	0.947932	−	0.947932i	−0.0507782	−	0.998710i	$-0.516170\pi$
$743$	25.8387	−	25.8387i	0.947932	−	0.947932i	0.998710	+	0.0507782i	$0.0161702\pi$
$744$	−1.30161			−0.0477195
$745$	10.3603	−	0.617024i	0.379572	−	0.0226060i
$746$	13.3085	+	13.3085i	0.487259	+	0.487259i
$747$	−5.88898	+	5.88898i	−0.215466	+	0.215466i
$748$		−	6.47463i		−	0.236736i
$749$			19.9637i			0.729459i
$750$	6.37678	−	9.18350i	0.232847	−	0.335334i
$751$		−	5.27898i		−	0.192633i	−0.995351	−	0.0963163i	$-0.969294\pi$
$751$		−	5.27898i		−	0.192633i	0.995351	−	0.0963163i	$-0.0307060\pi$
$752$	5.84077	−	5.84077i	0.212991	−	0.212991i
$753$		−	16.9795i		−	0.618766i
$754$	19.0713	+	19.0713i	0.694535	+	0.694535i
$755$	−32.3894	+	1.92900i	−1.17877	+	0.0702034i
$756$	2.09160			0.0760708
$757$	16.2149			0.589340			0.294670	−	0.955599i	$-0.404790\pi$
$757$	16.2149			0.589340			0.294670	+	0.955599i	$0.404790\pi$
$758$	−31.3641			−1.13920
$759$	2.20371	−	2.20371i	0.0799895	−	0.0799895i
$760$	2.77625	−	3.12787i	0.100705	−	0.113460i
$761$			10.2102i			0.370118i	0.982727	+	0.185059i	$0.0592476\pi$
$761$			10.2102i			0.370118i	−0.982727	+	0.185059i	$0.940752\pi$
$762$	−0.440822			−0.0159693
$763$		−	5.58374i		−	0.202145i
$764$	−17.8463	−	17.8463i	−0.645655	−	0.645655i
$765$	−12.5465	+	0.747224i	−0.453618	+	0.0270159i
$766$	7.04860			0.254676
$767$	−21.3126	−	21.3126i	−0.769552	−	0.769552i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−0.152750	−	0.152750i	−0.00550832	−	0.00550832i	0.704347	−	0.709856i	$-0.251240\pi$
$769$	−0.152750	−	0.152750i	−0.00550832	−	0.00550832i	−0.709856	+	0.704347i	$0.751240\pi$
$770$	−4.02915	−	3.57621i	−0.145201	−	0.128877i
$771$	6.21887	−	6.21887i	0.223967	−	0.223967i
$772$		−	5.07031i		−	0.182485i
$773$	11.9977	+	11.9977i	0.431529	+	0.431529i	0.889148	−	0.457619i	$-0.151298\pi$
$773$	11.9977	+	11.9977i	0.431529	+	0.431529i	−0.457619	+	0.889148i	$0.651298\pi$
$774$		−	8.92633i		−	0.320850i
$775$	4.02316	−	5.11558i	0.144516	−	0.183757i
$776$			14.2915i			0.513034i
$777$	9.88754	+	8.00650i	0.354714	+	0.287232i
$778$	18.3786	+	18.3786i	0.658904	+	0.658904i
$779$	9.05131	+	9.05131i	0.324297	+	0.324297i
$780$	4.28974	−	4.83306i	0.153597	−	0.173051i
$781$		−	5.36885i		−	0.192113i
$782$	−15.2077			−0.543827
$783$			9.33249i			0.333516i
$784$			2.62520i			0.0937572i
$785$	31.0116	+	27.5253i	1.10685	+	0.982422i
$786$	−17.6496			−0.629539
$787$	4.08657	−	4.08657i	0.145670	−	0.145670i	−0.630510	−	0.776181i	$-0.717154\pi$
$787$	4.08657	−	4.08657i	0.145670	−	0.145670i	0.776181	+	0.630510i	$0.217154\pi$
$788$	11.3573	−	11.3573i	0.404589	−	0.404589i
$789$			6.87106i			0.244616i
$790$	24.9775	−	28.1411i	0.888661	−	1.00122i
$791$	25.8757	−	25.8757i	0.920035	−	0.920035i
$792$			1.15189i			0.0409305i
$793$	−2.08552	−	2.08552i	−0.0740590	−	0.0740590i
$794$	−11.4488	+	11.4488i	−0.406304	+	0.406304i
$795$	0.803203	+	13.4864i	0.0284867	+	0.478313i
$796$	12.7174	+	12.7174i	0.450755	+	0.450755i
$797$		−	17.9557i		−	0.636024i	−0.948087	−	0.318012i	$-0.896985\pi$
$797$		−	17.9557i		−	0.636024i	0.948087	−	0.318012i	$-0.103015\pi$
$798$	−2.76623	+	2.76623i	−0.0979234	+	0.0979234i
$799$	32.8303	−	32.8303i	1.16145	−	1.16145i
$800$	0.593460	+	4.96466i	0.0209820	+	0.175527i
$801$	−6.87434	+	6.87434i	−0.242893	+	0.242893i
$802$	14.1357	+	14.1357i	0.499151	+	0.499151i
$803$	−0.939199	−	0.939199i	−0.0331436	−	0.0331436i
$804$	−6.11518			−0.215666
$805$	−8.39986	+	9.46375i	−0.296056	+	0.333553i
$806$	2.65989	−	2.65989i	0.0936908	−	0.0936908i
$807$	7.64191	+	7.64191i	0.269008	+	0.269008i
$808$	6.54373			0.230208
$809$	5.66008	+	5.66008i	0.198998	+	0.198998i	0.799570	−	0.600572i	$-0.205061\pi$
$809$	5.66008	+	5.66008i	0.198998	+	0.198998i	−0.600572	+	0.799570i	$0.705061\pi$
$810$	2.23211	−	0.132937i	0.0784285	−	0.00467092i
$811$	33.9490			1.19211			0.596054	−	0.802944i	$-0.296734\pi$
$811$	33.9490			1.19211			0.596054	+	0.802944i	$0.296734\pi$
$812$	19.5199			0.685013
$813$	14.8427	−	14.8427i	0.520555	−	0.520555i
$814$	−4.40934	+	5.44526i	−0.154547	+	0.190856i
$815$	1.17121	+	19.6656i	0.0410258	+	0.688855i
$816$	3.97457	−	3.97457i	0.139138	−	0.139138i
$817$	11.8054	+	11.8054i	0.413020	+	0.413020i
$818$	20.4751	−	20.4751i	0.715896	−	0.715896i
$819$	−4.27426	+	4.27426i	−0.149355	+	0.149355i
$820$	−15.2763	+	0.909804i	−0.533472	+	0.0317717i
$821$	−17.9270			−0.625658			−0.312829	−	0.949810i	$-0.601277\pi$
$821$	−17.9270			−0.625658			−0.312829	+	0.949810i	$0.601277\pi$
$822$	16.7917			0.585677
$823$	12.8847	+	12.8847i	0.449132	+	0.449132i	0.895066	−	0.445934i	$-0.147128\pi$
$823$	12.8847	+	12.8847i	0.449132	+	0.449132i	−0.445934	+	0.895066i	$0.647128\pi$
$824$			2.35550i			0.0820578i
$825$	−4.52712	−	3.56037i	−0.157614	−	0.123956i
$826$	−21.8139			−0.759002
$827$	24.0587			0.836605			0.418302	−	0.908308i	$-0.362625\pi$
$827$	24.0587			0.836605			0.418302	+	0.908308i	$0.362625\pi$
$828$	2.70557			0.0940251
$829$	6.84774	+	6.84774i	0.237832	+	0.237832i	0.815952	−	0.578120i	$-0.196213\pi$
$829$	6.84774	+	6.84774i	0.237832	+	0.237832i	−0.578120	+	0.815952i	$0.696213\pi$
$830$	13.9277	+	12.3620i	0.483438	+	0.429091i
$831$	1.65901	+	1.65901i	0.0575503	+	0.0575503i
$832$			2.88999i			0.100193i
$833$			14.7560i			0.511265i
$834$	−11.0316	−	11.0316i	−0.381991	−	0.381991i
$835$	−1.76618	−	29.6556i	−0.0611213	−	1.02627i
$836$	−1.52342	−	1.52342i	−0.0526885	−	0.0526885i
$837$	1.30161			0.0449904
$838$	−16.7209			−0.577614
$839$	33.9557			1.17228			0.586140	−	0.810210i	$-0.300647\pi$
$839$	33.9557			1.17228			0.586140	+	0.810210i	$0.300647\pi$
$840$	−0.278051	−	4.66869i	−0.00959367	−	0.161085i
$841$			58.0955i			2.00329i
$842$	−22.8919	−	22.8919i	−0.788909	−	0.788909i
$843$	17.6536			0.608024
$844$	−21.8632			−0.752562
$845$	−0.617882	−	10.3747i	−0.0212558	−	0.356901i
$846$	−5.84077	+	5.84077i	−0.200810	+	0.200810i
$847$	14.3065	−	14.3065i	0.491576	−	0.491576i
$848$	−4.27233	−	4.27233i	−0.146712	−	0.146712i
$849$	2.94770	−	2.94770i	0.101165	−	0.101165i
$850$	3.33578	+	27.9058i	0.114416	+	0.957161i
$851$	12.7899	+	10.3567i	0.438433	+	0.355024i
$852$	3.29577	−	3.29577i	0.112911	−	0.112911i
$853$	31.3903			1.07478			0.537391	−	0.843333i	$-0.319410\pi$
$853$	31.3903			1.07478			0.537391	+	0.843333i	$0.319410\pi$
$854$	−2.13457			−0.0730436
$855$	−2.77625	+	3.12787i	−0.0949456	+	0.106971i
$856$	−6.74914	−	6.74914i	−0.230681	−	0.230681i
$857$	8.66191			0.295885			0.147943	−	0.988996i	$-0.452735\pi$
$857$	8.66191			0.295885			0.147943	+	0.988996i	$0.452735\pi$
$858$	−2.35392	−	2.35392i	−0.0803615	−	0.0803615i
$859$	−17.7807	+	17.7807i	−0.606669	+	0.606669i	−0.942074	−	0.335405i	$-0.891127\pi$
$859$	−17.7807	+	17.7807i	−0.606669	+	0.606669i	0.335405	+	0.942074i	$0.391127\pi$
$860$	−19.9246	+	1.18664i	−0.679423	+	0.0404640i
$861$	14.3147			0.487843
$862$	5.61789	+	5.61789i	0.191346	+	0.191346i
$863$	17.8599	+	17.8599i	0.607959	+	0.607959i	0.942412	−	0.334454i	$-0.108552\pi$
$863$	17.8599	+	17.8599i	0.607959	+	0.607959i	−0.334454	+	0.942412i	$0.608552\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	−38.7227	−	34.3695i	−1.31661	−	1.16860i
$866$	4.80295	−	4.80295i	0.163211	−	0.163211i
$867$	10.3198	−	10.3198i	0.350480	−	0.350480i
$868$		−	2.72246i		−	0.0924063i
$869$	−13.7060	−	13.7060i	−0.464944	−	0.464944i
$870$	20.8312	−	1.24063i	0.706243	−	0.0420614i
$871$	12.4966	−	12.4966i	0.423430	−	0.423430i
$872$	1.88769	+	1.88769i	0.0639254	+	0.0639254i
$873$		−	14.2915i		−	0.483693i
$874$	−3.57823	+	3.57823i	−0.121035	+	0.121035i
$875$	19.2082	+	13.3377i	0.649357	+	0.450896i
$876$		−	1.15309i		−	0.0389593i
$877$	22.3059	−	22.3059i	0.753218	−	0.753218i	−0.221860	−	0.975078i	$-0.571213\pi$
$877$	22.3059	−	22.3059i	0.753218	−	0.753218i	0.975078	+	0.221860i	$0.0712129\pi$
$878$	−7.82626	+	7.82626i	−0.264123	+	0.264123i
$879$	5.55591			0.187396
$880$	2.57114	−	0.153128i	0.0866731	−	0.00516195i
$881$		−	50.8644i		−	1.71367i	−0.515594	−	0.856833i	$-0.672429\pi$
$881$		−	50.8644i		−	1.71367i	0.515594	−	0.856833i	$-0.327571\pi$
$882$		−	2.62520i		−	0.0883952i
$883$	−31.8341			−1.07130			−0.535652	−	0.844439i	$-0.679934\pi$
$883$	−31.8341			−1.07130			−0.535652	+	0.844439i	$0.679934\pi$
$884$			16.2443i			0.546357i
$885$	−23.2793	+	1.38643i	−0.782525	+	0.0466045i
$886$	13.6322	+	13.6322i	0.457981	+	0.457981i
$887$	−23.7032	−	23.7032i	−0.795875	−	0.795875i	0.186567	−	0.982442i	$-0.440264\pi$
$887$	−23.7032	−	23.7032i	−0.795875	−	0.795875i	−0.982442	+	0.186567i	$0.940264\pi$
$888$	−6.04943	+	0.635924i	−0.203006	+	0.0213402i
$889$		−	0.922024i		−	0.0309237i
$890$	16.2582	+	14.4304i	0.544975	+	0.483710i
$891$		−	1.15189i		−	0.0385896i
$892$	9.79908	+	9.79908i	0.328098	+	0.328098i
$893$		−	15.4493i		−	0.516991i
$894$	3.28202	−	3.28202i	0.109767	−	0.109767i
$895$	−13.4231	+	15.1232i	−0.448685	+	0.505514i
$896$	1.47899	+	1.47899i	0.0494094	+	0.0494094i
$897$	−5.52893	+	5.52893i	−0.184606	+	0.184606i
$898$	16.5631	+	16.5631i	0.552717	+	0.552717i
$899$	12.1473			0.405135
$900$	−0.593460	−	4.96466i	−0.0197820	−	0.165489i
$901$	−24.0143	−	24.0143i	−0.800033	−	0.800033i
$902$			7.88337i			0.262488i
$903$	18.6703			0.621310
$904$			17.4956i			0.581895i
$905$	−1.05557	−	17.7239i	−0.0350885	−	0.589163i
$906$	−10.2606	+	10.2606i	−0.340884	+	0.340884i
$907$	21.5811			0.716589			0.358294	−	0.933609i	$-0.383358\pi$
$907$	21.5811			0.716589			0.358294	+	0.933609i	$0.383358\pi$
$908$	−12.4848			−0.414322
$909$	−6.54373			−0.217042
$910$	10.1088	+	8.97242i	0.335105	+	0.297433i
$911$	−38.1307	−	38.1307i	−1.26332	−	1.26332i	−0.949471	−	0.313853i	$-0.898380\pi$
$911$	−38.1307	−	38.1307i	−1.26332	−	1.26332i	−0.313853	−	0.949471i	$-0.601620\pi$
$912$		−	1.87036i		−	0.0619337i
$913$	6.78343	−	6.78343i	0.224499	−	0.224499i
$914$			15.3145i			0.506558i
$915$	−2.27797	+	0.135668i	−0.0753074	+	0.00448505i
$916$		−	4.90899i		−	0.162197i
$917$		−	36.9158i		−	1.21907i
$918$	−3.97457	+	3.97457i	−0.131180	+	0.131180i
$919$	4.29529	+	4.29529i	0.141688	+	0.141688i	0.774393	−	0.632705i	$-0.218055\pi$
$919$	4.29529	+	4.29529i	0.141688	+	0.141688i	−0.632705	+	0.774393i	$0.718055\pi$
$920$	−0.359670	−	6.03914i	−0.0118580	−	0.199105i
$921$	0.718161			0.0236642
$922$	25.8489	−	25.8489i	0.851287	−	0.851287i
$923$			13.4700i			0.443372i
$924$	−2.40929			−0.0792597
$925$	16.1989	−	25.7409i	0.532617	−	0.846357i
$926$	23.9015			0.785454
$927$		−	2.35550i		−	0.0773648i
$928$	−6.59907	+	6.59907i	−0.216625	+	0.216625i
$929$	1.53246			0.0502783			0.0251392	−	0.999684i	$-0.491997\pi$
$929$	1.53246			0.0502783			0.0251392	+	0.999684i	$0.491997\pi$
$930$	−0.173033	−	2.90535i	−0.00567396	−	0.0952702i
$931$	3.47194	+	3.47194i	0.113788	+	0.113788i
$932$	−6.62951	+	6.62951i	−0.217157	+	0.217157i
$933$			0.613635i			0.0200895i
$934$		−	7.54639i		−	0.246925i
$935$	14.4521	−	0.860717i	0.472634	−	0.0281485i
$936$		−	2.88999i		−	0.0944624i
$937$	−39.9671	+	39.9671i	−1.30567	+	1.30567i	−0.381156	+	0.924511i	$0.624474\pi$
$937$	−39.9671	+	39.9671i	−1.30567	+	1.30567i	−0.924511	+	0.381156i	$0.875526\pi$
$938$		−	12.7905i		−	0.417625i
$939$	13.2988	+	13.2988i	0.433989	+	0.433989i
$940$	13.8137	+	12.2608i	0.450553	+	0.399903i
$941$	−46.4990			−1.51582			−0.757911	−	0.652358i	$-0.773780\pi$
$941$	−46.4990			−1.51582			−0.757911	+	0.652358i	$0.773780\pi$
$942$	18.5438			0.604190
$943$	18.5166			0.602984
$944$	7.37461	−	7.37461i	0.240023	−	0.240023i
$945$	0.278051	+	4.66869i	0.00904500	+	0.151873i
$946$			10.2821i			0.334301i
$947$	−30.4143			−0.988331			−0.494166	−	0.869368i	$-0.664526\pi$
$947$	−30.4143			−0.988331			−0.494166	+	0.869368i	$0.664526\pi$
$948$		−	16.8273i		−	0.546527i
$949$	2.35638	+	2.35638i	0.0764913	+	0.0764913i
$950$	7.35084	+	5.78108i	0.238493	+	0.187563i
$951$	−16.2948			−0.528395
$952$	8.31322	+	8.31322i	0.269433	+	0.269433i
$953$	−18.5452	+	18.5452i	−0.600738	+	0.600738i	−0.940509	−	0.339770i	$-0.889651\pi$
$953$	−18.5452	+	18.5452i	−0.600738	+	0.600738i	0.339770	+	0.940509i	$0.389651\pi$
$954$	4.27233	+	4.27233i	0.138322	+	0.138322i
$955$	37.4624	−	42.2073i	1.21226	−	1.36580i
$956$	−14.4055	+	14.4055i	−0.465908	+	0.465908i
$957$		−	10.7500i		−	0.347497i
$958$	24.1200	+	24.1200i	0.779283	+	0.779283i
$959$			35.1215i			1.13413i
$960$	1.67234	+	1.48434i	0.0539746	+	0.0479069i
$961$			29.3058i			0.945348i
$962$	11.0627	−	13.6618i	0.356675	−	0.440473i
$963$	6.74914	+	6.74914i	0.217488	+	0.217488i
$964$	5.83291	+	5.83291i	0.187865	+	0.187865i
$965$	11.3175	−	0.674031i	0.364324	−	0.0216978i
$966$			5.65898i			0.182075i
$967$	38.3059			1.23183			0.615917	−	0.787811i	$-0.288786\pi$
$967$	38.3059			1.23183			0.615917	+	0.787811i	$0.288786\pi$
$968$			9.67316i			0.310907i
$969$		−	10.5131i		−	0.337728i
$970$	−31.9002	+	1.89986i	−1.02425	+	0.0610009i
$971$	−42.4464			−1.36217			−0.681084	−	0.732205i	$-0.738491\pi$
$971$	−42.4464			−1.36217			−0.681084	+	0.732205i	$0.738491\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	23.0736	−	23.0736i	0.739706	−	0.739706i
$974$			1.74655i			0.0559631i
$975$	11.3582	+	8.93269i	0.363754	+	0.286075i
$976$	0.721634	−	0.721634i	0.0230990	−	0.0230990i
$977$			2.92825i			0.0936831i	0.998902	+	0.0468415i	$0.0149156\pi$
$977$			2.92825i			0.0936831i	−0.998902	+	0.0468415i	$0.985084\pi$
$978$	6.22982	+	6.22982i	0.199208	+	0.199208i
$979$	7.91846	−	7.91846i	0.253075	−	0.253075i
$980$	−5.85975	+	0.348986i	−0.187183	+	0.0111480i
$981$	−1.88769	−	1.88769i	−0.0602694	−	0.0602694i
$982$			6.46050i			0.206163i
$983$	−22.1302	+	22.1302i	−0.705843	+	0.705843i	−0.965658	−	0.259816i	$-0.916338\pi$
$983$	−22.1302	+	22.1302i	−0.705843	+	0.705843i	0.259816	+	0.965658i	$0.416338\pi$
$984$	−4.83935	+	4.83935i	−0.154273	+	0.154273i
$985$	26.8607	+	23.8411i	0.855853	+	0.759640i
$986$	−37.0927	+	37.0927i	−1.18127	+	1.18127i
$987$	−12.2166	−	12.2166i	−0.388857	−	0.388857i
$988$	3.82214	+	3.82214i	0.121598	+	0.121598i
$989$	24.1508			0.767952
$990$	−2.57114	+	0.153128i	−0.0817162	+	0.00486673i
$991$	12.2981	−	12.2981i	0.390663	−	0.390663i	−0.484261	−	0.874924i	$-0.660911\pi$
$991$	12.2981	−	12.2981i	0.390663	−	0.390663i	0.874924	+	0.484261i	$0.160911\pi$
$992$	0.920380	+	0.920380i	0.0292221	+	0.0292221i
$993$	−10.4535			−0.331731
$994$	6.89344	+	6.89344i	0.218647	+	0.218647i
$995$	−26.6960	+	30.0772i	−0.846320	+	0.953512i
$996$	8.32827			0.263891
$997$	12.8502			0.406971			0.203485	−	0.979078i	$-0.434773\pi$
$997$	12.8502			0.406971			0.203485	+	0.979078i	$0.434773\pi$
$998$	−11.4622	+	11.4622i	−0.362830	+	0.362830i
$999$	6.04943	−	0.635924i	0.191395	−	0.0201197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.b.43.16	✓	40
5.2	odd	4		1110.2.o.b.487.5	yes	40
37.31	odd	4		1110.2.o.b.253.5	yes	40
185.142	even	4	inner	1110.2.l.b.697.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.16	✓	40	1.1	even	1	trivial
1110.2.l.b.697.16	yes	40	185.142	even	4	inner
1110.2.o.b.253.5	yes	40	37.31	odd	4
1110.2.o.b.487.5	yes	40	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.132937 - 2.23211i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.47899 - 1.47899i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.132937 - 2.23211i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.47899 - 1.47899i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-2.23211 + 0.132937i) q^{10} +1.15189i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.88999i q^{13} +(-1.47899 - 1.47899i) q^{14} +(-1.67234 - 1.48434i) q^{15} +1.00000 q^{16} +5.62089 q^{17} -1.00000 q^{18} +(1.32254 - 1.32254i) q^{19} +(0.132937 + 2.23211i) q^{20} -2.09160i q^{21} +1.15189 q^{22} -2.70557i q^{23} +(0.707107 + 0.707107i) q^{24} +(-4.96466 + 0.593460i) q^{25} -2.88999 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.47899 + 1.47899i) q^{28} +(-6.59907 - 6.59907i) q^{29} +(-1.48434 + 1.67234i) q^{30} +(-0.920380 + 0.920380i) q^{31} -1.00000i q^{32} +(0.814507 + 0.814507i) q^{33} -5.62089i q^{34} +(-3.49787 - 3.10465i) q^{35} +1.00000i q^{36} +(-3.82793 + 4.72726i) q^{37} +(-1.32254 - 1.32254i) q^{38} +(-2.04353 - 2.04353i) q^{39} +(2.23211 - 0.132937i) q^{40} +6.84388i q^{41} -2.09160 q^{42} +8.92633i q^{43} -1.15189i q^{44} +(-2.23211 + 0.132937i) q^{45} -2.70557 q^{46} +(5.84077 - 5.84077i) q^{47} +(0.707107 - 0.707107i) q^{48} +2.62520i q^{49} +(0.593460 + 4.96466i) q^{50} +(3.97457 - 3.97457i) q^{51} +2.88999i q^{52} +(-4.27233 - 4.27233i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(2.57114 - 0.153128i) q^{55} +(1.47899 + 1.47899i) q^{56} -1.87036i q^{57} +(-6.59907 + 6.59907i) q^{58} +(7.37461 - 7.37461i) q^{59} +(1.67234 + 1.48434i) q^{60} +(0.721634 - 0.721634i) q^{61} +(0.920380 + 0.920380i) q^{62} +(-1.47899 - 1.47899i) q^{63} -1.00000 q^{64} +(-6.45079 + 0.384187i) q^{65} +(0.814507 - 0.814507i) q^{66} +(4.32408 + 4.32408i) q^{67} -5.62089 q^{68} +(-1.91313 - 1.91313i) q^{69} +(-3.10465 + 3.49787i) q^{70} -4.66092 q^{71} +1.00000 q^{72} +(-0.815358 + 0.815358i) q^{73} +(4.72726 + 3.82793i) q^{74} +(-3.09090 + 3.93018i) q^{75} +(-1.32254 + 1.32254i) q^{76} +(1.70362 + 1.70362i) q^{77} +(-2.04353 + 2.04353i) q^{78} +(-11.8987 + 11.8987i) q^{79} +(-0.132937 - 2.23211i) q^{80} -1.00000 q^{81} +6.84388 q^{82} +(-5.88898 - 5.88898i) q^{83} +2.09160i q^{84} +(-0.747224 - 12.5465i) q^{85} +8.92633 q^{86} -9.33249 q^{87} -1.15189 q^{88} +(-6.87434 - 6.87434i) q^{89} +(0.132937 + 2.23211i) q^{90} +(-4.27426 - 4.27426i) q^{91} +2.70557i q^{92} +1.30161i q^{93} +(-5.84077 - 5.84077i) q^{94} +(-3.12787 - 2.77625i) q^{95} +(-0.707107 - 0.707107i) q^{96} +14.2915 q^{97} +2.62520 q^{98} +1.15189 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) \) 40 * q - 40 * q^4 - 4 * q^7	\( 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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