LMFDB - Embedded newform 558.2.q.a.371.29

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			371.29
Character	$\chi$	$=$	558.371
Dual form			558.2.q.a.185.29

$q$-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} +(-3.19549 - 4.55948i) 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} +(0.397890 - 9.63544i) 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 $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	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	−0.0550544	−	0.998483i	$-0.517533\pi$
$5$	1.74890	−	1.00973i	0.782130	−	0.451563i	0.837185	+	0.546920i	$0.184200\pi$
$6$	0.665921	+	1.59892i	0.271861	+	0.652757i
$7$	−1.62183	+	2.80910i	−0.612995	+	1.06174i	0.377738	+	0.925913i	$0.376702\pi$
$7$	−1.62183	+	2.80910i	−0.612995	+	1.06174i	−0.990733	+	0.135826i	$0.956631\pi$
$8$			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	−0.00648152	−	0.999979i	$-0.502063\pi$
$11$	2.86147	−	4.95622i	0.862766	−	1.49436i	0.869248	−	0.494376i	$-0.164604\pi$
$12$	−0.222756	+	1.71767i	−0.0643040	+	0.495848i
$13$	−2.00587	+	1.15809i	−0.556329	+	0.321197i	−0.751671	−	0.659539i	$-0.770752\pi$
$13$	−2.00587	+	1.15809i	−0.556329	+	0.321197i	0.195342	+	0.980735i	$0.437418\pi$
$14$	−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	$-0.696854\pi$
$17$	−4.78084			−1.15952			−0.579762	+	0.814786i	$0.696854\pi$
$18$	−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	$-0.219234\pi$
$23$	−0.788409	−	1.36557i	−0.164395	−	0.284740i	−0.936440	+	0.350827i	$0.885900\pi$
$24$	−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	$-0.774378\pi$
$29$	0.991719	−	1.71771i	0.184158	−	0.318970i	0.943292	+	0.331963i	$0.107711\pi$
$30$	2.77910	+	2.12395i	0.507392	+	0.387778i
$31$	−3.19549	−	4.55948i	−0.573927	−	0.818907i
$31$	−3.19549	−	4.55948i	−0.573927	−	0.818907i
$32$	−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	0.136528	−	0.990636i	$-0.456406\pi$
$41$	6.80465	−	3.92867i	1.06271	−	0.613555i	0.926180	+	0.377082i	$0.123072\pi$
$42$	−5.57154	−	0.722545i	−0.859707	−	0.111491i
$43$	−3.65486	−	2.11013i	−0.557360	−	0.321792i	0.194725	−	0.980858i	$-0.437619\pi$
$43$	−3.65486	−	2.11013i	−0.557360	−	0.321792i	−0.752085	+	0.659066i	$0.770952\pi$
$44$	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	0.387085	−	0.922044i	$-0.373482\pi$
$47$	−1.49375	−	0.862419i	−0.217886	−	0.125797i	−0.604971	+	0.796247i	$0.706815\pi$
$48$	−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	$-0.163169\pi$
$53$	12.6888			1.74293			0.871467	+	0.490454i	$0.163169\pi$
$54$	−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	−0.681390	+	0.731921i	$0.738624\pi$
$59$	−12.7196	+	7.34365i	−1.65595	+	0.956061i	−0.974557	+	0.224141i	$0.928042\pi$
$60$	1.34480	+	3.22894i	0.173612	+	0.416855i
$61$	−4.68822	−	2.70674i	−0.600265	−	0.346563i	0.168881	−	0.985636i	$-0.445985\pi$
$61$	−4.68822	−	2.70674i	−0.600265	−	0.346563i	−0.769146	+	0.639073i	$0.779318\pi$
$62$	−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	0.969774	−	0.244003i	$-0.0784608\pi$
$67$	2.23930	+	3.87858i	0.273574	+	0.473844i	−0.696200	+	0.717848i	$0.745127\pi$
$68$	−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	$-0.842738\pi$
$71$		−	7.99135i		−	0.948398i	0.880418	−	0.474199i	$-0.157262\pi$
$72$	−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	$-0.512502\pi$
$79$	−8.21498	−	4.74292i	−0.924257	−	0.533620i	−0.884991	+	0.465609i	$0.845835\pi$
$80$			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	0.212573	+	0.977145i	$0.431816\pi$
$83$	−6.74123	+	11.6761i	−0.739946	+	1.28162i	−0.952519	+	0.304479i	$0.901518\pi$
$84$	−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	$-0.269573\pi$
$89$	12.4966			1.32464			0.662318	+	0.749222i	$0.269573\pi$
$90$	1.59065	+	5.84581i	0.167669	+	0.616203i
$91$		−	7.51292i		−	0.787568i
$92$	0.788409	−	1.36557i	0.0821974	−	0.142370i
$93$	0.397890	−	9.63544i	0.0412592	−	0.999148i
$94$	−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	−0.231024	−	0.972948i	$-0.574208\pi$
$97$	7.16097	−	12.4032i	0.727086	−	1.25935i	0.958110	−	0.286402i	$-0.0924592\pi$
$98$		−	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	−0.341951	−	0.939718i	$-0.611088\pi$
$101$	−13.3336	−	7.69818i	−1.32675	−	0.765997i	−0.984795	+	0.173721i	$0.944421\pi$
$102$	−3.18366	−	7.64418i	−0.315229	−	0.756887i
$103$	−3.62542	−	6.27941i	−0.357223	−	0.618729i	0.630273	−	0.776374i	$-0.282943\pi$
$103$	−3.62542	−	6.27941i	−0.357223	−	0.618729i	−0.987496	+	0.157645i	$0.949610\pi$
$104$	−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	$-0.953783\pi$
$107$		−	2.99327i		−	0.289371i	0.989478	−	0.144685i	$-0.0462170\pi$
$108$	−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	0.467810	−	0.883829i	$-0.345043\pi$
$113$	15.5958	−	9.00426i	1.46713	−	0.847050i	0.999323	+	0.0367793i	$0.0117099\pi$
$114$	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
$124$	2.35088	−	5.04711i	0.211115	−	0.453244i
$125$			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	−0.377822	−	0.925878i	$-0.623327\pi$
$131$	2.69085	−	1.55356i	0.235101	−	0.135735i	0.612923	+	0.790143i	$0.289994\pi$
$132$	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	$-0.962542\pi$
$137$	−4.62177	+	8.00513i	−0.394864	+	0.683925i	0.598220	+	0.801332i	$0.295875\pi$
$138$	1.65841	−	2.16996i	0.141173	−	0.184720i
$139$	2.87362	−	1.65909i	0.243737	−	0.140722i	−0.373156	−	0.927769i	$-0.621724\pi$
$139$	2.87362	−	1.65909i	0.243737	−	0.140722i	0.616893	+	0.787047i	$0.288391\pi$
$140$	−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	−0.688523	−	0.725214i	$-0.741741\pi$
$149$	−4.94037	+	2.85232i	−0.404731	+	0.233671i	0.283792	+	0.958886i	$0.408407\pi$
$150$	−1.58337	−	0.205339i	−0.129282	−	0.0167659i
$151$	−13.4475	−	7.76394i	−1.09435	−	0.631821i	−0.159616	−	0.987179i	$-0.551025\pi$
$151$	−13.4475	−	7.76394i	−1.09435	−	0.631821i	−0.934730	+	0.355358i	$0.884359\pi$
$152$			5.23392i			0.424527i
$153$	−3.76568	−	13.8393i	−0.304438	−	1.11884i
$154$			18.5633i			1.49587i
$155$	−10.1924	−	4.74749i	−0.818674	−	0.381327i
$156$	−1.54240	−	3.70339i	−0.123490	−	0.296509i
$157$	2.54810	+	4.41344i	0.203361	+	0.352231i	0.949609	−	0.313436i	$-0.101480\pi$
$157$	2.54810	+	4.41344i	0.203361	+	0.352231i	−0.746248	+	0.665667i	$0.768147\pi$
$158$	−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	$-0.0934065\pi$
$167$	2.94805	+	5.10618i	0.228127	+	0.395128i	−0.729126	+	0.684380i	$0.760073\pi$
$168$	−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	0.421323	−	0.906910i	$-0.361566\pi$
$173$	−2.01796	−	1.16507i	−0.153422	−	0.0885784i	−0.574746	+	0.818332i	$0.694899\pi$
$174$	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	$-0.498491\pi$
$179$	0.126838			0.00948033			0.00474016	+	0.999989i	$0.498491\pi$
$180$	−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
$186$	5.16230	−	8.14559i	0.378518	−	0.597264i
$187$	−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	0.235472	−	0.971881i	$-0.424337\pi$
$191$	−6.75074	−	3.89754i	−0.488466	−	0.282016i	−0.723938	+	0.689865i	$0.757670\pi$
$192$	−1.37617	−	1.05175i	−0.0993162	−	0.0759032i
$193$	9.81440	+	16.9990i	0.706456	+	1.22362i	0.966164	+	0.257930i	$0.0830404\pi$
$193$	9.81440	+	16.9990i	0.706456	+	1.22362i	−0.259708	+	0.965687i	$0.583626\pi$
$194$	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	$-0.546241\pi$
$197$	−4.06359			−0.289519			−0.144759	+	0.989467i	$0.546241\pi$
$198$	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	0.739759	−	0.672872i	$-0.234939\pi$
$211$	−3.09174	−	5.35505i	−0.212844	−	0.368657i	−0.952604	+	0.304215i	$0.901606\pi$
$212$	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	$-0.652553\pi$
$223$	−21.8045	−	12.5889i	−1.46014	−	0.843012i	−0.999017	+	0.0443246i	$0.985886\pi$
$224$		−	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	0.549534	−	0.835471i	$-0.314805\pi$
$227$	1.51813	+	0.876495i	0.100762	+	0.0581750i	−0.448772	+	0.893646i	$0.648139\pi$
$228$	−1.16589	+	8.99014i	−0.0772127	+	0.595387i
$229$	−11.7357	+	6.77559i	−0.775514	+	0.447743i	−0.834838	−	0.550496i	$-0.814439\pi$
$229$	−11.7357	+	6.77559i	−0.775514	+	0.447743i	0.0593240	+	0.998239i	$0.481105\pi$
$230$	−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	$0.268530\pi$
$233$			22.8064i			1.49410i	−0.664770	+	0.747048i	$0.731470\pi$
$234$	−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	0.995271	+	0.0971359i	$0.0309682\pi$
$239$	8.99376	+	15.5776i	0.581758	+	1.00763i	−0.413513	+	0.910498i	$0.635699\pi$
$240$	−2.12395	+	2.77910i	−0.137100	+	0.179390i
$241$	10.8438	+	6.26065i	0.698508	+	0.403284i	0.806791	−	0.590836i	$-0.201202\pi$
$241$	10.8438	+	6.26065i	0.698508	+	0.403284i	−0.108283	+	0.994120i	$0.534535\pi$
$242$		−	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
$248$	4.55948	−	3.19549i	0.289527	−	0.202914i
$249$	−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	$-0.418938\pi$
$251$	7.98232			0.503839			0.251920	+	0.967748i	$0.418938\pi$
$252$	−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	−0.199352	−	0.979928i	$-0.563884\pi$
$257$	8.81099	−	5.08702i	0.549614	−	0.317320i	0.748966	+	0.662608i	$0.230550\pi$
$258$	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	−0.165041	+	0.986287i	$0.552776\pi$
$263$	−15.1902	+	26.3103i	−0.936670	+	1.62236i	−0.771629	+	0.636073i	$0.780558\pi$
$264$	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	$-0.365922\pi$
$269$	13.4121			0.817748			0.408874	+	0.912591i	$0.365922\pi$
$270$	−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	$-0.420246\pi$
$277$	−7.77363	−	4.48811i	−0.467072	−	0.269664i	−0.715013	+	0.699111i	$0.753579\pi$
$278$	3.31817			0.199011
$279$	10.6816	−	12.8415i	0.639490	−	0.768799i
$280$	−6.55043			−0.391463
$281$	13.2999	+	7.67873i	0.793408	+	0.458074i	0.841161	−	0.540785i	$-0.181873\pi$
$281$	13.2999	+	7.67873i	0.793408	+	0.458074i	−0.0477529	+	0.998859i	$0.515206\pi$
$282$	0.384218	−	2.96270i	0.0228798	−	0.176426i
$283$	−6.05684	−	10.4908i	−0.360042	−	0.623611i	0.627926	−	0.778273i	$-0.283904\pi$
$283$	−6.05684	−	10.4908i	−0.360042	−	0.623611i	−0.987967	+	0.154663i	$0.950571\pi$
$284$	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	−0.987293	−	0.158913i	$-0.949201\pi$
$293$	−22.9939	+	13.2755i	−1.34332	+	0.775564i	−0.356024	+	0.934477i	$0.615868\pi$
$294$	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
$310$	−6.45314	−	9.20765i	−0.366514	−	0.522959i
$311$	−9.16823	+	5.29328i	−0.519882	+	0.300154i	−0.736887	−	0.676016i	$-0.763705\pi$
$311$	−9.16823	+	5.29328i	−0.519882	+	0.300154i	0.217004	+	0.976171i	$0.430372\pi$
$312$	0.515943	−	3.97843i	0.0292095	−	0.225234i
$313$	20.5416	+	11.8597i	1.16108	+	0.670350i	0.951563	−	0.307455i	$-0.0994773\pi$
$313$	20.5416	+	11.8597i	1.16108	+	0.670350i	0.209518	+	0.977805i	$0.432811\pi$
$314$			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	0.850805	−	0.525482i	$-0.176115\pi$
$317$	14.6197	+	8.44071i	0.821126	+	0.474077i	−0.0296786	+	0.999559i	$0.509448\pi$
$318$	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	$-0.0613017\pi$
$331$	23.7700	+	13.7236i	1.30651	+	0.754317i	0.325002	+	0.945713i	$0.394635\pi$
$332$	−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	−0.592536	+	0.805544i	$0.701873\pi$
$337$	−29.1229	+	16.8141i	−1.58643	+	0.915923i	−0.993890	+	0.110379i	$0.964793\pi$
$338$	−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	−0.859506	−	0.511125i	$-0.829229\pi$
$347$	−16.2510	−	28.1476i	−0.872400	−	1.51104i	−0.0128942	−	0.999917i	$-0.504104\pi$
$348$	2.72954	+	2.08607i	0.146319	+	0.111825i
$349$	−8.62749	+	14.9432i	−0.461819	+	0.799893i	−0.999052	−	0.0435404i	$-0.986136\pi$
$349$	−8.62749	+	14.9432i	−0.461819	+	0.799893i	0.537233	+	0.843434i	$0.319470\pi$
$350$		−	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	$-0.953255\pi$
$353$	−6.91214	+	11.9722i	−0.367896	+	0.637215i	0.621340	+	0.783541i	$0.286588\pi$
$354$	−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	$-0.810399\pi$
$359$		−	21.2606i		−	1.12209i	0.827785	−	0.561045i	$-0.189601\pi$
$360$	−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	$-0.518022\pi$
$367$	−18.1902	−	10.5021i	−0.949520	−	0.548205i	−0.892932	+	0.450192i	$0.851355\pi$
$368$	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
$372$	8.54348	−	4.47314i	0.442959	−	0.231921i
$373$	3.15200	+	5.45942i	0.163204	+	0.282678i	0.936016	−	0.351957i	$-0.114484\pi$
$373$	3.15200	+	5.45942i	0.163204	+	0.282678i	−0.772812	+	0.634635i	$0.781150\pi$
$374$	−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	$-0.118630\pi$
$383$	2.94220	+	5.09604i	0.150339	+	0.260395i	−0.781013	+	0.624515i	$0.785297\pi$
$384$	−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	$-0.899576\pi$
$389$	−4.07494	+	7.05800i	−0.206607	+	0.357855i	0.744036	+	0.668139i	$0.232909\pi$
$390$	−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	−0.857722	−	0.514114i	$-0.828121\pi$
$401$	−17.5038	−	30.3174i	−0.874097	−	1.51398i	−0.0163746	−	0.999866i	$-0.505212\pi$
$402$	−4.71035	+	6.16329i	−0.234931	+	0.307397i
$403$	11.6900	+	5.44507i	0.582322	+	0.271238i
$404$		−	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	$-0.776230\pi$
$409$	−11.8203	+	6.82443i	−0.584474	+	0.337446i	0.178435	+	0.983952i	$0.442896\pi$
$410$	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	0.135333	−	0.990800i	$-0.456790\pi$
$419$	21.7193	−	12.5396i	1.06106	−	0.612602i	0.925725	+	0.378199i	$0.123456\pi$
$420$	−11.2515	−	1.45914i	−0.549015	−	0.0711990i
$421$	1.08089	−	1.87215i	0.0526793	−	0.0912432i	−0.838483	−	0.544927i	$-0.816557\pi$
$421$	1.08089	−	1.87215i	0.0526793	−	0.0912432i	0.891163	+	0.453684i	$0.149891\pi$
$422$		−	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	$-0.995536\pi$
$431$		−	0.582229i		−	0.0280450i	0.999902	−	0.0140225i	$-0.00446364\pi$
$432$	−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	$-0.104678\pi$
$434$	16.3711	+	7.62547i	0.785840	+	0.366034i
$435$	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	−0.944721	−	0.327876i	$-0.893667\pi$
$439$	−3.94765	+	6.83753i	−0.188411	+	0.326337i	0.756310	+	0.654214i	$0.227000\pi$
$440$	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	0.169588	−	0.985515i	$-0.445756\pi$
$443$	−12.6096	−	7.28015i	−0.599099	−	0.345890i	−0.768687	+	0.639625i	$0.779090\pi$
$444$	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	$-0.531566\pi$
$449$	−4.19575			−0.198010			−0.0990049	+	0.995087i	$0.531566\pi$
$450$	−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	$-0.157583\pi$
$457$	19.4210	+	11.2127i	0.908474	+	0.524508i	0.0285340	+	0.999593i	$0.490916\pi$
$458$	−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	−0.429528	−	0.903053i	$-0.641320\pi$
$461$	12.1805	−	21.0973i	0.567303	−	0.982597i	0.996831	−	0.0795441i	$-0.0253465\pi$
$462$	−19.5239	+	25.5462i	−0.908333	+	1.18852i
$463$	14.0143	−	8.09115i	0.651299	−	0.376028i	−0.137655	−	0.990480i	$-0.543956\pi$
$463$	14.0143	−	8.09115i	0.651299	−	0.376028i	0.788954	+	0.614452i	$0.210623\pi$
$464$	0.991719	+	1.71771i	0.0460394	+	0.0797426i
$465$	−9.03329	−	17.2531i	−0.418909	−	0.800096i
$466$	−11.4032	+	19.7509i	−0.528243	+	0.914943i
$467$			1.66370i			0.0769867i	0.999259	+	0.0384933i	$0.0122558\pi$
$467$			1.66370i			0.0769867i	−0.999259	+	0.0384933i	$0.987744\pi$
$468$	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	0.546571	−	0.837413i	$-0.315933\pi$
$479$	2.07119	+	1.19580i	0.0946350	+	0.0546376i	−0.451936	+	0.892051i	$0.649266\pi$
$480$	−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	$-0.0817249\pi$
$491$	5.84312	+	10.1206i	0.263696	+	0.456736i	−0.703525	+	0.710671i	$0.748392\pi$
$492$	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	$-0.422244\pi$
$499$	26.8752	−	15.5164i	1.20310	−	0.694610i	0.961243	+	0.275702i	$0.0889103\pi$
$500$	−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	$0.0881774\pi$
$503$			12.2674i			0.546976i	−0.961875	+	0.273488i	$0.911823\pi$
$504$	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	$-0.139630\pi$
$509$	1.91401	+	3.31515i	0.0848368	+	0.146942i	−0.820485	+	0.571668i	$0.806296\pi$
$510$	−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	$-0.970998\pi$
$521$		−	4.15365i		−	0.181975i	0.995852	−	0.0909873i	$-0.0290023\pi$
$522$	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
$527$	15.2771	+	21.7981i	0.665481	+	0.949541i
$528$	−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	−0.785317	−	0.619094i	$-0.787500\pi$
$547$	3.35602	−	5.81280i	0.143493	−	0.248537i	0.928810	+	0.370557i	$0.120833\pi$
$548$	−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	$-0.359090\pi$
$557$	20.2195			0.856729			0.428364	+	0.903606i	$0.359090\pi$
$558$	15.6713	−	5.78025i	0.663418	−	0.244698i
$559$	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	−0.993036	−	0.117809i	$-0.962413\pi$
$563$	−32.9228	+	19.0080i	−1.38753	+	0.801090i	−0.394493	+	0.918899i	$0.629080\pi$
$564$	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	−0.243180	−	0.969981i	$-0.578191\pi$
$569$	17.1374	−	29.6829i	0.718438	−	1.24437i	0.961618	−	0.274390i	$-0.0884761\pi$
$570$	14.5456	+	11.1166i	0.609248	+	0.465623i
$571$	0.962168	−	0.555508i	0.0402655	−	0.0232473i	−0.479732	−	0.877415i	$-0.659266\pi$
$571$	0.962168	−	0.555508i	0.0402655	−	0.0232473i	0.519998	+	0.854168i	$0.325933\pi$
$572$	−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	$-0.785263\pi$
$587$	3.64494	−	6.31323i	0.150443	−	0.260575i	0.931390	+	0.364022i	$0.118597\pi$
$588$	5.63038	−	2.34495i	0.232193	−	0.0967042i
$589$	−16.7250	−	23.8640i	−0.689140	−	0.983298i
$590$	−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	$-0.901291\pi$
$593$		−	14.8621i		−	0.610315i	0.952302	−	0.305157i	$-0.0987090\pi$
$594$	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	0.216014	−	0.976390i	$-0.430694\pi$
$599$	28.6253	−	16.5269i	1.16960	−	0.675269i	0.953586	+	0.301121i	$0.0973609\pi$
$600$	−0.613855	−	1.47391i	−0.0250605	−	0.0601720i
$601$	−18.7777	−	10.8413i	−0.765959	−	0.442227i	0.0654721	−	0.997854i	$-0.479145\pi$
$601$	−18.7777	−	10.8413i	−0.765959	−	0.442227i	−0.831431	+	0.555628i	$0.812478\pi$
$602$	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	0.918710	−	0.394933i	$-0.129232\pi$
$607$	2.89077	+	5.00696i	0.117333	+	0.203226i	−0.801377	+	0.598160i	$0.795899\pi$
$608$	−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	−0.136300	−	0.990668i	$-0.543521\pi$
$617$	16.2324	−	9.37180i	0.653493	−	0.377295i	0.789793	+	0.613373i	$0.210188\pi$
$618$	7.62604	−	9.97836i	0.306764	−	0.401388i
$619$	7.39343	+	4.26860i	0.297167	+	0.171569i	0.641170	−	0.767399i	$-0.278450\pi$
$619$	7.39343	+	4.26860i	0.297167	+	0.171569i	−0.344003	+	0.938969i	$0.611783\pi$
$620$	−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	−0.408195	−	0.912895i	$-0.633842\pi$
$641$	14.8488	−	25.7189i	0.586493	−	1.01584i	0.994688	−	0.102940i	$-0.0328251\pi$
$642$	4.78601	−	1.99328i	0.188889	−	0.0786687i
$643$	−33.7394	+	19.4794i	−1.33055	+	0.768194i	−0.985384	−	0.170347i	$-0.945511\pi$
$643$	−33.7394	+	19.4794i	−1.33055	+	0.768194i	−0.345167	+	0.938541i	$0.612178\pi$
$644$	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	$-0.324806\pi$
$647$	26.6071			1.04603			0.523017	+	0.852322i	$0.324806\pi$
$648$	−4.56017	−	7.75918i	−0.179141	−	0.304809i
$649$			84.0546i			3.29943i
$650$	1.06754	−	1.84904i	0.0418725	−	0.0725253i
$651$	26.4216	+	16.7448i	1.03554	+	0.656280i
$652$	0.742663	+	1.28633i	0.0290849	+	0.0503766i
$653$	4.62141	−	2.66817i	0.180850	−	0.104414i	−0.406842	−	0.913499i	$-0.633370\pi$
$653$	4.62141	−	2.66817i	0.180850	−	0.104414i	0.587692	+	0.809085i	$0.300037\pi$
$654$	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	0.732104	−	0.681193i	$-0.238539\pi$
$659$	13.0467	+	7.53249i	0.508226	+	0.293424i	−0.223878	+	0.974617i	$0.571872\pi$
$660$	19.8514	+	2.57443i	0.772716	+	0.100210i
$661$	−15.2397	−	26.3959i	−0.592755	−	1.02668i	−0.993860	−	0.110649i	$-0.964707\pi$
$661$	−15.2397	−	26.3959i	−0.592755	−	1.02668i	0.401105	−	0.916032i	$-0.368626\pi$
$662$	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	$-0.459792\pi$
$673$	−17.3853	−	10.0374i	−0.670156	−	0.386915i	−0.796136	+	0.605118i	$0.793126\pi$
$674$	−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	−0.00744306	−	0.999972i	$-0.502369\pi$
$677$	22.4359	−	38.8600i	0.862280	−	1.49351i	0.869723	−	0.493540i	$-0.164297\pi$
$678$	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
$682$	−28.8844	−	13.4540i	−1.10604	−	0.515179i
$683$		−	21.9477i		−	0.839805i	−0.907569	−	0.419903i	$-0.862064\pi$
$683$		−	21.9477i		−	0.839805i	0.907569	−	0.419903i	$-0.137936\pi$
$684$	−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	−0.293561	−	0.955940i	$-0.594840\pi$
$691$	17.9037	−	31.0101i	0.681088	−	1.17968i	0.974649	−	0.223739i	$-0.0718262\pi$
$692$		−	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	$-0.890717\pi$
$701$		−	17.8249i		−	0.673236i	0.941641	−	0.336618i	$-0.109283\pi$
$702$	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	$-0.106101\pi$
$709$	30.1973	+	17.4344i	1.13408	+	0.654764i	0.189125	+	0.981953i	$0.439435\pi$
$710$		−	16.1381i		−	0.605654i
$711$	7.25894	−	27.5161i	0.272232	−	1.03194i
$712$			12.4966i			0.468330i
$713$	−3.70691	+	7.95839i	−0.138825	+	0.298044i
$714$	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	$-0.389881\pi$
$719$	18.1849			0.678181			0.339090	+	0.940754i	$0.389881\pi$
$720$	−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	0.314847	+	0.949142i	$0.398047\pi$
$727$	−17.9184	+	31.0356i	−0.664558	+	1.15105i	−0.979405	+	0.201905i	$0.935287\pi$
$728$	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	−0.987202	−	0.159477i	$-0.949019\pi$
$733$	−17.1030	−	29.6232i	−0.631712	−	1.09416i	0.355490	−	0.934680i	$-0.384314\pi$
$734$	−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	$-0.188985\pi$
$743$	−1.90960	−	3.30752i	−0.0700563	−	0.121341i	−0.898926	+	0.438101i	$0.855651\pi$
$744$	9.63544	+	0.397890i	0.353252	+	0.0145873i
$745$	−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	0.990804	−	0.135304i	$-0.0432012\pi$
$751$	10.3650	+	17.9527i	0.378225	+	0.655105i	−0.612579	+	0.790409i	$0.709868\pi$
$752$	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	−0.978434	−	0.206558i	$-0.933774\pi$
$761$	−18.4304	−	31.9224i	−0.668102	−	1.15719i	0.310332	−	0.950628i	$-0.399560\pi$
$762$	−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	0.934437	+	0.356128i	$0.115903\pi$
$769$	21.5090	+	37.2547i	0.775635	+	1.34344i	−0.158802	+	0.987310i	$0.550763\pi$
$770$	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	$-0.380593\pi$
$773$	20.3735			0.732785			0.366392	+	0.930460i	$0.380593\pi$
$774$	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	$-0.545564\pi$
$787$	18.0436	−	10.4175i	0.643186	−	0.371344i	0.785841	+	0.618429i	$0.212231\pi$
$788$	−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	0.925183	+	0.379522i	$0.123912\pi$
$797$	22.3384	+	38.6913i	0.791267	+	1.37051i	−0.133915	+	0.990993i	$0.542755\pi$
$798$	−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
$806$	7.40134	+	10.5606i	0.260701	+	0.371981i
$807$	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	$-0.157563\pi$
$809$	50.0578			1.75994			0.879969	+	0.475030i	$0.157563\pi$
$810$	−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	$-0.691325\pi$
$821$	12.3632	−	21.4137i	0.431480	−	0.747345i	0.997001	+	0.0773890i	$0.0246584\pi$
$822$	−15.8773	−	2.05905i	−0.553785	−	0.0718176i
$823$	−12.3905	+	7.15364i	−0.431905	+	0.249360i	−0.700158	−	0.713988i	$-0.746887\pi$
$823$	−12.3905	+	7.15364i	−0.431905	+	0.249360i	0.268253	+	0.963348i	$0.413554\pi$
$824$	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	$-0.580582\pi$
$827$	−14.4053			−0.500921			−0.250461	+	0.968127i	$0.580582\pi$
$828$	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
$837$	28.2056	−	6.43768i	0.974928	−	0.222519i
$838$	25.0793			0.866350
$839$	−49.1296	−	28.3650i	−1.69614	−	0.979267i	−0.949356	−	0.314202i	$-0.898263\pi$
$839$	−49.1296	−	28.3650i	−1.69614	−	0.979267i	−0.746785	−	0.665066i	$-0.768403\pi$
$840$	−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	−0.927613	−	0.373544i	$-0.878143\pi$
$853$	−4.09786	+	7.09770i	−0.140308	+	0.243021i	0.787305	+	0.616564i	$0.211476\pi$
$854$	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	0.887767	−	0.460294i	$-0.152256\pi$
$857$	27.3139	+	15.7697i	0.933024	+	0.538682i	0.0452574	+	0.998975i	$0.485589\pi$
$858$	−21.1943	+	8.82704i	−0.723562	+	0.301350i
$859$	−32.1588	+	18.5669i	−1.09724	+	0.633494i	−0.935496	−	0.353338i	$-0.885046\pi$
$859$	−32.1588	+	18.5669i	−1.09724	+	0.633494i	−0.161748	+	0.986832i	$0.551713\pi$
$860$	−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	$-0.462132\pi$
$863$	6.97322			0.237371			0.118686	+	0.992932i	$0.462132\pi$
$864$	−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
$868$	10.3651	+	14.7894i	0.351814	+	0.501986i
$869$	−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	0.585369	−	0.810767i	$-0.300949\pi$
$877$	−12.1258	−	21.0025i	−0.409460	−	0.709205i	−0.994829	+	0.101562i	$0.967616\pi$
$878$	−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	$-0.449844\pi$
$881$	9.31513			0.313835			0.156917	+	0.987612i	$0.449844\pi$
$882$	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	−0.166958	−	0.985964i	$-0.553394\pi$
$887$	17.9718	−	10.3760i	0.603433	−	0.348392i	0.770391	+	0.637572i	$0.220061\pi$
$888$	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	−0.913247	−	0.407406i	$-0.866433\pi$
$907$	−3.12607	+	5.41452i	−0.103800	+	0.179786i	0.809448	+	0.587192i	$0.199767\pi$
$908$			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	−0.436189	−	0.899855i	$-0.643672\pi$
$911$	16.9387	−	29.3386i	0.561203	−	0.972032i	0.997392	−	0.0721767i	$-0.0229946\pi$
$912$	−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	$-0.830647\pi$
$929$	0.257250	−	0.445570i	0.00844009	−	0.0146187i	0.870215	+	0.492673i	$0.163980\pi$
$930$	0.803519	−	19.4583i	0.0263484	−	0.638063i
$931$	−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	$-0.00220791\pi$
$941$	15.1532	+	26.2462i	0.493981	+	0.855600i	−0.505995	+	0.862536i	$0.668875\pi$
$942$	−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	$-0.872947\pi$
$947$	−3.81988	+	6.61623i	−0.124130	+	0.214999i	0.797263	+	0.603632i	$0.206280\pi$
$948$	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	$-0.483184\pi$
$953$	3.26013			0.105606			0.0528030	+	0.998605i	$0.483184\pi$
$954$	−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
$961$	−10.5777	+	29.1395i	−0.341216	+	0.939985i
$962$			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	$-0.376982\pi$
$967$	42.5258	−	24.5523i	1.36754	−	0.789548i	0.990613	+	0.136696i	$0.0436482\pi$
$968$	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	$0.112168\pi$
$971$			21.5097i			0.690278i	−0.938552	+	0.345139i	$0.887832\pi$
$972$	−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	−0.424360	−	0.905493i	$-0.639501\pi$
$977$	4.61478	−	2.66434i	0.147640	−	0.0852399i	0.572000	+	0.820254i	$0.306168\pi$
$978$	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	$-0.980491\pi$
$983$	−13.9839	+	24.2208i	−0.446017	+	0.772525i	0.552105	+	0.833774i	$0.313825\pi$
$984$	−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	$-0.0146811\pi$
$992$	5.04711	+	2.35088i	0.160246	+	0.0746405i
$993$	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	0.325648	+	0.945491i	$0.394418\pi$
$997$	−20.7133	+	35.8764i	−0.655996	+	1.13622i	−0.981643	+	0.190727i	$0.938916\pi$
$998$	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.371.29	yes	64
3.2	odd	2		1674.2.q.a.1115.2		64
9.4	even	3		1674.2.q.a.557.9		64
9.5	odd	6	inner	558.2.q.a.185.20	✓	64
31.30	odd	2	inner	558.2.q.a.371.20	yes	64
93.92	even	2		1674.2.q.a.1115.9		64
279.185	even	6	inner	558.2.q.a.185.29	yes	64
279.247	odd	6		1674.2.q.a.557.2		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.20	✓	64	9.5	odd	6	inner
558.2.q.a.185.29	yes	64	279.185	even	6	inner
558.2.q.a.371.20	yes	64	31.30	odd	2	inner
558.2.q.a.371.29	yes	64	1.1	even	1	trivial
1674.2.q.a.557.2		64	279.247	odd	6
1674.2.q.a.557.9		64	9.4	even	3
1674.2.q.a.1115.2		64	3.2	odd	2
1674.2.q.a.1115.9		64	93.92	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
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} +(-3.19549 - 4.55948i) 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} +(0.397890 - 9.63544i) 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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