LMFDB - Embedded newform 430.2.g.b.257.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(257,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("430.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.g (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:	$3.43356728692$
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			257.5
Character	$\chi$	$=$	430.257
Dual form			430.2.g.b.343.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.325226 - 0.325226i) q^{3} -1.00000i q^{4} +(2.06254 - 0.863667i) q^{5} +0.459939 q^{6} +(-2.30721 + 2.30721i) q^{7} +(0.707107 + 0.707107i) q^{8} -2.78846i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.325226 - 0.325226i) q^{3} -1.00000i q^{4} +(2.06254 - 0.863667i) q^{5} +0.459939 q^{6} +(-2.30721 + 2.30721i) q^{7} +(0.707107 + 0.707107i) q^{8} -2.78846i q^{9} +(-0.847732 + 2.06914i) q^{10} +5.14688 q^{11} +(-0.325226 + 0.325226i) q^{12} +(-1.01894 + 1.01894i) q^{13} -3.26289i q^{14} +(-0.951679 - 0.389905i) q^{15} -1.00000 q^{16} +(-1.10075 - 1.10075i) q^{17} +(1.97174 + 1.97174i) q^{18} +3.19382 q^{19} +(-0.863667 - 2.06254i) q^{20} +1.50073 q^{21} +(-3.63940 + 3.63940i) q^{22} +(5.12393 - 5.12393i) q^{23} -0.459939i q^{24} +(3.50816 - 3.56270i) q^{25} -1.44100i q^{26} +(-1.88256 + 1.88256i) q^{27} +(2.30721 + 2.30721i) q^{28} -1.35708 q^{29} +(0.948643 - 0.397234i) q^{30} +2.94914 q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.67390 - 1.67390i) q^{33} +1.55669 q^{34} +(-2.76605 + 6.75138i) q^{35} -2.78846 q^{36} +(7.77349 - 7.77349i) q^{37} +(-2.25837 + 2.25837i) q^{38} +0.662771 q^{39} +(2.06914 + 0.847732i) q^{40} -0.959493 q^{41} +(-1.06118 + 1.06118i) q^{42} +(-1.13974 + 6.45763i) q^{43} -5.14688i q^{44} +(-2.40830 - 5.75131i) q^{45} +7.24633i q^{46} +(9.36644 + 9.36644i) q^{47} +(0.325226 + 0.325226i) q^{48} -3.64643i q^{49} +(0.0385680 + 4.99985i) q^{50} +0.715982i q^{51} +(1.01894 + 1.01894i) q^{52} +(-3.85117 + 3.85117i) q^{53} -2.66234i q^{54} +(10.6157 - 4.44519i) q^{55} -3.26289 q^{56} +(-1.03871 - 1.03871i) q^{57} +(0.959602 - 0.959602i) q^{58} +7.97360i q^{59} +(-0.389905 + 0.951679i) q^{60} +1.09177i q^{61} +(-2.08535 + 2.08535i) q^{62} +(6.43355 + 6.43355i) q^{63} +1.00000i q^{64} +(-1.22158 + 2.98163i) q^{65} +2.36725 q^{66} +(-8.56974 - 8.56974i) q^{67} +(-1.10075 + 1.10075i) q^{68} -3.33287 q^{69} +(-2.81805 - 6.72984i) q^{70} -13.6345i q^{71} +(1.97174 - 1.97174i) q^{72} +(-5.49624 - 5.49624i) q^{73} +10.9934i q^{74} +(-2.29963 + 0.0177389i) q^{75} -3.19382i q^{76} +(-11.8749 + 11.8749i) q^{77} +(-0.468650 + 0.468650i) q^{78} -3.25832i q^{79} +(-2.06254 + 0.863667i) q^{80} -7.14086 q^{81} +(0.678464 - 0.678464i) q^{82} +(-8.65443 + 8.65443i) q^{83} -1.50073i q^{84} +(-3.22101 - 1.31966i) q^{85} +(-3.76032 - 5.37215i) q^{86} +(0.441358 + 0.441358i) q^{87} +(3.63940 + 3.63940i) q^{88} -17.2398 q^{89} +(5.76971 + 2.36386i) q^{90} -4.70182i q^{91} +(-5.12393 - 5.12393i) q^{92} +(-0.959136 - 0.959136i) q^{93} -13.2461 q^{94} +(6.58738 - 2.75840i) q^{95} -0.459939 q^{96} +(-5.34104 - 5.34104i) q^{97} +(2.57842 + 2.57842i) q^{98} -14.3519i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 8 q^{10} + 16 q^{11} - 24 q^{13} + 8 q^{15} - 40 q^{16} - 12 q^{17} - 16 q^{21} + 44 q^{23} + 24 q^{25} + 32 q^{31} - 64 q^{35} + 48 q^{36} - 28 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} - 28 q^{47} + 24 q^{52} - 80 q^{53} + 24 q^{56} + 64 q^{57} + 12 q^{58} + 24 q^{67} - 12 q^{68} + 40 q^{78} - 120 q^{81} + 48 q^{83} + 28 q^{87} - 44 q^{92} - 16 q^{95} - 60 q^{97}+O(q^{100}) $ 40 * q - 8 * q^10 + 16 * q^11 - 24 * q^13 + 8 * q^15 - 40 * q^16 - 12 * q^17 - 16 * q^21 + 44 * q^23 + 24 * q^25 + 32 * q^31 - 64 * q^35 + 48 * q^36 - 28 * q^38 - 4 * q^40 + 8 * q^41 - 16 * q^43 - 28 * q^47 + 24 * q^52 - 80 * q^53 + 24 * q^56 + 64 * q^57 + 12 * q^58 + 24 * q^67 - 12 * q^68 + 40 * q^78 - 120 * q^81 + 48 * q^83 + 28 * q^87 - 44 * q^92 - 16 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.325226	−	0.325226i	−0.187769	−	0.187769i	0.606962	−	0.794731i	$-0.292388\pi$
$3$	−0.325226	−	0.325226i	−0.187769	−	0.187769i	−0.794731	+	0.606962i	$0.792388\pi$
$4$		−	1.00000i		−	0.500000i
$5$	2.06254	−	0.863667i	0.922397	−	0.386244i
$5$	2.06254	−	0.863667i	0.922397	−	0.386244i
$6$	0.459939			0.187769
$7$	−2.30721	+	2.30721i	−0.872043	+	0.872043i	−0.992695	−	0.120652i	$-0.961502\pi$
$7$	−2.30721	+	2.30721i	−0.872043	+	0.872043i	0.120652	+	0.992695i	$0.461502\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	2.78846i		−	0.929485i
$10$	−0.847732	+	2.06914i	−0.268076	+	0.654320i
$11$	5.14688			1.55184			0.775922	−	0.630829i	$-0.217285\pi$
$11$	5.14688			1.55184			0.775922	+	0.630829i	$0.217285\pi$
$12$	−0.325226	+	0.325226i	−0.0938846	+	0.0938846i
$13$	−1.01894	+	1.01894i	−0.282603	+	0.282603i	−0.834146	−	0.551543i	$-0.814039\pi$
$13$	−1.01894	+	1.01894i	−0.282603	+	0.282603i	0.551543	+	0.834146i	$0.314039\pi$
$14$		−	3.26289i		−	0.872043i
$15$	−0.951679	−	0.389905i	−0.245722	−	0.100673i
$16$	−1.00000			−0.250000
$17$	−1.10075	−	1.10075i	−0.266970	−	0.266970i	0.560908	−	0.827878i	$-0.310452\pi$
$17$	−1.10075	−	1.10075i	−0.266970	−	0.266970i	−0.827878	+	0.560908i	$0.810452\pi$
$18$	1.97174	+	1.97174i	0.464743	+	0.464743i
$19$	3.19382			0.732712			0.366356	−	0.930475i	$-0.380605\pi$
$19$	3.19382			0.732712			0.366356	+	0.930475i	$0.380605\pi$
$20$	−0.863667	−	2.06254i	−0.193122	−	0.461198i
$21$	1.50073			0.327486
$22$	−3.63940	+	3.63940i	−0.775922	+	0.775922i
$23$	5.12393	−	5.12393i	1.06841	−	1.06841i	0.0709315	−	0.997481i	$-0.477403\pi$
$23$	5.12393	−	5.12393i	1.06841	−	1.06841i	0.997481	−	0.0709315i	$-0.0225972\pi$
$24$		−	0.459939i		−	0.0938846i
$25$	3.50816	−	3.56270i	0.701631	−	0.712540i
$26$		−	1.44100i		−	0.282603i
$27$	−1.88256	+	1.88256i	−0.362298	+	0.362298i
$28$	2.30721	+	2.30721i	0.436022	+	0.436022i
$29$	−1.35708			−0.252004			−0.126002	−	0.992030i	$-0.540215\pi$
$29$	−1.35708			−0.252004			−0.126002	+	0.992030i	$0.540215\pi$
$30$	0.948643	−	0.397234i	0.173198	−	0.0725247i
$31$	2.94914			0.529681			0.264840	−	0.964292i	$-0.414681\pi$
$31$	2.94914			0.529681			0.264840	+	0.964292i	$0.414681\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−1.67390	−	1.67390i	−0.291388	−	0.291388i
$34$	1.55669			0.266970
$35$	−2.76605	+	6.75138i	−0.467548	+	1.14119i
$36$	−2.78846			−0.464743
$37$	7.77349	−	7.77349i	1.27795	−	1.27795i	0.336144	−	0.941811i	$-0.390877\pi$
$37$	7.77349	−	7.77349i	1.27795	−	1.27795i	0.941811	−	0.336144i	$-0.109123\pi$
$38$	−2.25837	+	2.25837i	−0.366356	+	0.366356i
$39$	0.662771			0.106128
$40$	2.06914	+	0.847732i	0.327160	+	0.134038i
$41$	−0.959493			−0.149848			−0.0749238	−	0.997189i	$-0.523871\pi$
$41$	−0.959493			−0.149848			−0.0749238	+	0.997189i	$0.523871\pi$
$42$	−1.06118	+	1.06118i	−0.163743	+	0.163743i
$43$	−1.13974	+	6.45763i	−0.173809	+	0.984779i
$43$	−1.13974	+	6.45763i	−0.173809	+	0.984779i
$44$		−	5.14688i		−	0.775922i
$45$	−2.40830	−	5.75131i	−0.359008	−	0.857354i
$46$			7.24633i			1.06841i
$47$	9.36644	+	9.36644i	1.36624	+	1.36624i	0.865738	+	0.500498i	$0.166850\pi$
$47$	9.36644	+	9.36644i	1.36624	+	1.36624i	0.500498	+	0.865738i	$0.333150\pi$
$48$	0.325226	+	0.325226i	0.0469423	+	0.0469423i
$49$		−	3.64643i		−	0.520919i
$50$	0.0385680	+	4.99985i	0.00545434	+	0.707086i
$51$			0.715982i			0.100258i
$52$	1.01894	+	1.01894i	0.141302	+	0.141302i
$53$	−3.85117	+	3.85117i	−0.529000	+	0.529000i	−0.920274	−	0.391274i	$-0.872034\pi$
$53$	−3.85117	+	3.85117i	−0.529000	+	0.529000i	0.391274	+	0.920274i	$0.372034\pi$
$54$		−	2.66234i		−	0.362298i
$55$	10.6157	−	4.44519i	1.43142	−	0.599390i
$56$	−3.26289			−0.436022
$57$	−1.03871	−	1.03871i	−0.137581	−	0.137581i
$58$	0.959602	−	0.959602i	0.126002	−	0.126002i
$59$			7.97360i			1.03807i	0.854752	+	0.519037i	$0.173709\pi$
$59$			7.97360i			1.03807i	−0.854752	+	0.519037i	$0.826291\pi$
$60$	−0.389905	+	0.951679i	−0.0503365	+	0.122861i
$61$			1.09177i			0.139787i	0.997554	+	0.0698934i	$0.0222659\pi$
$61$			1.09177i			0.139787i	−0.997554	+	0.0698934i	$0.977734\pi$
$62$	−2.08535	+	2.08535i	−0.264840	+	0.264840i
$63$	6.43355	+	6.43355i	0.810551	+	0.810551i
$64$			1.00000i			0.125000i
$65$	−1.22158	+	2.98163i	−0.151518	+	0.369826i
$66$	2.36725			0.291388
$67$	−8.56974	−	8.56974i	−1.04696	−	1.04696i	−0.998842	−	0.0481191i	$-0.984677\pi$
$67$	−8.56974	−	8.56974i	−1.04696	−	1.04696i	−0.0481191	−	0.998842i	$-0.515323\pi$
$68$	−1.10075	+	1.10075i	−0.133485	+	0.133485i
$69$	−3.33287			−0.401230
$70$	−2.81805	−	6.72984i	−0.336821	−	0.804370i
$71$		−	13.6345i		−	1.61812i	−0.587728	−	0.809059i	$-0.699978\pi$
$71$		−	13.6345i		−	1.61812i	0.587728	−	0.809059i	$-0.300022\pi$
$72$	1.97174	−	1.97174i	0.232371	−	0.232371i
$73$	−5.49624	−	5.49624i	−0.643286	−	0.643286i	0.308076	−	0.951362i	$-0.400315\pi$
$73$	−5.49624	−	5.49624i	−0.643286	−	0.643286i	−0.951362	+	0.308076i	$0.900315\pi$
$74$			10.9934i			1.27795i
$75$	−2.29963	+	0.0177389i	−0.265538	+	0.00204831i
$76$		−	3.19382i		−	0.366356i
$77$	−11.8749	+	11.8749i	−1.35327	+	1.35327i
$78$	−0.468650	+	0.468650i	−0.0530642	+	0.0530642i
$79$		−	3.25832i		−	0.366589i	−0.983058	−	0.183295i	$-0.941324\pi$
$79$		−	3.25832i		−	0.366589i	0.983058	−	0.183295i	$-0.0586762\pi$
$80$	−2.06254	+	0.863667i	−0.230599	+	0.0965610i
$81$	−7.14086			−0.793429
$82$	0.678464	−	0.678464i	0.0749238	−	0.0749238i
$83$	−8.65443	+	8.65443i	−0.949947	+	0.949947i	−0.998806	−	0.0488589i	$-0.984442\pi$
$83$	−8.65443	+	8.65443i	−0.949947	+	0.949947i	0.0488589	+	0.998806i	$0.484442\pi$
$84$		−	1.50073i		−	0.163743i
$85$	−3.22101	−	1.31966i	−0.349368	−	0.143137i
$86$	−3.76032	−	5.37215i	−0.405485	−	0.579294i
$87$	0.441358	+	0.441358i	0.0473186	+	0.0473186i
$88$	3.63940	+	3.63940i	0.387961	+	0.387961i
$89$	−17.2398			−1.82742			−0.913710	−	0.406366i	$-0.866796\pi$
$89$	−17.2398			−1.82742			−0.913710	+	0.406366i	$0.866796\pi$
$90$	5.76971	+	2.36386i	0.608181	+	0.249173i
$91$		−	4.70182i		−	0.492884i
$92$	−5.12393	−	5.12393i	−0.534206	−	0.534206i
$93$	−0.959136	−	0.959136i	−0.0994577	−	0.0994577i
$94$	−13.2461			−1.36624
$95$	6.58738	−	2.75840i	0.675851	−	0.283005i
$96$	−0.459939			−0.0469423
$97$	−5.34104	−	5.34104i	−0.542301	−	0.542301i	0.381902	−	0.924203i	$-0.375269\pi$
$97$	−5.34104	−	5.34104i	−0.542301	−	0.542301i	−0.924203	+	0.381902i	$0.875269\pi$
$98$	2.57842	+	2.57842i	0.260459	+	0.260459i
$99$		−	14.3519i		−	1.44242i
$100$	−3.56270	−	3.50816i	−0.356270	−	0.350816i
$101$	9.84942			0.980053			0.490027	−	0.871707i	$-0.336987\pi$
$101$	9.84942			0.980053			0.490027	+	0.871707i	$0.336987\pi$
$102$	−0.506276	−	0.506276i	−0.0501288	−	0.0501288i
$103$	−4.98765	+	4.98765i	−0.491448	+	0.491448i	−0.908762	−	0.417314i	$-0.862971\pi$
$103$	−4.98765	+	4.98765i	−0.491448	+	0.491448i	0.417314	+	0.908762i	$0.362971\pi$
$104$	−1.44100			−0.141302
$105$	3.09532	−	1.29613i	0.302072	−	0.126489i
$106$		−	5.44638i		−	0.529000i
$107$	−6.59304	−	6.59304i	−0.637373	−	0.637373i	0.312534	−	0.949907i	$-0.398822\pi$
$107$	−6.59304	−	6.59304i	−0.637373	−	0.637373i	−0.949907	+	0.312534i	$0.898822\pi$
$108$	1.88256	+	1.88256i	0.181149	+	0.181149i
$109$		−	0.0739179i		−	0.00708005i	−0.999994	−	0.00354003i	$-0.998873\pi$
$109$		−	0.0739179i		−	0.00708005i	0.999994	−	0.00354003i	$-0.00112683\pi$
$110$	−4.36318	+	10.6496i	−0.416013	+	1.01540i
$111$	−5.05628			−0.479921
$112$	2.30721	−	2.30721i	0.218011	−	0.218011i
$113$	7.63485	+	7.63485i	0.718226	+	0.718226i	0.968242	−	0.250015i	$-0.0804357\pi$
$113$	7.63485	+	7.63485i	0.718226	+	0.718226i	−0.250015	+	0.968242i	$0.580436\pi$
$114$	1.46896			0.137581
$115$	6.14294	−	14.9937i	0.572833	−	1.39817i
$116$			1.35708i			0.126002i
$117$	2.84127	+	2.84127i	0.262676	+	0.262676i
$118$	−5.63818	−	5.63818i	−0.519037	−	0.519037i
$119$	5.07930			0.465619
$120$	−0.397234	−	0.948643i	−0.0362624	−	0.0865989i
$121$	15.4904			1.40822
$122$	−0.771998	−	0.771998i	−0.0698934	−	0.0698934i
$123$	0.312052	+	0.312052i	0.0281368	+	0.0281368i
$124$		−	2.94914i		−	0.264840i
$125$	4.15873	−	10.3781i	0.371968	−	0.928245i
$126$	−9.09842			−0.810551
$127$	2.90965	+	2.90965i	0.258190	+	0.258190i	0.824318	−	0.566128i	$-0.191559\pi$
$127$	2.90965	+	2.90965i	0.258190	+	0.258190i	−0.566128	+	0.824318i	$0.691559\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	2.47086	−	1.72952i	0.217547	−	0.152275i
$130$	−1.24454	−	2.97212i	−0.109154	−	0.260672i
$131$			17.8481i			1.55940i	0.626154	+	0.779699i	$0.284628\pi$
$131$			17.8481i			1.55940i	−0.626154	+	0.779699i	$0.715372\pi$
$132$	−1.67390	+	1.67390i	−0.145694	+	0.145694i
$133$	−7.36880	+	7.36880i	−0.638956	+	0.638956i
$134$	12.1194			1.04696
$135$	−2.25695	+	5.50875i	−0.194247	+	0.474118i
$136$		−	1.55669i		−	0.133485i
$137$	−10.1645	+	10.1645i	−0.868415	+	0.868415i	−0.992297	−	0.123882i	$-0.960466\pi$
$137$	−10.1645	+	10.1645i	−0.868415	+	0.868415i	0.123882	+	0.992297i	$0.460466\pi$
$138$	2.35669	−	2.35669i	0.200615	−	0.200615i
$139$			9.89852i			0.839582i	0.907621	+	0.419791i	$0.137897\pi$
$139$			9.89852i			0.839582i	−0.907621	+	0.419791i	$0.862103\pi$
$140$	6.75138	+	2.76605i	0.570596	+	0.233774i
$141$		−	6.09242i		−	0.513074i
$142$	9.64105	+	9.64105i	0.809059	+	0.809059i
$143$	−5.24436	+	5.24436i	−0.438556	+	0.438556i
$144$			2.78846i			0.232371i
$145$	−2.79904	+	1.17207i	−0.232447	+	0.0973349i
$146$	7.77286			0.643286
$147$	−1.18591	+	1.18591i	−0.0978125	+	0.0978125i
$148$	−7.77349	−	7.77349i	−0.638977	−	0.638977i
$149$	−20.8823			−1.71074			−0.855371	−	0.518016i	$-0.826671\pi$
$149$	−20.8823			−1.71074			−0.855371	+	0.518016i	$0.826671\pi$
$150$	1.61354	−	1.63862i	0.131745	−	0.133793i
$151$		−	1.08609i		−	0.0883851i	−0.999023	−	0.0441925i	$-0.985928\pi$
$151$		−	1.08609i		−	0.0883851i	0.999023	−	0.0441925i	$-0.0140715\pi$
$152$	2.25837	+	2.25837i	0.183178	+	0.183178i
$153$	−3.06938	+	3.06938i	−0.248145	+	0.248145i
$154$		−	16.7937i		−	1.35327i
$155$	6.08272	−	2.54707i	0.488576	−	0.204586i
$156$		−	0.662771i		−	0.0530642i
$157$	6.47795	−	6.47795i	0.516997	−	0.516997i	−0.399665	−	0.916661i	$-0.630873\pi$
$157$	6.47795	−	6.47795i	0.516997	−	0.516997i	0.916661	+	0.399665i	$0.130873\pi$
$158$	2.30398	+	2.30398i	0.183295	+	0.183295i
$159$	2.50500			0.198660
$160$	0.847732	−	2.06914i	0.0670191	−	0.163580i
$161$			23.6439i			1.86340i
$162$	5.04935	−	5.04935i	0.396714	−	0.396714i
$163$	3.44911	+	3.44911i	0.270155	+	0.270155i	0.829163	−	0.559007i	$-0.188818\pi$
$163$	3.44911	+	3.44911i	0.270155	+	0.270155i	−0.559007	+	0.829163i	$0.688818\pi$
$164$			0.959493i			0.0749238i
$165$	−4.89818	−	2.00679i	−0.381323	−	0.156229i
$166$		−	12.2392i		−	0.949947i
$167$	−4.17574	−	4.17574i	−0.323129	−	0.323129i	0.526837	−	0.849966i	$-0.323378\pi$
$167$	−4.17574	−	4.17574i	−0.323129	−	0.323129i	−0.849966	+	0.526837i	$0.823378\pi$
$168$	1.06118	+	1.06118i	0.0818715	+	0.0818715i
$169$			10.9235i			0.840271i
$170$	3.21074	−	1.34446i	0.246252	−	0.103116i
$171$		−	8.90582i		−	0.681045i
$172$	6.45763	+	1.13974i	0.492390	+	0.0869043i
$173$	−5.26440	+	5.26440i	−0.400245	+	0.400245i	−0.878319	−	0.478074i	$-0.841335\pi$
$173$	−5.26440	+	5.26440i	−0.400245	+	0.400245i	0.478074	+	0.878319i	$0.341335\pi$
$174$	−0.624175			−0.0473186
$175$	0.125843	+	16.3139i	0.00951284	+	1.23322i
$176$	−5.14688			−0.387961
$177$	2.59322	−	2.59322i	0.194918	−	0.194918i
$178$	12.1904	−	12.1904i	0.913710	−	0.913710i
$179$	−17.9971			−1.34517			−0.672583	−	0.740022i	$-0.734815\pi$
$179$	−17.9971			−1.34517			−0.672583	+	0.740022i	$0.734815\pi$
$180$	−5.75131	+	2.40830i	−0.428677	+	0.179504i
$181$	9.73176			0.723356			0.361678	−	0.932303i	$-0.382204\pi$
$181$	9.73176			0.723356			0.361678	+	0.932303i	$0.382204\pi$
$182$	3.32469	+	3.32469i	0.246442	+	0.246442i
$183$	0.355072	−	0.355072i	0.0262477	−	0.0262477i
$184$	7.24633			0.534206
$185$	9.31944	−	22.7469i	0.685179	−	1.67238i
$186$	1.35642			0.0994577
$187$	−5.66541	−	5.66541i	−0.414296	−	0.414296i
$188$	9.36644	−	9.36644i	0.683118	−	0.683118i
$189$		−	8.68690i		−	0.631879i
$190$	−2.70750	+	6.60846i	−0.196423	+	0.479428i
$191$			15.5933i			1.12829i	0.825676	+	0.564145i	$0.190794\pi$
$191$			15.5933i			1.12829i	−0.825676	+	0.564145i	$0.809206\pi$
$192$	0.325226	−	0.325226i	0.0234712	−	0.0234712i
$193$	5.31679	−	5.31679i	0.382711	−	0.382711i	−0.489367	−	0.872078i	$-0.662772\pi$
$193$	5.31679	−	5.31679i	0.382711	−	0.382711i	0.872078	+	0.489367i	$0.162772\pi$
$194$	7.55338			0.542301
$195$	1.36699	−	0.572414i	0.0978925	−	0.0409914i
$196$	−3.64643			−0.260459
$197$	2.76661	+	2.76661i	0.197113	+	0.197113i	0.798761	−	0.601648i	$-0.205489\pi$
$197$	2.76661	+	2.76661i	0.197113	+	0.197113i	−0.601648	+	0.798761i	$0.705489\pi$
$198$	10.1483	+	10.1483i	0.721208	+	0.721208i
$199$	−0.374772			−0.0265669			−0.0132834	−	0.999912i	$-0.504228\pi$
$199$	−0.374772			−0.0265669			−0.0132834	+	0.999912i	$0.504228\pi$
$200$	4.99985	−	0.0385680i	0.353543	−	0.00272717i
$201$			5.57420i			0.393174i
$202$	−6.96459	+	6.96459i	−0.490027	+	0.490027i
$203$	3.13107	−	3.13107i	0.219758	−	0.219758i
$204$	0.715982			0.0501288
$205$	−1.97899	+	0.828683i	−0.138219	+	0.0578777i
$206$		−	7.05361i		−	0.491448i
$207$	−14.2878	−	14.2878i	−0.993074	−	0.993074i
$208$	1.01894	−	1.01894i	0.0706508	−	0.0706508i
$209$	16.4382			1.13705
$210$	−1.27222	+	3.10522i	−0.0877912	+	0.214281i
$211$		−	3.51599i		−	0.242051i	−0.992649	−	0.121025i	$-0.961382\pi$
$211$		−	3.51599i		−	0.242051i	0.992649	−	0.121025i	$-0.0386183\pi$
$212$	3.85117	+	3.85117i	0.264500	+	0.264500i
$213$	−4.43429	+	4.43429i	−0.303833	+	0.303833i
$214$	9.32396			0.637373
$215$	3.22649	+	14.3035i	0.220044	+	0.975490i
$216$	−2.66234			−0.181149
$217$	−6.80428	+	6.80428i	−0.461904	+	0.461904i
$218$	0.0522679	+	0.0522679i	0.00354003	+	0.00354003i
$219$			3.57504i			0.241579i
$220$	−4.44519	−	10.6157i	−0.299695	−	0.715708i
$221$	2.24319			0.150893
$222$	3.57533	−	3.57533i	0.239961	−	0.239961i
$223$	7.13863	+	7.13863i	0.478038	+	0.478038i	0.904504	−	0.426466i	$-0.140241\pi$
$223$	7.13863	+	7.13863i	0.478038	+	0.478038i	−0.426466	+	0.904504i	$0.640241\pi$
$224$			3.26289i			0.218011i
$225$	−9.93443	−	9.78234i	−0.662296	−	0.652156i
$226$	−10.7973			−0.718226
$227$	14.6735	−	14.6735i	0.973917	−	0.973917i	−0.0257516	−	0.999668i	$-0.508198\pi$
$227$	14.6735	−	14.6735i	0.973917	−	0.973917i	0.999668	+	0.0257516i	$0.00819790\pi$
$228$	−1.03871	+	1.03871i	−0.0687904	+	0.0687904i
$229$			2.66498i			0.176107i	0.996116	+	0.0880534i	$0.0280646\pi$
$229$			2.66498i			0.176107i	−0.996116	+	0.0880534i	$0.971935\pi$
$230$	6.25842	+	14.9459i	0.412668	+	0.985500i
$231$	7.72407			0.508207
$232$	−0.959602	−	0.959602i	−0.0630009	−	0.0630009i
$233$	3.79924	+	3.79924i	0.248897	+	0.248897i	0.820518	−	0.571621i	$-0.193685\pi$
$233$	3.79924	+	3.79924i	0.248897	+	0.248897i	−0.571621	+	0.820518i	$0.693685\pi$
$234$	−4.01816			−0.262676
$235$	27.4082	+	11.2292i	1.78791	+	0.732511i
$236$	7.97360			0.519037
$237$	−1.05969	+	1.05969i	−0.0688342	+	0.0688342i
$238$	−3.59161	+	3.59161i	−0.232809	+	0.232809i
$239$			16.1584i			1.04520i	0.852577	+	0.522602i	$0.175038\pi$
$239$			16.1584i			1.04520i	−0.852577	+	0.522602i	$0.824962\pi$
$240$	0.951679	+	0.389905i	0.0614306	+	0.0251683i
$241$			0.784965i			0.0505640i	0.999680	+	0.0252820i	$0.00804837\pi$
$241$			0.784965i			0.0505640i	−0.999680	+	0.0252820i	$0.991952\pi$
$242$	−10.9534	+	10.9534i	−0.704109	+	0.704109i
$243$	7.97006	+	7.97006i	0.511280	+	0.511280i
$244$	1.09177			0.0698934
$245$	−3.14930	−	7.52092i	−0.201202	−	0.480494i
$246$	−0.441308			−0.0281368
$247$	−3.25431	+	3.25431i	−0.207067	+	0.207067i
$248$	2.08535	+	2.08535i	0.132420	+	0.132420i
$249$	5.62929			0.356742
$250$	4.39776	+	10.2791i	0.278139	+	0.650107i
$251$	15.4014			0.972129			0.486065	−	0.873923i	$-0.338432\pi$
$251$	15.4014			0.972129			0.486065	+	0.873923i	$0.338432\pi$
$252$	6.43355	−	6.43355i	0.405276	−	0.405276i
$253$	26.3723	−	26.3723i	1.65801	−	1.65801i
$254$	−4.11487			−0.258190
$255$	0.618370	+	1.47674i	0.0387239	+	0.0924772i
$256$	1.00000			0.0625000
$257$	18.8940	−	18.8940i	1.17858	−	1.17858i	0.198471	−	0.980107i	$-0.436403\pi$
$257$	18.8940	−	18.8940i	1.17858	−	1.17858i	0.980107	−	0.198471i	$-0.0635975\pi$
$258$	−0.524210	+	2.97012i	−0.0326359	+	0.184911i
$259$			35.8702i			2.22886i
$260$	2.98163	+	1.22158i	0.184913	+	0.0757592i
$261$			3.78416i			0.234234i
$262$	−12.6205	−	12.6205i	−0.779699	−	0.779699i
$263$	−5.48051	−	5.48051i	−0.337942	−	0.337942i	0.517650	−	0.855592i	$-0.326807\pi$
$263$	−5.48051	−	5.48051i	−0.337942	−	0.337942i	−0.855592	+	0.517650i	$0.826807\pi$
$264$		−	2.36725i		−	0.145694i
$265$	−4.61707	+	11.2693i	−0.283625	+	0.692270i
$266$		−	10.4211i		−	0.638956i
$267$	5.60685	+	5.60685i	0.343133	+	0.343133i
$268$	−8.56974	+	8.56974i	−0.523480	+	0.523480i
$269$		−	18.2253i		−	1.11122i	−0.831444	−	0.555608i	$-0.812486\pi$
$269$		−	18.2253i		−	1.11122i	0.831444	−	0.555608i	$-0.187514\pi$
$270$	−2.29937	−	5.49118i	−0.139935	−	0.334183i
$271$	−15.7115			−0.954407			−0.477203	−	0.878793i	$-0.658349\pi$
$271$	−15.7115			−0.954407			−0.477203	+	0.878793i	$0.658349\pi$
$272$	1.10075	+	1.10075i	0.0667425	+	0.0667425i
$273$	−1.52915	+	1.52915i	−0.0925485	+	0.0925485i
$274$		−	14.3748i		−	0.868415i
$275$	18.0561	−	18.3368i	1.08882	−	1.10575i
$276$			3.33287i			0.200615i
$277$	−4.81860	+	4.81860i	−0.289522	+	0.289522i	−0.836891	−	0.547369i	$-0.815629\pi$
$277$	−4.81860	+	4.81860i	−0.289522	+	0.289522i	0.547369	+	0.836891i	$0.315629\pi$
$278$	−6.99931	−	6.99931i	−0.419791	−	0.419791i
$279$		−	8.22354i		−	0.492330i
$280$	−6.72984	+	2.81805i	−0.402185	+	0.168411i
$281$	−16.2149			−0.967302			−0.483651	−	0.875261i	$-0.660690\pi$
$281$	−16.2149			−0.967302			−0.483651	+	0.875261i	$0.660690\pi$
$282$	4.30799	+	4.30799i	0.256537	+	0.256537i
$283$	1.78668	−	1.78668i	0.106207	−	0.106207i	−0.652007	−	0.758213i	$-0.726073\pi$
$283$	1.78668	−	1.78668i	0.106207	−	0.106207i	0.758213	+	0.652007i	$0.226073\pi$
$284$	−13.6345			−0.809059
$285$	−3.03949	−	1.24528i	−0.180044	−	0.0737643i
$286$		−	7.41665i		−	0.438556i
$287$	2.21375	−	2.21375i	0.130674	−	0.130674i
$288$	−1.97174	−	1.97174i	−0.116186	−	0.116186i
$289$		−	14.5767i		−	0.857454i
$290$	1.15044	−	2.80800i	0.0675563	−	0.164891i
$291$			3.47409i			0.203655i
$292$	−5.49624	+	5.49624i	−0.321643	+	0.321643i
$293$	11.7195	−	11.7195i	0.684658	−	0.684658i	−0.276388	−	0.961046i	$-0.589138\pi$
$293$	11.7195	−	11.7195i	0.684658	−	0.684658i	0.961046	+	0.276388i	$0.0891376\pi$
$294$		−	1.67714i		−	0.0978125i
$295$	6.88654	+	16.4459i	0.400950	+	0.957516i
$296$	10.9934			0.638977
$297$	−9.68929	+	9.68929i	−0.562230	+	0.562230i
$298$	14.7660	−	14.7660i	0.855371	−	0.855371i
$299$			10.4420i			0.603874i
$300$	0.0177389	+	2.29963i	0.00102416	+	0.132769i
$301$	−12.2695	−	17.5287i	−0.707202	−	1.01034i
$302$	0.767985	+	0.767985i	0.0441925	+	0.0441925i
$303$	−3.20328	−	3.20328i	−0.184024	−	0.184024i
$304$	−3.19382			−0.183178
$305$	0.942926	+	2.25182i	0.0539918	+	0.128939i
$306$		−	4.34076i		−	0.248145i
$307$	−11.6458	−	11.6458i	−0.664659	−	0.664659i	0.291816	−	0.956475i	$-0.405741\pi$
$307$	−11.6458	−	11.6458i	−0.664659	−	0.664659i	−0.956475	+	0.291816i	$0.905741\pi$
$308$	11.8749	+	11.8749i	0.676637	+	0.676637i
$309$	3.24423			0.184558
$310$	−2.50008	+	6.10218i	−0.141995	+	0.346581i
$311$	−14.0317			−0.795666			−0.397833	−	0.917458i	$-0.630238\pi$
$311$	−14.0317			−0.795666			−0.397833	+	0.917458i	$0.630238\pi$
$312$	0.468650	+	0.468650i	0.0265321	+	0.0265321i
$313$	−1.39774	−	1.39774i	−0.0790051	−	0.0790051i	0.666500	−	0.745505i	$-0.267792\pi$
$313$	−1.39774	−	1.39774i	−0.0790051	−	0.0790051i	−0.745505	+	0.666500i	$0.767792\pi$
$314$			9.16121i			0.516997i
$315$	18.8259	+	7.71302i	1.06072	+	0.434580i
$316$	−3.25832			−0.183295
$317$	9.22054	+	9.22054i	0.517877	+	0.517877i	0.916929	−	0.399052i	$-0.130661\pi$
$317$	9.22054	+	9.22054i	0.517877	+	0.517877i	−0.399052	+	0.916929i	$0.630661\pi$
$318$	−1.77130	+	1.77130i	−0.0993299	+	0.0993299i
$319$	−6.98474			−0.391070
$320$	0.863667	+	2.06254i	0.0482805	+	0.115300i
$321$			4.28845i			0.239358i
$322$	−16.7188	−	16.7188i	−0.931702	−	0.931702i
$323$	−3.51558	−	3.51558i	−0.195612	−	0.195612i
$324$			7.14086i			0.396714i
$325$	0.0555765	+	7.20478i	0.00308283	+	0.399649i
$326$	−4.87778			−0.270155
$327$	−0.0240400	+	0.0240400i	−0.00132942	+	0.00132942i
$328$	−0.678464	−	0.678464i	−0.0374619	−	0.0374619i
$329$	−43.2207			−2.38283
$330$	4.88255	−	2.04452i	0.268776	−	0.112547i
$331$		−	2.90939i		−	0.159915i	−0.996798	−	0.0799573i	$-0.974522\pi$
$331$		−	2.90939i		−	0.159915i	0.996798	−	0.0799573i	$-0.0254784\pi$
$332$	8.65443	+	8.65443i	0.474973	+	0.474973i
$333$	−21.6760	−	21.6760i	−1.18784	−	1.18784i
$334$	5.90539			0.323129
$335$	−25.0769	−	10.2740i	−1.37010	−	0.561331i
$336$	−1.50073			−0.0818715
$337$	−14.5477	−	14.5477i	−0.792466	−	0.792466i	0.189429	−	0.981894i	$-0.439336\pi$
$337$	−14.5477	−	14.5477i	−0.792466	−	0.792466i	−0.981894	+	0.189429i	$0.939336\pi$
$338$	−7.72410	−	7.72410i	−0.420135	−	0.420135i
$339$		−	4.96610i		−	0.269722i
$340$	−1.31966	+	3.22101i	−0.0715684	+	0.174684i
$341$	15.1789			0.821981
$342$	6.29736	+	6.29736i	0.340522	+	0.340522i
$343$	−7.73739	−	7.73739i	−0.417780	−	0.417780i
$344$	−5.37215	+	3.76032i	−0.289647	+	0.202743i
$345$	−6.87418	+	2.87849i	−0.370093	+	0.154973i
$346$		−	7.44498i		−	0.400245i
$347$	−6.14246	+	6.14246i	−0.329745	+	0.329745i	−0.852489	−	0.522745i	$-0.824908\pi$
$347$	−6.14246	+	6.14246i	−0.329745	+	0.329745i	0.522745	+	0.852489i	$0.324908\pi$
$348$	0.441358	−	0.441358i	0.0236593	−	0.0236593i
$349$	25.5138			1.36572			0.682861	−	0.730549i	$-0.260736\pi$
$349$	25.5138			1.36572			0.682861	+	0.730549i	$0.260736\pi$
$350$	−11.6247	−	11.4467i	−0.621366	−	0.611853i
$351$		−	3.83642i		−	0.204773i
$352$	3.63940	−	3.63940i	0.193980	−	0.193980i
$353$	−22.9647	+	22.9647i	−1.22229	+	1.22229i	−0.255468	+	0.966817i	$0.582230\pi$
$353$	−22.9647	+	22.9647i	−1.22229	+	1.22229i	−0.966817	+	0.255468i	$0.917770\pi$
$354$			3.66737i			0.194918i
$355$	−11.7757	−	28.1217i	−0.624988	−	1.49255i
$356$			17.2398i			0.913710i
$357$	−1.65192	−	1.65192i	−0.0874289	−	0.0874289i
$358$	12.7259	−	12.7259i	0.672583	−	0.672583i
$359$			32.2310i			1.70109i	0.525905	+	0.850543i	$0.323727\pi$
$359$			32.2310i			1.70109i	−0.525905	+	0.850543i	$0.676273\pi$
$360$	2.36386	−	5.76971i	0.124587	−	0.304091i
$361$	−8.79954			−0.463134
$362$	−6.88139	+	6.88139i	−0.361678	+	0.361678i
$363$	−5.03788	−	5.03788i	−0.264420	−	0.264420i
$364$	−4.70182			−0.246442
$365$	−16.0831	−	6.58930i	−0.841830	−	0.344900i
$366$			0.502147i			0.0262477i
$367$	19.7863	+	19.7863i	1.03283	+	1.03283i	0.999442	+	0.0333923i	$0.0106311\pi$
$367$	19.7863	+	19.7863i	1.03283	+	1.03283i	0.0333923	+	0.999442i	$0.489369\pi$
$368$	−5.12393	+	5.12393i	−0.267103	+	0.267103i
$369$			2.67550i			0.139281i
$370$	9.49463	+	22.6743i	0.493602	+	1.17878i
$371$		−	17.7709i		−	0.922621i
$372$	−0.959136	+	0.959136i	−0.0497289	+	0.0497289i
$373$	−11.9657	−	11.9657i	−0.619558	−	0.619558i	0.325860	−	0.945418i	$-0.394346\pi$
$373$	−11.9657	−	11.9657i	−0.619558	−	0.619558i	−0.945418	+	0.325860i	$0.894346\pi$
$374$	8.01210			0.414296
$375$	−4.72775	+	2.02270i	−0.244140	+	0.104452i
$376$			13.2461i			0.683118i
$377$	1.38279	−	1.38279i	0.0712171	−	0.0712171i
$378$	6.14257	+	6.14257i	0.315940	+	0.315940i
$379$			8.29131i			0.425896i	0.977064	+	0.212948i	$0.0683065\pi$
$379$			8.29131i			0.425896i	−0.977064	+	0.212948i	$0.931694\pi$
$380$	−2.75840	−	6.58738i	−0.141503	−	0.337925i
$381$		−	1.89259i		−	0.0969603i
$382$	−11.0261	−	11.0261i	−0.564145	−	0.564145i
$383$	−2.22003	−	2.22003i	−0.113438	−	0.113438i	0.648109	−	0.761547i	$-0.275560\pi$
$383$	−2.22003	−	2.22003i	−0.113438	−	0.113438i	−0.761547	+	0.648109i	$0.775560\pi$
$384$			0.459939i			0.0234712i
$385$	−14.2366	+	34.7485i	−0.725562	+	1.77095i
$386$			7.51907i			0.382711i
$387$	18.0068	+	3.17811i	0.915338	+	0.161553i
$388$	−5.34104	+	5.34104i	−0.271150	+	0.271150i
$389$	36.7148			1.86152			0.930758	−	0.365635i	$-0.119148\pi$
$389$	36.7148			1.86152			0.930758	+	0.365635i	$0.119148\pi$
$390$	−0.561853	+	1.37137i	−0.0284505	+	0.0694419i
$391$	−11.2803			−0.570468
$392$	2.57842	−	2.57842i	0.130230	−	0.130230i
$393$	5.80468	−	5.80468i	0.292807	−	0.292807i
$394$	−3.91258			−0.197113
$395$	−2.81410	−	6.72041i	−0.141593	−	0.338141i
$396$	−14.3519			−0.721208
$397$	7.91729	+	7.91729i	0.397357	+	0.397357i	0.877300	−	0.479943i	$-0.159343\pi$
$397$	7.91729	+	7.91729i	0.397357	+	0.397357i	−0.479943	+	0.877300i	$0.659343\pi$
$398$	0.265004	−	0.265004i	0.0132834	−	0.0132834i
$399$	4.79305			0.239953
$400$	−3.50816	+	3.56270i	−0.175408	+	0.178135i
$401$	29.2692			1.46163			0.730817	−	0.682574i	$-0.239139\pi$
$401$	29.2692			1.46163			0.730817	+	0.682574i	$0.239139\pi$
$402$	−3.94156	−	3.94156i	−0.196587	−	0.196587i
$403$	−3.00499	+	3.00499i	−0.149689	+	0.149689i
$404$		−	9.84942i		−	0.490027i
$405$	−14.7283	+	6.16733i	−0.731856	+	0.306457i
$406$			4.42800i			0.219758i
$407$	40.0093	−	40.0093i	1.98319	−	1.98319i
$408$	−0.506276	+	0.506276i	−0.0250644	+	0.0250644i
$409$	33.5533			1.65910			0.829552	−	0.558430i	$-0.188596\pi$
$409$	33.5533			1.65910			0.829552	+	0.558430i	$0.188596\pi$
$410$	0.813393	−	1.98533i	0.0401706	−	0.0980484i
$411$	6.61154			0.326123
$412$	4.98765	+	4.98765i	0.245724	+	0.245724i
$413$	−18.3968	−	18.3968i	−0.905245	−	0.905245i
$414$	20.2061			0.993074
$415$	−10.3756	+	25.3247i	−0.509317	+	1.24314i
$416$			1.44100i			0.0706508i
$417$	3.21926	−	3.21926i	0.157648	−	0.157648i
$418$	−11.6236	+	11.6236i	−0.568527	+	0.568527i
$419$	−25.5182			−1.24665			−0.623323	−	0.781964i	$-0.714218\pi$
$419$	−25.5182			−1.24665			−0.623323	+	0.781964i	$0.714218\pi$
$420$	−1.29613	−	3.09532i	−0.0632447	−	0.151036i
$421$			15.1343i			0.737601i	0.929508	+	0.368801i	$0.120232\pi$
$421$			15.1343i			0.737601i	−0.929508	+	0.368801i	$0.879768\pi$
$422$	2.48618	+	2.48618i	0.121025	+	0.121025i
$423$	26.1179	−	26.1179i	1.26990	−	1.26990i
$424$	−5.44638			−0.264500
$425$	−7.78322	+	0.0600384i	−0.377541	+	0.00291229i
$426$		−	6.27104i		−	0.303833i
$427$	−2.51894	−	2.51894i	−0.121900	−	0.121900i
$428$	−6.59304	+	6.59304i	−0.318686	+	0.318686i
$429$	3.41121			0.164695
$430$	−12.3956	−	7.83262i	−0.597767	−	0.377723i
$431$	−29.3180			−1.41220			−0.706100	−	0.708112i	$-0.749547\pi$
$431$	−29.3180			−1.41220			−0.706100	+	0.708112i	$0.749547\pi$
$432$	1.88256	−	1.88256i	0.0905745	−	0.0905745i
$433$	−18.8478	−	18.8478i	−0.905765	−	0.905765i	0.0901619	−	0.995927i	$-0.471262\pi$
$433$	−18.8478	−	18.8478i	−0.905765	−	0.905765i	−0.995927	+	0.0901619i	$0.971262\pi$
$434$		−	9.62270i		−	0.461904i
$435$	1.29151	+	0.529133i	0.0619230	+	0.0253700i
$436$	−0.0739179			−0.00354003
$437$	16.3649	−	16.3649i	0.782839	−	0.782839i
$438$	−2.52793	−	2.52793i	−0.120789	−	0.120789i
$439$			11.5536i			0.551423i	0.961240	+	0.275712i	$0.0889135\pi$
$439$			11.5536i			0.551423i	−0.961240	+	0.275712i	$0.911087\pi$
$440$	10.6496	+	4.36318i	0.507701	+	0.208006i
$441$	−10.1679			−0.484186
$442$	−1.58617	+	1.58617i	−0.0754466	+	0.0754466i
$443$	3.99598	−	3.99598i	0.189855	−	0.189855i	−0.605779	−	0.795633i	$-0.707138\pi$
$443$	3.99598	−	3.99598i	0.189855	−	0.189855i	0.795633	+	0.605779i	$0.207138\pi$
$444$			5.05628i			0.239961i
$445$	−35.5579	+	14.8895i	−1.68561	+	0.705830i
$446$	−10.0955			−0.478038
$447$	6.79145	+	6.79145i	0.321225	+	0.321225i
$448$	−2.30721	−	2.30721i	−0.109005	−	0.109005i
$449$	8.24906			0.389297			0.194649	−	0.980873i	$-0.437643\pi$
$449$	8.24906			0.389297			0.194649	+	0.980873i	$0.437643\pi$
$450$	13.9419	−	0.107545i	0.657226	−	0.00506973i
$451$	−4.93840			−0.232540
$452$	7.63485	−	7.63485i	0.359113	−	0.359113i
$453$	−0.353226	+	0.353226i	−0.0165960	+	0.0165960i
$454$			20.7515i			0.973917i
$455$	−4.06081	−	9.69769i	−0.190374	−	0.454635i
$456$		−	1.46896i		−	0.0687904i
$457$	−19.9660	+	19.9660i	−0.933971	+	0.933971i	−0.997951	−	0.0639803i	$-0.979621\pi$
$457$	−19.9660	+	19.9660i	−0.933971	+	0.933971i	0.0639803	+	0.997951i	$0.479621\pi$
$458$	−1.88443	−	1.88443i	−0.0880534	−	0.0880534i
$459$	4.14443			0.193445
$460$	−14.9937	−	6.14294i	−0.699084	−	0.286416i
$461$	4.03862			0.188097			0.0940487	−	0.995568i	$-0.470019\pi$
$461$	4.03862			0.188097			0.0940487	+	0.995568i	$0.470019\pi$
$462$	−5.46174	+	5.46174i	−0.254103	+	0.254103i
$463$	−16.3398	−	16.3398i	−0.759375	−	0.759375i	0.216834	−	0.976208i	$-0.430427\pi$
$463$	−16.3398	−	16.3398i	−0.759375	−	0.759375i	−0.976208	+	0.216834i	$0.930427\pi$
$464$	1.35708			0.0630009
$465$	−2.80663	−	1.14988i	−0.130154	−	0.0533245i
$466$	−5.37294			−0.248897
$467$	−6.92312	+	6.92312i	−0.320364	+	0.320364i	−0.848907	−	0.528543i	$-0.822739\pi$
$467$	−6.92312	+	6.92312i	−0.320364	+	0.320364i	0.528543	+	0.848907i	$0.322739\pi$
$468$	2.84127	−	2.84127i	0.131338	−	0.131338i
$469$	39.5444			1.82599
$470$	−27.3207	+	11.4403i	−1.26021	+	0.527700i
$471$	−4.21360			−0.194152
$472$	−5.63818	+	5.63818i	−0.259518	+	0.259518i
$473$	−5.86610	+	33.2367i	−0.269724	+	1.52822i
$474$		−	1.49863i		−	0.0688342i
$475$	11.2044	−	11.3786i	0.514094	−	0.522086i
$476$		−	5.07930i		−	0.232809i
$477$	10.7388	+	10.7388i	0.491697	+	0.491697i
$478$	−11.4257	−	11.4257i	−0.522602	−	0.522602i
$479$		−	24.7655i		−	1.13157i	−0.824554	−	0.565783i	$-0.808574\pi$
$479$		−	24.7655i		−	1.13157i	0.824554	−	0.565783i	$-0.191426\pi$
$480$	−0.948643	+	0.397234i	−0.0432994	+	0.0181312i
$481$			15.8415i			0.722308i
$482$	−0.555054	−	0.555054i	−0.0252820	−	0.0252820i
$483$	7.68962	−	7.68962i	0.349890	−	0.349890i
$484$		−	15.4904i		−	0.704109i
$485$	−15.6290	−	6.40324i	−0.709677	−	0.290756i
$486$	−11.2714			−0.511280
$487$	−9.48334	−	9.48334i	−0.429731	−	0.429731i	0.458806	−	0.888537i	$-0.348277\pi$
$487$	−9.48334	−	9.48334i	−0.429731	−	0.429731i	−0.888537	+	0.458806i	$0.848277\pi$
$488$	−0.771998	+	0.771998i	−0.0349467	+	0.0349467i
$489$		−	2.24348i		−	0.101454i
$490$	7.54499	+	3.09120i	0.340848	+	0.139646i
$491$			17.2655i			0.779180i	0.920988	+	0.389590i	$0.127383\pi$
$491$			17.2655i			0.779180i	−0.920988	+	0.389590i	$0.872617\pi$
$492$	0.312052	−	0.312052i	0.0140684	−	0.0140684i
$493$	1.49380	+	1.49380i	0.0672775	+	0.0672775i
$494$		−	4.60229i		−	0.207067i
$495$	−12.3952	−	29.6013i	−0.557124	−	1.33048i
$496$	−2.94914			−0.132420
$497$	31.4576	+	31.4576i	1.41107	+	1.41107i
$498$	−3.98051	+	3.98051i	−0.178371	+	0.178371i
$499$	−15.0151			−0.672169			−0.336084	−	0.941832i	$-0.609103\pi$
$499$	−15.0151			−0.672169			−0.336084	+	0.941832i	$0.609103\pi$
$500$	−10.3781	−	4.15873i	−0.464123	−	0.185984i
$501$			2.71612i			0.121347i
$502$	−10.8905	+	10.8905i	−0.486065	+	0.486065i
$503$	17.0349	+	17.0349i	0.759549	+	0.759549i	0.976240	−	0.216691i	$-0.0695264\pi$
$503$	17.0349	+	17.0349i	0.759549	+	0.759549i	−0.216691	+	0.976240i	$0.569526\pi$
$504$			9.09842i			0.405276i
$505$	20.3148	−	8.50662i	0.903998	−	0.378540i
$506$			37.2960i			1.65801i
$507$	3.55261	−	3.55261i	0.157777	−	0.157777i
$508$	2.90965	−	2.90965i	0.129095	−	0.129095i
$509$		−	20.1675i		−	0.893907i	−0.894557	−	0.446953i	$-0.852509\pi$
$509$		−	20.1675i		−	0.893907i	0.894557	−	0.446953i	$-0.147491\pi$
$510$	−1.48147	−	0.606961i	−0.0656005	−	0.0268767i
$511$	25.3619			1.12195
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−6.01254	+	6.01254i	−0.265460	+	0.265460i
$514$			26.7202i			1.17858i
$515$	−5.97957	+	14.5949i	−0.263491	+	0.643129i
$516$	−1.72952	−	2.47086i	−0.0761377	−	0.108774i
$517$	48.2080	+	48.2080i	2.12018	+	2.12018i
$518$	−25.3640	−	25.3640i	−1.11443	−	1.11443i
$519$	3.42424			0.150307
$520$	−2.97212	+	1.24454i	−0.130336	+	0.0545769i
$521$			8.32287i			0.364631i	0.983240	+	0.182316i	$0.0583593\pi$
$521$			8.32287i			0.364631i	−0.983240	+	0.182316i	$0.941641\pi$
$522$	−2.67581	−	2.67581i	−0.117117	−	0.117117i
$523$	16.5694	+	16.5694i	0.724531	+	0.724531i	0.969525	−	0.244994i	$-0.0787859\pi$
$523$	16.5694	+	16.5694i	0.724531	+	0.724531i	−0.244994	+	0.969525i	$0.578786\pi$
$524$	17.8481			0.779699
$525$	5.26479	−	5.34665i	0.229774	−	0.233347i
$526$	7.75061			0.337942
$527$	−3.24625	−	3.24625i	−0.141409	−	0.141409i
$528$	1.67390	+	1.67390i	0.0728471	+	0.0728471i
$529$		−	29.5093i		−	1.28301i
$530$	−4.70386	−	11.2334i	−0.204323	−	0.487947i
$531$	22.2340			0.964874
$532$	7.36880	+	7.36880i	0.319478	+	0.319478i
$533$	0.977666	−	0.977666i	0.0423474	−	0.0423474i
$534$	−7.92928			−0.343133
$535$	−19.2926	−	7.90422i	−0.834092	−	0.341729i
$536$		−	12.1194i		−	0.523480i
$537$	5.85312	+	5.85312i	0.252581	+	0.252581i
$538$	12.8872	+	12.8872i	0.555608	+	0.555608i
$539$		−	18.7678i		−	0.808384i
$540$	5.50875	+	2.25695i	0.237059	+	0.0971236i
$541$	28.9270			1.24367			0.621834	−	0.783149i	$-0.286388\pi$
$541$	28.9270			1.24367			0.621834	+	0.783149i	$0.286388\pi$
$542$	11.1097	−	11.1097i	0.477203	−	0.477203i
$543$	−3.16502	−	3.16502i	−0.135824	−	0.135824i
$544$	−1.55669			−0.0667425
$545$	−0.0638405	−	0.152459i	−0.00273463	−	0.00653062i
$546$		−	2.16255i		−	0.0925485i
$547$	−22.9895	−	22.9895i	−0.982962	−	0.982962i	0.0168956	−	0.999857i	$-0.494622\pi$
$547$	−22.9895	−	22.9895i	−0.982962	−	0.982962i	−0.999857	+	0.0168956i	$0.994622\pi$
$548$	10.1645	+	10.1645i	0.434208	+	0.434208i
$549$	3.04435			0.129930
$550$	0.198505	+	25.7336i	0.00846428	+	1.09729i
$551$	−4.33427			−0.184646
$552$	−2.35669	−	2.35669i	−0.100308	−	0.100308i
$553$	7.51762	+	7.51762i	0.319682	+	0.319682i
$554$		−	6.81453i		−	0.289522i
$555$	−10.4288	+	4.36695i	−0.442678	+	0.185367i
$556$	9.89852			0.419791
$557$	−19.9269	−	19.9269i	−0.844328	−	0.844328i	0.145090	−	0.989418i	$-0.453653\pi$
$557$	−19.9269	−	19.9269i	−0.844328	−	0.844328i	−0.989418	+	0.145090i	$0.953653\pi$
$558$	5.81492	+	5.81492i	0.246165	+	0.246165i
$559$	−5.41861	−	7.74127i	−0.229183	−	0.327421i
$560$	2.76605	−	6.75138i	0.116887	−	0.285298i
$561$			3.68508i			0.155584i
$562$	11.4657	−	11.4657i	0.483651	−	0.483651i
$563$	−7.76358	+	7.76358i	−0.327196	+	0.327196i	−0.851519	−	0.524323i	$-0.824318\pi$
$563$	−7.76358	+	7.76358i	−0.327196	+	0.327196i	0.524323	+	0.851519i	$0.324318\pi$
$564$	−6.09242			−0.256537
$565$	22.3412	+	9.15323i	0.939900	+	0.385079i
$566$			2.52674i			0.106207i
$567$	16.4755	−	16.4755i	0.691904	−	0.691904i
$568$	9.64105	−	9.64105i	0.404529	−	0.404529i
$569$			20.6471i			0.865570i	0.901497	+	0.432785i	$0.142469\pi$
$569$			20.6471i			0.865570i	−0.901497	+	0.432785i	$0.857531\pi$
$570$	3.02979	−	1.26869i	0.126904	−	0.0531397i
$571$			7.12147i			0.298024i	0.988835	+	0.149012i	$0.0476093\pi$
$571$			7.12147i			0.298024i	−0.988835	+	0.149012i	$0.952391\pi$
$572$	5.24436	+	5.24436i	0.219278	+	0.219278i
$573$	5.07134	−	5.07134i	0.211858	−	0.211858i
$574$			3.13072i			0.130674i
$575$	−0.279476	−	36.2306i	−0.0116550	−	1.51092i
$576$	2.78846			0.116186
$577$	−16.4057	+	16.4057i	−0.682980	+	0.682980i	−0.960671	−	0.277690i	$-0.910431\pi$
$577$	−16.4057	+	16.4057i	−0.682980	+	0.682980i	0.277690	+	0.960671i	$0.410431\pi$
$578$	10.3073	+	10.3073i	0.428727	+	0.428727i
$579$	−3.45831			−0.143723
$580$	1.17207	+	2.79904i	0.0486674	+	0.116224i
$581$		−	39.9352i		−	1.65679i
$582$	−2.45655	−	2.45655i	−0.101827	−	0.101827i
$583$	−19.8215	+	19.8215i	−0.820924	+	0.820924i
$584$		−	7.77286i		−	0.321643i
$585$	8.31415	+	3.40633i	0.343748	+	0.140834i
$586$			16.5738i			0.684658i
$587$	−6.83639	+	6.83639i	−0.282168	+	0.282168i	−0.833973	−	0.551805i	$-0.813939\pi$
$587$	−6.83639	+	6.83639i	−0.282168	+	0.282168i	0.551805	+	0.833973i	$0.313939\pi$
$588$	1.18591	+	1.18591i	0.0489063	+	0.0489063i
$589$	9.41900			0.388103
$590$	−16.4985	−	6.75947i	−0.679233	−	0.278283i
$591$		−	1.79955i		−	0.0740236i
$592$	−7.77349	+	7.77349i	−0.319489	+	0.319489i
$593$	−7.84518	−	7.84518i	−0.322163	−	0.322163i	0.527433	−	0.849596i	$-0.323154\pi$
$593$	−7.84518	−	7.84518i	−0.322163	−	0.322163i	−0.849596	+	0.527433i	$0.823154\pi$
$594$		−	13.7027i		−	0.562230i
$595$	10.4763	−	4.38683i	0.429485	−	0.179842i
$596$			20.8823i			0.855371i
$597$	0.121886	+	0.121886i	0.00498844	+	0.00498844i
$598$	−7.38357	−	7.38357i	−0.301937	−	0.301937i
$599$			31.5794i			1.29030i	0.764055	+	0.645151i	$0.223205\pi$
$599$			31.5794i			1.29030i	−0.764055	+	0.645151i	$0.776795\pi$
$600$	−1.63862	−	1.61354i	−0.0668966	−	0.0658724i
$601$		−	42.7552i		−	1.74402i	−0.489488	−	0.872010i	$-0.662816\pi$
$601$		−	42.7552i		−	1.74402i	0.489488	−	0.872010i	$-0.337184\pi$
$602$	21.0705	+	3.71884i	0.858770	+	0.151569i
$603$	−23.8964	+	23.8964i	−0.973135	+	0.973135i
$604$	−1.08609			−0.0441925
$605$	31.9496	−	13.3786i	1.29894	−	0.543915i
$606$	4.53013			0.184024
$607$	2.69524	−	2.69524i	0.109396	−	0.109396i	−0.650290	−	0.759686i	$-0.725353\pi$
$607$	2.69524	−	2.69524i	0.109396	−	0.109396i	0.759686	+	0.650290i	$0.225353\pi$
$608$	2.25837	−	2.25837i	0.0915890	−	0.0915890i
$609$	−2.03661			−0.0825277
$610$	−2.25903	−	0.925529i	−0.0914654	−	0.0374736i
$611$	−19.0877			−0.772205
$612$	3.06938	+	3.06938i	0.124072	+	0.124072i
$613$	24.8913	−	24.8913i	1.00535	−	1.00535i	0.00536555	−	0.999986i	$-0.498292\pi$
$613$	24.8913	−	24.8913i	1.00535	−	1.00535i	0.999986	−	0.00536555i	$-0.00170792\pi$
$614$	16.4696			0.664659
$615$	0.913129	+	0.374111i	0.0368209	+	0.0150856i
$616$	−16.7937			−0.676637
$617$	−18.2701	−	18.2701i	−0.735527	−	0.735527i	0.236182	−	0.971709i	$-0.424104\pi$
$617$	−18.2701	−	18.2701i	−0.735527	−	0.735527i	−0.971709	+	0.236182i	$0.924104\pi$
$618$	−2.29402	+	2.29402i	−0.0922788	+	0.0922788i
$619$		−	30.9074i		−	1.24227i	−0.783703	−	0.621136i	$-0.786672\pi$
$619$		−	30.9074i		−	1.24227i	0.783703	−	0.621136i	$-0.213328\pi$
$620$	−2.54707	−	6.08272i	−0.102293	−	0.244288i
$621$			19.2922i			0.774168i
$622$	9.92193	−	9.92193i	0.397833	−	0.397833i
$623$	39.7759	−	39.7759i	1.59359	−	1.59359i
$624$	−0.662771			−0.0265321
$625$	−0.385669	−	24.9970i	−0.0154267	−	0.999881i
$626$	1.97671			0.0790051
$627$	−5.34613	−	5.34613i	−0.213504	−	0.213504i
$628$	−6.47795	−	6.47795i	−0.258498	−	0.258498i
$629$	−17.1133			−0.682351
$630$	−18.7659	+	7.85801i	−0.747650	+	0.313070i
$631$			6.60151i			0.262802i	0.991329	+	0.131401i	$0.0419475\pi$
$631$			6.60151i			0.262802i	−0.991329	+	0.131401i	$0.958052\pi$
$632$	2.30398	−	2.30398i	0.0916473	−	0.0916473i
$633$	−1.14349	+	1.14349i	−0.0454497	+	0.0454497i
$634$	−13.0398			−0.517877
$635$	8.51425	+	3.48831i	0.337878	+	0.138429i
$636$		−	2.50500i		−	0.0993299i
$637$	3.71550	+	3.71550i	0.147213	+	0.147213i
$638$	4.93896	−	4.93896i	0.195535	−	0.195535i
$639$	−38.0192			−1.50402
$640$	−2.06914	−	0.847732i	−0.0817900	−	0.0335096i
$641$			41.1815i			1.62657i	0.581864	+	0.813286i	$0.302324\pi$
$641$			41.1815i			1.62657i	−0.581864	+	0.813286i	$0.697676\pi$
$642$	−3.03239	−	3.03239i	−0.119679	−	0.119679i
$643$	6.21229	−	6.21229i	0.244989	−	0.244989i	−0.573921	−	0.818910i	$-0.694579\pi$
$643$	6.21229	−	6.21229i	0.244989	−	0.244989i	0.818910	+	0.573921i	$0.194579\pi$
$644$	23.6439			0.931702
$645$	3.60253	−	5.70120i	0.141849	−	0.224485i
$646$	4.97178			0.195612
$647$	16.2534	−	16.2534i	0.638985	−	0.638985i	−0.311320	−	0.950305i	$-0.600771\pi$
$647$	16.2534	−	16.2534i	0.638985	−	0.638985i	0.950305	+	0.311320i	$0.100771\pi$
$648$	−5.04935	−	5.04935i	−0.198357	−	0.198357i
$649$			41.0392i			1.61093i
$650$	−5.13385	−	5.05525i	−0.201366	−	0.198283i
$651$	4.42585			0.173463
$652$	3.44911	−	3.44911i	0.135078	−	0.135078i
$653$	−20.0625	−	20.0625i	−0.785106	−	0.785106i	0.195581	−	0.980688i	$-0.437341\pi$
$653$	−20.0625	−	20.0625i	−0.785106	−	0.785106i	−0.980688	+	0.195581i	$0.937341\pi$
$654$		−	0.0339977i		−	0.00132942i
$655$	15.4149	+	36.8125i	0.602308	+	1.43838i
$656$	0.959493			0.0374619
$657$	−15.3260	+	15.3260i	−0.597925	+	0.597925i
$658$	30.5616	−	30.5616i	1.19142	−	1.19142i
$659$		−	25.2180i		−	0.982354i	−0.871060	−	0.491177i	$-0.836567\pi$
$659$		−	25.2180i		−	0.982354i	0.871060	−	0.491177i	$-0.163433\pi$
$660$	−2.00679	+	4.89818i	−0.0781144	+	0.190661i
$661$	−31.3587			−1.21971			−0.609856	−	0.792512i	$-0.708773\pi$
$661$	−31.3587			−1.21971			−0.609856	+	0.792512i	$0.708773\pi$
$662$	2.05725	+	2.05725i	0.0799573	+	0.0799573i
$663$	−0.729543	−	0.729543i	−0.0283331	−	0.0283331i
$664$	−12.2392			−0.474973
$665$	−8.83427	+	21.5627i	−0.342578	+	0.836164i
$666$	30.6546			1.18784
$667$	−6.95359	+	6.95359i	−0.269244	+	0.269244i
$668$	−4.17574	+	4.17574i	−0.161564	+	0.161564i
$669$		−	4.64334i		−	0.179522i
$670$	24.9969	−	10.4672i	0.965713	−	0.404382i
$671$			5.61921i			0.216927i
$672$	1.06118	−	1.06118i	0.0409357	−	0.0409357i
$673$	2.51840	+	2.51840i	0.0970772	+	0.0970772i	0.753977	−	0.656900i	$-0.228133\pi$
$673$	2.51840	+	2.51840i	0.0970772	+	0.0970772i	−0.656900	+	0.753977i	$0.728133\pi$
$674$	20.5736			0.792466
$675$	0.102681	+	13.3113i	0.00395219	+	0.512352i
$676$	10.9235			0.420135
$677$	−1.21444	+	1.21444i	−0.0466748	+	0.0466748i	−0.730059	−	0.683384i	$-0.760507\pi$
$677$	−1.21444	+	1.21444i	−0.0466748	+	0.0466748i	0.683384	+	0.730059i	$0.260507\pi$
$678$	3.51157	+	3.51157i	0.134861	+	0.134861i
$679$	24.6458			0.945820
$680$	−1.34446	−	3.21074i	−0.0515578	−	0.123126i
$681$	−9.54443			−0.365743
$682$	−10.7331	+	10.7331i	−0.410991	+	0.410991i
$683$	−0.877908	+	0.877908i	−0.0335922	+	0.0335922i	−0.723703	−	0.690111i	$-0.757562\pi$
$683$	−0.877908	+	0.877908i	−0.0335922	+	0.0335922i	0.690111	+	0.723703i	$0.257562\pi$
$684$	−8.90582			−0.340522
$685$	−12.1860	+	29.7436i	−0.465603	+	1.13644i
$686$	10.9423			0.417780
$687$	0.866721	−	0.866721i	0.0330675	−	0.0330675i
$688$	1.13974	−	6.45763i	0.0434522	−	0.246195i
$689$		−	7.84823i		−	0.298994i
$690$	2.82538	−	6.89618i	0.107560	−	0.262533i
$691$			15.9216i			0.605685i	0.953041	+	0.302842i	$0.0979356\pi$
$691$			15.9216i			0.605685i	−0.953041	+	0.302842i	$0.902064\pi$
$692$	5.26440	+	5.26440i	0.200122	+	0.200122i
$693$	33.1127	+	33.1127i	1.25785	+	1.25785i
$694$		−	8.68675i		−	0.329745i
$695$	8.54903	+	20.4161i	0.324283	+	0.774427i
$696$			0.624175i			0.0236593i
$697$	1.05616	+	1.05616i	0.0400048	+	0.0400048i
$698$	−18.0410	+	18.0410i	−0.682861	+	0.682861i
$699$		−	2.47122i		−	0.0934703i
$700$	16.3139	−	0.125843i	0.616609	−	0.00475642i
$701$	28.6904			1.08362			0.541810	−	0.840501i	$-0.317739\pi$
$701$	28.6904			1.08362			0.541810	+	0.840501i	$0.317739\pi$
$702$	2.71276	+	2.71276i	0.102387	+	0.102387i
$703$	24.8271	−	24.8271i	0.936372	−	0.936372i
$704$			5.14688i			0.193980i
$705$	−5.26182	−	12.5659i	−0.198172	−	0.473258i
$706$		−	32.4769i		−	1.22229i
$707$	−22.7247	+	22.7247i	−0.854649	+	0.854649i
$708$	−2.59322	−	2.59322i	−0.0974592	−	0.0974592i
$709$		−	26.6237i		−	0.999874i	−0.866062	−	0.499937i	$-0.833356\pi$
$709$		−	26.6237i		−	0.999874i	0.866062	−	0.499937i	$-0.166644\pi$
$710$	28.2117	+	11.5584i	1.05877	+	0.433779i
$711$	−9.08567			−0.340739
$712$	−12.1904	−	12.1904i	−0.456855	−	0.456855i
$713$	15.1112	−	15.1112i	0.565917	−	0.565917i
$714$	2.33617			0.0874289
$715$	−6.28733	+	15.3461i	−0.235133	+	0.573912i
$716$			17.9971i			0.672583i
$717$	5.25515	−	5.25515i	0.196257	−	0.196257i
$718$	−22.7908	−	22.7908i	−0.850543	−	0.850543i
$719$			40.2114i			1.49963i	0.661646	+	0.749816i	$0.269858\pi$
$719$			40.2114i			1.49963i	−0.661646	+	0.749816i	$0.730142\pi$
$720$	2.40830	+	5.75131i	0.0897520	+	0.214339i
$721$		−	23.0151i		−	0.857128i
$722$	6.22221	−	6.22221i	0.231567	−	0.231567i
$723$	0.255291	−	0.255291i	0.00949437	−	0.00949437i
$724$		−	9.73176i		−	0.361678i
$725$	−4.76086	+	4.83488i	−0.176814	+	0.179563i
$726$	7.12464			0.264420
$727$	−17.3364	+	17.3364i	−0.642970	+	0.642970i	−0.951285	−	0.308314i	$-0.900235\pi$
$727$	−17.3364	+	17.3364i	−0.642970	+	0.642970i	0.308314	+	0.951285i	$0.400235\pi$
$728$	3.32469	−	3.32469i	0.123221	−	0.123221i
$729$			16.2384i			0.601423i
$730$	16.0318	−	6.71316i	0.593365	−	0.248465i
$731$	8.36277	−	5.85365i	0.309308	−	0.216505i
$732$	−0.355072	−	0.355072i	−0.0131238	−	0.0131238i
$733$	22.4458	+	22.4458i	0.829054	+	0.829054i	0.987386	−	0.158332i	$-0.0506115\pi$
$733$	22.4458	+	22.4458i	0.829054	+	0.829054i	−0.158332	+	0.987386i	$0.550612\pi$
$734$	−27.9820			−1.03283
$735$	−1.42176	+	3.47023i	−0.0524425	+	0.128001i
$736$		−	7.24633i		−	0.267103i
$737$	−44.1075	−	44.1075i	−1.62472	−	1.62472i
$738$	−1.89187	−	1.89187i	−0.0696406	−	0.0696406i
$739$	46.6413			1.71573			0.857864	−	0.513877i	$-0.171791\pi$
$739$	46.6413			1.71573			0.857864	+	0.513877i	$0.171791\pi$
$740$	−22.7469	−	9.31944i	−0.836192	−	0.342590i
$741$	2.11677			0.0777615
$742$	12.5659	+	12.5659i	0.461310	+	0.461310i
$743$	−33.2170	−	33.2170i	−1.21861	−	1.21861i	−0.968118	−	0.250493i	$-0.919407\pi$
$743$	−33.2170	−	33.2170i	−1.21861	−	1.21861i	−0.250493	−	0.968118i	$-0.580593\pi$
$744$		−	1.35642i		−	0.0497289i
$745$	−43.0705	+	18.0353i	−1.57798	+	0.660764i
$746$	16.9220			0.619558
$747$	24.1325	+	24.1325i	0.882962	+	0.882962i
$748$	−5.66541	+	5.66541i	−0.207148	+	0.207148i
$749$	30.4230			1.11163
$750$	1.91276	−	4.77329i	0.0698442	−	0.174296i
$751$		−	6.05719i		−	0.221030i	−0.993874	−	0.110515i	$-0.964750\pi$
$751$		−	6.05719i		−	0.221030i	0.993874	−	0.110515i	$-0.0352500\pi$
$752$	−9.36644	−	9.36644i	−0.341559	−	0.341559i
$753$	−5.00894	−	5.00894i	−0.182536	−	0.182536i
$754$			1.95555i			0.0712171i
$755$	−0.938024	−	2.24011i	−0.0341382	−	0.0815261i
$756$	−8.68690			−0.315940
$757$	10.3923	−	10.3923i	0.377714	−	0.377714i	−0.492563	−	0.870277i	$-0.663940\pi$
$757$	10.3923	−	10.3923i	0.377714	−	0.377714i	0.870277	+	0.492563i	$0.163940\pi$
$758$	−5.86284	−	5.86284i	−0.212948	−	0.212948i
$759$	−17.1539			−0.622646
$760$	6.60846	+	2.70750i	0.239714	+	0.0982114i
$761$			48.0148i			1.74053i	0.492581	+	0.870267i	$0.336054\pi$
$761$			48.0148i			1.74053i	−0.492581	+	0.870267i	$0.663946\pi$
$762$	1.33826	+	1.33826i	0.0484801	+	0.0484801i
$763$	0.170544	+	0.170544i	0.00617411	+	0.00617411i
$764$	15.5933			0.564145
$765$	−3.67980	+	8.98165i	−0.133044	+	0.324732i
$766$	3.13959			0.113438
$767$	−8.12462	−	8.12462i	−0.293363	−	0.293363i
$768$	−0.325226	−	0.325226i	−0.0117356	−	0.0117356i
$769$		−	11.7653i		−	0.424269i	−0.977241	−	0.212134i	$-0.931959\pi$
$769$		−	11.7653i		−	0.424269i	0.977241	−	0.212134i	$-0.0680414\pi$
$770$	−14.5042	−	34.6377i	−0.522694	−	1.24826i
$771$	−12.2897			−0.442601
$772$	−5.31679	−	5.31679i	−0.191355	−	0.191355i
$773$	18.5190	+	18.5190i	0.666082	+	0.666082i	0.956807	−	0.290725i	$-0.0938964\pi$
$773$	18.5190	+	18.5190i	0.666082	+	0.666082i	−0.290725	+	0.956807i	$0.593896\pi$
$774$	−14.9800	+	10.4855i	−0.538445	+	0.376893i
$775$	10.3460	−	10.5069i	0.371641	−	0.377419i
$776$		−	7.55338i		−	0.271150i
$777$	11.6659	−	11.6659i	0.418512	−	0.418512i
$778$	−25.9613	+	25.9613i	−0.930758	+	0.930758i
$779$	−3.06444			−0.109795
$780$	−0.572414	−	1.36699i	−0.0204957	−	0.0489462i
$781$		−	70.1751i		−	2.51106i
$782$	7.97636	−	7.97636i	0.285234	−	0.285234i
$783$	2.55478	−	2.55478i	0.0913005	−	0.0913005i
$784$			3.64643i			0.130230i
$785$	7.76625	−	18.9558i	0.277189	−	0.676563i
$786$			8.20905i			0.292807i
$787$	−21.5431	−	21.5431i	−0.767928	−	0.767928i	0.209813	−	0.977742i	$-0.432714\pi$
$787$	−21.5431	−	21.5431i	−0.767928	−	0.767928i	−0.977742	+	0.209813i	$0.932714\pi$
$788$	2.76661	−	2.76661i	0.0985566	−	0.0985566i
$789$			3.56480i			0.126910i
$790$	6.74192	+	2.76218i	0.239867	+	0.0982739i
$791$	−35.2304			−1.25265
$792$	10.1483	−	10.1483i	0.360604	−	0.360604i
$793$	−1.11245	−	1.11245i	−0.0395042	−	0.0395042i
$794$	−11.1967			−0.397357
$795$	5.16667	−	2.16349i	0.183243	−	0.0767311i
$796$			0.374772i			0.0132834i
$797$	7.46237	+	7.46237i	0.264331	+	0.264331i	0.826811	−	0.562480i	$-0.190153\pi$
$797$	7.46237	+	7.46237i	0.264331	+	0.264331i	−0.562480	+	0.826811i	$0.690153\pi$
$798$	−3.38920	+	3.38920i	−0.119976	+	0.119976i
$799$		−	20.6201i		−	0.729488i
$800$	−0.0385680	−	4.99985i	−0.00136358	−	0.176771i
$801$			48.0726i			1.69856i
$802$	−20.6964	+	20.6964i	−0.730817	+	0.730817i
$803$	−28.2885	−	28.2885i	−0.998279	−	0.998279i
$804$	5.57420			0.196587
$805$	20.4205	+	48.7666i	0.719728	+	1.71880i
$806$		−	4.24970i		−	0.149689i
$807$	−5.92734	+	5.92734i	−0.208652	+	0.208652i
$808$	6.96459	+	6.96459i	0.245013	+	0.245013i
$809$			46.4026i			1.63143i	0.578454	+	0.815715i	$0.303656\pi$
$809$			46.4026i			1.63143i	−0.578454	+	0.815715i	$0.696344\pi$
$810$	6.05353	−	14.7754i	0.212699	−	0.519156i
$811$			1.91005i			0.0670710i	0.999438	+	0.0335355i	$0.0106767\pi$
$811$			1.91005i			0.0670710i	−0.999438	+	0.0335355i	$0.989323\pi$
$812$	−3.13107	−	3.13107i	−0.109879	−	0.109879i
$813$	5.10979	+	5.10979i	0.179208	+	0.179208i
$814$			56.5816i			1.98319i
$815$	10.0928	+	4.13505i	0.353536	+	0.144845i
$816$		−	0.715982i		−	0.0250644i
$817$	−3.64012	+	20.6245i	−0.127352	+	0.721559i
$818$	−23.7258	+	23.7258i	−0.829552	+	0.829552i
$819$	−13.1108			−0.458129
$820$	0.828683	+	1.97899i	0.0289389	+	0.0691095i
$821$	3.86216			0.134790			0.0673952	−	0.997726i	$-0.478531\pi$
$821$	3.86216			0.134790			0.0673952	+	0.997726i	$0.478531\pi$
$822$	−4.67507	+	4.67507i	−0.163062	+	0.163062i
$823$	9.34126	−	9.34126i	0.325616	−	0.325616i	−0.525301	−	0.850917i	$-0.676047\pi$
$823$	9.34126	−	9.34126i	0.325616	−	0.325616i	0.850917	+	0.525301i	$0.176047\pi$
$824$	−7.05361			−0.245724
$825$	−11.8359	+	0.0913001i	−0.412073	+	0.00317866i
$826$	26.0169			0.905245
$827$	14.4681	+	14.4681i	0.503106	+	0.503106i	0.912402	−	0.409296i	$-0.134226\pi$
$827$	14.4681	+	14.4681i	0.503106	+	0.503106i	−0.409296	+	0.912402i	$0.634226\pi$
$828$	−14.2878	+	14.2878i	−0.496537	+	0.496537i
$829$	15.7313			0.546371			0.273186	−	0.961961i	$-0.411923\pi$
$829$	15.7313			0.546371			0.273186	+	0.961961i	$0.411923\pi$
$830$	−10.5706	−	25.2439i	−0.366911	−	0.876228i
$831$	3.13427			0.108727
$832$	−1.01894	−	1.01894i	−0.0353254	−	0.0353254i
$833$	−4.01379	+	4.01379i	−0.139070	+	0.139070i
$834$			4.55271i			0.157648i
$835$	−12.2191	−	5.00619i	−0.422859	−	0.173246i
$836$		−	16.4382i		−	0.568527i
$837$	−5.55191	+	5.55191i	−0.191902	+	0.191902i
$838$	18.0441	−	18.0441i	0.623323	−	0.623323i
$839$	25.7877			0.890292			0.445146	−	0.895458i	$-0.353152\pi$
$839$	25.7877			0.890292			0.445146	+	0.895458i	$0.353152\pi$
$840$	3.10522	+	1.27222i	0.107140	+	0.0438956i
$841$	−27.1583			−0.936494
$842$	−10.7016	−	10.7016i	−0.368801	−	0.368801i
$843$	5.27351	+	5.27351i	0.181630	+	0.181630i
$844$	−3.51599			−0.121025
$845$	9.43429	+	22.5302i	0.324549	+	0.775063i
$846$			36.9363i			1.26990i
$847$	−35.7396	+	35.7396i	−1.22803	+	1.22803i
$848$	3.85117	−	3.85117i	0.132250	−	0.132250i
$849$	−1.16215			−0.0398848
$850$	5.46111	−	5.54602i	0.187315	−	0.190227i
$851$		−	79.6616i		−	2.73077i
$852$	4.43429	+	4.43429i	0.151916	+	0.151916i
$853$	−20.2029	+	20.2029i	−0.691736	+	0.691736i	−0.962614	−	0.270878i	$-0.912686\pi$
$853$	−20.2029	+	20.2029i	−0.691736	+	0.691736i	0.270878	+	0.962614i	$0.412686\pi$
$854$	3.56232			0.121900
$855$	−7.69166	−	18.3686i	−0.263049	−	0.628194i
$856$		−	9.32396i		−	0.318686i
$857$	−0.872147	−	0.872147i	−0.0297920	−	0.0297920i	0.692054	−	0.721846i	$-0.256706\pi$
$857$	−0.872147	−	0.872147i	−0.0297920	−	0.0297920i	−0.721846	+	0.692054i	$0.756706\pi$
$858$	−2.41209	+	2.41209i	−0.0823473	+	0.0823473i
$859$	−24.1402			−0.823654			−0.411827	−	0.911262i	$-0.635109\pi$
$859$	−24.1402			−0.823654			−0.411827	+	0.911262i	$0.635109\pi$
$860$	14.3035	−	3.22649i	0.487745	−	0.110022i
$861$	−1.43994			−0.0490730
$862$	20.7310	−	20.7310i	0.706100	−	0.706100i
$863$	12.9671	+	12.9671i	0.441407	+	0.441407i	0.892485	−	0.451078i	$-0.148960\pi$
$863$	12.9671	+	12.9671i	0.441407	+	0.441407i	−0.451078	+	0.892485i	$0.648960\pi$
$864$			2.66234i			0.0905745i
$865$	−6.31135	+	15.4047i	−0.214592	+	0.523777i
$866$	26.6547			0.905765
$867$	−4.74073	+	4.74073i	−0.161003	+	0.161003i
$868$	6.80428	+	6.80428i	0.230952	+	0.230952i
$869$		−	16.7702i		−	0.568889i
$870$	−1.28739	+	0.539079i	−0.0436465	+	0.0182765i
$871$	17.4641			0.591749
$872$	0.0522679	−	0.0522679i	0.00177001	−	0.00177001i
$873$	−14.8933	+	14.8933i	−0.504061	+	0.504061i
$874$			23.1434i			0.782839i
$875$	14.3494	+	33.5395i	0.485098	+	1.13384i
$876$	3.57504			0.120789
$877$	27.5391	+	27.5391i	0.929929	+	0.929929i	0.997701	−	0.0677723i	$-0.0215891\pi$
$877$	27.5391	+	27.5391i	0.929929	+	0.929929i	−0.0677723	+	0.997701i	$0.521589\pi$
$878$	−8.16963	−	8.16963i	−0.275712	−	0.275712i
$879$	−7.62294			−0.257115
$880$	−10.6157	+	4.44519i	−0.357854	+	0.149847i
$881$	6.94329			0.233926			0.116963	−	0.993136i	$-0.462684\pi$
$881$	6.94329			0.233926			0.116963	+	0.993136i	$0.462684\pi$
$882$	7.18980	−	7.18980i	0.242093	−	0.242093i
$883$	5.17439	−	5.17439i	0.174132	−	0.174132i	−0.614660	−	0.788792i	$-0.710707\pi$
$883$	5.17439	−	5.17439i	0.174132	−	0.174132i	0.788792	+	0.614660i	$0.210707\pi$
$884$		−	2.24319i		−	0.0754466i
$885$	3.10894	−	7.58830i	0.104506	−	0.255078i
$886$			5.65116i			0.189855i
$887$	18.6190	−	18.6190i	0.625163	−	0.625163i	−0.321684	−	0.946847i	$-0.604249\pi$
$887$	18.6190	−	18.6190i	0.625163	−	0.625163i	0.946847	+	0.321684i	$0.104249\pi$
$888$	−3.57533	−	3.57533i	−0.119980	−	0.119980i
$889$	−13.4264			−0.450306
$890$	14.6148	−	35.6717i	0.489888	−	1.19572i
$891$	−36.7531			−1.23128
$892$	7.13863	−	7.13863i	0.239019	−	0.239019i
$893$	29.9147	+	29.9147i	1.00106	+	1.00106i
$894$	−9.60457			−0.321225
$895$	−37.1197	+	15.5435i	−1.24078	+	0.519562i
$896$	3.26289			0.109005
$897$	3.39599	−	3.39599i	0.113389	−	0.113389i
$898$	−5.83297	+	5.83297i	−0.194649	+	0.194649i
$899$	−4.00222			−0.133481
$900$	−9.78234	+	9.93443i	−0.326078	+	0.331148i
$901$	8.47833			0.282454
$902$	3.49197	−	3.49197i	0.116270	−	0.116270i
$903$	−1.71044	+	9.69115i	−0.0569199	+	0.322501i
$904$			10.7973i			0.359113i
$905$	20.0722	−	8.40500i	0.667221	−	0.279392i
$906$		−	0.499537i		−	0.0165960i
$907$	12.0983	+	12.0983i	0.401717	+	0.401717i	0.878838	−	0.477120i	$-0.158319\pi$
$907$	12.0983	+	12.0983i	0.401717	+	0.401717i	−0.477120	+	0.878838i	$0.658319\pi$
$908$	−14.6735	−	14.6735i	−0.486958	−	0.486958i
$909$		−	27.4647i		−	0.910945i
$910$	9.72873	+	3.98588i	0.322504	+	0.132131i
$911$		−	24.0309i		−	0.796179i	−0.917347	−	0.398090i	$-0.869673\pi$
$911$		−	24.0309i		−	0.796179i	0.917347	−	0.398090i	$-0.130327\pi$
$912$	1.03871	+	1.03871i	0.0343952	+	0.0343952i
$913$	−44.5433	+	44.5433i	−1.47417	+	1.47417i
$914$		−	28.2362i		−	0.933971i
$915$	0.425687	−	1.03901i	0.0140728	−	0.0343488i
$916$	2.66498			0.0880534
$917$	−41.1794	−	41.1794i	−1.35986	−	1.35986i
$918$	−2.93056	+	2.93056i	−0.0967227	+	0.0967227i
$919$		−	23.9720i		−	0.790765i	−0.918517	−	0.395382i	$-0.870612\pi$
$919$		−	23.9720i		−	0.790765i	0.918517	−	0.395382i	$-0.129388\pi$
$920$	14.9459	−	6.25842i	0.492750	−	0.206334i
$921$			7.57501i			0.249605i
$922$	−2.85574	+	2.85574i	−0.0940487	+	0.0940487i
$923$	13.8927	+	13.8927i	0.457285	+	0.457285i
$924$		−	7.72407i		−	0.254103i
$925$	−0.423993	−	54.9653i	−0.0139408	−	1.80725i
$926$	23.1080			0.759375
$927$	13.9079	+	13.9079i	0.456794	+	0.456794i
$928$	−0.959602	+	0.959602i	−0.0315005	+	0.0315005i
$929$	−5.61863			−0.184341			−0.0921707	−	0.995743i	$-0.529381\pi$
$929$	−5.61863			−0.184341			−0.0921707	+	0.995743i	$0.529381\pi$
$930$	2.79768	−	1.17150i	0.0917395	−	0.0384149i
$931$		−	11.6460i		−	0.381683i
$932$	3.79924	−	3.79924i	0.124448	−	0.124448i
$933$	4.56348	+	4.56348i	0.149402	+	0.149402i
$934$		−	9.79076i		−	0.320364i
$935$	−16.5782	−	6.79211i	−0.542164	−	0.222126i
$936$			4.01816i			0.131338i
$937$	17.3728	−	17.3728i	0.567546	−	0.567546i	−0.363894	−	0.931440i	$-0.618553\pi$
$937$	17.3728	−	17.3728i	0.567546	−	0.567546i	0.931440	+	0.363894i	$0.118553\pi$
$938$	−27.9621	+	27.9621i	−0.912995	+	0.912995i
$939$			0.909164i			0.0296695i
$940$	11.2292	−	27.4082i	0.366256	−	0.893956i
$941$	−51.6850			−1.68488			−0.842441	−	0.538789i	$-0.818882\pi$
$941$	−51.6850			−1.68488			−0.842441	+	0.538789i	$0.818882\pi$
$942$	2.97946	−	2.97946i	0.0970761	−	0.0970761i
$943$	−4.91637	+	4.91637i	−0.160099	+	0.160099i
$944$		−	7.97360i		−	0.259518i
$945$	−7.50259	−	17.9171i	−0.244059	−	0.582843i
$946$	−19.3539	−	27.6498i	−0.629250	−	0.898974i
$947$	−3.12994	−	3.12994i	−0.101710	−	0.101710i	0.654421	−	0.756130i	$-0.272912\pi$
$947$	−3.12994	−	3.12994i	−0.101710	−	0.101710i	−0.756130	+	0.654421i	$0.772912\pi$
$948$	1.05969	+	1.05969i	0.0344171	+	0.0344171i
$949$	11.2007			0.363589
$950$	0.123179	+	15.9686i	0.00399646	+	0.518090i
$951$		−	5.99752i		−	0.194483i
$952$	3.59161	+	3.59161i	0.116405	+	0.116405i
$953$	2.81089	+	2.81089i	0.0910537	+	0.0910537i	0.751166	−	0.660113i	$-0.229492\pi$
$953$	2.81089	+	2.81089i	0.0910537	+	0.0910537i	−0.660113	+	0.751166i	$0.729492\pi$
$954$	−15.1870			−0.491697
$955$	13.4674	+	32.1618i	0.435795	+	1.04073i
$956$	16.1584			0.522602
$957$	2.27162	+	2.27162i	0.0734310	+	0.0734310i
$958$	17.5119	+	17.5119i	0.565783	+	0.565783i
$959$		−	46.9034i		−	1.51459i
$960$	0.389905	−	0.951679i	0.0125841	−	0.0307153i
$961$	−22.3026			−0.719438
$962$	−11.2016	−	11.2016i	−0.361154	−	0.361154i
$963$	−18.3844	+	18.3844i	−0.592429	+	0.592429i
$964$	0.784965			0.0252820
$965$	6.37416	−	15.5580i	0.205192	−	0.500831i
$966$			10.8748i			0.349890i
$967$	−31.7123	−	31.7123i	−1.01980	−	1.01980i	−0.999800	−	0.0199986i	$-0.993634\pi$
$967$	−31.7123	−	31.7123i	−1.01980	−	1.01980i	−0.0199986	−	0.999800i	$-0.506366\pi$
$968$	10.9534	+	10.9534i	0.352054	+	0.352054i
$969$			2.28672i			0.0734599i
$970$	15.5792	−	6.52361i	0.500217	−	0.209460i
$971$	−55.7450			−1.78894			−0.894471	−	0.447125i	$-0.852448\pi$
$971$	−55.7450			−1.78894			−0.894471	+	0.447125i	$0.852448\pi$
$972$	7.97006	−	7.97006i	0.255640	−	0.255640i
$973$	−22.8380	−	22.8380i	−0.732151	−	0.732151i
$974$	13.4115			0.429731
$975$	2.32511	−	2.36126i	0.0744630	−	0.0756207i
$976$		−	1.09177i		−	0.0349467i
$977$	23.5517	+	23.5517i	0.753486	+	0.753486i	0.975128	−	0.221642i	$-0.0711415\pi$
$977$	23.5517	+	23.5517i	0.753486	+	0.753486i	−0.221642	+	0.975128i	$0.571142\pi$
$978$	1.58638	+	1.58638i	0.0507269	+	0.0507269i
$979$	−88.7315			−2.83587
$980$	−7.52092	+	3.14930i	−0.240247	+	0.100601i
$981$	−0.206117			−0.00658081
$982$	−12.2085	−	12.2085i	−0.389590	−	0.389590i
$983$	39.8624	+	39.8624i	1.27141	+	1.27141i	0.945347	+	0.326066i	$0.105723\pi$
$983$	39.8624	+	39.8624i	1.27141	+	1.27141i	0.326066	+	0.945347i	$0.394277\pi$
$984$			0.441308i			0.0140684i
$985$	8.09569	+	3.31682i	0.257950	+	0.105683i
$986$	−2.11255			−0.0672775
$987$	14.0565	+	14.0565i	0.447423	+	0.447423i
$988$	3.25431	+	3.25431i	0.103533	+	0.103533i
$989$	27.2485	+	38.9284i	0.866452	+	1.23785i
$990$	29.6960	+	12.1665i	0.943802	+	0.386678i
$991$			39.9840i			1.27014i	0.772457	+	0.635068i	$0.219028\pi$
$991$			39.9840i			1.27014i	−0.772457	+	0.635068i	$0.780972\pi$
$992$	2.08535	−	2.08535i	0.0662101	−	0.0662101i
$993$	−0.946210	+	0.946210i	−0.0300271	+	0.0300271i
$994$	−44.4878			−1.41107
$995$	−0.772983	+	0.323678i	−0.0245052	+	0.0102613i
$996$		−	5.62929i		−	0.178371i
$997$	−31.3161	+	31.3161i	−0.991790	+	0.991790i	−0.999967	−	0.00817688i	$-0.997397\pi$
$997$	−31.3161	+	31.3161i	−0.991790	+	0.991790i	0.00817688	+	0.999967i	$0.497397\pi$
$998$	10.6173	−	10.6173i	0.336084	−	0.336084i
$999$			29.2681i			0.926001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.g.b.257.5	✓	40
5.3	odd	4	inner	430.2.g.b.343.16	yes	40
43.42	odd	2	inner	430.2.g.b.257.16	yes	40
215.128	even	4	inner	430.2.g.b.343.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.g.b.257.5	✓	40	1.1	even	1	trivial
430.2.g.b.257.16	yes	40	43.42	odd	2	inner
430.2.g.b.343.5	yes	40	215.128	even	4	inner
430.2.g.b.343.16	yes	40	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.325226 - 0.325226i) q^{3} -1.00000i q^{4} +(2.06254 - 0.863667i) q^{5} +0.459939 q^{6} +(-2.30721 + 2.30721i) q^{7} +(0.707107 + 0.707107i) q^{8} -2.78846i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.325226 - 0.325226i) q^{3} -1.00000i q^{4} +(2.06254 - 0.863667i) q^{5} +0.459939 q^{6} +(-2.30721 + 2.30721i) q^{7} +(0.707107 + 0.707107i) q^{8} -2.78846i q^{9} +(-0.847732 + 2.06914i) q^{10} +5.14688 q^{11} +(-0.325226 + 0.325226i) q^{12} +(-1.01894 + 1.01894i) q^{13} -3.26289i q^{14} +(-0.951679 - 0.389905i) q^{15} -1.00000 q^{16} +(-1.10075 - 1.10075i) q^{17} +(1.97174 + 1.97174i) q^{18} +3.19382 q^{19} +(-0.863667 - 2.06254i) q^{20} +1.50073 q^{21} +(-3.63940 + 3.63940i) q^{22} +(5.12393 - 5.12393i) q^{23} -0.459939i q^{24} +(3.50816 - 3.56270i) q^{25} -1.44100i q^{26} +(-1.88256 + 1.88256i) q^{27} +(2.30721 + 2.30721i) q^{28} -1.35708 q^{29} +(0.948643 - 0.397234i) q^{30} +2.94914 q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.67390 - 1.67390i) q^{33} +1.55669 q^{34} +(-2.76605 + 6.75138i) q^{35} -2.78846 q^{36} +(7.77349 - 7.77349i) q^{37} +(-2.25837 + 2.25837i) q^{38} +0.662771 q^{39} +(2.06914 + 0.847732i) q^{40} -0.959493 q^{41} +(-1.06118 + 1.06118i) q^{42} +(-1.13974 + 6.45763i) q^{43} -5.14688i q^{44} +(-2.40830 - 5.75131i) q^{45} +7.24633i q^{46} +(9.36644 + 9.36644i) q^{47} +(0.325226 + 0.325226i) q^{48} -3.64643i q^{49} +(0.0385680 + 4.99985i) q^{50} +0.715982i q^{51} +(1.01894 + 1.01894i) q^{52} +(-3.85117 + 3.85117i) q^{53} -2.66234i q^{54} +(10.6157 - 4.44519i) q^{55} -3.26289 q^{56} +(-1.03871 - 1.03871i) q^{57} +(0.959602 - 0.959602i) q^{58} +7.97360i q^{59} +(-0.389905 + 0.951679i) q^{60} +1.09177i q^{61} +(-2.08535 + 2.08535i) q^{62} +(6.43355 + 6.43355i) q^{63} +1.00000i q^{64} +(-1.22158 + 2.98163i) q^{65} +2.36725 q^{66} +(-8.56974 - 8.56974i) q^{67} +(-1.10075 + 1.10075i) q^{68} -3.33287 q^{69} +(-2.81805 - 6.72984i) q^{70} -13.6345i q^{71} +(1.97174 - 1.97174i) q^{72} +(-5.49624 - 5.49624i) q^{73} +10.9934i q^{74} +(-2.29963 + 0.0177389i) q^{75} -3.19382i q^{76} +(-11.8749 + 11.8749i) q^{77} +(-0.468650 + 0.468650i) q^{78} -3.25832i q^{79} +(-2.06254 + 0.863667i) q^{80} -7.14086 q^{81} +(0.678464 - 0.678464i) q^{82} +(-8.65443 + 8.65443i) q^{83} -1.50073i q^{84} +(-3.22101 - 1.31966i) q^{85} +(-3.76032 - 5.37215i) q^{86} +(0.441358 + 0.441358i) q^{87} +(3.63940 + 3.63940i) q^{88} -17.2398 q^{89} +(5.76971 + 2.36386i) q^{90} -4.70182i q^{91} +(-5.12393 - 5.12393i) q^{92} +(-0.959136 - 0.959136i) q^{93} -13.2461 q^{94} +(6.58738 - 2.75840i) q^{95} -0.459939 q^{96} +(-5.34104 - 5.34104i) q^{97} +(2.57842 + 2.57842i) q^{98} -14.3519i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 8 q^{10} + 16 q^{11} - 24 q^{13} + 8 q^{15} - 40 q^{16} - 12 q^{17} - 16 q^{21} + 44 q^{23} + 24 q^{25} + 32 q^{31} - 64 q^{35} + 48 q^{36} - 28 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} - 28 q^{47} + 24 q^{52} - 80 q^{53} + 24 q^{56} + 64 q^{57} + 12 q^{58} + 24 q^{67} - 12 q^{68} + 40 q^{78} - 120 q^{81} + 48 q^{83} + 28 q^{87} - 44 q^{92} - 16 q^{95} - 60 q^{97}+O(q^{100}) \) 40 * q - 8 * q^10 + 16 * q^11 - 24 * q^13 + 8 * q^15 - 40 * q^16 - 12 * q^17 - 16 * q^21 + 44 * q^23 + 24 * q^25 + 32 * q^31 - 64 * q^35 + 48 * q^36 - 28 * q^38 - 4 * q^40 + 8 * q^41 - 16 * q^43 - 28 * q^47 + 24 * q^52 - 80 * q^53 + 24 * q^56 + 64 * q^57 + 12 * q^58 + 24 * q^67 - 12 * q^68 + 40 * q^78 - 120 * q^81 + 48 * q^83 + 28 * q^87 - 44 * q^92 - 16 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more