LMFDB - Embedded newform 558.2.q.a.185.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(185,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.185"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.20
Character	$\chi$	$=$	558.185
Dual form			558.2.q.a.371.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.37617 + 1.05175i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.74890 + 1.00973i) q^{5} +(-0.665921 + 1.59892i) q^{6} +(-1.62183 - 2.80910i) q^{7} -1.00000i q^{8} +(0.787662 - 2.89475i) q^{9} +2.01945 q^{10} +(-2.86147 - 4.95622i) q^{11} +(0.222756 + 1.71767i) q^{12} +(2.00587 + 1.15809i) q^{13} +(-2.80910 - 1.62183i) q^{14} +(-3.46875 + 0.449844i) q^{15} +(-0.500000 - 0.866025i) q^{16} +4.78084 q^{17} +(-0.765240 - 2.90076i) q^{18} +5.23392 q^{19} +(1.74890 - 1.00973i) q^{20} +(5.18636 + 2.16003i) q^{21} +(-4.95622 - 2.86147i) q^{22} +(0.788409 - 1.36557i) q^{23} +(1.05175 + 1.37617i) q^{24} +(-0.460907 - 0.798314i) q^{25} +2.31618 q^{26} +(1.96059 + 4.81208i) q^{27} -3.24367 q^{28} +(-0.991719 - 1.71771i) q^{29} +(-2.77910 + 2.12395i) q^{30} +(-2.35088 + 5.04711i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(9.15054 + 3.81103i) q^{33} +(4.14033 - 2.39042i) q^{34} -6.55043i q^{35} +(-2.11310 - 2.12951i) q^{36} -3.80460i q^{37} +(4.53271 - 2.61696i) q^{38} +(-3.97843 + 0.515943i) q^{39} +(1.00973 - 1.74890i) q^{40} +(6.80465 + 3.92867i) q^{41} +(5.57154 - 0.722545i) q^{42} +(3.65486 - 2.11013i) q^{43} -5.72295 q^{44} +(4.30045 - 4.26730i) q^{45} -1.57682i q^{46} +(-1.49375 + 0.862419i) q^{47} +(1.59892 + 0.665921i) q^{48} +(-1.76068 + 3.04959i) q^{49} +(-0.798314 - 0.460907i) q^{50} +(-6.57922 + 5.02822i) q^{51} +(2.00587 - 1.15809i) q^{52} -12.6888 q^{53} +(4.10396 + 3.18709i) q^{54} -11.5572i q^{55} +(-2.80910 + 1.62183i) q^{56} +(-7.20275 + 5.50476i) q^{57} +(-1.71771 - 0.991719i) q^{58} +(-12.7196 - 7.34365i) q^{59} +(-1.34480 + 3.22894i) q^{60} +(4.68822 - 2.70674i) q^{61} +(0.487636 + 5.54637i) q^{62} +(-9.40909 + 2.48218i) q^{63} -1.00000 q^{64} +(2.33871 + 4.05076i) q^{65} +(9.83011 - 1.27482i) q^{66} +(2.23930 - 3.87858i) q^{67} +(2.39042 - 4.14033i) q^{68} +(0.351245 + 2.70845i) q^{69} +(-3.27521 - 5.67284i) q^{70} +7.99135i q^{71} +(-2.89475 - 0.787662i) q^{72} +3.40825i q^{73} +(-1.90230 - 3.29488i) q^{74} +(1.47391 + 0.613855i) q^{75} +(2.61696 - 4.53271i) q^{76} +(-9.28166 + 16.0763i) q^{77} +(-3.18745 + 2.43603i) q^{78} +(8.21498 - 4.74292i) q^{79} -2.01945i q^{80} +(-7.75918 - 4.56017i) q^{81} +7.85733 q^{82} +(6.74123 + 11.6761i) q^{83} +(4.46382 - 3.41151i) q^{84} +(8.36119 + 4.82733i) q^{85} +(2.11013 - 3.65486i) q^{86} +(3.17136 + 1.32081i) q^{87} +(-4.95622 + 2.86147i) q^{88} -12.4966 q^{89} +(1.59065 - 5.84581i) q^{90} -7.51292i q^{91} +(-0.788409 - 1.36557i) q^{92} +(-2.07308 - 9.41819i) q^{93} +(-0.862419 + 1.49375i) q^{94} +(9.15359 + 5.28483i) q^{95} +(1.71767 - 0.222756i) q^{96} +(7.16097 + 12.4032i) q^{97} +3.52136i q^{98} +(-16.6009 + 4.37943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) $ 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.37617	+	1.05175i	−0.794529	+	0.607226i
$3$	−1.37617	+	1.05175i	−0.794529	+	0.607226i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.74890	+	1.00973i	0.782130	+	0.451563i	0.837185	−	0.546920i	$-0.184200\pi$
$5$	1.74890	+	1.00973i	0.782130	+	0.451563i	−0.0550544	+	0.998483i	$0.517533\pi$
$6$	−0.665921	+	1.59892i	−0.271861	+	0.652757i
$7$	−1.62183	−	2.80910i	−0.612995	−	1.06174i	−0.990733	−	0.135826i	$-0.956631\pi$
$7$	−1.62183	−	2.80910i	−0.612995	−	1.06174i	0.377738	−	0.925913i	$-0.376702\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.787662	−	2.89475i	0.262554	−	0.964917i
$10$	2.01945			0.638607
$11$	−2.86147	−	4.95622i	−0.862766	−	1.49436i	−0.869248	−	0.494376i	$-0.835396\pi$
$11$	−2.86147	−	4.95622i	−0.862766	−	1.49436i	0.00648152	−	0.999979i	$-0.497937\pi$
$12$	0.222756	+	1.71767i	0.0643040	+	0.495848i
$13$	2.00587	+	1.15809i	0.556329	+	0.321197i	0.751671	−	0.659539i	$-0.229248\pi$
$13$	2.00587	+	1.15809i	0.556329	+	0.321197i	−0.195342	+	0.980735i	$0.562582\pi$
$14$	−2.80910	−	1.62183i	−0.750763	−	0.433453i
$15$	−3.46875	+	0.449844i	−0.895626	+	0.116149i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.78084			1.15952			0.579762	−	0.814786i	$-0.303146\pi$
$17$	4.78084			1.15952			0.579762	+	0.814786i	$0.303146\pi$
$18$	−0.765240	−	2.90076i	−0.180369	−	0.683716i
$19$	5.23392			1.20074			0.600372	−	0.799721i	$-0.295019\pi$
$19$	5.23392			1.20074			0.600372	+	0.799721i	$0.295019\pi$
$20$	1.74890	−	1.00973i	0.391065	−	0.225782i
$21$	5.18636	+	2.16003i	1.13176	+	0.471356i
$22$	−4.95622	−	2.86147i	−1.05667	−	0.610068i
$23$	0.788409	−	1.36557i	0.164395	−	0.284740i	−0.772045	−	0.635567i	$-0.780766\pi$
$23$	0.788409	−	1.36557i	0.164395	−	0.284740i	0.936440	+	0.350827i	$0.114100\pi$
$24$	1.05175	+	1.37617i	0.214687	+	0.280909i
$25$	−0.460907	−	0.798314i	−0.0921814	−	0.159663i
$26$	2.31618			0.454241
$27$	1.96059	+	4.81208i	0.377315	+	0.926085i
$28$	−3.24367			−0.612995
$29$	−0.991719	−	1.71771i	−0.184158	−	0.318970i	0.759135	−	0.650934i	$-0.225622\pi$
$29$	−0.991719	−	1.71771i	−0.184158	−	0.318970i	−0.943292	+	0.331963i	$0.892289\pi$
$30$	−2.77910	+	2.12395i	−0.507392	+	0.387778i
$31$	−2.35088	+	5.04711i	−0.422230	+	0.906489i
$31$	−2.35088	+	5.04711i	−0.422230	+	0.906489i
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	9.15054	+	3.81103i	1.59290	+	0.663415i
$34$	4.14033	−	2.39042i	0.710060	−	0.409953i
$35$		−	6.55043i		−	1.10722i
$36$	−2.11310	−	2.12951i	−0.352183	−	0.354919i
$37$		−	3.80460i		−	0.625473i	−0.949840	−	0.312737i	$-0.898754\pi$
$37$		−	3.80460i		−	0.625473i	0.949840	−	0.312737i	$-0.101246\pi$
$38$	4.53271	−	2.61696i	0.735303	−	0.424527i
$39$	−3.97843	+	0.515943i	−0.637059	+	0.0826170i
$40$	1.00973	−	1.74890i	0.159652	−	0.276525i
$41$	6.80465	+	3.92867i	1.06271	+	0.613555i	0.926180	−	0.377082i	$-0.123072\pi$
$41$	6.80465	+	3.92867i	1.06271	+	0.613555i	0.136528	+	0.990636i	$0.456406\pi$
$42$	5.57154	−	0.722545i	0.859707	−	0.111491i
$43$	3.65486	−	2.11013i	0.557360	−	0.321792i	−0.194725	−	0.980858i	$-0.562381\pi$
$43$	3.65486	−	2.11013i	0.557360	−	0.321792i	0.752085	+	0.659066i	$0.229048\pi$
$44$	−5.72295			−0.862766
$45$	4.30045	−	4.26730i	0.641073	−	0.636131i
$46$		−	1.57682i		−	0.232489i
$47$	−1.49375	+	0.862419i	−0.217886	+	0.125797i	−0.604971	−	0.796247i	$-0.706815\pi$
$47$	−1.49375	+	0.862419i	−0.217886	+	0.125797i	0.387085	+	0.922044i	$0.373482\pi$
$48$	1.59892	+	0.665921i	0.230784	+	0.0961175i
$49$	−1.76068	+	3.04959i	−0.251526	+	0.435656i
$50$	−0.798314	−	0.460907i	−0.112899	−	0.0651821i
$51$	−6.57922	+	5.02822i	−0.921275	+	0.704092i
$52$	2.00587	−	1.15809i	0.278164	−	0.160598i
$53$	−12.6888			−1.74293			−0.871467	−	0.490454i	$-0.836831\pi$
$53$	−12.6888			−1.74293			−0.871467	+	0.490454i	$0.836831\pi$
$54$	4.10396	+	3.18709i	0.558478	+	0.433708i
$55$		−	11.5572i		−	1.55837i
$56$	−2.80910	+	1.62183i	−0.375381	+	0.216727i
$57$	−7.20275	+	5.50476i	−0.954027	+	0.729123i
$58$	−1.71771	−	0.991719i	−0.225546	−	0.130219i
$59$	−12.7196	−	7.34365i	−1.65595	−	0.956061i	−0.974557	−	0.224141i	$-0.928042\pi$
$59$	−12.7196	−	7.34365i	−1.65595	−	0.956061i	−0.681390	−	0.731921i	$-0.738624\pi$
$60$	−1.34480	+	3.22894i	−0.173612	+	0.416855i
$61$	4.68822	−	2.70674i	0.600265	−	0.346563i	−0.168881	−	0.985636i	$-0.554015\pi$
$61$	4.68822	−	2.70674i	0.600265	−	0.346563i	0.769146	+	0.639073i	$0.220682\pi$
$62$	0.487636	+	5.54637i	0.0619298	+	0.704390i
$63$	−9.40909	+	2.48218i	−1.18543	+	0.312726i
$64$	−1.00000			−0.125000
$65$	2.33871	+	4.05076i	0.290081	+	0.502435i
$66$	9.83011	−	1.27482i	1.21000	−	0.156919i
$67$	2.23930	−	3.87858i	0.273574	−	0.473844i	−0.696200	−	0.717848i	$-0.745127\pi$
$67$	2.23930	−	3.87858i	0.273574	−	0.473844i	0.969774	+	0.244003i	$0.0784608\pi$
$68$	2.39042	−	4.14033i	0.289881	−	0.502088i
$69$	0.351245	+	2.70845i	0.0422850	+	0.326059i
$70$	−3.27521	−	5.67284i	−0.391463	−	0.678034i
$71$			7.99135i			0.948398i	0.880418	+	0.474199i	$0.157262\pi$
$71$			7.99135i			0.948398i	−0.880418	+	0.474199i	$0.842738\pi$
$72$	−2.89475	−	0.787662i	−0.341150	−	0.0928269i
$73$			3.40825i			0.398905i	0.979907	+	0.199453i	$0.0639164\pi$
$73$			3.40825i			0.398905i	−0.979907	+	0.199453i	$0.936084\pi$
$74$	−1.90230	−	3.29488i	−0.221138	−	0.383023i
$75$	1.47391	+	0.613855i	0.170192	+	0.0708819i
$76$	2.61696	−	4.53271i	0.300186	−	0.519938i
$77$	−9.28166	+	16.0763i	−1.05774	+	1.83207i
$78$	−3.18745	+	2.43603i	−0.360908	+	0.275827i
$79$	8.21498	−	4.74292i	0.924257	−	0.533620i	0.0392664	−	0.999229i	$-0.487498\pi$
$79$	8.21498	−	4.74292i	0.924257	−	0.533620i	0.884991	+	0.465609i	$0.154165\pi$
$80$		−	2.01945i		−	0.225782i
$81$	−7.75918	−	4.56017i	−0.862131	−	0.506686i
$82$	7.85733			0.867697
$83$	6.74123	+	11.6761i	0.739946	+	1.28162i	0.952519	+	0.304479i	$0.0984823\pi$
$83$	6.74123	+	11.6761i	0.739946	+	1.28162i	−0.212573	+	0.977145i	$0.568184\pi$
$84$	4.46382	−	3.41151i	0.487043	−	0.372226i
$85$	8.36119	+	4.82733i	0.906898	+	0.523598i
$86$	2.11013	−	3.65486i	0.227541	−	0.394113i
$87$	3.17136	+	1.32081i	0.340006	+	0.141606i
$88$	−4.95622	+	2.86147i	−0.528334	+	0.305034i
$89$	−12.4966			−1.32464			−0.662318	−	0.749222i	$-0.730427\pi$
$89$	−12.4966			−1.32464			−0.662318	+	0.749222i	$0.730427\pi$
$90$	1.59065	−	5.84581i	0.167669	−	0.616203i
$91$		−	7.51292i		−	0.787568i
$92$	−0.788409	−	1.36557i	−0.0821974	−	0.142370i
$93$	−2.07308	−	9.41819i	−0.214968	−	0.976621i
$94$	−0.862419	+	1.49375i	−0.0889517	+	0.154069i
$95$	9.15359	+	5.28483i	0.939139	+	0.542212i
$96$	1.71767	−	0.222756i	0.175309	−	0.0227349i
$97$	7.16097	+	12.4032i	0.727086	+	1.25935i	0.958110	+	0.286402i	$0.0924592\pi$
$97$	7.16097	+	12.4032i	0.727086	+	1.25935i	−0.231024	+	0.972948i	$0.574208\pi$
$98$			3.52136i			0.355712i
$99$	−16.6009	+	4.37943i	−1.66845	+	0.440149i
$100$	−0.921814			−0.0921814
$101$	−13.3336	+	7.69818i	−1.32675	+	0.765997i	−0.984795	−	0.173721i	$-0.944421\pi$
$101$	−13.3336	+	7.69818i	−1.32675	+	0.765997i	−0.341951	+	0.939718i	$0.611088\pi$
$102$	−3.18366	+	7.64418i	−0.315229	+	0.756887i
$103$	−3.62542	+	6.27941i	−0.357223	+	0.618729i	−0.987496	−	0.157645i	$-0.949610\pi$
$103$	−3.62542	+	6.27941i	−0.357223	+	0.618729i	0.630273	+	0.776374i	$0.282943\pi$
$104$	1.15809	−	2.00587i	0.113560	−	0.196692i
$105$	6.88938	+	9.01447i	0.672335	+	0.879722i
$106$	−10.9888	+	6.34438i	−1.06732	+	0.616220i
$107$			2.99327i			0.289371i	0.989478	+	0.144685i	$0.0462170\pi$
$107$			2.99327i			0.289371i	−0.989478	+	0.144685i	$0.953783\pi$
$108$	5.14768	+	0.708119i	0.495335	+	0.0681388i
$109$	8.31180			0.796126			0.398063	−	0.917358i	$-0.369683\pi$
$109$	8.31180			0.796126			0.398063	+	0.917358i	$0.369683\pi$
$110$	−5.77861	−	10.0088i	−0.550969	−	0.954305i
$111$	4.00148	+	5.23577i	0.379803	+	0.496957i
$112$	−1.62183	+	2.80910i	−0.153249	+	0.265435i
$113$	15.5958	+	9.00426i	1.46713	+	0.847050i	0.999323	−	0.0367793i	$-0.0117099\pi$
$113$	15.5958	+	9.00426i	1.46713	+	0.847050i	0.467810	+	0.883829i	$0.345043\pi$
$114$	−3.48538	+	8.36863i	−0.326436	+	0.783794i
$115$	2.75769	−	1.59216i	0.257156	−	0.148469i
$116$	−1.98344			−0.184158
$117$	4.93234	−	4.89432i	0.455995	−	0.452480i
$118$	−14.6873			−1.35207
$119$	−7.75372	−	13.4298i	−0.710782	−	1.23111i
$120$	0.449844	+	3.46875i	0.0410650	+	0.316652i
$121$	−10.8761	+	18.8379i	−0.988732	+	1.71253i
$122$	2.70674	−	4.68822i	0.245057	−	0.424451i
$123$	−13.4963	+	1.75027i	−1.21692	+	0.157816i
$124$	3.19549	+	4.55948i	0.286963	+	0.409453i
$125$		−	11.9588i		−	1.06963i
$126$	−6.90742	+	6.85418i	−0.615362	+	0.610619i
$127$			4.43220i			0.393294i	0.980474	+	0.196647i	$0.0630053\pi$
$127$			4.43220i			0.393294i	−0.980474	+	0.196647i	$0.936995\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−2.81037	+	6.74787i	−0.247439	+	0.594117i
$130$	4.05076	+	2.33871i	0.355275	+	0.205118i
$131$	2.69085	+	1.55356i	0.235101	+	0.135735i	0.612923	−	0.790143i	$-0.289994\pi$
$131$	2.69085	+	1.55356i	0.235101	+	0.135735i	−0.377822	+	0.925878i	$0.623327\pi$
$132$	7.87572	−	6.01908i	0.685493	−	0.523894i
$133$	−8.48855	−	14.7026i	−0.736051	−	1.27488i
$134$		−	4.47860i		−	0.386892i
$135$	−1.43001	+	10.3955i	−0.123076	+	0.894701i
$136$		−	4.78084i		−	0.409953i
$137$	4.62177	+	8.00513i	0.394864	+	0.683925i	0.993084	−	0.117407i	$-0.0374583\pi$
$137$	4.62177	+	8.00513i	0.394864	+	0.683925i	−0.598220	+	0.801332i	$0.704125\pi$
$138$	1.65841	+	2.16996i	0.141173	+	0.184720i
$139$	−2.87362	−	1.65909i	−0.243737	−	0.140722i	0.373156	−	0.927769i	$-0.378276\pi$
$139$	−2.87362	−	1.65909i	−0.243737	−	0.140722i	−0.616893	+	0.787047i	$0.711609\pi$
$140$	−5.67284	−	3.27521i	−0.479442	−	0.276806i
$141$	1.14861	−	2.75788i	0.0967301	−	0.232255i
$142$	3.99567	+	6.92071i	0.335309	+	0.580773i
$143$		−	13.2554i		−	1.10847i
$144$	−2.90076	+	0.765240i	−0.241730	+	0.0637700i
$145$		−	4.00546i		−	0.332635i
$146$	1.70412	+	2.95163i	0.141034	+	0.244279i
$147$	−0.784404	−	6.04853i	−0.0646965	−	0.498874i
$148$	−3.29488	−	1.90230i	−0.270838	−	0.156368i
$149$	−4.94037	−	2.85232i	−0.404731	−	0.233671i	0.283792	−	0.958886i	$-0.408407\pi$
$149$	−4.94037	−	2.85232i	−0.404731	−	0.233671i	−0.688523	+	0.725214i	$0.741741\pi$
$150$	1.58337	−	0.205339i	0.129282	−	0.0167659i
$151$	13.4475	−	7.76394i	1.09435	−	0.631821i	0.159616	−	0.987179i	$-0.448975\pi$
$151$	13.4475	−	7.76394i	1.09435	−	0.631821i	0.934730	+	0.355358i	$0.115641\pi$
$152$		−	5.23392i		−	0.424527i
$153$	3.76568	−	13.8393i	0.304438	−	1.11884i
$154$			18.5633i			1.49587i
$155$	−9.20765	+	6.45314i	−0.739576	+	0.518328i
$156$	−1.54240	+	3.70339i	−0.123490	+	0.296509i
$157$	2.54810	−	4.41344i	0.203361	−	0.352231i	−0.746248	−	0.665667i	$-0.768147\pi$
$157$	2.54810	−	4.41344i	0.203361	−	0.352231i	0.949609	+	0.313436i	$0.101480\pi$
$158$	4.74292	−	8.21498i	0.377326	−	0.653548i
$159$	17.4618	−	13.3453i	1.38481	−	1.05835i
$160$	−1.00973	−	1.74890i	−0.0798258	−	0.138262i
$161$	−5.11467			−0.403093
$162$	−8.99973	−	0.0696391i	−0.707086	−	0.00547137i
$163$	1.48533			0.116340			0.0581698	−	0.998307i	$-0.481474\pi$
$163$	1.48533			0.116340			0.0581698	+	0.998307i	$0.481474\pi$
$164$	6.80465	−	3.92867i	0.531354	−	0.306777i
$165$	12.1552	+	15.9046i	0.946285	+	1.23817i
$166$	11.6761	+	6.74123i	0.906245	+	0.523221i
$167$	−2.94805	+	5.10618i	−0.228127	+	0.395128i	−0.957253	−	0.289252i	$-0.906594\pi$
$167$	−2.94805	+	5.10618i	−0.228127	+	0.395128i	0.729126	+	0.684380i	$0.239927\pi$
$168$	2.16003	−	5.18636i	0.166650	−	0.400137i
$169$	−3.81765	−	6.61236i	−0.293665	−	0.508643i
$170$	9.65467			0.740479
$171$	4.12257	−	15.1509i	0.315260	−	1.15862i
$172$		−	4.22027i		−	0.321792i
$173$	−2.01796	+	1.16507i	−0.153422	+	0.0885784i	−0.574746	−	0.818332i	$-0.694899\pi$
$173$	−2.01796	+	1.16507i	−0.153422	+	0.0885784i	0.421323	+	0.906910i	$0.361566\pi$
$174$	3.40689	−	0.441822i	0.258275	−	0.0334945i
$175$	−1.49503	+	2.58946i	−0.113013	+	0.195745i
$176$	−2.86147	+	4.95622i	−0.215692	+	0.373589i
$177$	25.2279	−	3.27168i	1.89624	−	0.245914i
$178$	−10.8224	+	6.24830i	−0.811171	+	0.468330i
$179$	−0.126838			−0.00948033			−0.00474016	−	0.999989i	$-0.501509\pi$
$179$	−0.126838			−0.00948033			−0.00474016	+	0.999989i	$0.501509\pi$
$180$	−1.54537	−	5.85795i	−0.115185	−	0.436625i
$181$			24.1210i			1.79290i	0.443148	+	0.896449i	$0.353862\pi$
$181$			24.1210i			1.79290i	−0.443148	+	0.896449i	$0.646138\pi$
$182$	−3.75646	−	6.50638i	−0.278447	−	0.482285i
$183$	−3.60496	+	8.65574i	−0.266486	+	0.639851i
$184$	−1.36557	−	0.788409i	−0.100671	−	0.0581223i
$185$	3.84161	−	6.65386i	0.282441	−	0.489202i
$186$	−6.50444	−	7.11985i	−0.476928	−	0.522053i
$187$	−13.6802	−	23.6949i	−1.00040	−	1.73274i
$188$			1.72484i			0.125797i
$189$	10.3378	−	13.3119i	0.751968	−	0.968296i
$190$	10.5697			0.766804
$191$	−6.75074	+	3.89754i	−0.488466	+	0.282016i	−0.723938	−	0.689865i	$-0.757670\pi$
$191$	−6.75074	+	3.89754i	−0.488466	+	0.282016i	0.235472	+	0.971881i	$0.424337\pi$
$192$	1.37617	−	1.05175i	0.0993162	−	0.0759032i
$193$	9.81440	−	16.9990i	0.706456	−	1.22362i	−0.259708	−	0.965687i	$-0.583626\pi$
$193$	9.81440	−	16.9990i	0.706456	−	1.22362i	0.966164	−	0.257930i	$-0.0830404\pi$
$194$	12.4032	+	7.16097i	0.890495	+	0.514127i
$195$	−7.47882	−	3.11479i	−0.535570	−	0.223055i
$196$	1.76068	+	3.04959i	0.125763	+	0.217828i
$197$	4.06359			0.289519			0.144759	−	0.989467i	$-0.453759\pi$
$197$	4.06359			0.289519			0.144759	+	0.989467i	$0.453759\pi$
$198$	−12.1871	+	12.0931i	−0.866098	+	0.859422i
$199$		−	6.46253i		−	0.458117i	−0.973413	−	0.229058i	$-0.926435\pi$
$199$		−	6.46253i		−	0.458117i	0.973413	−	0.229058i	$-0.0735647\pi$
$200$	−0.798314	+	0.460907i	−0.0564493	+	0.0325910i
$201$	0.997633	+	7.69274i	0.0703676	+	0.542604i
$202$	−7.69818	+	13.3336i	−0.541642	+	0.938151i
$203$	−3.21681	+	5.57167i	−0.225776	+	0.391055i
$204$	1.06496	+	8.21188i	0.0745620	+	0.574947i
$205$	7.93375	+	13.7417i	0.554117	+	0.959759i
$206$			7.25084i			0.505190i
$207$	−3.33197	−	3.35785i	−0.231588	−	0.233387i
$208$		−	2.31618i		−	0.160598i
$209$	−14.9767	−	25.9405i	−1.03596	−	1.79434i
$210$	10.4736	+	4.36207i	0.722748	+	0.301011i
$211$	−3.09174	+	5.35505i	−0.212844	+	0.368657i	−0.952604	−	0.304215i	$-0.901606\pi$
$211$	−3.09174	+	5.35505i	−0.212844	+	0.368657i	0.739759	+	0.672872i	$0.234939\pi$
$212$	−6.34438	+	10.9888i	−0.435734	+	0.754713i
$213$	−8.40486	−	10.9974i	−0.575892	−	0.753530i
$214$	1.49664	+	2.59225i	0.102308	+	0.177203i
$215$	8.52262			0.581238
$216$	4.81208	−	1.96059i	0.327420	−	0.133401i
$217$	17.9906	−	1.58173i	1.22128	−	0.107375i
$218$	7.19823	−	4.15590i	0.487526	−	0.281473i
$219$	−3.58461	−	4.69031i	−0.242225	−	0.316942i
$220$	−10.0088	−	5.77861i	−0.674796	−	0.389594i
$221$	9.58975	+	5.53664i	0.645076	+	0.372435i
$222$	6.08326	+	2.53357i	0.408282	+	0.170042i
$223$	21.8045	−	12.5889i	1.46014	−	0.843012i	0.461122	−	0.887337i	$-0.347447\pi$
$223$	21.8045	−	12.5889i	1.46014	−	0.843012i	0.999017	+	0.0443246i	$0.0141136\pi$
$224$			3.24367i			0.216727i
$225$	−2.67396	+	0.705409i	−0.178264	+	0.0470273i
$226$	18.0085			1.19791
$227$	1.51813	−	0.876495i	0.100762	−	0.0581750i	−0.448772	−	0.893646i	$-0.648139\pi$
$227$	1.51813	−	0.876495i	0.100762	−	0.0581750i	0.549534	+	0.835471i	$0.314805\pi$
$228$	1.16589	+	8.99014i	0.0772127	+	0.595387i
$229$	11.7357	+	6.77559i	0.775514	+	0.447743i	0.834838	−	0.550496i	$-0.185561\pi$
$229$	11.7357	+	6.77559i	0.775514	+	0.447743i	−0.0593240	+	0.998239i	$0.518895\pi$
$230$	1.59216	−	2.75769i	0.104984	−	0.181837i
$231$	−4.13508	−	31.8856i	−0.272069	−	2.09792i
$232$	−1.71771	+	0.991719i	−0.112773	+	0.0651096i
$233$		−	22.8064i		−	1.49410i	−0.664770	−	0.747048i	$-0.731470\pi$
$233$		−	22.8064i		−	1.49410i	0.664770	−	0.747048i	$-0.268530\pi$
$234$	1.82437	−	6.70477i	0.119263	−	0.438305i
$235$	−3.48323			−0.227221
$236$	−12.7196	+	7.34365i	−0.827973	+	0.478031i
$237$	−6.31682	+	15.1671i	−0.410322	+	0.985209i
$238$	−13.4298	−	7.75372i	−0.870527	−	0.502599i
$239$	−8.99376	+	15.5776i	−0.581758	+	1.00763i	0.413513	+	0.910498i	$0.364301\pi$
$239$	−8.99376	+	15.5776i	−0.581758	+	1.00763i	−0.995271	+	0.0971359i	$0.969032\pi$
$240$	2.12395	+	2.77910i	0.137100	+	0.179390i
$241$	−10.8438	+	6.26065i	−0.698508	+	0.403284i	−0.806791	−	0.590836i	$-0.798798\pi$
$241$	−10.8438	+	6.26065i	−0.698508	+	0.403284i	0.108283	+	0.994120i	$0.465465\pi$
$242$			21.7521i			1.39828i
$243$	15.4741	−	1.88512i	0.992661	−	0.120931i
$244$		−	5.41349i		−	0.346563i
$245$	−6.15850	+	3.55561i	−0.393452	+	0.227160i
$246$	−10.8130	+	8.26391i	−0.689411	+	0.526888i
$247$	10.4986	+	6.06136i	0.668009	+	0.385675i
$248$	5.04711	+	2.35088i	0.320492	+	0.149281i
$249$	−21.5574	−	8.97826i	−1.36614	−	0.568974i
$250$	−5.97941	−	10.3566i	−0.378171	−	0.655011i
$251$	−7.98232			−0.503839			−0.251920	−	0.967748i	$-0.581062\pi$
$251$	−7.98232			−0.503839			−0.251920	+	0.967748i	$0.581062\pi$
$252$	−2.55491	+	9.38961i	−0.160944	+	0.591490i
$253$	−9.02405			−0.567337
$254$	2.21610	+	3.83840i	0.139050	+	0.240843i
$255$	−16.5835	+	2.15063i	−1.03850	+	0.134678i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.81099	+	5.08702i	0.549614	+	0.317320i	0.748966	−	0.662608i	$-0.230550\pi$
$257$	8.81099	+	5.08702i	0.549614	+	0.317320i	−0.199352	+	0.979928i	$0.563884\pi$
$258$	0.940088	+	7.24901i	0.0585273	+	0.451304i
$259$	−10.6875	+	6.17043i	−0.664089	+	0.383412i
$260$	4.67742			0.290081
$261$	−5.75348	+	1.51781i	−0.356131	+	0.0939499i
$262$	3.10713			0.191959
$263$	15.1902	+	26.3103i	0.936670	+	1.62236i	0.771629	+	0.636073i	$0.219442\pi$
$263$	15.1902	+	26.3103i	0.936670	+	1.62236i	0.165041	+	0.986287i	$0.447224\pi$
$264$	3.81103	−	9.15054i	0.234553	−	0.563177i
$265$	−22.1913	−	12.8122i	−1.36320	−	0.787045i
$266$	−14.7026	−	8.48855i	−0.901474	−	0.520466i
$267$	17.1974	−	13.1432i	1.05246	−	0.804353i
$268$	−2.23930	−	3.87858i	−0.136787	−	0.236922i
$269$	−13.4121			−0.817748			−0.408874	−	0.912591i	$-0.634078\pi$
$269$	−13.4121			−0.817748			−0.408874	+	0.912591i	$0.634078\pi$
$270$	3.95931	+	9.71776i	0.240956	+	0.591404i
$271$			29.7260i			1.80572i	0.429929	+	0.902862i	$0.358538\pi$
$271$			29.7260i			1.80572i	−0.429929	+	0.902862i	$0.641462\pi$
$272$	−2.39042	−	4.14033i	−0.144940	−	0.251044i
$273$	7.90168	+	10.3390i	0.478231	+	0.625746i
$274$	8.00513	+	4.62177i	0.483608	+	0.279211i
$275$	−2.63774	+	4.56871i	−0.159062	+	0.275503i
$276$	2.52121	+	1.05004i	0.151759	+	0.0632048i
$277$	7.77363	−	4.48811i	0.467072	−	0.269664i	−0.247941	−	0.968775i	$-0.579754\pi$
$277$	7.77363	−	4.48811i	0.467072	−	0.269664i	0.715013	+	0.699111i	$0.246421\pi$
$278$	−3.31817			−0.199011
$279$	12.7584	+	10.7806i	0.763828	+	0.645420i
$280$	−6.55043			−0.391463
$281$	13.2999	−	7.67873i	0.793408	−	0.458074i	−0.0477529	−	0.998859i	$-0.515206\pi$
$281$	13.2999	−	7.67873i	0.793408	−	0.458074i	0.841161	+	0.540785i	$0.181873\pi$
$282$	−0.384218	−	2.96270i	−0.0228798	−	0.176426i
$283$	−6.05684	+	10.4908i	−0.360042	+	0.623611i	−0.987967	−	0.154663i	$-0.950571\pi$
$283$	−6.05684	+	10.4908i	−0.360042	+	0.623611i	0.627926	+	0.778273i	$0.283904\pi$
$284$	6.92071	+	3.99567i	0.410669	+	0.237100i
$285$	−18.1552	+	2.35445i	−1.07542	+	0.139466i
$286$	−6.62769	−	11.4795i	−0.391904	−	0.678797i
$287$		−	25.4866i		−	1.50442i
$288$	−2.12951	+	2.11310i	−0.125483	+	0.124515i
$289$	5.85639			0.344494
$290$	−2.00273	−	3.46883i	−0.117604	−	0.203697i
$291$	−22.8996	−	9.53728i	−1.34240	−	0.559085i
$292$	2.95163	+	1.70412i	0.172731	+	0.0997263i
$293$	−22.9939	−	13.2755i	−1.34332	−	0.775564i	−0.356024	−	0.934477i	$-0.615868\pi$
$293$	−22.9939	−	13.2755i	−1.34332	−	0.775564i	−0.987293	+	0.158913i	$0.949201\pi$
$294$	−3.70358	−	4.84598i	−0.215997	−	0.282623i
$295$	−14.8301	−	25.6866i	−0.863444	−	1.49553i
$296$	−3.80460			−0.221138
$297$	18.2395	−	23.4867i	1.05836	−	1.36284i
$298$	−5.70465			−0.330461
$299$	3.16290	−	1.82610i	0.182915	−	0.105606i
$300$	1.26857	−	0.969513i	0.0732408	−	0.0559749i
$301$	−11.8551	−	6.84456i	−0.683318	−	0.394514i
$302$	7.76394	−	13.4475i	0.446765	−	0.773819i
$303$	10.2528	−	24.6175i	0.589006	−	1.41424i
$304$	−2.61696	−	4.53271i	−0.150093	−	0.259969i
$305$	10.9323			0.625981
$306$	−3.65849	−	13.8681i	−0.209142	−	0.792784i
$307$	25.3501			1.44680			0.723402	−	0.690427i	$-0.242577\pi$
$307$	25.3501			1.44680			0.723402	+	0.690427i	$0.242577\pi$
$308$	9.28166	+	16.0763i	0.528872	+	0.916033i
$309$	−1.61517	−	12.4545i	−0.0918836	−	0.708513i
$310$	−4.74749	+	10.1924i	−0.269639	+	0.578890i
$311$	−9.16823	−	5.29328i	−0.519882	−	0.300154i	0.217004	−	0.976171i	$-0.430372\pi$
$311$	−9.16823	−	5.29328i	−0.519882	−	0.300154i	−0.736887	+	0.676016i	$0.763705\pi$
$312$	0.515943	+	3.97843i	0.0292095	+	0.225234i
$313$	−20.5416	+	11.8597i	−1.16108	+	0.670350i	−0.951563	−	0.307455i	$-0.900523\pi$
$313$	−20.5416	+	11.8597i	−1.16108	+	0.670350i	−0.209518	+	0.977805i	$0.567189\pi$
$314$		−	5.09620i		−	0.287595i
$315$	−18.9619	−	5.15952i	−1.06838	−	0.290706i
$316$		−	9.48584i		−	0.533620i
$317$	14.6197	−	8.44071i	0.821126	−	0.474077i	−0.0296786	−	0.999559i	$-0.509448\pi$
$317$	14.6197	−	8.44071i	0.821126	−	0.474077i	0.850805	+	0.525482i	$0.176115\pi$
$318$	8.44971	−	20.2883i	0.473836	−	1.13771i
$319$	−5.67556	+	9.83035i	−0.317770	+	0.550394i
$320$	−1.74890	−	1.00973i	−0.0977663	−	0.0564454i
$321$	−3.14816	−	4.11924i	−0.175713	−	0.229914i
$322$	−4.42944	+	2.55734i	−0.246843	+	0.142515i
$323$	25.0225			1.39229
$324$	−7.82881	+	4.43956i	−0.434934	+	0.246642i
$325$		−	2.13509i		−	0.118433i
$326$	1.28633	−	0.742663i	0.0712432	−	0.0411323i
$327$	−11.4384	+	8.74190i	−0.632545	+	0.483428i
$328$	3.92867	−	6.80465i	0.216924	−	0.375724i
$329$	4.84524	+	2.79740i	0.267127	+	0.154226i
$330$	18.4791	+	7.69620i	1.01724	+	0.423662i
$331$	−23.7700	+	13.7236i	−1.30651	+	0.754317i	−0.981513	−	0.191397i	$-0.938698\pi$
$331$	−23.7700	+	13.7236i	−1.30651	+	0.754317i	−0.325002	+	0.945713i	$0.605365\pi$
$332$	13.4825			0.739946
$333$	−11.0134	−	2.99674i	−0.603530	−	0.164221i
$334$			5.89610i			0.322620i
$335$	7.83261	−	4.52216i	0.427941	−	0.247072i
$336$	−0.722545	−	5.57154i	−0.0394181	−	0.303952i
$337$	29.1229	+	16.8141i	1.58643	+	0.915923i	0.993890	+	0.110379i	$0.0352065\pi$
$337$	29.1229	+	16.8141i	1.58643	+	0.915923i	0.592536	+	0.805544i	$0.298127\pi$
$338$	−6.61236	−	3.81765i	−0.359665	−	0.207653i
$339$	−30.9326	+	4.01150i	−1.68003	+	0.217875i
$340$	8.36119	−	4.82733i	0.453449	−	0.261799i
$341$	31.7416	−	2.79071i	1.71890	−	0.151126i
$342$	−4.00521	−	15.1824i	−0.216577	−	0.820968i
$343$	−11.2835			−0.609253
$344$	−2.11013	−	3.65486i	−0.113771	−	0.197057i
$345$	−2.12050	+	5.09146i	−0.114164	+	0.274115i
$346$	−1.16507	+	2.01796i	−0.0626344	+	0.108486i
$347$	16.2510	−	28.1476i	0.872400	−	1.51104i	0.0128942	−	0.999917i	$-0.495896\pi$
$347$	16.2510	−	28.1476i	0.872400	−	1.51104i	0.859506	−	0.511125i	$-0.170771\pi$
$348$	2.72954	−	2.08607i	0.146319	−	0.111825i
$349$	−8.62749	−	14.9432i	−0.461819	−	0.799893i	0.537233	−	0.843434i	$-0.319470\pi$
$349$	−8.62749	−	14.9432i	−0.461819	−	0.799893i	−0.999052	+	0.0435404i	$0.986136\pi$
$350$			2.99006i			0.159825i
$351$	−1.64013	+	11.9230i	−0.0875438	+	0.636400i
$352$			5.72295i			0.305034i
$353$	6.91214	+	11.9722i	0.367896	+	0.637215i	0.989236	−	0.146326i	$-0.0467449\pi$
$353$	6.91214	+	11.9722i	0.367896	+	0.637215i	−0.621340	+	0.783541i	$0.713412\pi$
$354$	20.2121	−	15.4473i	1.07426	−	0.821014i
$355$	−8.06907	+	13.9760i	−0.428262	+	0.741771i
$356$	−6.24830	+	10.8224i	−0.331159	+	0.573585i
$357$	24.7952	+	10.3267i	1.31230	+	0.546549i
$358$	−0.109845	+	0.0634191i	−0.00580549	+	0.00335180i
$359$			21.2606i			1.12209i	0.827785	+	0.561045i	$0.189601\pi$
$359$			21.2606i			1.12209i	−0.827785	+	0.561045i	$0.810399\pi$
$360$	−4.26730	−	4.30045i	−0.224906	−	0.226653i
$361$	8.39396			0.441788
$362$	12.0605	+	20.8894i	0.633885	+	1.09792i
$363$	−4.84540	−	37.3629i	−0.254318	−	1.96104i
$364$	−6.50638	−	3.75646i	−0.341027	−	0.196892i
$365$	−3.44140	+	5.96067i	−0.180131	+	0.311996i
$366$	1.20589	+	9.29857i	0.0630326	+	0.486044i
$367$	18.1902	−	10.5021i	0.949520	−	0.548205i	0.0565879	−	0.998398i	$-0.481978\pi$
$367$	18.1902	−	10.5021i	0.949520	−	0.548205i	0.892932	+	0.450192i	$0.148645\pi$
$368$	−1.57682			−0.0821974
$369$	16.7323	−	16.6033i	0.871048	−	0.864334i
$370$		−	7.68322i		−	0.399431i
$371$	20.5790	+	35.6439i	1.06841	+	1.85054i
$372$	−9.19293	−	2.91375i	−0.476631	−	0.151071i
$373$	3.15200	−	5.45942i	0.163204	−	0.282678i	−0.772812	−	0.634635i	$-0.781150\pi$
$373$	3.15200	−	5.45942i	0.163204	−	0.282678i	0.936016	+	0.351957i	$0.114484\pi$
$374$	−23.6949	−	13.6802i	−1.22523	−	0.707388i
$375$	12.5776	+	16.4573i	0.649506	+	0.849852i
$376$	0.862419	+	1.49375i	0.0444759	+	0.0770345i
$377$		−	4.59401i		−	0.236603i
$378$	2.29690	−	16.6973i	0.118140	−	0.858818i
$379$	1.09716			0.0563572			0.0281786	−	0.999603i	$-0.491029\pi$
$379$	1.09716			0.0563572			0.0281786	+	0.999603i	$0.491029\pi$
$380$	9.15359	−	5.28483i	0.469569	−	0.271106i
$381$	−4.66155	−	6.09944i	−0.238818	−	0.312484i
$382$	−3.89754	+	6.75074i	−0.199416	+	0.345398i
$383$	−2.94220	+	5.09604i	−0.150339	+	0.260395i	−0.931352	−	0.364120i	$-0.881370\pi$
$383$	−2.94220	+	5.09604i	−0.150339	+	0.260395i	0.781013	+	0.624515i	$0.214703\pi$
$384$	0.665921	−	1.59892i	0.0339827	−	0.0815946i
$385$	−32.4653	+	18.7439i	−1.65459	+	0.955276i
$386$		−	19.6288i		−	0.999079i
$387$	−3.22952	−	12.2420i	−0.164166	−	0.622295i
$388$	14.3219			0.727086
$389$	4.07494	+	7.05800i	0.206607	+	0.357855i	0.950644	−	0.310285i	$-0.100424\pi$
$389$	4.07494	+	7.05800i	0.206607	+	0.357855i	−0.744036	+	0.668139i	$0.767091\pi$
$390$	−8.03425	+	1.04192i	−0.406830	+	0.0527598i
$391$	3.76926	−	6.52854i	0.190619	−	0.330163i
$392$	3.04959	+	1.76068i	0.154028	+	0.0889279i
$393$	−5.33701	+	0.692130i	−0.269216	+	0.0349133i
$394$	3.51917	−	2.03179i	0.177293	−	0.102360i
$395$	19.1562			0.963853
$396$	−4.50775	+	16.5665i	−0.226523	+	0.832498i
$397$	37.4113			1.87762			0.938810	−	0.344437i	$-0.111930\pi$
$397$	37.4113			1.87762			0.938810	+	0.344437i	$0.111930\pi$
$398$	−3.23127	−	5.59672i	−0.161969	−	0.280538i
$399$	27.1450	+	11.3054i	1.35895	+	0.565979i
$400$	−0.460907	+	0.798314i	−0.0230453	+	0.0399157i
$401$	17.5038	−	30.3174i	0.874097	−	1.51398i	0.0163746	−	0.999866i	$-0.494788\pi$
$401$	17.5038	−	30.3174i	0.874097	−	1.51398i	0.857722	−	0.514114i	$-0.171879\pi$
$402$	4.71035	+	6.16329i	0.234931	+	0.307397i
$403$	−10.5606	+	7.40134i	−0.526060	+	0.368687i
$404$			15.3964i			0.765997i
$405$	−8.96547	−	15.8099i	−0.445498	−	0.785601i
$406$			6.43361i			0.319295i
$407$	−18.8564	+	10.8868i	−0.934679	+	0.539637i
$408$	5.02822	+	6.57922i	0.248934	+	0.325720i
$409$	11.8203	+	6.82443i	0.584474	+	0.337446i	0.762909	−	0.646505i	$-0.223770\pi$
$409$	11.8203	+	6.82443i	0.584474	+	0.337446i	−0.178435	+	0.983952i	$0.557104\pi$
$410$	13.7417	+	7.93375i	0.678652	+	0.391820i
$411$	−14.7797	−	6.15547i	−0.729028	−	0.303627i
$412$	3.62542	+	6.27941i	0.178612	+	0.309364i
$413$			47.6407i			2.34424i
$414$	−4.56450	−	1.24200i	−0.224333	−	0.0610410i
$415$			27.2272i			1.33653i
$416$	−1.15809	−	2.00587i	−0.0567801	−	0.0983460i
$417$	5.69951	−	0.739142i	0.279106	−	0.0361959i
$418$	−25.9405	−	14.9767i	−1.26879	−	0.732536i
$419$	21.7193	+	12.5396i	1.06106	+	0.612602i	0.925725	−	0.378199i	$-0.123456\pi$
$419$	21.7193	+	12.5396i	1.06106	+	0.612602i	0.135333	+	0.990800i	$0.456790\pi$
$420$	11.2515	−	1.45914i	0.549015	−	0.0711990i
$421$	1.08089	+	1.87215i	0.0526793	+	0.0912432i	0.891163	−	0.453684i	$-0.149891\pi$
$421$	1.08089	+	1.87215i	0.0526793	+	0.0912432i	−0.838483	+	0.544927i	$0.816557\pi$
$422$			6.18348i			0.301007i
$423$	1.31992	+	5.00334i	0.0641765	+	0.243271i
$424$			12.6888i			0.616220i
$425$	−2.20352	−	3.81661i	−0.106886	−	0.185133i
$426$	−12.7775	−	5.32161i	−0.619074	−	0.257833i
$427$	−15.2070	−	8.77977i	−0.735919	−	0.424883i
$428$	2.59225	+	1.49664i	0.125301	+	0.0723427i
$429$	13.9413	+	18.2416i	0.673092	+	0.880713i
$430$	7.38081	−	4.26131i	0.355934	−	0.205499i
$431$			0.582229i			0.0280450i	0.999902	+	0.0140225i	$0.00446364\pi$
$431$			0.582229i			0.0280450i	−0.999902	+	0.0140225i	$0.995536\pi$
$432$	3.18709	−	4.10396i	0.153339	−	0.197452i
$433$		−	13.4408i		−	0.645923i	−0.946412	−	0.322961i	$-0.895322\pi$
$433$		−	13.4408i		−	0.645923i	0.946412	−	0.322961i	$-0.104678\pi$
$434$	14.7894	−	10.3651i	0.709915	−	0.497541i
$435$	4.21272	+	5.51218i	0.201985	+	0.264289i
$436$	4.15590	−	7.19823i	0.199031	−	0.344733i
$437$	4.12648	−	7.14726i	0.197396	−	0.341900i
$438$	−5.44952	−	2.26962i	−0.260388	−	0.108447i
$439$	−3.94765	−	6.83753i	−0.188411	−	0.326337i	0.756310	−	0.654214i	$-0.227000\pi$
$439$	−3.94765	−	6.83753i	−0.188411	−	0.326337i	−0.944721	+	0.327876i	$0.893667\pi$
$440$	−11.5572			−0.550969
$441$	7.44099	+	7.49879i	0.354333	+	0.357085i
$442$	11.0733			0.526703
$443$	−12.6096	+	7.28015i	−0.599099	+	0.345890i	−0.768687	−	0.639625i	$-0.779090\pi$
$443$	−12.6096	+	7.28015i	−0.599099	+	0.345890i	0.169588	+	0.985515i	$0.445756\pi$
$444$	6.53504	−	0.847497i	0.310139	−	0.0402204i
$445$	−21.8553	−	12.6181i	−1.03604	−	0.598157i
$446$	12.5889	−	21.8045i	0.596099	−	1.03247i
$447$	9.79868	−	1.27074i	0.463462	−	0.0601040i
$448$	1.62183	+	2.80910i	0.0766244	+	0.132717i
$449$	4.19575			0.198010			0.0990049	−	0.995087i	$-0.468434\pi$
$449$	4.19575			0.198010			0.0990049	+	0.995087i	$0.468434\pi$
$450$	−1.96301	+	1.94788i	−0.0925373	+	0.0918240i
$451$		−	44.9671i		−	2.11742i
$452$	15.5958	−	9.00426i	0.733567	−	0.423525i
$453$	−10.3404	+	24.8279i	−0.485832	+	1.16651i
$454$	0.876495	−	1.51813i	0.0411359	−	0.0712495i
$455$	7.58599	−	13.1393i	0.355637	−	0.615981i
$456$	5.50476	+	7.20275i	0.257784	+	0.337299i
$457$	−19.4210	+	11.2127i	−0.908474	+	0.524508i	−0.879940	−	0.475085i	$-0.842417\pi$
$457$	−19.4210	+	11.2127i	−0.908474	+	0.524508i	−0.0285340	+	0.999593i	$0.509084\pi$
$458$	13.5512			0.633205
$459$	9.37325	+	23.0058i	0.437506	+	1.07382i
$460$		−	3.18431i		−	0.148469i
$461$	−12.1805	−	21.0973i	−0.567303	−	0.982597i	−0.996831	−	0.0795441i	$-0.974654\pi$
$461$	−12.1805	−	21.0973i	−0.567303	−	0.982597i	0.429528	−	0.903053i	$-0.358680\pi$
$462$	−19.5239	−	25.5462i	−0.908333	−	1.18852i
$463$	−14.0143	−	8.09115i	−0.651299	−	0.376028i	0.137655	−	0.990480i	$-0.456044\pi$
$463$	−14.0143	−	8.09115i	−0.651299	−	0.376028i	−0.788954	+	0.614452i	$0.789377\pi$
$464$	−0.991719	+	1.71771i	−0.0460394	+	0.0797426i
$465$	5.88419	−	18.5647i	0.272873	−	0.860917i
$466$	−11.4032	−	19.7509i	−0.528243	−	0.914943i
$467$		−	1.66370i		−	0.0769867i	−0.999259	−	0.0384933i	$-0.987744\pi$
$467$		−	1.66370i		−	0.0769867i	0.999259	−	0.0384933i	$-0.0122558\pi$
$468$	−1.77244	−	6.71869i	−0.0819309	−	0.310571i
$469$	−14.5271			−0.670798
$470$	−3.01656	+	1.74161i	−0.139144	+	0.0803347i
$471$	1.13521	+	8.75358i	0.0523077	+	0.403344i
$472$	−7.34365	+	12.7196i	−0.338019	+	0.585466i
$473$	−20.9165	−	12.0762i	−0.961744	−	0.555263i
$474$	2.11302	+	16.2935i	0.0970544	+	0.748386i
$475$	−2.41235	−	4.17832i	−0.110686	−	0.191714i
$476$	−15.5074			−0.710782
$477$	−9.99445	+	36.7308i	−0.457615	+	1.68179i
$478$			17.9875i			0.822730i
$479$	2.07119	−	1.19580i	0.0946350	−	0.0546376i	−0.451936	−	0.892051i	$-0.649266\pi$
$479$	2.07119	−	1.19580i	0.0946350	−	0.0546376i	0.546571	+	0.837413i	$0.315933\pi$
$480$	3.22894	+	1.34480i	0.147380	+	0.0613813i
$481$	4.40608	−	7.63155i	0.200900	−	0.347969i
$482$	−6.26065	+	10.8438i	−0.285165	+	0.493920i
$483$	7.03864	−	5.37933i	0.320269	−	0.244768i
$484$	10.8761	+	18.8379i	0.494366	+	0.856267i
$485$			28.9225i			1.31330i
$486$	12.4584	−	9.36959i	0.565123	−	0.425013i
$487$		−	6.53725i		−	0.296231i	−0.988970	−	0.148116i	$-0.952679\pi$
$487$		−	6.53725i		−	0.296231i	0.988970	−	0.148116i	$-0.0473208\pi$
$488$	−2.70674	−	4.68822i	−0.122529	−	0.212226i
$489$	−2.04405	+	1.56218i	−0.0924353	+	0.0706444i
$490$	−3.55561	+	6.15850i	−0.160626	+	0.278213i
$491$	−5.84312	+	10.1206i	−0.263696	+	0.456736i	−0.967221	−	0.253935i	$-0.918275\pi$
$491$	−5.84312	+	10.1206i	−0.263696	+	0.456736i	0.703525	+	0.710671i	$0.251608\pi$
$492$	−5.23237	+	12.5633i	−0.235893	+	0.566395i
$493$	−4.74125	−	8.21208i	−0.213535	−	0.369854i
$494$	12.1227			0.545427
$495$	−33.4553	−	9.10318i	−1.50370	−	0.409158i
$496$	5.54637	−	0.487636i	0.249039	−	0.0218955i
$497$	22.4485	−	12.9606i	1.00695	−	0.581364i
$498$	−23.1584	+	3.00329i	−1.03775	+	0.134581i
$499$	−26.8752	−	15.5164i	−1.20310	−	0.694610i	−0.241857	−	0.970312i	$-0.577756\pi$
$499$	−26.8752	−	15.5164i	−1.20310	−	0.694610i	−0.961243	+	0.275702i	$0.911090\pi$
$500$	−10.3566	−	5.97941i	−0.463163	−	0.267407i
$501$	−1.31339	−	10.1275i	−0.0586780	−	0.452465i
$502$	−6.91289	+	3.99116i	−0.308537	+	0.178134i
$503$		−	12.2674i		−	0.546976i	−0.961875	−	0.273488i	$-0.911823\pi$
$503$		−	12.2674i		−	0.546976i	0.961875	−	0.273488i	$-0.0881774\pi$
$504$	2.48218	+	9.40909i	0.110565	+	0.419114i
$505$	−31.0922			−1.38358
$506$	−7.81505	+	4.51202i	−0.347422	+	0.200584i
$507$	12.2082	+	5.08451i	0.542187	+	0.225811i
$508$	3.83840	+	2.21610i	0.170301	+	0.0983235i
$509$	−1.91401	+	3.31515i	−0.0848368	+	0.146942i	−0.905322	−	0.424727i	$-0.860370\pi$
$509$	−1.91401	+	3.31515i	−0.0848368	+	0.146942i	0.820485	+	0.571668i	$0.193704\pi$
$510$	−13.2864	+	10.1543i	−0.588333	+	0.449638i
$511$	9.57409	−	5.52761i	0.423533	−	0.244527i
$512$			1.00000i			0.0441942i
$513$	10.2616	+	25.1861i	0.453059	+	1.11199i
$514$	10.1740			0.448758
$515$	−12.6810	+	7.32136i	−0.558790	+	0.322618i
$516$	4.43865	+	5.80778i	0.195400	+	0.255673i
$517$	8.54867	+	4.93558i	0.375970	+	0.217066i
$518$	−6.17043	+	10.6875i	−0.271113	+	0.469582i
$519$	1.55169	−	3.72570i	0.0681115	−	0.163540i
$520$	4.05076	−	2.33871i	0.177638	−	0.102559i
$521$			4.15365i			0.181975i	0.995852	+	0.0909873i	$0.0290023\pi$
$521$			4.15365i			0.181975i	−0.995852	+	0.0909873i	$0.970998\pi$
$522$	−4.22376	+	4.19120i	−0.184869	+	0.183444i
$523$			27.0846i			1.18433i	0.805818	+	0.592164i	$0.201726\pi$
$523$			27.0846i			1.18433i	−0.805818	+	0.592164i	$0.798274\pi$
$524$	2.69085	−	1.55356i	0.117550	−	0.0678677i
$525$	−0.666052	−	5.13592i	−0.0290689	−	0.224150i
$526$	26.3103	+	15.1902i	1.14718	+	0.662326i
$527$	−11.2392	+	24.1294i	−0.489586	+	1.05109i
$528$	−1.27482	−	9.83011i	−0.0554794	−	0.427801i
$529$	10.2568	+	17.7653i	0.445949	+	0.772406i
$530$	−25.6243			−1.11305
$531$	−31.2768	+	31.0357i	−1.35730	+	1.34683i
$532$	−16.9771			−0.736051
$533$	9.09951	+	15.7608i	0.394143	+	0.682676i
$534$	8.32175	−	19.9811i	0.360117	−	0.864666i
$535$	−3.02239	+	5.23493i	−0.130669	+	0.226326i
$536$	−3.87858	−	2.23930i	−0.167529	−	0.0967230i
$537$	0.174550	−	0.133401i	0.00753240	−	0.00575670i
$538$	−11.6152	+	6.70603i	−0.500766	+	0.289118i
$539$	20.1526			0.868033
$540$	8.28775	+	6.43617i	0.356648	+	0.276969i
$541$	−42.1713			−1.81309			−0.906543	−	0.422114i	$-0.861288\pi$
$541$	−42.1713			−1.81309			−0.906543	+	0.422114i	$0.861288\pi$
$542$	14.8630	+	25.7435i	0.638420	+	1.10578i
$543$	−25.3691	−	33.1944i	−1.08869	−	1.42451i
$544$	−4.14033	−	2.39042i	−0.177515	−	0.102488i
$545$	14.5365	+	8.39264i	0.622674	+	0.359501i
$546$	12.0126	+	5.00301i	0.514090	+	0.214109i
$547$	3.35602	+	5.81280i	0.143493	+	0.248537i	0.928810	−	0.370557i	$-0.120833\pi$
$547$	3.35602	+	5.81280i	0.143493	+	0.248537i	−0.785317	+	0.619094i	$0.787500\pi$
$548$	9.24353			0.394864
$549$	−4.14262	−	15.7032i	−0.176803	−	0.670197i
$550$			5.27549i			0.224948i
$551$	−5.19058	−	8.99036i	−0.221126	−	0.383002i
$552$	2.70845	−	0.351245i	0.115279	−	0.0149500i
$553$	−26.6466	−	15.3844i	−1.13313	−	0.654213i
$554$	4.48811	−	7.77363i	0.190681	−	0.330270i
$555$	1.71148	+	13.1972i	0.0726483	+	0.560190i
$556$	−2.87362	+	1.65909i	−0.121869	+	0.0703609i
$557$	−20.2195			−0.856729			−0.428364	−	0.903606i	$-0.640910\pi$
$557$	−20.2195			−0.856729			−0.428364	+	0.903606i	$0.640910\pi$
$558$	16.4395	+	2.95708i	0.695938	+	0.125183i
$559$	9.77490			0.413434
$560$	−5.67284	+	3.27521i	−0.239721	+	0.138403i
$561$	43.7472	+	18.2199i	1.84701	+	0.769246i
$562$	7.67873	−	13.2999i	0.323908	−	0.561024i
$563$	−32.9228	−	19.0080i	−1.38753	−	0.801090i	−0.394493	−	0.918899i	$-0.629080\pi$
$563$	−32.9228	−	19.0080i	−1.38753	−	0.801090i	−0.993036	+	0.117809i	$0.962413\pi$
$564$	−1.81409	−	2.37366i	−0.0763870	−	0.0999492i
$565$	18.1837	+	31.4951i	0.764993	+	1.32501i
$566$			12.1137i			0.509176i
$567$	−0.225886	+	29.1921i	−0.00948632	+	1.22595i
$568$	7.99135			0.335309
$569$	−17.1374	−	29.6829i	−0.718438	−	1.24437i	−0.961618	−	0.274390i	$-0.911524\pi$
$569$	−17.1374	−	29.6829i	−0.718438	−	1.24437i	0.243180	−	0.969981i	$-0.421809\pi$
$570$	−14.5456	+	11.1166i	−0.609248	+	0.465623i
$571$	−0.962168	−	0.555508i	−0.0402655	−	0.0232473i	0.479732	−	0.877415i	$-0.340734\pi$
$571$	−0.962168	−	0.555508i	−0.0402655	−	0.0232473i	−0.519998	+	0.854168i	$0.674067\pi$
$572$	−11.4795	−	6.62769i	−0.479982	−	0.277118i
$573$	5.19091	−	12.4637i	0.216854	−	0.520680i
$574$	−12.7433	−	22.0720i	−0.531894	−	0.921268i
$575$	−1.45353			−0.0606165
$576$	−0.787662	+	2.89475i	−0.0328193	+	0.120615i
$577$	−31.5055			−1.31159			−0.655796	−	0.754938i	$-0.727667\pi$
$577$	−31.5055			−1.31159			−0.655796	+	0.754938i	$0.727667\pi$
$578$	5.07178	−	2.92820i	0.210958	−	0.121797i
$579$	4.37243	+	33.7157i	0.181712	+	1.40118i
$580$	−3.46883	−	2.00273i	−0.144035	−	0.0831588i
$581$	21.8663	−	37.8735i	0.907166	−	1.57126i
$582$	−24.6003	+	3.19029i	−1.01972	+	0.132242i
$583$	36.3085	+	62.8882i	1.50375	+	2.60456i
$584$	3.40825			0.141034
$585$	13.5681	−	3.57935i	0.560971	−	0.147988i
$586$	−26.5510			−1.09681
$587$	−3.64494	−	6.31323i	−0.150443	−	0.260575i	0.780947	−	0.624597i	$-0.214737\pi$
$587$	−3.64494	−	6.31323i	−0.150443	−	0.260575i	−0.931390	+	0.364022i	$0.881403\pi$
$588$	−5.63038	−	2.34495i	−0.232193	−	0.0967042i
$589$	−12.3043	+	26.4162i	−0.506991	+	1.08846i
$590$	−25.6866	−	14.8301i	−1.05750	−	0.610547i
$591$	−5.59217	+	4.27386i	−0.230031	+	0.175803i
$592$	−3.29488	+	1.90230i	−0.135419	+	0.0781841i
$593$			14.8621i			0.610315i	0.952302	+	0.305157i	$0.0987090\pi$
$593$			14.8621i			0.610315i	−0.952302	+	0.305157i	$0.901291\pi$
$594$	4.05253	−	29.4599i	0.166277	−	1.20875i
$595$		−	31.3165i		−	1.28385i
$596$	−4.94037	+	2.85232i	−0.202365	+	0.116836i
$597$	6.79694	+	8.89351i	0.278180	+	0.363987i
$598$	1.82610	−	3.16290i	0.0746748	−	0.129341i
$599$	28.6253	+	16.5269i	1.16960	+	0.675269i	0.953586	−	0.301121i	$-0.0973609\pi$
$599$	28.6253	+	16.5269i	1.16960	+	0.675269i	0.216014	+	0.976390i	$0.430694\pi$
$600$	0.613855	−	1.47391i	0.0250605	−	0.0601720i
$601$	18.7777	−	10.8413i	0.765959	−	0.442227i	−0.0654721	−	0.997854i	$-0.520855\pi$
$601$	18.7777	−	10.8413i	0.765959	−	0.442227i	0.831431	+	0.555628i	$0.187522\pi$
$602$	−13.6891			−0.557927
$603$	−9.46372	−	9.53723i	−0.385392	−	0.388386i
$604$		−	15.5279i		−	0.631821i
$605$	−38.0422	+	21.9637i	−1.54663	+	0.892950i
$606$	−3.42962	−	26.4458i	−0.139319	−	1.07429i
$607$	2.89077	−	5.00696i	0.117333	−	0.203226i	−0.801377	−	0.598160i	$-0.795899\pi$
$607$	2.89077	−	5.00696i	0.117333	−	0.203226i	0.918710	+	0.394933i	$0.129232\pi$
$608$	−4.53271	−	2.61696i	−0.183826	−	0.106132i
$609$	−1.43312	−	11.0508i	−0.0580731	−	0.447801i
$610$	9.46763	−	5.46614i	0.383333	−	0.221318i
$611$	−3.99504			−0.161622
$612$	−10.1024	−	10.1808i	−0.408364	−	0.411536i
$613$		−	15.1905i		−	0.613539i	−0.951784	−	0.306769i	$-0.900752\pi$
$613$		−	15.1905i		−	0.613539i	0.951784	−	0.306769i	$-0.0992481\pi$
$614$	21.9538	−	12.6750i	0.885983	−	0.511522i
$615$	−25.3709	−	10.5665i	−1.02305	−	0.426083i
$616$	16.0763	+	9.28166i	0.647733	+	0.373969i
$617$	16.2324	+	9.37180i	0.653493	+	0.377295i	0.789793	−	0.613373i	$-0.210188\pi$
$617$	16.2324	+	9.37180i	0.653493	+	0.377295i	−0.136300	+	0.990668i	$0.543521\pi$
$618$	−7.62604	−	9.97836i	−0.306764	−	0.401388i
$619$	−7.39343	+	4.26860i	−0.297167	+	0.171569i	−0.641170	−	0.767399i	$-0.721550\pi$
$619$	−7.39343	+	4.26860i	−0.297167	+	0.171569i	0.344003	+	0.938969i	$0.388217\pi$
$620$	0.984757	+	11.2006i	0.0395488	+	0.449828i
$621$	8.11695	+	1.11658i	0.325722	+	0.0448066i
$622$	−10.5866			−0.424482
$623$	20.2674	+	35.1042i	0.811996	+	1.40642i
$624$	2.43603	+	3.18745i	0.0975194	+	0.127600i
$625$	9.77060	−	16.9232i	0.390824	−	0.676927i
$626$	−11.8597	+	20.5416i	−0.474009	+	0.821008i
$627$	47.8932	+	19.9467i	1.91267	+	0.796593i
$628$	−2.54810	−	4.41344i	−0.101680	−	0.176116i
$629$		−	18.1892i		−	0.725251i
$630$	−19.0012	+	5.01265i	−0.757026	+	0.199709i
$631$		−	29.9304i		−	1.19151i	−0.803167	−	0.595755i	$-0.796853\pi$
$631$		−	29.9304i		−	1.19151i	0.803167	−	0.595755i	$-0.203147\pi$
$632$	−4.74292	−	8.21498i	−0.188663	−	0.326774i
$633$	−1.37741	−	10.6212i	−0.0547470	−	0.422153i
$634$	8.44071	−	14.6197i	0.335223	−	0.580624i
$635$	−4.47531	+	7.75146i	−0.177597	+	0.307607i
$636$	−2.82649	−	21.7951i	−0.112078	−	0.864230i
$637$	−7.06341	+	4.07806i	−0.279862	+	0.161579i
$638$			11.3511i			0.449395i
$639$	23.1330	+	6.29448i	0.915126	+	0.249006i
$640$	−2.01945			−0.0798258
$641$	−14.8488	−	25.7189i	−0.586493	−	1.01584i	−0.994688	−	0.102940i	$-0.967175\pi$
$641$	−14.8488	−	25.7189i	−0.586493	−	1.01584i	0.408195	−	0.912895i	$-0.366158\pi$
$642$	−4.78601	−	1.99328i	−0.188889	−	0.0786687i
$643$	33.7394	+	19.4794i	1.33055	+	0.768194i	0.985384	−	0.170347i	$-0.0544889\pi$
$643$	33.7394	+	19.4794i	1.33055	+	0.768194i	0.345167	+	0.938541i	$0.387822\pi$
$644$	−2.55734	+	4.42944i	−0.100773	+	0.174544i
$645$	−11.7285	+	8.96363i	−0.461811	+	0.352943i
$646$	21.6701	−	12.5113i	0.852601	−	0.492249i
$647$	−26.6071			−1.04603			−0.523017	−	0.852322i	$-0.675194\pi$
$647$	−26.6071			−1.04603			−0.523017	+	0.852322i	$0.675194\pi$
$648$	−4.56017	+	7.75918i	−0.179141	+	0.304809i
$649$			84.0546i			3.29943i
$650$	−1.06754	−	1.84904i	−0.0418725	−	0.0725253i
$651$	−23.0944	+	21.0982i	−0.905142	+	0.826904i
$652$	0.742663	−	1.28633i	0.0290849	−	0.0503766i
$653$	4.62141	+	2.66817i	0.180850	+	0.104414i	0.587692	−	0.809085i	$-0.300037\pi$
$653$	4.62141	+	2.66817i	0.180850	+	0.104414i	−0.406842	+	0.913499i	$0.633370\pi$
$654$	−5.53500	+	13.2899i	−0.216436	+	0.519677i
$655$	3.13735	+	5.43404i	0.122586	+	0.212326i
$656$		−	7.85733i		−	0.306777i
$657$	9.86603	+	2.68455i	0.384910	+	0.104734i
$658$	5.59480			0.218108
$659$	13.0467	−	7.53249i	0.508226	−	0.293424i	−0.223878	−	0.974617i	$-0.571872\pi$
$659$	13.0467	−	7.53249i	0.508226	−	0.293424i	0.732104	+	0.681193i	$0.238539\pi$
$660$	19.8514	−	2.57443i	0.772716	−	0.100210i
$661$	−15.2397	+	26.3959i	−0.592755	+	1.02668i	0.401105	+	0.916032i	$0.368626\pi$
$661$	−15.2397	+	26.3959i	−0.592755	+	1.02668i	−0.993860	+	0.110649i	$0.964707\pi$
$662$	−13.7236	+	23.7700i	−0.533382	+	0.923846i
$663$	−19.0202	+	2.46664i	−0.738684	+	0.0957963i
$664$	11.6761	−	6.74123i	0.453122	−	0.261610i
$665$		−	34.2844i		−	1.32949i
$666$	−11.0362	+	2.91144i	−0.427646	+	0.112816i
$667$	−3.12752			−0.121098
$668$	2.94805	+	5.10618i	0.114064	+	0.197564i
$669$	−16.7664	+	40.2572i	−0.648225	+	1.55643i
$670$	4.52216	−	7.83261i	0.174706	−	0.302600i
$671$	−26.8304	−	15.4905i	−1.03578	−	0.598006i
$672$	−3.41151	−	4.46382i	−0.131602	−	0.172196i
$673$	17.3853	−	10.0374i	0.670156	−	0.386915i	−0.125980	−	0.992033i	$-0.540208\pi$
$673$	17.3853	−	10.0374i	0.670156	−	0.386915i	0.796136	+	0.605118i	$0.206874\pi$
$674$	33.6282			1.29531
$675$	2.93790	−	3.78309i	0.113080	−	0.145611i
$676$	−7.63530			−0.293665
$677$	−22.4359	−	38.8600i	−0.862280	−	1.49351i	−0.869723	−	0.493540i	$-0.835703\pi$
$677$	−22.4359	−	38.8600i	−0.862280	−	1.49351i	0.00744306	−	0.999972i	$-0.497631\pi$
$678$	−24.7827	+	18.9404i	−0.951774	+	0.727401i
$679$	23.2278	−	40.2317i	0.891400	−	1.54395i
$680$	4.82733	−	8.36119i	0.185120	−	0.320637i
$681$	−1.16735	+	2.80289i	−0.0447331	+	0.107407i
$682$	26.0936	−	18.2876i	0.999177	−	0.700269i
$683$			21.9477i			0.839805i	0.907569	+	0.419903i	$0.137936\pi$
$683$			21.9477i			0.839805i	−0.907569	+	0.419903i	$0.862064\pi$
$684$	−11.0598	−	11.1457i	−0.422882	−	0.426167i
$685$			18.6669i			0.713224i
$686$	−9.77182	+	5.64176i	−0.373090	+	0.215404i
$687$	−23.2764	+	3.01860i	−0.888050	+	0.115167i
$688$	−3.65486	−	2.11013i	−0.139340	−	0.0804481i
$689$	−25.4520	−	14.6947i	−0.969645	−	0.559825i
$690$	0.709323	+	5.46958i	0.0270035	+	0.208224i
$691$	17.9037	+	31.0101i	0.681088	+	1.17968i	0.974649	+	0.223739i	$0.0718262\pi$
$691$	17.9037	+	31.0101i	0.681088	+	1.17968i	−0.293561	+	0.955940i	$0.594840\pi$
$692$			2.33013i			0.0885784i
$693$	39.2261	+	39.5308i	1.49008	+	1.50165i
$694$		−	32.5020i		−	1.23376i
$695$	−3.35044	−	5.80314i	−0.127090	−	0.220126i
$696$	1.32081	−	3.17136i	0.0500653	−	0.120210i
$697$	32.5319	+	18.7823i	1.23223	+	0.711431i
$698$	−14.9432	−	8.62749i	−0.565610	−	0.326555i
$699$	23.9865	+	31.3854i	0.907253	+	1.18710i
$700$	1.49503	+	2.58946i	0.0565067	+	0.0978725i
$701$			17.8249i			0.673236i	0.941641	+	0.336618i	$0.109283\pi$
$701$			17.8249i			0.673236i	−0.941641	+	0.336618i	$0.890717\pi$
$702$	4.54108	+	11.1456i	0.171392	+	0.420665i
$703$		−	19.9130i		−	0.751034i
$704$	2.86147	+	4.95622i	0.107846	+	0.186794i
$705$	4.79350	−	3.66347i	0.180534	−	0.137974i
$706$	11.9722	+	6.91214i	0.450579	+	0.260142i
$707$	43.2498	+	24.9703i	1.62658	+	0.939105i
$708$	9.78058	−	23.4838i	0.367577	−	0.882576i
$709$	−30.1973	+	17.4344i	−1.13408	+	0.654764i	−0.944959	−	0.327189i	$-0.893899\pi$
$709$	−30.1973	+	17.4344i	−1.13408	+	0.654764i	−0.189125	+	0.981953i	$0.560565\pi$
$710$			16.1381i			0.605654i
$711$	−7.25894	−	27.5161i	−0.272232	−	1.03194i
$712$			12.4966i			0.468330i
$713$	5.03871	+	7.18947i	0.188701	+	0.269248i
$714$	26.6366	−	3.45437i	0.996850	−	0.129276i
$715$	13.3843	−	23.1823i	0.500545	−	0.866969i
$716$	−0.0634191	+	0.109845i	−0.00237008	+	0.00410510i
$717$	−4.00682	−	30.8966i	−0.149637	−	1.15385i
$718$	10.6303	+	18.4122i	0.396719	+	0.687137i
$719$	−18.1849			−0.678181			−0.339090	−	0.940754i	$-0.610119\pi$
$719$	−18.1849			−0.678181			−0.339090	+	0.940754i	$0.610119\pi$
$720$	−5.84581	−	1.59065i	−0.217861	−	0.0592799i
$721$	23.5193			0.875905
$722$	7.26939	−	4.19698i	0.270539	−	0.156195i
$723$	8.33820	−	20.0206i	0.310101	−	0.744573i
$724$	20.8894	+	12.0605i	0.776347	+	0.448224i
$725$	−0.914181	+	1.58341i	−0.0339518	+	0.0588063i
$726$	−22.8777	−	29.9345i	−0.849070	−	1.11097i
$727$	−17.9184	−	31.0356i	−0.664558	−	1.15105i	−0.979405	−	0.201905i	$-0.935287\pi$
$727$	−17.9184	−	31.0356i	−0.664558	−	1.15105i	0.314847	−	0.949142i	$-0.398047\pi$
$728$	−7.51292			−0.278447
$729$	−19.3122	+	18.8690i	−0.715266	+	0.698852i
$730$			6.88279i			0.254744i
$731$	17.4733	−	10.0882i	0.646272	−	0.373125i
$732$	5.69361	+	7.44986i	0.210442	+	0.275355i
$733$	−17.1030	+	29.6232i	−0.631712	+	1.09416i	0.355490	+	0.934680i	$0.384314\pi$
$733$	−17.1030	+	29.6232i	−0.631712	+	1.09416i	−0.987202	+	0.159477i	$0.949019\pi$
$734$	10.5021	−	18.1902i	0.387640	−	0.671412i
$735$	4.73552	−	11.3703i	0.174672	−	0.419399i
$736$	−1.36557	+	0.788409i	−0.0503354	+	0.0290612i
$737$	−25.6308			−0.944122
$738$	6.18893	−	22.7450i	0.227817	−	0.837256i
$739$		−	26.3634i		−	0.969795i	−0.874571	−	0.484897i	$-0.838857\pi$
$739$		−	26.3634i		−	0.969795i	0.874571	−	0.484897i	$-0.161143\pi$
$740$	−3.84161	−	6.65386i	−0.141220	−	0.244601i
$741$	−20.8228	+	2.70041i	−0.764945	+	0.0992019i
$742$	35.6439	+	20.5790i	1.30853	+	0.755480i
$743$	1.90960	−	3.30752i	0.0700563	−	0.121341i	−0.828869	−	0.559442i	$-0.811015\pi$
$743$	1.90960	−	3.30752i	0.0700563	−	0.121341i	0.898926	+	0.438101i	$0.144349\pi$
$744$	−9.41819	+	2.07308i	−0.345288	+	0.0760028i
$745$	−5.76013	−	9.97684i	−0.211035	−	0.365523i
$746$		−	6.30399i		−	0.230806i
$747$	39.1094	−	10.3173i	1.43094	−	0.377491i
$748$	−27.3605			−1.00040
$749$	8.40839	−	4.85459i	0.307236	−	0.177383i
$750$	19.1212	+	7.96363i	0.698208	+	0.290791i
$751$	10.3650	−	17.9527i	0.378225	−	0.655105i	−0.612579	−	0.790409i	$-0.709868\pi$
$751$	10.3650	−	17.9527i	0.378225	−	0.655105i	0.990804	+	0.135304i	$0.0432012\pi$
$752$	1.49375	+	0.862419i	0.0544716	+	0.0314492i
$753$	10.9850	−	8.39537i	0.400315	−	0.305944i
$754$	−2.29700	−	3.97853i	−0.0836519	−	0.144889i
$755$	31.3578			1.14123
$756$	−6.35949	−	15.6088i	−0.231293	−	0.567685i
$757$			15.5810i			0.566302i	0.959075	+	0.283151i	$0.0913798\pi$
$757$			15.5810i			0.566302i	−0.959075	+	0.283151i	$0.908620\pi$
$758$	0.950166	−	0.548578i	0.0345116	−	0.0199253i
$759$	12.4186	−	9.49100i	0.450766	−	0.344502i
$760$	5.28483	−	9.15359i	0.191701	−	0.332036i
$761$	18.4304	−	31.9224i	0.668102	−	1.15719i	−0.310332	−	0.950628i	$-0.600440\pi$
$761$	18.4304	−	31.9224i	0.668102	−	1.15719i	0.978434	−	0.206558i	$-0.0662264\pi$
$762$	−7.08674	−	2.95150i	−0.256725	−	0.106921i
$763$	−13.4803	−	23.3486i	−0.488021	−	0.845278i
$764$			7.79508i			0.282016i
$765$	20.5597	−	20.4013i	0.743339	−	0.737609i
$766$			5.88440i			0.212612i
$767$	−17.0092	−	29.4608i	−0.614167	−	1.06377i
$768$	−0.222756	−	1.71767i	−0.00803800	−	0.0619810i
$769$	21.5090	−	37.2547i	0.775635	−	1.34344i	−0.158802	−	0.987310i	$-0.550763\pi$
$769$	21.5090	−	37.2547i	0.775635	−	1.34344i	0.934437	−	0.356128i	$-0.115903\pi$
$770$	−18.7439	+	32.4653i	−0.675482	+	1.16997i
$771$	−17.4756	+	2.26633i	−0.629369	+	0.0816198i
$772$	−9.81440	−	16.9990i	−0.353228	−	0.611809i
$773$	−20.3735			−0.732785			−0.366392	−	0.930460i	$-0.619407\pi$
$773$	−20.3735			−0.732785			−0.366392	+	0.930460i	$0.619407\pi$
$774$	−8.91783	−	8.98710i	−0.320545	−	0.323035i
$775$	5.11272	−	0.449509i	0.183654	−	0.0161468i
$776$	12.4032	−	7.16097i	0.445247	−	0.257064i
$777$	8.21805	−	19.7321i	0.294821	−	0.707884i
$778$	7.05800	+	4.07494i	0.253041	+	0.146094i
$779$	35.6150	+	20.5623i	1.27604	+	0.736722i
$780$	−6.43690	+	4.91945i	−0.230478	+	0.176145i
$781$	39.6068	−	22.8670i	1.41724	−	0.818246i
$782$		−	7.53851i		−	0.269577i
$783$	6.32139	−	8.13995i	0.225908	−	0.290898i
$784$	3.52136			0.125763
$785$	8.91274	−	5.14577i	0.318109	−	0.183660i
$786$	−4.27592	+	3.26791i	−0.152517	+	0.116562i
$787$	−18.0436	−	10.4175i	−0.643186	−	0.371344i	0.142655	−	0.989773i	$-0.454436\pi$
$787$	−18.0436	−	10.4175i	−0.643186	−	0.371344i	−0.785841	+	0.618429i	$0.787769\pi$
$788$	2.03179	−	3.51917i	0.0723796	−	0.125365i
$789$	−48.5760	−	20.2310i	−1.72935	−	0.720243i
$790$	16.5898	−	9.57810i	0.590237	−	0.340773i
$791$		−	58.4136i		−	2.07695i
$792$	4.37943	+	16.6009i	0.155616	+	0.589887i
$793$	12.5386			0.445260
$794$	32.3991	−	18.7056i	1.14980	−	0.663839i
$795$	44.0141	−	5.70797i	1.56102	−	0.202441i
$796$	−5.59672	−	3.23127i	−0.198370	−	0.114529i
$797$	−22.3384	+	38.6913i	−0.791267	+	1.37051i	0.133915	+	0.990993i	$0.457245\pi$
$797$	−22.3384	+	38.6913i	−0.791267	+	1.37051i	−0.925183	+	0.379522i	$0.876088\pi$
$798$	29.1610	−	3.78175i	1.03229	−	0.133872i
$799$	−7.14139	+	4.12308i	−0.252644	+	0.145864i
$800$			0.921814i			0.0325910i
$801$	−9.84310	+	36.1746i	−0.347789	+	1.27816i
$802$		−	35.0075i		−	1.23616i
$803$	16.8920	−	9.75261i	0.596106	−	0.344162i
$804$	7.16093	+	2.98240i	0.252546	+	0.105181i
$805$	−8.94503	−	5.16442i	−0.315271	−	0.182022i
$806$	−5.44507	+	11.6900i	−0.191794	+	0.411764i
$807$	18.4572	−	14.1061i	0.649725	−	0.496558i
$808$	7.69818	+	13.3336i	0.270821	+	0.469075i
$809$	−50.0578			−1.75994			−0.879969	−	0.475030i	$-0.842437\pi$
$809$	−50.0578			−1.75994			−0.879969	+	0.475030i	$0.842437\pi$
$810$	−15.6693	−	9.20905i	−0.550562	−	0.323573i
$811$	−35.4859			−1.24608			−0.623039	−	0.782191i	$-0.714102\pi$
$811$	−35.4859			−1.24608			−0.623039	+	0.782191i	$0.714102\pi$
$812$	3.21681	+	5.57167i	0.112888	+	0.195527i
$813$	−31.2642	−	40.9079i	−1.09648	−	1.43470i
$814$	−10.8868	+	18.8564i	−0.381581	+	0.660918i
$815$	2.59768	+	1.49977i	0.0909928	+	0.0525347i
$816$	7.64418	+	3.18366i	0.267600	+	0.111450i
$817$	19.1292	−	11.0443i	0.669248	−	0.386390i
$818$	13.6489			0.477221
$819$	−21.7480	−	5.91764i	−0.759938	−	0.206779i
$820$	15.8675			0.554117
$821$	−12.3632	−	21.4137i	−0.431480	−	0.747345i	0.565521	−	0.824734i	$-0.308675\pi$
$821$	−12.3632	−	21.4137i	−0.431480	−	0.747345i	−0.997001	+	0.0773890i	$0.975342\pi$
$822$	−15.8773	+	2.05905i	−0.553785	+	0.0718176i
$823$	12.3905	+	7.15364i	0.431905	+	0.249360i	0.700158	−	0.713988i	$-0.253113\pi$
$823$	12.3905	+	7.15364i	0.431905	+	0.249360i	−0.268253	+	0.963348i	$0.586446\pi$
$824$	6.27941	+	3.62542i	0.218754	+	0.126298i
$825$	−1.17515	−	9.06153i	−0.0409133	−	0.315482i
$826$	23.8203	+	41.2580i	0.828815	+	1.43555i
$827$	14.4053			0.500921			0.250461	−	0.968127i	$-0.419418\pi$
$827$	14.4053			0.500921			0.250461	+	0.968127i	$0.419418\pi$
$828$	−4.57397	+	1.20665i	−0.158957	+	0.0419338i
$829$			40.2751i			1.39881i	0.714724	+	0.699407i	$0.246552\pi$
$829$			40.2751i			1.39881i	−0.714724	+	0.699407i	$0.753448\pi$
$830$	13.6136	+	23.5794i	0.472534	+	0.818454i
$831$	−5.97745	+	14.3523i	−0.207356	+	0.497874i
$832$	−2.00587	−	1.15809i	−0.0695411	−	0.0401496i
$833$	−8.41753	+	14.5796i	−0.291650	+	0.505153i
$834$	4.56635	−	3.48987i	0.158120	−	0.120844i
$835$	−10.3117	+	5.95345i	−0.356850	+	0.206028i
$836$	−29.9535			−1.03596
$837$	−28.8962	−	1.41730i	−0.998799	−	0.0489891i
$838$	25.0793			0.866350
$839$	−49.1296	+	28.3650i	−1.69614	+	0.979267i	−0.746785	+	0.665066i	$0.768403\pi$
$839$	−49.1296	+	28.3650i	−1.69614	+	0.979267i	−0.949356	+	0.314202i	$0.898263\pi$
$840$	9.01447	−	6.88938i	0.311029	−	0.237706i
$841$	12.5330	−	21.7078i	0.432172	−	0.748544i
$842$	1.87215	+	1.08089i	0.0645187	+	0.0372499i
$843$	−10.2269	+	24.5554i	−0.352232	+	0.845731i
$844$	3.09174	+	5.35505i	0.106422	+	0.184329i
$845$		−	15.4191i		−	0.530434i
$846$	3.64475	+	3.67306i	0.125309	+	0.126283i
$847$	70.5565			2.42435
$848$	6.34438	+	10.9888i	0.217867	+	0.377356i
$849$	−2.69839	−	20.8073i	−0.0926085	−	0.714104i
$850$	−3.81661	−	2.20352i	−0.130909	−	0.0755801i
$851$	−5.19544	−	2.99959i	−0.178097	−	0.102824i
$852$	−13.7265	+	1.78012i	−0.470261	+	0.0609858i
$853$	−4.09786	−	7.09770i	−0.140308	−	0.243021i	0.787305	−	0.616564i	$-0.211476\pi$
$853$	−4.09786	−	7.09770i	−0.140308	−	0.243021i	−0.927613	+	0.373544i	$0.878143\pi$
$854$	−17.5595			−0.600875
$855$	22.5082	−	22.3347i	0.769765	−	0.763831i
$856$	2.99327			0.102308
$857$	27.3139	−	15.7697i	0.933024	−	0.538682i	0.0452574	−	0.998975i	$-0.485589\pi$
$857$	27.3139	−	15.7697i	0.933024	−	0.538682i	0.887767	+	0.460294i	$0.152256\pi$
$858$	21.1943	+	8.82704i	0.723562	+	0.301350i
$859$	32.1588	+	18.5669i	1.09724	+	0.633494i	0.935496	−	0.353338i	$-0.114954\pi$
$859$	32.1588	+	18.5669i	1.09724	+	0.633494i	0.161748	+	0.986832i	$0.448287\pi$
$860$	4.26131	−	7.38081i	0.145310	−	0.251683i
$861$	26.8054	+	35.0737i	0.913525	+	1.19531i
$862$	0.291115	+	0.504225i	0.00991540	+	0.0171740i
$863$	−6.97322			−0.237371			−0.118686	−	0.992932i	$-0.537868\pi$
$863$	−6.97322			−0.237371			−0.118686	+	0.992932i	$0.537868\pi$
$864$	0.708119	−	5.14768i	0.0240907	−	0.175127i
$865$	−4.70559			−0.159995
$866$	−6.72039	−	11.6401i	−0.228368	−	0.395545i
$867$	−8.05936	+	6.15943i	−0.273710	+	0.209185i
$868$	7.62547	−	16.3711i	0.258825	−	0.555673i
$869$	−47.0139	−	27.1435i	−1.59484	−	0.920779i
$870$	6.40441	+	2.66732i	0.217130	+	0.0904307i
$871$	8.98350	−	5.18663i	0.304394	−	0.175742i
$872$		−	8.31180i		−	0.281473i
$873$	41.5445	−	10.9597i	1.40607	−	0.370930i
$874$		−	8.25295i		−	0.279160i
$875$	−33.5935	+	19.3952i	−1.13567	+	0.655677i
$876$	−5.85423	+	0.759206i	−0.197796	+	0.0256512i
$877$	−12.1258	+	21.0025i	−0.409460	+	0.709205i	−0.994829	−	0.101562i	$-0.967616\pi$
$877$	−12.1258	+	21.0025i	−0.409460	+	0.709205i	0.585369	+	0.810767i	$0.300949\pi$
$878$	−6.83753	−	3.94765i	−0.230755	−	0.133227i
$879$	45.6058	−	5.91439i	1.53825	−	0.199488i
$880$	−10.0088	+	5.77861i	−0.337398	+	0.194797i
$881$	−9.31513			−0.313835			−0.156917	−	0.987612i	$-0.550156\pi$
$881$	−9.31513			−0.313835			−0.156917	+	0.987612i	$0.550156\pi$
$882$	10.1935	+	2.77365i	0.343232	+	0.0933935i
$883$		−	51.4915i		−	1.73283i	−0.499328	−	0.866413i	$-0.666420\pi$
$883$		−	51.4915i		−	1.73283i	0.499328	−	0.866413i	$-0.333580\pi$
$884$	9.58975	−	5.53664i	0.322538	−	0.186217i
$885$	47.4245	+	19.7514i	1.59416	+	0.663937i
$886$	−7.28015	+	12.6096i	−0.244581	+	0.423627i
$887$	17.9718	+	10.3760i	0.603433	+	0.348392i	0.770391	−	0.637572i	$-0.220061\pi$
$887$	17.9718	+	10.3760i	0.603433	+	0.348392i	−0.166958	+	0.985964i	$0.553394\pi$
$888$	5.23577	−	4.00148i	0.175701	−	0.134281i
$889$	12.4505	−	7.18829i	0.417576	−	0.241087i
$890$	−25.2363			−0.845922
$891$	−0.398541	+	51.5050i	−0.0133516	+	1.72548i
$892$		−	25.1777i		−	0.843012i
$893$	−7.81819	+	4.51384i	−0.261626	+	0.151050i
$894$	7.85054	−	5.99984i	0.262561	−	0.200665i
$895$	−0.221827	−	0.128072i	−0.00741485	−	0.00428097i
$896$	2.80910	+	1.62183i	0.0938453	+	0.0541816i
$897$	−2.43208	+	5.83958i	−0.0812047	+	0.194978i
$898$	3.63363	−	2.09788i	0.121256	−	0.0700070i
$899$	11.0009	−	0.967196i	0.366900	−	0.0322578i
$900$	−0.726078	+	2.66842i	−0.0242026	+	0.0889474i
$901$	−60.6628			−2.02097
$902$	−22.4835	−	38.9426i	−0.748620	−	1.29665i
$903$	23.5134	−	3.04933i	0.782476	−	0.101475i
$904$	9.00426	−	15.5958i	0.299477	−	0.518710i
$905$	−24.3556	+	42.1851i	−0.809606	+	1.40228i
$906$	3.45893	+	26.6717i	0.114915	+	0.886109i
$907$	−3.12607	−	5.41452i	−0.103800	−	0.179786i	0.809448	−	0.587192i	$-0.199767\pi$
$907$	−3.12607	−	5.41452i	−0.103800	−	0.179786i	−0.913247	+	0.407406i	$0.866433\pi$
$908$		−	1.75299i		−	0.0581750i
$909$	11.7819	+	44.6611i	0.390781	+	1.48132i
$910$		−	15.1720i		−	0.502946i
$911$	−16.9387	−	29.3386i	−0.561203	−	0.972032i	−0.997392	−	0.0721767i	$-0.977005\pi$
$911$	−16.9387	−	29.3386i	−0.561203	−	0.972032i	0.436189	−	0.899855i	$-0.356328\pi$
$912$	8.36863	+	3.48538i	0.277113	+	0.115413i
$913$	38.5797	−	66.8220i	1.27680	−	2.21148i
$914$	−11.2127	+	19.4210i	−0.370883	+	0.642388i
$915$	−15.0446	+	11.4980i	−0.497360	+	0.380111i
$916$	11.7357	−	6.77559i	0.387757	−	0.223872i
$917$		−	10.0785i		−	0.332821i
$918$	19.6204	+	15.2369i	0.647568	+	0.502894i
$919$	−25.3725			−0.836963			−0.418481	−	0.908225i	$-0.637437\pi$
$919$	−25.3725			−0.836963			−0.418481	+	0.908225i	$0.637437\pi$
$920$	−1.59216	−	2.75769i	−0.0524918	−	0.0909185i
$921$	−34.8859	+	26.6618i	−1.14953	+	0.878536i
$922$	−21.0973	−	12.1805i	−0.694801	−	0.401144i
$923$	−9.25471	+	16.0296i	−0.304622	+	0.527621i
$924$	−29.6813	−	12.3617i	−0.976442	−	0.406670i
$925$	−3.03727	+	1.75357i	−0.0998648	+	0.0576570i
$926$	−16.1823			−0.531784
$927$	15.3217	+	15.4407i	0.503232	+	0.507141i
$928$			1.98344i			0.0651096i
$929$	−0.257250	−	0.445570i	−0.00844009	−	0.0146187i	0.861775	−	0.507292i	$-0.169353\pi$
$929$	−0.257250	−	0.445570i	−0.00844009	−	0.0146187i	−0.870215	+	0.492673i	$0.836020\pi$
$930$	−4.18649	−	19.0196i	−0.137280	−	0.623677i
$931$	−9.21528	+	15.9613i	−0.302019	+	0.523111i
$932$	−19.7509	−	11.4032i	−0.646963	−	0.373524i
$933$	18.1842	−	2.35822i	0.595323	−	0.0772045i
$934$	−0.831848	−	1.44080i	−0.0272189	−	0.0471445i
$935$		−	55.2531i		−	1.80697i
$936$	−4.89432	−	4.93234i	−0.159976	−	0.161218i
$937$	−15.2745			−0.498995			−0.249498	−	0.968375i	$-0.580265\pi$
$937$	−15.2745			−0.498995			−0.249498	+	0.968375i	$0.580265\pi$
$938$	−12.5808	+	7.26354i	−0.410778	+	0.237163i
$939$	15.7953	−	37.9255i	0.515459	−	1.23765i
$940$	−1.74161	+	3.01656i	−0.0568052	+	0.0983895i
$941$	−15.1532	+	26.2462i	−0.493981	+	0.855600i	−0.999976	−	0.00693629i	$-0.997792\pi$
$941$	−15.1532	+	26.2462i	−0.493981	+	0.855600i	0.505995	+	0.862536i	$0.331125\pi$
$942$	5.35991	+	7.01322i	0.174635	+	0.228503i
$943$	10.7297	−	6.19479i	0.349407	−	0.201730i
$944$			14.6873i			0.478031i
$945$	31.5212	−	12.8427i	1.02538	−	0.417773i
$946$	−24.1523			−0.785261
$947$	3.81988	+	6.61623i	0.124130	+	0.214999i	0.921392	−	0.388634i	$-0.127053\pi$
$947$	3.81988	+	6.61623i	0.124130	+	0.214999i	−0.797263	+	0.603632i	$0.793720\pi$
$948$	9.97669	+	13.0541i	0.324028	+	0.423977i
$949$	−3.94706	+	6.83651i	−0.128127	+	0.221922i
$950$	−4.17832	−	2.41235i	−0.135562	−	0.0782670i
$951$	−11.2417	+	26.9921i	−0.364537	+	0.875277i
$952$	−13.4298	+	7.75372i	−0.435263	+	0.251299i
$953$	−3.26013			−0.105606			−0.0528030	−	0.998605i	$-0.516816\pi$
$953$	−3.26013			−0.105606			−0.0528030	+	0.998605i	$0.516816\pi$
$954$	9.70994	+	36.8070i	0.314371	+	1.19167i
$955$	−15.7418			−0.509393
$956$	8.99376	+	15.5776i	0.290879	+	0.503817i
$957$	−2.52852	−	19.4974i	−0.0817356	−	0.630262i
$958$	1.19580	−	2.07119i	0.0386346	−	0.0669171i
$959$	14.9915	−	25.9660i	0.484100	−	0.838485i
$960$	3.46875	−	0.449844i	0.111953	−	0.0145187i
$961$	−19.9467	−	23.7303i	−0.643443	−	0.765494i
$962$		−	8.81216i		−	0.284115i
$963$	8.66478	+	2.35769i	0.279219	+	0.0759755i
$964$			12.5213i			0.403284i
$965$	34.3287	−	19.8197i	1.10508	−	0.638019i
$966$	3.40597	−	8.17796i	0.109585	−	0.263121i
$967$	−42.5258	−	24.5523i	−1.36754	−	0.789548i	−0.376925	−	0.926244i	$-0.623018\pi$
$967$	−42.5258	−	24.5523i	−1.36754	−	0.789548i	−0.990613	+	0.136696i	$0.956352\pi$
$968$	18.8379	+	10.8761i	0.605472	+	0.349570i
$969$	−34.4351	+	26.3173i	−1.10622	+	0.845435i
$970$	14.4612	+	25.0476i	0.464322	+	0.804229i
$971$		−	21.5097i		−	0.690278i	−0.938552	−	0.345139i	$-0.887832\pi$
$971$		−	21.5097i		−	0.690278i	0.938552	−	0.345139i	$-0.112168\pi$
$972$	6.10446	−	14.3435i	0.195801	−	0.460067i
$973$			10.7630i			0.345047i
$974$	−3.26863	−	5.66143i	−0.104734	−	0.181404i
$975$	2.24557	+	2.93823i	0.0719158	+	0.0940988i
$976$	−4.68822	−	2.70674i	−0.150066	−	0.0866408i
$977$	4.61478	+	2.66434i	0.147640	+	0.0852399i	0.572000	−	0.820254i	$-0.306168\pi$
$977$	4.61478	+	2.66434i	0.147640	+	0.0852399i	−0.424360	+	0.905493i	$0.639501\pi$
$978$	−0.989110	+	2.37492i	−0.0316283	+	0.0759415i
$979$	35.7587	+	61.9358i	1.14285	+	1.97948i
$980$			7.11123i			0.227160i
$981$	6.54689	−	24.0606i	0.209026	−	0.768196i
$982$			11.6862i			0.372923i
$983$	13.9839	+	24.2208i	0.446017	+	0.772525i	0.998122	−	0.0612499i	$-0.0195086\pi$
$983$	13.9839	+	24.2208i	0.446017	+	0.772525i	−0.552105	+	0.833774i	$0.686175\pi$
$984$	1.75027	+	13.4963i	0.0557964	+	0.430246i
$985$	7.10679	+	4.10311i	0.226441	+	0.130736i
$986$	−8.21208	−	4.74125i	−0.261526	−	0.150992i
$987$	−9.61000	+	1.24627i	−0.305890	+	0.0396693i
$988$	10.4986	−	6.06136i	0.334004	−	0.192838i
$989$		−	6.65459i		−	0.211604i
$990$	−33.5247	+	8.84404i	−1.06548	+	0.281082i
$991$		−	2.90283i		−	0.0922115i	−0.998937	−	0.0461058i	$-0.985319\pi$
$991$		−	2.90283i		−	0.0922115i	0.998937	−	0.0461058i	$-0.0146811\pi$
$992$	4.55948	−	3.19549i	0.144764	−	0.101457i
$993$	18.2777	−	43.8859i	0.580024	−	1.39268i
$994$	12.9606	−	22.4485i	0.411086	−	0.712022i
$995$	6.52539	−	11.3023i	0.206869	−	0.358307i
$996$	−18.5541	+	14.1801i	−0.587909	+	0.449314i
$997$	−20.7133	−	35.8764i	−0.655996	−	1.13622i	−0.981643	−	0.190727i	$-0.938916\pi$
$997$	−20.7133	−	35.8764i	−0.655996	−	1.13622i	0.325648	−	0.945491i	$-0.394418\pi$
$998$	−31.0328			−0.982327
$999$	18.3081	−	7.45926i	0.579241	−	0.236001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.q.a.185.20	✓	64
3.2	odd	2		1674.2.q.a.557.9		64
9.2	odd	6	inner	558.2.q.a.371.29	yes	64
9.7	even	3		1674.2.q.a.1115.2		64
31.30	odd	2	inner	558.2.q.a.185.29	yes	64
93.92	even	2		1674.2.q.a.557.2		64
279.61	odd	6		1674.2.q.a.1115.9		64
279.92	even	6	inner	558.2.q.a.371.20	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.20	✓	64	1.1	even	1	trivial
558.2.q.a.185.29	yes	64	31.30	odd	2	inner
558.2.q.a.371.20	yes	64	279.92	even	6	inner
558.2.q.a.371.29	yes	64	9.2	odd	6	inner
1674.2.q.a.557.2		64	93.92	even	2
1674.2.q.a.557.9		64	3.2	odd	2
1674.2.q.a.1115.2		64	9.7	even	3
1674.2.q.a.1115.9		64	279.61	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.37617 + 1.05175i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.74890 + 1.00973i) q^{5} +(-0.665921 + 1.59892i) q^{6} +(-1.62183 - 2.80910i) q^{7} -1.00000i q^{8} +(0.787662 - 2.89475i) q^{9} +2.01945 q^{10} +(-2.86147 - 4.95622i) q^{11} +(0.222756 + 1.71767i) q^{12} +(2.00587 + 1.15809i) q^{13} +(-2.80910 - 1.62183i) q^{14} +(-3.46875 + 0.449844i) q^{15} +(-0.500000 - 0.866025i) q^{16} +4.78084 q^{17} +(-0.765240 - 2.90076i) q^{18} +5.23392 q^{19} +(1.74890 - 1.00973i) q^{20} +(5.18636 + 2.16003i) q^{21} +(-4.95622 - 2.86147i) q^{22} +(0.788409 - 1.36557i) q^{23} +(1.05175 + 1.37617i) q^{24} +(-0.460907 - 0.798314i) q^{25} +2.31618 q^{26} +(1.96059 + 4.81208i) q^{27} -3.24367 q^{28} +(-0.991719 - 1.71771i) q^{29} +(-2.77910 + 2.12395i) q^{30} +(-2.35088 + 5.04711i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(9.15054 + 3.81103i) q^{33} +(4.14033 - 2.39042i) q^{34} -6.55043i q^{35} +(-2.11310 - 2.12951i) q^{36} -3.80460i q^{37} +(4.53271 - 2.61696i) q^{38} +(-3.97843 + 0.515943i) q^{39} +(1.00973 - 1.74890i) q^{40} +(6.80465 + 3.92867i) q^{41} +(5.57154 - 0.722545i) q^{42} +(3.65486 - 2.11013i) q^{43} -5.72295 q^{44} +(4.30045 - 4.26730i) q^{45} -1.57682i q^{46} +(-1.49375 + 0.862419i) q^{47} +(1.59892 + 0.665921i) q^{48} +(-1.76068 + 3.04959i) q^{49} +(-0.798314 - 0.460907i) q^{50} +(-6.57922 + 5.02822i) q^{51} +(2.00587 - 1.15809i) q^{52} -12.6888 q^{53} +(4.10396 + 3.18709i) q^{54} -11.5572i q^{55} +(-2.80910 + 1.62183i) q^{56} +(-7.20275 + 5.50476i) q^{57} +(-1.71771 - 0.991719i) q^{58} +(-12.7196 - 7.34365i) q^{59} +(-1.34480 + 3.22894i) q^{60} +(4.68822 - 2.70674i) q^{61} +(0.487636 + 5.54637i) q^{62} +(-9.40909 + 2.48218i) q^{63} -1.00000 q^{64} +(2.33871 + 4.05076i) q^{65} +(9.83011 - 1.27482i) q^{66} +(2.23930 - 3.87858i) q^{67} +(2.39042 - 4.14033i) q^{68} +(0.351245 + 2.70845i) q^{69} +(-3.27521 - 5.67284i) q^{70} +7.99135i q^{71} +(-2.89475 - 0.787662i) q^{72} +3.40825i q^{73} +(-1.90230 - 3.29488i) q^{74} +(1.47391 + 0.613855i) q^{75} +(2.61696 - 4.53271i) q^{76} +(-9.28166 + 16.0763i) q^{77} +(-3.18745 + 2.43603i) q^{78} +(8.21498 - 4.74292i) q^{79} -2.01945i q^{80} +(-7.75918 - 4.56017i) q^{81} +7.85733 q^{82} +(6.74123 + 11.6761i) q^{83} +(4.46382 - 3.41151i) q^{84} +(8.36119 + 4.82733i) q^{85} +(2.11013 - 3.65486i) q^{86} +(3.17136 + 1.32081i) q^{87} +(-4.95622 + 2.86147i) q^{88} -12.4966 q^{89} +(1.59065 - 5.84581i) q^{90} -7.51292i q^{91} +(-0.788409 - 1.36557i) q^{92} +(-2.07308 - 9.41819i) q^{93} +(-0.862419 + 1.49375i) q^{94} +(9.15359 + 5.28483i) q^{95} +(1.71767 - 0.222756i) q^{96} +(7.16097 + 12.4032i) q^{97} +3.52136i q^{98} +(-16.6009 + 4.37943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) \) 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Introduction

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