LMFDB - Embedded newform 187.2.e.b.89.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(89,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("187.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.3
Character	$\chi$	$=$	187.89
Dual form			187.2.e.b.166.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90463i q^{2} +(-1.14033 + 1.14033i) q^{3} -1.62763 q^{4} +(-2.29152 + 2.29152i) q^{5} +(2.17192 + 2.17192i) q^{6} +(3.32922 + 3.32922i) q^{7} -0.709222i q^{8} +0.399285i q^{9} +O(q^{10})$	\(q-1.90463i q^{2} +(-1.14033 + 1.14033i) q^{3} -1.62763 q^{4} +(-2.29152 + 2.29152i) q^{5} +(2.17192 + 2.17192i) q^{6} +(3.32922 + 3.32922i) q^{7} -0.709222i q^{8} +0.399285i q^{9} +(4.36451 + 4.36451i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(1.85604 - 1.85604i) q^{12} +2.85253 q^{13} +(6.34095 - 6.34095i) q^{14} -5.22619i q^{15} -4.60608 q^{16} +(-3.62388 + 1.96660i) q^{17} +0.760491 q^{18} +3.83050i q^{19} +(3.72975 - 3.72975i) q^{20} -7.59283 q^{21} +(-1.34678 + 1.34678i) q^{22} +(3.28150 + 3.28150i) q^{23} +(0.808748 + 0.808748i) q^{24} -5.50212i q^{25} -5.43302i q^{26} +(-3.87631 - 3.87631i) q^{27} +(-5.41875 - 5.41875i) q^{28} +(3.14919 - 3.14919i) q^{29} -9.95398 q^{30} +(1.43907 - 1.43907i) q^{31} +7.35445i q^{32} +1.61267 q^{33} +(3.74565 + 6.90216i) q^{34} -15.2579 q^{35} -0.649889i q^{36} +(1.52989 - 1.52989i) q^{37} +7.29570 q^{38} +(-3.25283 + 3.25283i) q^{39} +(1.62519 + 1.62519i) q^{40} +(5.52729 + 5.52729i) q^{41} +14.4616i q^{42} -12.7194i q^{43} +(1.15091 + 1.15091i) q^{44} +(-0.914968 - 0.914968i) q^{45} +(6.25006 - 6.25006i) q^{46} -5.54760 q^{47} +(5.25246 - 5.25246i) q^{48} +15.1674i q^{49} -10.4795 q^{50} +(1.88985 - 6.37500i) q^{51} -4.64287 q^{52} -4.51499i q^{53} +(-7.38296 + 7.38296i) q^{54} +3.24070 q^{55} +(2.36115 - 2.36115i) q^{56} +(-4.36804 - 4.36804i) q^{57} +(-5.99806 - 5.99806i) q^{58} -0.104183i q^{59} +8.50632i q^{60} +(3.14970 + 3.14970i) q^{61} +(-2.74091 - 2.74091i) q^{62} +(-1.32931 + 1.32931i) q^{63} +4.79539 q^{64} +(-6.53662 + 6.53662i) q^{65} -3.07155i q^{66} -2.20907 q^{67} +(5.89835 - 3.20090i) q^{68} -7.48400 q^{69} +29.0608i q^{70} +(3.31785 - 3.31785i) q^{71} +0.283181 q^{72} +(2.33617 - 2.33617i) q^{73} +(-2.91388 - 2.91388i) q^{74} +(6.27424 + 6.27424i) q^{75} -6.23465i q^{76} -4.70823i q^{77} +(6.19545 + 6.19545i) q^{78} +(-4.15365 - 4.15365i) q^{79} +(10.5549 - 10.5549i) q^{80} +7.64272 q^{81} +(10.5275 - 10.5275i) q^{82} -15.1373i q^{83} +12.3584 q^{84} +(3.79769 - 12.8107i) q^{85} -24.2257 q^{86} +7.18225i q^{87} +(-0.501495 + 0.501495i) q^{88} +18.3246 q^{89} +(-1.74268 + 1.74268i) q^{90} +(9.49669 + 9.49669i) q^{91} +(-5.34108 - 5.34108i) q^{92} +3.28205i q^{93} +10.5661i q^{94} +(-8.77765 - 8.77765i) q^{95} +(-8.38652 - 8.38652i) q^{96} +(-3.71120 + 3.71120i) q^{97} +28.8884 q^{98} +(0.282337 - 0.282337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.90463i		−	1.34678i	−0.739287	−	0.673390i	$-0.764837\pi$
$2$		−	1.90463i		−	1.34678i	0.739287	−	0.673390i	$-0.235163\pi$
$3$	−1.14033	+	1.14033i	−0.658371	+	0.658371i	−0.954995	−	0.296623i	$-0.904139\pi$
$3$	−1.14033	+	1.14033i	−0.658371	+	0.658371i	0.296623	+	0.954995i	$0.404139\pi$
$4$	−1.62763			−0.813817
$5$	−2.29152	+	2.29152i	−1.02480	+	1.02480i	−0.0251137	+	0.999685i	$0.507995\pi$
$5$	−2.29152	+	2.29152i	−1.02480	+	1.02480i	−0.999685	+	0.0251137i	$0.992005\pi$
$6$	2.17192	+	2.17192i	0.886681	+	0.886681i
$7$	3.32922	+	3.32922i	1.25833	+	1.25833i	0.951892	+	0.306435i	$0.0991363\pi$
$7$	3.32922	+	3.32922i	1.25833	+	1.25833i	0.306435	+	0.951892i	$0.400864\pi$
$8$		−	0.709222i		−	0.250748i
$9$			0.399285i			0.133095i
$10$	4.36451	+	4.36451i	1.38018	+	1.38018i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$12$	1.85604	−	1.85604i	0.535794	−	0.535794i
$13$	2.85253			0.791149			0.395574	−	0.918434i	$-0.370546\pi$
$13$	2.85253			0.791149			0.395574	+	0.918434i	$0.370546\pi$
$14$	6.34095	−	6.34095i	1.69469	−	1.69469i
$15$		−	5.22619i		−	1.34940i
$16$	−4.60608			−1.15152
$17$	−3.62388	+	1.96660i	−0.878919	+	0.476970i
$17$	−3.62388	+	1.96660i	−0.878919	+	0.476970i
$18$	0.760491			0.179249
$19$			3.83050i			0.878776i	0.898297	+	0.439388i	$0.144805\pi$
$19$			3.83050i			0.878776i	−0.898297	+	0.439388i	$0.855195\pi$
$20$	3.72975	−	3.72975i	0.833998	−	0.833998i
$21$	−7.59283			−1.65689
$22$	−1.34678	+	1.34678i	−0.287135	+	0.287135i
$23$	3.28150	+	3.28150i	0.684240	+	0.684240i	0.960953	−	0.276712i	$-0.0892450\pi$
$23$	3.28150	+	3.28150i	0.684240	+	0.684240i	−0.276712	+	0.960953i	$0.589245\pi$
$24$	0.808748	+	0.808748i	0.165085	+	0.165085i
$25$		−	5.50212i		−	1.10042i
$26$		−	5.43302i		−	1.06550i
$27$	−3.87631	−	3.87631i	−0.745997	−	0.745997i
$28$	−5.41875	−	5.41875i	−1.02405	−	1.02405i
$29$	3.14919	−	3.14919i	0.584791	−	0.584791i	−0.351425	−	0.936216i	$-0.614303\pi$
$29$	3.14919	−	3.14919i	0.584791	−	0.584791i	0.936216	+	0.351425i	$0.114303\pi$
$30$	−9.95398			−1.81734
$31$	1.43907	−	1.43907i	0.258465	−	0.258465i	−0.565964	−	0.824430i	$-0.691496\pi$
$31$	1.43907	−	1.43907i	0.258465	−	0.258465i	0.824430	+	0.565964i	$0.191496\pi$
$32$			7.35445i			1.30010i
$33$	1.61267			0.280730
$34$	3.74565	+	6.90216i	0.642374	+	1.18371i
$35$	−15.2579			−2.57906
$36$		−	0.649889i		−	0.108315i
$37$	1.52989	−	1.52989i	0.251512	−	0.251512i	−0.570078	−	0.821590i	$-0.693087\pi$
$37$	1.52989	−	1.52989i	0.251512	−	0.251512i	0.821590	+	0.570078i	$0.193087\pi$
$38$	7.29570			1.18352
$39$	−3.25283	+	3.25283i	−0.520870	+	0.520870i
$40$	1.62519	+	1.62519i	0.256966	+	0.256966i
$41$	5.52729	+	5.52729i	0.863217	+	0.863217i	0.991710	−	0.128493i	$-0.0410141\pi$
$41$	5.52729	+	5.52729i	0.863217	+	0.863217i	−0.128493	+	0.991710i	$0.541014\pi$
$42$			14.4616i			2.23147i
$43$		−	12.7194i		−	1.93968i	−0.243736	−	0.969842i	$-0.578373\pi$
$43$		−	12.7194i		−	1.93968i	0.243736	−	0.969842i	$-0.421627\pi$
$44$	1.15091	+	1.15091i	0.173506	+	0.173506i
$45$	−0.914968	−	0.914968i	−0.136395	−	0.136395i
$46$	6.25006	−	6.25006i	0.921521	−	0.921521i
$47$	−5.54760			−0.809200			−0.404600	−	0.914494i	$-0.632589\pi$
$47$	−5.54760			−0.809200			−0.404600	+	0.914494i	$0.632589\pi$
$48$	5.25246	−	5.25246i	0.758127	−	0.758127i
$49$			15.1674i			2.16677i
$50$	−10.4795			−1.48203
$51$	1.88985	−	6.37500i	0.264632	−	0.892679i
$52$	−4.64287			−0.643850
$53$		−	4.51499i		−	0.620182i	−0.950707	−	0.310091i	$-0.899641\pi$
$53$		−	4.51499i		−	0.620182i	0.950707	−	0.310091i	$-0.100359\pi$
$54$	−7.38296	+	7.38296i	−1.00469	+	1.00469i
$55$	3.24070			0.436975
$56$	2.36115	−	2.36115i	0.315523	−	0.315523i
$57$	−4.36804	−	4.36804i	−0.578561	−	0.578561i
$58$	−5.99806	−	5.99806i	−0.787584	−	0.787584i
$59$		−	0.104183i		−	0.0135635i	−0.999977	−	0.00678175i	$-0.997841\pi$
$59$		−	0.104183i		−	0.0135635i	0.999977	−	0.00678175i	$-0.00215872\pi$
$60$			8.50632i			1.09816i
$61$	3.14970	+	3.14970i	0.403277	+	0.403277i	0.879386	−	0.476109i	$-0.157953\pi$
$61$	3.14970	+	3.14970i	0.403277	+	0.403277i	−0.476109	+	0.879386i	$0.657953\pi$
$62$	−2.74091	−	2.74091i	−0.348096	−	0.348096i
$63$	−1.32931	+	1.32931i	−0.167477	+	0.167477i
$64$	4.79539			0.599424
$65$	−6.53662	+	6.53662i	−0.810768	+	0.810768i
$66$		−	3.07155i		−	0.378082i
$67$	−2.20907			−0.269881			−0.134941	−	0.990854i	$-0.543084\pi$
$67$	−2.20907			−0.269881			−0.134941	+	0.990854i	$0.543084\pi$
$68$	5.89835	−	3.20090i	0.715280	−	0.388166i
$69$	−7.48400			−0.900968
$70$			29.0608i			3.47343i
$71$	3.31785	−	3.31785i	0.393756	−	0.393756i	−0.482268	−	0.876024i	$-0.660187\pi$
$71$	3.31785	−	3.31785i	0.393756	−	0.393756i	0.876024	+	0.482268i	$0.160187\pi$
$72$	0.283181			0.0333732
$73$	2.33617	−	2.33617i	0.273428	−	0.273428i	−0.557050	−	0.830479i	$-0.688067\pi$
$73$	2.33617	−	2.33617i	0.273428	−	0.273428i	0.830479	+	0.557050i	$0.188067\pi$
$74$	−2.91388	−	2.91388i	−0.338732	−	0.338732i
$75$	6.27424	+	6.27424i	0.724487	+	0.724487i
$76$		−	6.23465i		−	0.715163i
$77$		−	4.70823i		−	0.536552i
$78$	6.19545	+	6.19545i	0.701497	+	0.701497i
$79$	−4.15365	−	4.15365i	−0.467322	−	0.467322i	0.433724	−	0.901046i	$-0.357199\pi$
$79$	−4.15365	−	4.15365i	−0.467322	−	0.467322i	−0.901046	+	0.433724i	$0.857199\pi$
$80$	10.5549	−	10.5549i	1.18007	−	1.18007i
$81$	7.64272			0.849191
$82$	10.5275	−	10.5275i	1.16256	−	1.16256i
$83$		−	15.1373i		−	1.66153i	−0.556620	−	0.830767i	$-0.687902\pi$
$83$		−	15.1373i		−	1.66153i	0.556620	−	0.830767i	$-0.312098\pi$
$84$	12.3584			1.34841
$85$	3.79769	−	12.8107i	0.411917	−	1.38951i
$86$	−24.2257			−2.61233
$87$			7.18225i			0.770019i
$88$	−0.501495	+	0.501495i	−0.0534596	+	0.0534596i
$89$	18.3246			1.94240			0.971200	−	0.238267i	$-0.0765793\pi$
$89$	18.3246			1.94240			0.971200	+	0.238267i	$0.0765793\pi$
$90$	−1.74268	+	1.74268i	−0.183695	+	0.183695i
$91$	9.49669	+	9.49669i	0.995524	+	0.995524i
$92$	−5.34108	−	5.34108i	−0.556846	−	0.556846i
$93$			3.28205i			0.340332i
$94$			10.5661i			1.08981i
$95$	−8.77765	−	8.77765i	−0.900568	−	0.900568i
$96$	−8.38652	−	8.38652i	−0.855945	−	0.855945i
$97$	−3.71120	+	3.71120i	−0.376816	+	0.376816i	−0.869952	−	0.493136i	$-0.835850\pi$
$97$	−3.71120	+	3.71120i	−0.376816	+	0.376816i	0.493136	+	0.869952i	$0.335850\pi$
$98$	28.8884			2.91817
$99$	0.282337	−	0.282337i	0.0283759	−	0.0283759i
$100$			8.95543i			0.895543i
$101$	16.8030			1.67196			0.835982	−	0.548756i	$-0.184898\pi$
$101$	16.8030			1.67196			0.835982	+	0.548756i	$0.184898\pi$
$102$	−12.1420	−	3.59947i	−1.20224	−	0.356401i
$103$	9.95958			0.981346			0.490673	−	0.871344i	$-0.336751\pi$
$103$	9.95958			0.981346			0.490673	+	0.871344i	$0.336751\pi$
$104$		−	2.02307i		−	0.198379i
$105$	17.3991	−	17.3991i	1.69798	−	1.69798i
$106$	−8.59941			−0.835249
$107$	−8.42743	+	8.42743i	−0.814711	+	0.814711i	−0.985336	−	0.170625i	$-0.945421\pi$
$107$	−8.42743	+	8.42743i	−0.814711	+	0.814711i	0.170625	+	0.985336i	$0.445421\pi$
$108$	6.30922	+	6.30922i	0.607105	+	0.607105i
$109$	8.46035	+	8.46035i	0.810354	+	0.810354i	0.984687	−	0.174333i	$-0.0557768\pi$
$109$	8.46035	+	8.46035i	0.810354	+	0.810354i	−0.174333	+	0.984687i	$0.555777\pi$
$110$		−	6.17234i		−	0.588510i
$111$			3.48917i			0.331177i
$112$	−15.3346	−	15.3346i	−1.44899	−	1.44899i
$113$	1.16546	+	1.16546i	0.109637	+	0.109637i	0.759797	−	0.650160i	$-0.225298\pi$
$113$	1.16546	+	1.16546i	0.109637	+	0.109637i	−0.650160	+	0.759797i	$0.725298\pi$
$114$	−8.31952	+	8.31952i	−0.779194	+	0.779194i
$115$	−15.0392			−1.40242
$116$	−5.12573	+	5.12573i	−0.475913	+	0.475913i
$117$			1.13897i			0.105298i
$118$	−0.198431			−0.0182671
$119$	−18.6119	−	5.51745i	−1.70615	−	0.505783i
$120$	−3.70652			−0.338358
$121$			1.00000i			0.0909091i
$122$	5.99902	−	5.99902i	0.543126	−	0.543126i
$123$	−12.6059			−1.13663
$124$	−2.34229	+	2.34229i	−0.210343	+	0.210343i
$125$	1.15061	+	1.15061i	0.102914	+	0.102914i
$126$	2.53184	+	2.53184i	0.225554	+	0.225554i
$127$		−	8.01721i		−	0.711413i	−0.934598	−	0.355706i	$-0.884240\pi$
$127$		−	8.01721i		−	0.711413i	0.934598	−	0.355706i	$-0.115760\pi$
$128$			5.57543i			0.492803i
$129$	14.5043	+	14.5043i	1.27703	+	1.27703i
$130$	12.4499	+	12.4499i	1.09193	+	1.09193i
$131$	−6.61845	+	6.61845i	−0.578257	+	0.578257i	−0.934423	−	0.356166i	$-0.884084\pi$
$131$	−6.61845	+	6.61845i	−0.578257	+	0.578257i	0.356166	+	0.934423i	$0.384084\pi$
$132$	−2.62484			−0.228463
$133$	−12.7526	+	12.7526i	−1.10579	+	1.10579i
$134$			4.20748i			0.363471i
$135$	17.7653			1.52899
$136$	1.39475	+	2.57013i	0.119599	+	0.220387i
$137$	14.0491			1.20029			0.600147	−	0.799890i	$-0.295109\pi$
$137$	14.0491			1.20029			0.600147	+	0.799890i	$0.295109\pi$
$138$			14.2543i			1.21341i
$139$	−3.31741	+	3.31741i	−0.281379	+	0.281379i	−0.833659	−	0.552280i	$-0.813758\pi$
$139$	−3.31741	+	3.31741i	−0.281379	+	0.281379i	0.552280	+	0.833659i	$0.313758\pi$
$140$	24.8343			2.09888
$141$	6.32610	−	6.32610i	0.532754	−	0.532754i
$142$	−6.31929	−	6.31929i	−0.530303	−	0.530303i
$143$	−2.01704	−	2.01704i	−0.168673	−	0.168673i
$144$		−	1.83913i		−	0.153261i
$145$			14.4329i			1.19858i
$146$	−4.44955	−	4.44955i	−0.368248	−	0.368248i
$147$	−17.2959	−	17.2959i	−1.42654	−	1.42654i
$148$	−2.49010	+	2.49010i	−0.204685	+	0.204685i
$149$	−5.60556			−0.459225			−0.229612	−	0.973282i	$-0.573746\pi$
$149$	−5.60556			−0.459225			−0.229612	+	0.973282i	$0.573746\pi$
$150$	11.9501	−	11.9501i	0.975725	−	0.975725i
$151$			6.24868i			0.508510i	0.967137	+	0.254255i	$0.0818303\pi$
$151$			6.24868i			0.508510i	−0.967137	+	0.254255i	$0.918170\pi$
$152$	2.71667			0.220351
$153$	−0.785232	−	1.44696i	−0.0634823	−	0.116980i
$154$	−8.96745			−0.722618
$155$			6.59533i			0.529750i
$156$	5.29442	−	5.29442i	0.423892	−	0.423892i
$157$	−8.79044			−0.701554			−0.350777	−	0.936459i	$-0.614082\pi$
$157$	−8.79044			−0.701554			−0.350777	+	0.936459i	$0.614082\pi$
$158$	−7.91118	+	7.91118i	−0.629380	+	0.629380i
$159$	5.14859	+	5.14859i	0.408310	+	0.408310i
$160$	−16.8529	−	16.8529i	−1.33234	−	1.33234i
$161$			21.8497i			1.72200i
$162$		−	14.5566i		−	1.14367i
$163$	2.78327	+	2.78327i	0.218003	+	0.218003i	0.807656	−	0.589654i	$-0.200736\pi$
$163$	2.78327	+	2.78327i	0.218003	+	0.218003i	−0.589654	+	0.807656i	$0.700736\pi$
$164$	−8.99640	−	8.99640i	−0.702501	−	0.702501i
$165$	−3.69547	+	3.69547i	−0.287692	+	0.287692i
$166$	−28.8310			−2.23772
$167$	−10.0304	+	10.0304i	−0.776173	+	0.776173i	−0.979178	−	0.203005i	$-0.934929\pi$
$167$	−10.0304	+	10.0304i	−0.776173	+	0.776173i	0.203005	+	0.979178i	$0.434929\pi$
$168$			5.38500i			0.415462i
$169$	−4.86309			−0.374084
$170$	−24.3997	−	7.23321i	−1.87137	−	0.554762i
$171$	−1.52946			−0.116961
$172$			20.7024i			1.57855i
$173$	2.17831	−	2.17831i	0.165614	−	0.165614i	−0.619434	−	0.785048i	$-0.712638\pi$
$173$	2.17831	−	2.17831i	0.165614	−	0.165614i	0.785048	+	0.619434i	$0.212638\pi$
$174$	13.6796			1.03705
$175$	18.3178	−	18.3178i	1.38469	−	1.38469i
$176$	3.25699	+	3.25699i	0.245505	+	0.245505i
$177$	0.118804	+	0.118804i	0.00892982	+	0.00892982i
$178$		−	34.9016i		−	2.61599i
$179$			4.53200i			0.338738i	0.985553	+	0.169369i	$0.0541729\pi$
$179$			4.53200i			0.338738i	−0.985553	+	0.169369i	$0.945827\pi$
$180$	1.48923	+	1.48923i	0.111001	+	0.111001i
$181$	−9.95002	−	9.95002i	−0.739579	−	0.739579i	0.232917	−	0.972497i	$-0.425173\pi$
$181$	−9.95002	−	9.95002i	−0.739579	−	0.739579i	−0.972497	+	0.232917i	$0.925173\pi$
$182$	18.0877	−	18.0877i	1.34075	−	1.34075i
$183$	−7.18340			−0.531012
$184$	2.32731	−	2.32731i	0.171572	−	0.171572i
$185$			7.01154i			0.515499i
$186$	6.25110			0.458353
$187$	3.95306	+	1.17187i	0.289077	+	0.0856959i
$188$	9.02946			0.658541
$189$		−	25.8102i		−	1.87742i
$190$	−16.7182	+	16.7182i	−1.21287	+	1.21287i
$191$	−2.48308			−0.179669			−0.0898346	−	0.995957i	$-0.528634\pi$
$191$	−2.48308			−0.179669			−0.0898346	+	0.995957i	$0.528634\pi$
$192$	−5.46834	+	5.46834i	−0.394643	+	0.394643i
$193$	−4.07547	−	4.07547i	−0.293358	−	0.293358i	0.545047	−	0.838405i	$-0.316512\pi$
$193$	−4.07547	−	4.07547i	−0.293358	−	0.293358i	−0.838405	+	0.545047i	$0.816512\pi$
$194$	7.06849	+	7.06849i	0.507488	+	0.507488i
$195$		−	14.9078i		−	1.06757i
$196$		−	24.6870i		−	1.76336i
$197$	10.5674	+	10.5674i	0.752894	+	0.752894i	0.975018	−	0.222124i	$-0.0712991\pi$
$197$	10.5674	+	10.5674i	0.752894	+	0.752894i	−0.222124	+	0.975018i	$0.571299\pi$
$198$	−0.537748	−	0.537748i	−0.0382161	−	0.0382161i
$199$	12.3517	−	12.3517i	0.875586	−	0.875586i	−0.117489	−	0.993074i	$-0.537484\pi$
$199$	12.3517	−	12.3517i	0.875586	−	0.875586i	0.993074	+	0.117489i	$0.0374844\pi$
$200$	−3.90222			−0.275929
$201$	2.51908	−	2.51908i	0.177682	−	0.177682i
$202$		−	32.0037i		−	2.25177i
$203$	20.9687			1.47172
$204$	−3.07598	+	10.3762i	−0.215362	+	0.726477i
$205$	−25.3318			−1.76925
$206$		−	18.9694i		−	1.32166i
$207$	−1.31025	+	1.31025i	−0.0910689	+	0.0910689i
$208$	−13.1390			−0.911023
$209$	2.70857	−	2.70857i	0.187356	−	0.187356i
$210$	−33.1390	−	33.1390i	−2.28681	−	2.28681i
$211$	12.1673	+	12.1673i	0.837630	+	0.837630i	0.988546	−	0.150917i	$-0.0482225\pi$
$211$	12.1673	+	12.1673i	0.837630	+	0.837630i	−0.150917	+	0.988546i	$0.548223\pi$
$212$			7.34875i			0.504714i
$213$			7.56690i			0.518475i
$214$	16.0512	+	16.0512i	1.09724	+	1.09724i
$215$	29.1466	+	29.1466i	1.98778	+	1.98778i
$216$	−2.74917	+	2.74917i	−0.187057	+	0.187057i
$217$	9.58199			0.650468
$218$	16.1139	−	16.1139i	1.09137	−	1.09137i
$219$			5.32802i			0.360035i
$220$	−5.27467			−0.355618
$221$	−10.3372	+	5.60978i	−0.695356	+	0.377354i
$222$	6.64559			0.446022
$223$		−	6.77020i		−	0.453366i	−0.973969	−	0.226683i	$-0.927212\pi$
$223$		−	6.77020i		−	0.453366i	0.973969	−	0.226683i	$-0.0727881\pi$
$224$	−24.4846	+	24.4846i	−1.63594	+	1.63594i
$225$	2.19691			0.146461
$226$	2.21977	−	2.21977i	0.147657	−	0.147657i
$227$	−16.6386	−	16.6386i	−1.10434	−	1.10434i	−0.993880	−	0.110462i	$-0.964767\pi$
$227$	−16.6386	−	16.6386i	−1.10434	−	1.10434i	−0.110462	−	0.993880i	$-0.535233\pi$
$228$	7.10957	+	7.10957i	0.470843	+	0.470843i
$229$		−	3.01597i		−	0.199301i	−0.995023	−	0.0996504i	$-0.968228\pi$
$229$		−	3.01597i		−	0.199301i	0.995023	−	0.0996504i	$-0.0317725\pi$
$230$			28.6443i			1.88875i
$231$	5.36894	+	5.36894i	0.353251	+	0.353251i
$232$	−2.23348	−	2.23348i	−0.146635	−	0.146635i
$233$	4.93982	−	4.93982i	0.323618	−	0.323618i	−0.526535	−	0.850153i	$-0.676509\pi$
$233$	4.93982	−	4.93982i	0.323618	−	0.323618i	0.850153	+	0.526535i	$0.176509\pi$
$234$	2.16932			0.141813
$235$	12.7124	−	12.7124i	0.829267	−	0.829267i
$236$			0.169572i			0.0110382i
$237$	9.47308			0.615342
$238$	−10.5087	+	35.4489i	−0.681179	+	2.29781i
$239$	−8.82716			−0.570982			−0.285491	−	0.958381i	$-0.592157\pi$
$239$	−8.82716			−0.570982			−0.285491	+	0.958381i	$0.592157\pi$
$240$			24.0722i			1.55385i
$241$	−7.71115	+	7.71115i	−0.496719	+	0.496719i	−0.910415	−	0.413696i	$-0.864238\pi$
$241$	−7.71115	+	7.71115i	−0.496719	+	0.496719i	0.413696	+	0.910415i	$0.364238\pi$
$242$	1.90463			0.122435
$243$	2.91370	−	2.91370i	0.186914	−	0.186914i
$244$	−5.12655	−	5.12655i	−0.328194	−	0.328194i
$245$	−34.7564	−	34.7564i	−2.22050	−	2.22050i
$246$			24.0096i			1.53080i
$247$			10.9266i			0.695243i
$248$	−1.02062	−	1.02062i	−0.0648096	−	0.0648096i
$249$	17.2615	+	17.2615i	1.09391	+	1.09391i
$250$	2.19149	−	2.19149i	0.138602	−	0.138602i
$251$	5.99482			0.378390			0.189195	−	0.981940i	$-0.439412\pi$
$251$	5.99482			0.378390			0.189195	+	0.981940i	$0.439412\pi$
$252$	2.16362	−	2.16362i	0.136295	−	0.136295i
$253$		−	4.64074i		−	0.291761i
$254$	−15.2699			−0.958117
$255$	10.2778	+	18.9391i	0.643621	+	1.18601i
$256$	20.2099			1.26312
$257$		−	6.90411i		−	0.430667i	−0.976541	−	0.215333i	$-0.930916\pi$
$257$		−	6.90411i		−	0.430667i	0.976541	−	0.215333i	$-0.0690838\pi$
$258$	27.6254	−	27.6254i	1.71988	−	1.71988i
$259$	10.1867			0.632969
$260$	10.6392	−	10.6392i	0.659817	−	0.659817i
$261$	1.25742	+	1.25742i	0.0778326	+	0.0778326i
$262$	12.6057	+	12.6057i	0.778785	+	0.778785i
$263$		−	16.5475i		−	1.02036i	−0.860067	−	0.510181i	$-0.829578\pi$
$263$		−	16.5475i		−	1.02036i	0.860067	−	0.510181i	$-0.170422\pi$
$264$		−	1.14374i		−	0.0703925i
$265$	10.3462	+	10.3462i	0.635561	+	0.635561i
$266$	24.2890	+	24.2890i	1.48925	+	1.48925i
$267$	−20.8961	+	20.8961i	−1.27882	+	1.27882i
$268$	3.59556			0.219634
$269$	−7.03563	+	7.03563i	−0.428970	+	0.428970i	−0.888277	−	0.459308i	$-0.848098\pi$
$269$	−7.03563	+	7.03563i	−0.428970	+	0.428970i	0.459308	+	0.888277i	$0.348098\pi$
$270$		−	33.8364i		−	2.05922i
$271$	−20.1423			−1.22356			−0.611780	−	0.791028i	$-0.709546\pi$
$271$	−20.1423			−1.22356			−0.611780	+	0.791028i	$0.709546\pi$
$272$	16.6919	−	9.05830i	1.01209	−	0.549240i
$273$	−21.6588			−1.31085
$274$		−	26.7584i		−	1.61653i
$275$	−3.89058	+	3.89058i	−0.234611	+	0.234611i
$276$	12.1812			0.733223
$277$	−14.0043	+	14.0043i	−0.841435	+	0.841435i	−0.989046	−	0.147611i	$-0.952842\pi$
$277$	−14.0043	+	14.0043i	−0.841435	+	0.841435i	0.147611	+	0.989046i	$0.452842\pi$
$278$	6.31845	+	6.31845i	0.378955	+	0.378955i
$279$	0.574600	+	0.574600i	0.0344004	+	0.0344004i
$280$			10.8213i			0.646694i
$281$			14.0335i			0.837169i	0.908178	+	0.418585i	$0.137474\pi$
$281$			14.0335i			0.837169i	−0.908178	+	0.418585i	$0.862526\pi$
$282$	−12.0489	−	12.0489i	−0.717503	−	0.717503i
$283$	−11.0694	−	11.0694i	−0.658006	−	0.658006i	0.296902	−	0.954908i	$-0.404046\pi$
$283$	−11.0694	−	11.0694i	−0.658006	−	0.658006i	−0.954908	+	0.296902i	$0.904046\pi$
$284$	−5.40024	+	5.40024i	−0.320445	+	0.320445i
$285$	20.0189			1.18582
$286$	−3.84173	+	3.84173i	−0.227166	+	0.227166i
$287$			36.8031i			2.17242i
$288$	−2.93652			−0.173036
$289$	9.26498	−	14.2534i	0.544999	−	0.838437i
$290$	27.4894			1.61423
$291$		−	8.46401i		−	0.496169i
$292$	−3.80243	+	3.80243i	−0.222521	+	0.222521i
$293$	−9.06181			−0.529397			−0.264698	−	0.964331i	$-0.585272\pi$
$293$	−9.06181			−0.529397			−0.264698	+	0.964331i	$0.585272\pi$
$294$	−32.9423	+	32.9423i	−1.92124	+	1.92124i
$295$	0.238738	+	0.238738i	0.0138999	+	0.0138999i
$296$	−1.08503	−	1.08503i	−0.0630661	−	0.0630661i
$297$			5.48194i			0.318094i
$298$			10.6765i			0.618475i
$299$	9.36057	+	9.36057i	0.541336	+	0.541336i
$300$	−10.2122	−	10.2122i	−0.589600	−	0.589600i
$301$	42.3455	−	42.3455i	2.44076	−	2.44076i
$302$	11.9015			0.684852
$303$	−19.1610	+	19.1610i	−1.10077	+	1.10077i
$304$		−	17.6436i		−	1.01193i
$305$	−14.4352			−0.826556
$306$	−2.75593	+	1.49558i	−0.157546	+	0.0854967i
$307$	23.5369			1.34332			0.671661	−	0.740859i	$-0.265581\pi$
$307$	23.5369			1.34332			0.671661	+	0.740859i	$0.265581\pi$
$308$			7.66327i			0.436655i
$309$	−11.3572	+	11.3572i	−0.646090	+	0.646090i
$310$	12.5617			0.713456
$311$	−6.39363	+	6.39363i	−0.362549	+	0.362549i	−0.864751	−	0.502201i	$-0.832524\pi$
$311$	−6.39363	+	6.39363i	−0.362549	+	0.362549i	0.502201	+	0.864751i	$0.332524\pi$
$312$	2.30698	+	2.30698i	0.130607	+	0.130607i
$313$	−11.1588	−	11.1588i	−0.630735	−	0.630735i	0.317518	−	0.948252i	$-0.397151\pi$
$313$	−11.1588	−	11.1588i	−0.630735	−	0.630735i	−0.948252	+	0.317518i	$0.897151\pi$
$314$			16.7426i			0.944838i
$315$		−	6.09226i		−	0.343260i
$316$	6.76062	+	6.76062i	0.380314	+	0.380314i
$317$	−17.2668	−	17.2668i	−0.969799	−	0.969799i	0.0297584	−	0.999557i	$-0.490526\pi$
$317$	−17.2668	−	17.2668i	−0.969799	−	0.969799i	−0.999557	+	0.0297584i	$0.990526\pi$
$318$	9.80619	−	9.80619i	0.549904	−	0.549904i
$319$	−4.45363			−0.249356
$320$	−10.9887	+	10.9887i	−0.614288	+	0.614288i
$321$		−	19.2202i		−	1.07276i
$322$	41.6157			2.31915
$323$	−7.53305	−	13.8812i	−0.419150	−	0.772373i
$324$	−12.4395			−0.691086
$325$		−	15.6949i		−	0.870599i
$326$	5.30112	−	5.30112i	0.293602	−	0.293602i
$327$	−19.2952			−1.06703
$328$	3.92007	−	3.92007i	0.216450	−	0.216450i
$329$	−18.4692	−	18.4692i	−1.01824	−	1.01824i
$330$	7.03852	+	7.03852i	0.387458	+	0.387458i
$331$		−	26.3920i		−	1.45063i	−0.688415	−	0.725317i	$-0.741693\pi$
$331$		−	26.3920i		−	1.45063i	0.688415	−	0.725317i	$-0.258307\pi$
$332$			24.6380i			1.35218i
$333$	0.610861	+	0.610861i	0.0334750	+	0.0334750i
$334$	19.1042	+	19.1042i	1.04533	+	1.04533i
$335$	5.06213	−	5.06213i	0.276574	−	0.276574i
$336$	34.9732			1.90794
$337$	9.50651	−	9.50651i	0.517852	−	0.517852i	−0.399069	−	0.916921i	$-0.630667\pi$
$337$	9.50651	−	9.50651i	0.517852	−	0.517852i	0.916921	+	0.399069i	$0.130667\pi$
$338$			9.26240i			0.503808i
$339$	−2.65802			−0.144364
$340$	−6.18124	+	20.8511i	−0.335225	+	1.13081i
$341$	−2.03516			−0.110210
$342$			2.91306i			0.157520i
$343$	−27.1911	+	27.1911i	−1.46818	+	1.46818i
$344$	−9.02084			−0.486371
$345$	17.1497	−	17.1497i	0.923311	−	0.923311i
$346$	−4.14889	−	4.14889i	−0.223046	−	0.223046i
$347$	15.2952	+	15.2952i	0.821090	+	0.821090i	0.986264	−	0.165175i	$-0.0528188\pi$
$347$	15.2952	+	15.2952i	0.821090	+	0.821090i	−0.165175	+	0.986264i	$0.552819\pi$
$348$		−	11.6901i		−	0.626654i
$349$			21.3538i			1.14304i	0.820588	+	0.571521i	$0.193646\pi$
$349$			21.3538i			1.14304i	−0.820588	+	0.571521i	$0.806354\pi$
$350$	−34.8886	−	34.8886i	−1.86488	−	1.86488i
$351$	−11.0573	−	11.0573i	−0.590195	−	0.590195i
$352$	5.20038	−	5.20038i	0.277181	−	0.277181i
$353$	21.1209			1.12415			0.562076	−	0.827085i	$-0.310003\pi$
$353$	21.1209			1.12415			0.562076	+	0.827085i	$0.310003\pi$
$354$	0.226277	−	0.226277i	0.0120265	−	0.0120265i
$355$			15.2058i			0.807041i
$356$	−29.8257			−1.58076
$357$	27.5155	−	14.9321i	1.45627	−	0.790288i
$358$	8.63181			0.456205
$359$		−	33.9945i		−	1.79416i	−0.441869	−	0.897080i	$-0.645684\pi$
$359$		−	33.9945i		−	1.79416i	0.441869	−	0.897080i	$-0.354316\pi$
$360$	−0.648915	+	0.648915i	−0.0342008	+	0.0342008i
$361$	4.32730			0.227753
$362$	−18.9512	+	18.9512i	−0.996050	+	0.996050i
$363$	−1.14033	−	1.14033i	−0.0598519	−	0.0598519i
$364$	−15.4571	−	15.4571i	−0.810174	−	0.810174i
$365$			10.7068i			0.560418i
$366$			13.6818i			0.715157i
$367$	3.39226	+	3.39226i	0.177075	+	0.177075i	0.790079	−	0.613005i	$-0.210039\pi$
$367$	3.39226	+	3.39226i	0.177075	+	0.177075i	−0.613005	+	0.790079i	$0.710039\pi$
$368$	−15.1148	−	15.1148i	−0.787916	−	0.787916i
$369$	−2.20696	+	2.20696i	−0.114890	+	0.114890i
$370$	13.3544			0.694264
$371$	15.0314	−	15.0314i	0.780391	−	0.780391i
$372$		−	5.34197i		−	0.276968i
$373$	−20.4116			−1.05687			−0.528435	−	0.848974i	$-0.677221\pi$
$373$	−20.4116			−1.05687			−0.528435	+	0.848974i	$0.677221\pi$
$374$	2.23199	−	7.52914i	0.115413	−	0.389323i
$375$	−2.62415			−0.135511
$376$			3.93448i			0.202905i
$377$	8.98316	−	8.98316i	0.462656	−	0.462656i
$378$	−49.1590			−2.52847
$379$	17.0011	−	17.0011i	0.873289	−	0.873289i	−0.119541	−	0.992829i	$-0.538142\pi$
$379$	17.0011	−	17.0011i	0.873289	−	0.873289i	0.992829	+	0.119541i	$0.0381422\pi$
$380$	14.2868	+	14.2868i	0.732898	+	0.732898i
$381$	9.14229	+	9.14229i	0.468374	+	0.468374i
$382$			4.72936i			0.241975i
$383$		−	26.7526i		−	1.36699i	−0.729953	−	0.683497i	$-0.760458\pi$
$383$		−	26.7526i		−	1.36699i	0.729953	−	0.683497i	$-0.239542\pi$
$384$	−6.35785	−	6.35785i	−0.324448	−	0.324448i
$385$	10.7890	+	10.7890i	0.549858	+	0.549858i
$386$	−7.76228	+	7.76228i	−0.395089	+	0.395089i
$387$	5.07864			0.258162
$388$	6.04048	−	6.04048i	0.306659	−	0.306659i
$389$			27.3082i			1.38458i	0.721618	+	0.692291i	$0.243399\pi$
$389$			27.3082i			1.38458i	−0.721618	+	0.692291i	$0.756601\pi$
$390$	−28.3940			−1.43779
$391$	−18.3452	−	5.43836i	−0.927754	−	0.275030i
$392$	10.7571			0.543313
$393$		−	15.0945i		−	0.761415i
$394$	20.1270	−	20.1270i	1.01398	−	1.01398i
$395$	19.0363			0.957821
$396$	−0.459541	+	0.459541i	−0.0230928	+	0.0230928i
$397$	−14.9437	−	14.9437i	−0.750005	−	0.750005i	0.224475	−	0.974480i	$-0.427933\pi$
$397$	−14.9437	−	14.9437i	−0.750005	−	0.750005i	−0.974480	+	0.224475i	$0.927933\pi$
$398$	−23.5254	−	23.5254i	−1.17922	−	1.17922i
$399$		−	29.0843i		−	1.45604i
$400$			25.3432i			1.26716i
$401$	−8.23862	−	8.23862i	−0.411417	−	0.411417i	0.470815	−	0.882232i	$-0.343960\pi$
$401$	−8.23862	−	8.23862i	−0.411417	−	0.411417i	−0.882232	+	0.470815i	$0.843960\pi$
$402$	−4.79792	−	4.79792i	−0.239299	−	0.239299i
$403$	4.10500	−	4.10500i	0.204485	−	0.204485i
$404$	−27.3492			−1.36067
$405$	−17.5134	+	17.5134i	−0.870249	+	0.870249i
$406$		−	39.9377i		−	1.98208i
$407$	−2.16359			−0.107245
$408$	−4.52129	−	1.34032i	−0.223837	−	0.0663558i
$409$	10.2212			0.505408			0.252704	−	0.967544i	$-0.418680\pi$
$409$	10.2212			0.505408			0.252704	+	0.967544i	$0.418680\pi$
$410$			48.2477i			2.38279i
$411$	−16.0206	+	16.0206i	−0.790239	+	0.790239i
$412$	−16.2105			−0.798636
$413$	0.346849	−	0.346849i	0.0170673	−	0.0170673i
$414$	2.49555	+	2.49555i	0.122650	+	0.122650i
$415$	34.6874	+	34.6874i	1.70274	+	1.70274i
$416$			20.9788i			1.02857i
$417$		−	7.56589i		−	0.370503i
$418$	−5.15884	−	5.15884i	−0.252327	−	0.252327i
$419$	5.45540	+	5.45540i	0.266514	+	0.266514i	0.827694	−	0.561180i	$-0.189652\pi$
$419$	5.45540	+	5.45540i	0.266514	+	0.266514i	−0.561180	+	0.827694i	$0.689652\pi$
$420$	−28.3194	+	28.3194i	−1.38185	+	1.38185i
$421$	7.09316			0.345700			0.172850	−	0.984948i	$-0.444702\pi$
$421$	7.09316			0.345700			0.172850	+	0.984948i	$0.444702\pi$
$422$	23.1742	−	23.1742i	1.12810	−	1.12810i
$423$		−	2.21507i		−	0.107700i
$424$	−3.20213			−0.155509
$425$	10.8205	+	19.9390i	0.524869	+	0.967183i
$426$	14.4122			0.698272
$427$			20.9721i			1.01491i
$428$	13.7168	−	13.7168i	0.663025	−	0.663025i
$429$	4.60020			0.222100
$430$	55.5137	−	55.5137i	2.67711	−	2.67711i
$431$	1.16872	+	1.16872i	0.0562952	+	0.0562952i	0.734694	−	0.678399i	$-0.237326\pi$
$431$	1.16872	+	1.16872i	0.0562952	+	0.0562952i	−0.678399	+	0.734694i	$0.737326\pi$
$432$	17.8546	+	17.8546i	0.859030	+	0.859030i
$433$			18.2106i			0.875147i	0.899183	+	0.437574i	$0.144162\pi$
$433$			18.2106i			0.875147i	−0.899183	+	0.437574i	$0.855838\pi$
$434$		−	18.2502i		−	0.876037i
$435$	−16.4583	−	16.4583i	−0.789114	−	0.789114i
$436$	−13.7703	−	13.7703i	−0.659480	−	0.659480i
$437$	−12.5698	+	12.5698i	−0.601294	+	0.601294i
$438$	10.1479			0.484887
$439$	−26.8606	+	26.8606i	−1.28199	+	1.28199i	−0.342450	+	0.939536i	$0.611257\pi$
$439$	−26.8606	+	26.8606i	−1.28199	+	1.28199i	−0.939536	+	0.342450i	$0.888743\pi$
$440$		−	2.29837i		−	0.109571i
$441$	−6.05611			−0.288386
$442$	10.6846	+	19.6886i	0.508213	+	0.936492i
$443$	2.11177			0.100333			0.0501666	−	0.998741i	$-0.484025\pi$
$443$	2.11177			0.100333			0.0501666	+	0.998741i	$0.484025\pi$
$444$		−	5.67908i		−	0.269517i
$445$	−41.9911	+	41.9911i	−1.99057	+	1.99057i
$446$	−12.8948			−0.610584
$447$	6.39220	−	6.39220i	0.302340	−	0.302340i
$448$	15.9649	+	15.9649i	0.754271	+	0.754271i
$449$	−2.69949	−	2.69949i	−0.127397	−	0.127397i	0.640534	−	0.767930i	$-0.278713\pi$
$449$	−2.69949	−	2.69949i	−0.127397	−	0.127397i	−0.767930	+	0.640534i	$0.778713\pi$
$450$		−	4.18431i		−	0.197250i
$451$		−	7.81676i		−	0.368077i
$452$	−1.89694	−	1.89694i	−0.0892245	−	0.0892245i
$453$	−7.12557	−	7.12557i	−0.334789	−	0.334789i
$454$	−31.6904	+	31.6904i	−1.48731	+	1.48731i
$455$	−43.5237			−2.04042
$456$	−3.09791	+	3.09791i	−0.145073	+	0.145073i
$457$		−	34.3225i		−	1.60554i	−0.596289	−	0.802770i	$-0.703359\pi$
$457$		−	34.3225i		−	1.60554i	0.596289	−	0.802770i	$-0.296641\pi$
$458$	−5.74432			−0.268414
$459$	21.6704	+	6.42413i	1.01149	+	0.299853i
$460$	24.4784			1.14131
$461$			9.89821i			0.461006i	0.973072	+	0.230503i	$0.0740371\pi$
$461$			9.89821i			0.461006i	−0.973072	+	0.230503i	$0.925963\pi$
$462$	10.2259	−	10.2259i	0.475751	−	0.475751i
$463$	−16.3162			−0.758280			−0.379140	−	0.925339i	$-0.623780\pi$
$463$	−16.3162			−0.758280			−0.379140	+	0.925339i	$0.623780\pi$
$464$	−14.5054	+	14.5054i	−0.673397	+	0.673397i
$465$	−7.52087	−	7.52087i	−0.348772	−	0.348772i
$466$	−9.40855	−	9.40855i	−0.435842	−	0.435842i
$467$		−	10.6415i		−	0.492432i	−0.969215	−	0.246216i	$-0.920813\pi$
$467$		−	10.6415i		−	0.492432i	0.969215	−	0.246216i	$-0.0791873\pi$
$468$		−	1.85383i		−	0.0856932i
$469$	−7.35449	−	7.35449i	−0.339599	−	0.339599i
$470$	−24.2125	−	24.2125i	−1.11684	−	1.11684i
$471$	10.0240	−	10.0240i	0.461883	−	0.461883i
$472$	−0.0738890			−0.00340102
$473$	−8.99394	+	8.99394i	−0.413542	+	0.413542i
$474$		−	18.0428i		−	0.828731i
$475$	21.0758			0.967026
$476$	30.2934	+	8.98038i	1.38850	+	0.411615i
$477$	1.80277			0.0825430
$478$			16.8125i			0.768987i
$479$	−20.3159	+	20.3159i	−0.928257	+	0.928257i	−0.997593	−	0.0693361i	$-0.977912\pi$
$479$	−20.3159	+	20.3159i	−0.928257	+	0.928257i	0.0693361	+	0.997593i	$0.477912\pi$
$480$	38.4357			1.75434
$481$	4.36405	−	4.36405i	0.198984	−	0.198984i
$482$	14.6869	+	14.6869i	0.668971	+	0.668971i
$483$	−24.9159	−	24.9159i	−1.13371	−	1.13371i
$484$		−	1.62763i		−	0.0739834i
$485$		−	17.0086i		−	0.772320i
$486$	−5.54954	−	5.54954i	−0.251732	−	0.251732i
$487$	22.6530	+	22.6530i	1.02650	+	1.02650i	0.999639	+	0.0268645i	$0.00855228\pi$
$487$	22.6530	+	22.6530i	1.02650	+	1.02650i	0.0268645	+	0.999639i	$0.491448\pi$
$488$	2.23383	−	2.23383i	0.101121	−	0.101121i
$489$	−6.34771			−0.287053
$490$	−66.1982	+	66.1982i	−2.99053	+	2.99053i
$491$			15.4718i			0.698232i	0.937080	+	0.349116i	$0.113518\pi$
$491$			15.4718i			0.698232i	−0.937080	+	0.349116i	$0.886482\pi$
$492$	20.5178			0.925012
$493$	−5.21909	+	17.6055i	−0.235056	+	0.792912i
$494$	20.8112			0.936339
$495$			1.29396i			0.0581592i
$496$	−6.62848	+	6.62848i	−0.297628	+	0.297628i
$497$	22.0917			0.990948
$498$	32.8769	−	32.8769i	1.47325	−	1.47325i
$499$	−20.5236	−	20.5236i	−0.918761	−	0.918761i	0.0781788	−	0.996939i	$-0.475090\pi$
$499$	−20.5236	−	20.5236i	−0.918761	−	0.918761i	−0.996939	+	0.0781788i	$0.975090\pi$
$500$	−1.87277	−	1.87277i	−0.0837528	−	0.0837528i
$501$		−	22.8759i		−	1.02202i
$502$		−	11.4179i		−	0.509608i
$503$	3.94936	+	3.94936i	0.176093	+	0.176093i	0.789650	−	0.613557i	$-0.210262\pi$
$503$	3.94936	+	3.94936i	0.176093	+	0.176093i	−0.613557	+	0.789650i	$0.710262\pi$
$504$	0.942772	+	0.942772i	0.0419944	+	0.0419944i
$505$	−38.5045	+	38.5045i	−1.71343	+	1.71343i
$506$	−8.83892			−0.392938
$507$	5.54553	−	5.54553i	0.246286	−	0.246286i
$508$			13.0491i			0.578960i
$509$	18.6491			0.826609			0.413304	−	0.910593i	$-0.364375\pi$
$509$	18.6491			0.826609			0.413304	+	0.910593i	$0.364375\pi$
$510$	36.0720	−	19.5755i	1.59729	−	0.866817i
$511$	15.5553			0.688124
$512$		−	27.3417i		−	1.20834i
$513$	14.8482	−	14.8482i	0.655564	−	0.655564i
$514$	−13.1498			−0.580013
$515$	−22.8226	+	22.8226i	−1.00568	+	1.00568i
$516$	−23.6077	−	23.6077i	−1.03927	−	1.03927i
$517$	3.92274	+	3.92274i	0.172522	+	0.172522i
$518$		−	19.4019i		−	0.852471i
$519$			4.96800i			0.218071i
$520$	4.63591	+	4.63591i	0.203298	+	0.203298i
$521$	−3.25111	−	3.25111i	−0.142434	−	0.142434i	0.632295	−	0.774728i	$-0.282113\pi$
$521$	−3.25111	−	3.25111i	−0.142434	−	0.142434i	−0.774728	+	0.632295i	$0.782113\pi$
$522$	2.39493	−	2.39493i	0.104823	−	0.104823i
$523$	5.60838			0.245237			0.122619	−	0.992454i	$-0.460871\pi$
$523$	5.60838			0.245237			0.122619	+	0.992454i	$0.460871\pi$
$524$	10.7724	−	10.7724i	0.470595	−	0.470595i
$525$			41.7766i			1.82328i
$526$	−31.5169			−1.37420
$527$	−2.38495	+	8.04511i	−0.103890	+	0.350450i
$528$	−7.42810			−0.323266
$529$		−	1.46350i		−	0.0636304i
$530$	19.7057	−	19.7057i	0.855961	−	0.855961i
$531$	0.0415988			0.00180523
$532$	20.7565	−	20.7565i	0.899909	−	0.899909i
$533$	15.7667	+	15.7667i	0.682933	+	0.682933i
$534$	39.7994	+	39.7994i	1.72229	+	1.72229i
$535$		−	38.6232i		−	1.66983i
$536$			1.56672i			0.0676721i
$537$	−5.16799	−	5.16799i	−0.223015	−	0.223015i
$538$	13.4003	+	13.4003i	0.577728	+	0.577728i
$539$	10.7250	−	10.7250i	0.461957	−	0.461957i
$540$	−28.9154			−1.24432
$541$	11.1646	−	11.1646i	0.480003	−	0.480003i	−0.425130	−	0.905132i	$-0.639772\pi$
$541$	11.1646	−	11.1646i	0.480003	−	0.480003i	0.905132	+	0.425130i	$0.139772\pi$
$542$			38.3638i			1.64787i
$543$	22.6927			0.973835
$544$	−14.4632	−	26.6516i	−0.620107	−	1.14268i
$545$	−38.7741			−1.66090
$546$			41.2520i			1.76542i
$547$	9.39303	−	9.39303i	0.401617	−	0.401617i	−0.477185	−	0.878803i	$-0.658343\pi$
$547$	9.39303	−	9.39303i	0.401617	−	0.401617i	0.878803	+	0.477185i	$0.158343\pi$
$548$	−22.8668			−0.976820
$549$	−1.25763	+	1.25763i	−0.0536741	+	0.0536741i
$550$	7.41014	+	7.41014i	0.315969	+	0.315969i
$551$	12.0630	+	12.0630i	0.513900	+	0.513900i
$552$			5.30782i			0.225916i
$553$		−	27.6568i		−	1.17609i
$554$	26.6730	+	26.6730i	1.13323	+	1.13323i
$555$	−7.99549	−	7.99549i	−0.339390	−	0.339390i
$556$	5.39952	−	5.39952i	0.228991	−	0.228991i
$557$	−2.01230			−0.0852638			−0.0426319	−	0.999091i	$-0.513574\pi$
$557$	−2.01230			−0.0852638			−0.0426319	+	0.999091i	$0.513574\pi$
$558$	1.09440	−	1.09440i	0.0463298	−	0.0463298i
$559$		−	36.2823i		−	1.53458i
$560$	70.2792			2.96984
$561$	−5.84413	+	3.17148i	−0.246739	+	0.133900i
$562$	26.7287			1.12748
$563$			21.7386i			0.916172i	0.888908	+	0.458086i	$0.151465\pi$
$563$			21.7386i			0.916172i	−0.888908	+	0.458086i	$0.848535\pi$
$564$	−10.2966	+	10.2966i	−0.433564	+	0.433564i
$565$	−5.34134			−0.224712
$566$	−21.0831	+	21.0831i	−0.886189	+	0.886189i
$567$	25.4443	+	25.4443i	1.06856	+	1.06856i
$568$	−2.35309	−	2.35309i	−0.0987334	−	0.0987334i
$569$			26.6428i			1.11692i	0.829530	+	0.558462i	$0.188608\pi$
$569$			26.6428i			1.11692i	−0.829530	+	0.558462i	$0.811392\pi$
$570$		−	38.1287i		−	1.59703i
$571$	−20.5454	−	20.5454i	−0.859798	−	0.859798i	0.131516	−	0.991314i	$-0.458016\pi$
$571$	−20.5454	−	20.5454i	−0.859798	−	0.859798i	−0.991314	+	0.131516i	$0.958016\pi$
$572$	3.28301	+	3.28301i	0.137269	+	0.137269i
$573$	2.83153	−	2.83153i	0.118289	−	0.118289i
$574$	70.0965			2.92577
$575$	18.0552	−	18.0552i	0.752954	−	0.752954i
$576$			1.91472i			0.0797802i
$577$	−6.74815			−0.280929			−0.140465	−	0.990086i	$-0.544860\pi$
$577$	−6.74815			−0.280929			−0.140465	+	0.990086i	$0.544860\pi$
$578$	−27.1476	−	17.6464i	−1.12919	−	0.733994i
$579$	9.29477			0.386278
$580$		−	23.4914i		−	0.975429i
$581$	50.3954	−	50.3954i	2.09075	−	2.09075i
$582$	−16.1208			−0.668231
$583$	−3.19258	+	3.19258i	−0.132223	+	0.132223i
$584$	−1.65686	−	1.65686i	−0.0685615	−	0.0685615i
$585$	−2.60997	−	2.60997i	−0.107909	−	0.107909i
$586$			17.2594i			0.712981i
$587$			39.1668i			1.61659i	0.588779	+	0.808294i	$0.299609\pi$
$587$			39.1668i			1.61659i	−0.588779	+	0.808294i	$0.700391\pi$
$588$	28.1514	+	28.1514i	1.16094	+	1.16094i
$589$	5.51237	+	5.51237i	0.227133	+	0.227133i
$590$	0.454709	−	0.454709i	0.0187201	−	0.0187201i
$591$	−24.1006			−0.991367
$592$	−7.04679	+	7.04679i	−0.289621	+	0.289621i
$593$			43.8432i			1.80043i	0.435450	+	0.900213i	$0.356589\pi$
$593$			43.8432i			1.80043i	−0.435450	+	0.900213i	$0.643411\pi$
$594$	10.4411			0.428403
$595$	55.2929	−	30.0062i	2.26679	−	1.23014i
$596$	9.12379			0.373725
$597$			28.1700i			1.15292i
$598$	17.8285	−	17.8285i	0.729060	−	0.729060i
$599$	−9.43117			−0.385347			−0.192674	−	0.981263i	$-0.561716\pi$
$599$	−9.43117			−0.385347			−0.192674	+	0.981263i	$0.561716\pi$
$600$	4.44983	−	4.44983i	0.181663	−	0.181663i
$601$	9.93877	+	9.93877i	0.405411	+	0.405411i	0.880135	−	0.474724i	$-0.157452\pi$
$601$	9.93877	+	9.93877i	0.405411	+	0.405411i	−0.474724	+	0.880135i	$0.657452\pi$
$602$	−80.6527	−	80.6527i	−3.28716	−	3.28716i
$603$		−	0.882048i		−	0.0359198i
$604$		−	10.1706i		−	0.413834i
$605$	−2.29152	−	2.29152i	−0.0931635	−	0.0931635i
$606$	36.4948	+	36.4948i	1.48250	+	1.48250i
$607$	16.0296	−	16.0296i	0.650622	−	0.650622i	−0.302521	−	0.953143i	$-0.597828\pi$
$607$	16.0296	−	16.0296i	0.650622	−	0.650622i	0.953143	+	0.302521i	$0.0978282\pi$
$608$	−28.1712			−1.14249
$609$	−23.9113	+	23.9113i	−0.968935	+	0.968935i
$610$			27.4937i			1.11319i
$611$	−15.8247			−0.640198
$612$	1.27807	+	2.35512i	0.0516629	+	0.0952000i
$613$	−6.66183			−0.269069			−0.134534	−	0.990909i	$-0.542954\pi$
$613$	−6.66183			−0.269069			−0.134534	+	0.990909i	$0.542954\pi$
$614$		−	44.8292i		−	1.80916i
$615$	28.8866	−	28.8866i	1.16482	−	1.16482i
$616$	−3.33918			−0.134539
$617$	6.94729	−	6.94729i	0.279687	−	0.279687i	−0.553297	−	0.832984i	$-0.686630\pi$
$617$	6.94729	−	6.94729i	0.279687	−	0.279687i	0.832984	+	0.553297i	$0.186630\pi$
$618$	21.6314	+	21.6314i	0.870141	+	0.870141i
$619$	−32.7108	−	32.7108i	−1.31476	−	1.31476i	−0.917866	−	0.396890i	$-0.870089\pi$
$619$	−32.7108	−	32.7108i	−1.31476	−	1.31476i	−0.396890	−	0.917866i	$-0.629911\pi$
$620$		−	10.7348i		−	0.431119i
$621$		−	25.4403i		−	1.02088i
$622$	12.1775	+	12.1775i	0.488274	+	0.488274i
$623$	61.0065	+	61.0065i	2.44417	+	2.44417i
$624$	14.9828	−	14.9828i	0.599791	−	0.599791i
$625$	22.2373			0.889492
$626$	−21.2535	+	21.2535i	−0.849461	+	0.849461i
$627$			6.17734i			0.246699i
$628$	14.3076			0.570936
$629$	−2.53545	+	8.55281i	−0.101095	+	0.341023i
$630$	−11.6035			−0.462296
$631$		−	38.5254i		−	1.53367i	−0.641843	−	0.766836i	$-0.721830\pi$
$631$		−	38.5254i		−	1.53367i	0.641843	−	0.766836i	$-0.278170\pi$
$632$	−2.94586	+	2.94586i	−0.117180	+	0.117180i
$633$	−27.7495			−1.10294
$634$	−32.8869	+	32.8869i	−1.30611	+	1.30611i
$635$	18.3716	+	18.3716i	0.729055	+	0.729055i
$636$	−8.38002	−	8.38002i	−0.332289	−	0.332289i
$637$			43.2654i			1.71424i
$638$			8.48254i			0.335827i
$639$	1.32477	+	1.32477i	0.0524069	+	0.0524069i
$640$	−12.7762	−	12.7762i	−0.505024	−	0.505024i
$641$	21.5038	−	21.5038i	0.849347	−	0.849347i	−0.140704	−	0.990052i	$-0.544937\pi$
$641$	21.5038	−	21.5038i	0.849347	−	0.849347i	0.990052	+	0.140704i	$0.0449367\pi$
$642$	−36.6074			−1.44478
$643$	−5.14467	+	5.14467i	−0.202886	+	0.202886i	−0.801235	−	0.598349i	$-0.795823\pi$
$643$	−5.14467	+	5.14467i	−0.202886	+	0.202886i	0.598349	+	0.801235i	$0.295823\pi$
$644$		−	35.5633i		−	1.40139i
$645$	−66.4737			−2.61740
$646$	−26.4387	+	14.3477i	−1.04022	+	0.564503i
$647$	−45.7496			−1.79860			−0.899302	−	0.437329i	$-0.855925\pi$
$647$	−45.7496			−1.79860			−0.899302	+	0.437329i	$0.855925\pi$
$648$		−	5.42038i		−	0.212933i
$649$	−0.0736687	+	0.0736687i	−0.00289175	+	0.00289175i
$650$	−29.8931			−1.17250
$651$	−10.9266	+	10.9266i	−0.428249	+	0.428249i
$652$	−4.53015	−	4.53015i	−0.177414	−	0.177414i
$653$	6.82403	+	6.82403i	0.267045	+	0.267045i	0.827908	−	0.560863i	$-0.189531\pi$
$653$	6.82403	+	6.82403i	0.267045	+	0.267045i	−0.560863	+	0.827908i	$0.689531\pi$
$654$			36.7503i			1.43705i
$655$		−	30.3326i		−	1.18519i
$656$	−25.4591	−	25.4591i	−0.994011	−	0.994011i
$657$	0.932797	+	0.932797i	0.0363919	+	0.0363919i
$658$	−35.1770	+	35.1770i	−1.37134	+	1.37134i
$659$	−10.8591			−0.423010			−0.211505	−	0.977377i	$-0.567836\pi$
$659$	−10.8591			−0.423010			−0.211505	+	0.977377i	$0.567836\pi$
$660$	6.01487	−	6.01487i	0.234129	−	0.234129i
$661$		−	50.0727i		−	1.94760i	−0.227404	−	0.973801i	$-0.573024\pi$
$661$		−	50.0727i		−	1.94760i	0.227404	−	0.973801i	$-0.426976\pi$
$662$	−50.2671			−1.95369
$663$	5.39085	−	18.1849i	0.209363	−	0.706242i
$664$	−10.7357			−0.416626
$665$		−	58.4455i		−	2.26642i
$666$	1.16347	−	1.16347i	0.0450835	−	0.0450835i
$667$	20.6682			0.800275
$668$	16.3258	−	16.3258i	0.631663	−	0.631663i
$669$	7.72028	+	7.72028i	0.298483	+	0.298483i
$670$	−9.64151	−	9.64151i	−0.372484	−	0.372484i
$671$		−	4.45434i		−	0.171958i
$672$		−	55.8411i		−	2.15412i
$673$	7.16146	+	7.16146i	0.276054	+	0.276054i	0.831532	−	0.555478i	$-0.187465\pi$
$673$	7.16146	+	7.16146i	0.276054	+	0.276054i	−0.555478	+	0.831532i	$0.687465\pi$
$674$	−18.1064	−	18.1064i	−0.697433	−	0.697433i
$675$	−21.3279	+	21.3279i	−0.820912	+	0.820912i
$676$	7.91532			0.304436
$677$	−21.9759	+	21.9759i	−0.844604	+	0.844604i	−0.989454	−	0.144849i	$-0.953730\pi$
$677$	−21.9759	+	21.9759i	−0.844604	+	0.844604i	0.144849	+	0.989454i	$0.453730\pi$
$678$			5.06256i			0.194426i
$679$	−24.7108			−0.948314
$680$	−9.08561	−	2.69340i	−0.348417	−	0.103287i
$681$	37.9471			1.45413
$682$			3.87623i			0.148429i
$683$	−8.21090	+	8.21090i	−0.314181	+	0.314181i	−0.846527	−	0.532346i	$-0.821311\pi$
$683$	−8.21090	+	8.21090i	−0.314181	+	0.314181i	0.532346	+	0.846527i	$0.321311\pi$
$684$	2.48940			0.0951845
$685$	−32.1937	+	32.1937i	−1.23006	+	1.23006i
$686$	51.7891	+	51.7891i	1.97732	+	1.97732i
$687$	3.43921	+	3.43921i	0.131214	+	0.131214i
$688$			58.5863i			2.23358i
$689$		−	12.8791i		−	0.490656i
$690$	−32.6640	−	32.6640i	−1.24350	−	1.24350i
$691$	27.9054	+	27.9054i	1.06157	+	1.06157i	0.997976	+	0.0635954i	$0.0202567\pi$
$691$	27.9054	+	27.9054i	1.06157	+	1.06157i	0.0635954	+	0.997976i	$0.479743\pi$
$692$	−3.54550	+	3.54550i	−0.134780	+	0.134780i
$693$	1.87992			0.0714123
$694$	29.1318	−	29.1318i	1.10583	−	1.10583i
$695$		−	15.2038i		−	0.576713i
$696$	5.09381			0.193080
$697$	−30.9002	−	9.16025i	−1.17043	−	0.346969i
$698$	40.6711			1.53943
$699$			11.2661i			0.426122i
$700$	−29.8146	+	29.8146i	−1.12689	+	1.12689i
$701$	16.6176			0.627638			0.313819	−	0.949483i	$-0.398391\pi$
$701$	16.6176			0.627638			0.313819	+	0.949483i	$0.398391\pi$
$702$	−21.0601	+	21.0601i	−0.794862	+	0.794862i
$703$	5.86024	+	5.86024i	0.221023	+	0.221023i
$704$	−3.39085	−	3.39085i	−0.127798	−	0.127798i
$705$			28.9928i			1.09193i
$706$		−	40.2276i		−	1.51399i
$707$	55.9410	+	55.9410i	2.10388	+	2.10388i
$708$	−0.193369	−	0.193369i	−0.00726724	−	0.00726724i
$709$	−23.7662	+	23.7662i	−0.892557	+	0.892557i	−0.994763	−	0.102206i	$-0.967410\pi$
$709$	−23.7662	+	23.7662i	−0.892557	+	0.892557i	0.102206	+	0.994763i	$0.467410\pi$
$710$	28.9615			1.08691
$711$	1.65849	−	1.65849i	0.0621981	−	0.0621981i
$712$		−	12.9962i		−	0.487052i
$713$	9.44465			0.353705
$714$	−28.4401	−	52.4070i	−1.06434	−	1.96128i
$715$	9.24418			0.345713
$716$		−	7.37644i		−	0.275670i
$717$	10.0659	−	10.0659i	0.375918	−	0.375918i
$718$	−64.7470			−2.41634
$719$	17.9571	−	17.9571i	0.669687	−	0.669687i	−0.287956	−	0.957644i	$-0.592976\pi$
$719$	17.9571	−	17.9571i	0.669687	−	0.669687i	0.957644	+	0.287956i	$0.0929758\pi$
$720$	4.21441	+	4.21441i	0.157062	+	0.157062i
$721$	33.1576	+	33.1576i	1.23485	+	1.23485i
$722$		−	8.24192i		−	0.306733i
$723$		−	17.5866i		−	0.654051i
$724$	16.1950	+	16.1950i	0.601882	+	0.601882i
$725$	−17.3272	−	17.3272i	−0.643517	−	0.643517i
$726$	−2.17192	+	2.17192i	−0.0806074	+	0.0806074i
$727$	−3.91340			−0.145140			−0.0725700	−	0.997363i	$-0.523120\pi$
$727$	−3.91340			−0.145140			−0.0725700	+	0.997363i	$0.523120\pi$
$728$	6.73526	−	6.73526i	0.249625	−	0.249625i
$729$			29.5733i			1.09531i
$730$	20.3925			0.754759
$731$	25.0139	+	46.0934i	0.925171	+	1.70483i
$732$	11.6920			0.432147
$733$			2.90011i			0.107118i	0.998565	+	0.0535589i	$0.0170565\pi$
$733$			2.90011i			0.107118i	−0.998565	+	0.0535589i	$0.982944\pi$
$734$	6.46102	−	6.46102i	0.238480	−	0.238480i
$735$	79.2677			2.92383
$736$	−24.1336	+	24.1336i	−0.889578	+	0.889578i
$737$	1.56205	+	1.56205i	0.0575389	+	0.0575389i
$738$	4.20345	+	4.20345i	0.154731	+	0.154731i
$739$		−	19.4576i		−	0.715759i	−0.933768	−	0.357879i	$-0.883500\pi$
$739$		−	19.4576i		−	0.715759i	0.933768	−	0.357879i	$-0.116500\pi$
$740$		−	11.4122i		−	0.419522i
$741$	−12.4600	−	12.4600i	−0.457728	−	0.457728i
$742$	−28.6293	−	28.6293i	−1.05102	−	1.05102i
$743$	33.3169	−	33.3169i	1.22228	−	1.22228i	0.255457	−	0.966820i	$-0.417774\pi$
$743$	33.3169	−	33.3169i	1.22228	−	1.22228i	0.966820	−	0.255457i	$-0.0822259\pi$
$744$	2.32770			0.0853375
$745$	12.8452	−	12.8452i	0.470613	−	0.470613i
$746$			38.8766i			1.42337i
$747$	6.04409			0.221142
$748$	−6.43414	−	1.90738i	−0.235255	−	0.0697407i
$749$	−56.1136			−2.05034
$750$			4.99805i			0.182503i
$751$	−13.8227	+	13.8227i	−0.504398	+	0.504398i	−0.912801	−	0.408404i	$-0.866086\pi$
$751$	−13.8227	+	13.8227i	−0.504398	+	0.504398i	0.408404	+	0.912801i	$0.366086\pi$
$752$	25.5526			0.931809
$753$	−6.83609	+	6.83609i	−0.249121	+	0.249121i
$754$	−17.1096	−	17.1096i	−0.623096	−	0.623096i
$755$	−14.3190	−	14.3190i	−0.521121	−	0.521121i
$756$			42.0096i			1.52787i
$757$			9.02549i			0.328037i	0.986457	+	0.164018i	$0.0524457\pi$
$757$			9.02549i			0.328037i	−0.986457	+	0.164018i	$0.947554\pi$
$758$	−32.3809	−	32.3809i	−1.17613	−	1.17613i
$759$	5.29199	+	5.29199i	0.192087	+	0.192087i
$760$	−6.22530	+	6.22530i	−0.225815	+	0.225815i
$761$	−40.1420			−1.45515			−0.727573	−	0.686030i	$-0.759352\pi$
$761$	−40.1420			−1.45515			−0.727573	+	0.686030i	$0.759352\pi$
$762$	17.4127	−	17.4127i	0.630796	−	0.630796i
$763$			56.3327i			2.03938i
$764$	4.04154			0.146218
$765$	5.11511	+	1.51636i	0.184937	+	0.0548240i
$766$	−50.9539			−1.84104
$767$		−	0.297186i		−	0.0107308i
$768$	−23.0461	+	23.0461i	−0.831603	+	0.831603i
$769$	28.7056			1.03515			0.517576	−	0.855637i	$-0.326834\pi$
$769$	28.7056			1.03515			0.517576	+	0.855637i	$0.326834\pi$
$770$	20.5491	−	20.5491i	0.740538	−	0.740538i
$771$	7.87298	+	7.87298i	0.283539	+	0.283539i
$772$	6.63337	+	6.63337i	0.238740	+	0.238740i
$773$			6.93496i			0.249433i	0.992192	+	0.124717i	$0.0398022\pi$
$773$			6.93496i			0.249433i	−0.992192	+	0.124717i	$0.960198\pi$
$774$		−	9.67296i		−	0.347687i
$775$	−7.91795	−	7.91795i	−0.284421	−	0.284421i
$776$	2.63207	+	2.63207i	0.0944856	+	0.0944856i
$777$	−11.6162	+	11.6162i	−0.416729	+	0.416729i
$778$	52.0122			1.86473
$779$	−21.1722	+	21.1722i	−0.758574	+	0.758574i
$780$			24.2645i			0.868809i
$781$	−4.69215			−0.167898
$782$	−10.3581	+	34.9408i	−0.370405	+	1.24948i
$783$	−24.4145			−0.872504
$784$		−	69.8622i		−	2.49508i
$785$	20.1435	−	20.1435i	0.718951	−	0.718951i
$786$	−28.7495			−1.02546
$787$	−21.4837	+	21.4837i	−0.765810	+	0.765810i	−0.977366	−	0.211556i	$-0.932147\pi$
$787$	−21.4837	+	21.4837i	−0.765810	+	0.765810i	0.211556	+	0.977366i	$0.432147\pi$
$788$	−17.1998	−	17.1998i	−0.612718	−	0.612718i
$789$	18.8696	+	18.8696i	0.671777	+	0.671777i
$790$		−	36.2572i		−	1.28997i
$791$			7.76013i			0.275919i
$792$	−0.200239	−	0.200239i	−0.00711520	−	0.00711520i
$793$	8.98460	+	8.98460i	0.319052	+	0.319052i
$794$	−28.4624	+	28.4624i	−1.01009	+	1.01009i
$795$	−23.5962			−0.836870
$796$	−20.1040	+	20.1040i	−0.712566	+	0.712566i
$797$		−	39.7877i		−	1.40935i	−0.709530	−	0.704676i	$-0.751093\pi$
$797$		−	39.7877i		−	1.40935i	0.709530	−	0.704676i	$-0.248907\pi$
$798$	−55.3950			−1.96096
$799$	20.1038	−	10.9099i	0.711222	−	0.385964i
$800$	40.4650			1.43065
$801$			7.31671i			0.258523i
$802$	−15.6916	+	15.6916i	−0.554088	+	0.554088i
$803$	−3.30385			−0.116590
$804$	−4.10013	+	4.10013i	−0.144601	+	0.144601i
$805$	−50.0689	−	50.0689i	−1.76470	−	1.76470i
$806$	−7.81852	−	7.81852i	−0.275396	−	0.275396i
$807$		−	16.0459i		−	0.564842i
$808$		−	11.9171i		−	0.419241i
$809$	18.2470	+	18.2470i	0.641530	+	0.641530i	0.950932	−	0.309401i	$-0.100129\pi$
$809$	18.2470	+	18.2470i	0.641530	+	0.641530i	−0.309401	+	0.950932i	$0.600129\pi$
$810$	33.3567	+	33.3567i	1.17203	+	1.17203i
$811$	7.63145	−	7.63145i	0.267976	−	0.267976i	−0.560308	−	0.828284i	$-0.689317\pi$
$811$	7.63145	−	7.63145i	0.267976	−	0.267976i	0.828284	+	0.560308i	$0.189317\pi$
$812$	−34.1294			−1.19771
$813$	22.9689	−	22.9689i	0.805556	−	0.805556i
$814$			4.12085i			0.144436i
$815$	−12.7558			−0.446818
$816$	−8.70479	+	29.3637i	−0.304729	+	1.02794i
$817$	48.7214			1.70455
$818$		−	19.4677i		−	0.680673i
$819$	−3.79188	+	3.79188i	−0.132499	+	0.132499i
$820$	41.2308			1.43984
$821$	28.7580	−	28.7580i	1.00366	−	1.00366i	0.00366742	−	0.999993i	$-0.498833\pi$
$821$	28.7580	−	28.7580i	1.00366	−	1.00366i	0.999993	−	0.00366742i	$-0.00116738\pi$
$822$	30.5134	+	30.5134i	1.06428	+	1.06428i
$823$	4.40891	+	4.40891i	0.153685	+	0.153685i	0.779762	−	0.626077i	$-0.215340\pi$
$823$	4.40891	+	4.40891i	0.153685	+	0.153685i	−0.626077	+	0.779762i	$0.715340\pi$
$824$		−	7.06355i		−	0.246070i
$825$		−	8.87312i		−	0.308922i
$826$	−0.660621	−	0.660621i	−0.0229859	−	0.0229859i
$827$	12.1283	+	12.1283i	0.421744	+	0.421744i	0.885804	−	0.464060i	$-0.153608\pi$
$827$	12.1283	+	12.1283i	0.421744	+	0.421744i	−0.464060	+	0.885804i	$0.653608\pi$
$828$	2.13261	−	2.13261i	0.0741134	−	0.0741134i
$829$	−46.5777			−1.61771			−0.808855	−	0.588009i	$-0.799912\pi$
$829$	−46.5777			−1.61771			−0.808855	+	0.588009i	$0.799912\pi$
$830$	66.0668	−	66.0668i	2.29321	−	2.29321i
$831$		−	31.9390i		−	1.10795i
$832$	13.6790			0.474233
$833$	−29.8282	−	54.9648i	−1.03349	−	1.90442i
$834$	−14.4103			−0.498987
$835$		−	45.9695i		−	1.59084i
$836$	−4.40856	+	4.40856i	−0.152473	+	0.152473i
$837$	−11.1566			−0.385629
$838$	10.3905	−	10.3905i	0.358936	−	0.358936i
$839$	−17.1351	−	17.1351i	−0.591570	−	0.591570i	0.346486	−	0.938055i	$-0.387375\pi$
$839$	−17.1351	−	17.1351i	−0.591570	−	0.591570i	−0.938055	+	0.346486i	$0.887375\pi$
$840$	−12.3398	−	12.3398i	−0.425765	−	0.425765i
$841$			9.16516i			0.316040i
$842$		−	13.5099i		−	0.465581i
$843$	−16.0029	−	16.0029i	−0.551168	−	0.551168i
$844$	−19.8039	−	19.8039i	−0.681677	−	0.681677i
$845$	11.1439	−	11.1439i	0.383360	−	0.383360i
$846$	−4.21890			−0.145049
$847$	−3.32922	+	3.32922i	−0.114393	+	0.114393i
$848$			20.7964i			0.714151i
$849$	25.2455			0.866424
$850$	37.9765	−	20.6090i	1.30258	−	0.706883i
$851$	10.0407			0.344190
$852$		−	12.3161i		−	0.421944i
$853$	34.8373	−	34.8373i	1.19281	−	1.19281i	0.216531	−	0.976276i	$-0.430526\pi$
$853$	34.8373	−	34.8373i	1.19281	−	1.19281i	0.976276	−	0.216531i	$-0.0694742\pi$
$854$	39.9441			1.36686
$855$	3.50478	−	3.50478i	0.119861	−	0.119861i
$856$	5.97692	+	5.97692i	0.204287	+	0.204287i
$857$	−21.0889	−	21.0889i	−0.720382	−	0.720382i	0.248301	−	0.968683i	$-0.420128\pi$
$857$	−21.0889	−	21.0889i	−0.720382	−	0.720382i	−0.968683	+	0.248301i	$0.920128\pi$
$858$		−	8.76169i		−	0.299119i
$859$			49.6079i			1.69260i	0.532708	+	0.846299i	$0.321174\pi$
$859$			49.6079i			1.69260i	−0.532708	+	0.846299i	$0.678826\pi$
$860$	−47.4400	−	47.4400i	−1.61769	−	1.61769i
$861$	−41.9678	−	41.9678i	−1.43026	−	1.43026i
$862$	2.22598	−	2.22598i	0.0758172	−	0.0758172i
$863$	6.13104			0.208703			0.104351	−	0.994540i	$-0.466723\pi$
$863$	6.13104			0.208703			0.104351	+	0.994540i	$0.466723\pi$
$864$	28.5082	−	28.5082i	0.969867	−	0.969867i
$865$			9.98330i			0.339442i
$866$	34.6846			1.17863
$867$	5.68849	+	26.8188i	0.193191	+	0.910814i
$868$	−15.5960			−0.529362
$869$			5.87414i			0.199267i
$870$	−31.3470	+	31.3470i	−1.06276	+	1.06276i
$871$	−6.30144			−0.213516
$872$	6.00026	−	6.00026i	0.203194	−	0.203194i
$873$	−1.48183	−	1.48183i	−0.0501522	−	0.0501522i
$874$	23.9408	+	23.9408i	0.809811	+	0.809811i
$875$			7.66126i			0.258998i
$876$		−	8.67207i		−	0.293002i
$877$	14.2260	+	14.2260i	0.480377	+	0.480377i	0.905252	−	0.424875i	$-0.139682\pi$
$877$	14.2260	+	14.2260i	0.480377	+	0.480377i	−0.424875	+	0.905252i	$0.639682\pi$
$878$	51.1596	+	51.1596i	1.72655	+	1.72655i
$879$	10.3335	−	10.3335i	0.348540	−	0.348540i
$880$	−14.9269			−0.503186
$881$	30.0632	−	30.0632i	1.01285	−	1.01285i	0.0129383	−	0.999916i	$-0.495882\pi$
$881$	30.0632	−	30.0632i	1.01285	−	1.01285i	0.999916	−	0.0129383i	$-0.00411850\pi$
$882$			11.5347i			0.388393i
$883$	−15.7538			−0.530158			−0.265079	−	0.964227i	$-0.585398\pi$
$883$	−15.7538			−0.530158			−0.265079	+	0.964227i	$0.585398\pi$
$884$	16.8252	−	9.13066i	0.565893	−	0.307097i
$885$	−0.544481			−0.0183025
$886$		−	4.02215i		−	0.135127i
$887$	23.5055	−	23.5055i	0.789238	−	0.789238i	−0.192131	−	0.981369i	$-0.561540\pi$
$887$	23.5055	−	23.5055i	0.789238	−	0.789238i	0.981369	+	0.192131i	$0.0615399\pi$
$888$	2.47459			0.0830418
$889$	26.6911	−	26.6911i	0.895190	−	0.895190i
$890$	79.9777	+	79.9777i	2.68086	+	2.68086i
$891$	−5.40422	−	5.40422i	−0.181048	−	0.181048i
$892$			11.0194i			0.368957i
$893$		−	21.2500i		−	0.711106i
$894$	−12.1748	−	12.1748i	−0.407186	−	0.407186i
$895$	−10.3852	−	10.3852i	−0.347138	−	0.347138i
$896$	−18.5618	+	18.5618i	−0.620108	+	0.620108i
$897$	−21.3483			−0.712800
$898$	−5.14154	+	5.14154i	−0.171575	+	0.171575i
$899$		−	9.06385i		−	0.302296i
$900$	−3.57576			−0.119192
$901$	8.87918	+	16.3618i	0.295808	+	0.545090i
$902$	−14.8881			−0.495719
$903$			96.5759i			3.21385i
$904$	0.826568	−	0.826568i	0.0274913	−	0.0274913i
$905$	45.6013			1.51584
$906$	−13.5716	+	13.5716i	−0.450887	+	0.450887i
$907$	9.80888	+	9.80888i	0.325698	+	0.325698i	0.850948	−	0.525250i	$-0.176028\pi$
$907$	9.80888	+	9.80888i	0.325698	+	0.325698i	−0.525250	+	0.850948i	$0.676028\pi$
$908$	27.0815	+	27.0815i	0.898732	+	0.898732i
$909$			6.70919i			0.222530i
$910$			82.8967i			2.74800i
$911$	−30.3215	−	30.3215i	−1.00460	−	1.00460i	−0.999989	−	0.00460592i	$-0.998534\pi$
$911$	−30.3215	−	30.3215i	−1.00460	−	1.00460i	−0.00460592	−	0.999989i	$-0.501466\pi$
$912$	20.1195	+	20.1195i	0.666224	+	0.666224i
$913$	−10.7037	+	10.7037i	−0.354240	+	0.354240i
$914$	−65.3719			−2.16231
$915$	16.4609	−	16.4609i	0.544181	−	0.544181i
$916$			4.90889i			0.162194i
$917$	−44.0686			−1.45527
$918$	12.2356	−	41.2743i	0.403836	−	1.36225i
$919$	31.3774			1.03504			0.517522	−	0.855670i	$-0.326854\pi$
$919$	31.3774			1.03504			0.517522	+	0.855670i	$0.326854\pi$
$920$			10.6662i			0.351653i
$921$	−26.8399	+	26.8399i	−0.884404	+	0.884404i
$922$	18.8525			0.620873
$923$	9.46425	−	9.46425i	0.311520	−	0.311520i
$924$	−8.73867	−	8.73867i	−0.287481	−	0.287481i
$925$	−8.41763	−	8.41763i	−0.276770	−	0.276770i
$926$			31.0765i			1.02124i
$927$			3.97670i			0.130612i
$928$	23.1606	+	23.1606i	0.760284	+	0.760284i
$929$	−25.8750	−	25.8750i	−0.848931	−	0.848931i	0.141069	−	0.990000i	$-0.454946\pi$
$929$	−25.8750	−	25.8750i	−0.848931	−	0.848931i	−0.990000	+	0.141069i	$0.954946\pi$
$930$	−14.3245	+	14.3245i	−0.469719	+	0.469719i
$931$	−58.0987			−1.90411
$932$	−8.04021	+	8.04021i	−0.263366	+	0.263366i
$933$		−	14.5817i		−	0.477384i
$934$	−20.2683			−0.663198
$935$	−11.7439	+	6.37315i	−0.384066	+	0.208424i
$936$	0.807782			0.0264032
$937$		−	29.3987i		−	0.960415i	−0.877155	−	0.480208i	$-0.840561\pi$
$937$		−	29.3987i		−	0.960415i	0.877155	−	0.480208i	$-0.159439\pi$
$938$	−14.0076	+	14.0076i	−0.457365	+	0.457365i
$939$	25.4496			0.830515
$940$	−20.6912	+	20.6912i	−0.674871	+	0.674871i
$941$	15.0419	+	15.0419i	0.490353	+	0.490353i	0.908418	−	0.418064i	$-0.137291\pi$
$941$	15.0419	+	15.0419i	0.490353	+	0.490353i	−0.418064	+	0.908418i	$0.637291\pi$
$942$	−19.0921	−	19.0921i	−0.622054	−	0.622054i
$943$			36.2756i			1.18130i
$944$			0.479876i			0.0156186i
$945$	59.1446	+	59.1446i	1.92397	+	1.92397i
$946$	17.1302	+	17.1302i	0.556950	+	0.556950i
$947$	−25.2408	+	25.2408i	−0.820215	+	0.820215i	−0.986139	−	0.165923i	$-0.946940\pi$
$947$	−25.2408	+	25.2408i	−0.820215	+	0.820215i	0.165923	+	0.986139i	$0.446940\pi$
$948$	−15.4187			−0.500776
$949$	6.66400	−	6.66400i	0.216322	−	0.216322i
$950$		−	40.1418i		−	1.30237i
$951$	39.3797			1.27698
$952$	−3.91309	+	13.2000i	−0.126824	+	0.427814i
$953$	−17.4705			−0.565926			−0.282963	−	0.959131i	$-0.591317\pi$
$953$	−17.4705			−0.565926			−0.282963	+	0.959131i	$0.591317\pi$
$954$		−	3.43361i		−	0.111167i
$955$	5.69002	−	5.69002i	0.184125	−	0.184125i
$956$	14.3674			0.464674
$957$	5.07862	−	5.07862i	0.164169	−	0.164169i
$958$	38.6944	+	38.6944i	1.25016	+	1.25016i
$959$	46.7725	+	46.7725i	1.51036	+	1.51036i
$960$		−	25.0616i		−	0.808859i
$961$			26.8581i			0.866391i
$962$	−8.31193	−	8.31193i	−0.267987	−	0.267987i
$963$	−3.36494	−	3.36494i	−0.108434	−	0.108434i
$964$	12.5509	−	12.5509i	0.404238	−	0.404238i
$965$	18.6780			0.601267
$966$	−47.4557	+	47.4557i	−1.52686	+	1.52686i
$967$		−	8.41879i		−	0.270730i	−0.990796	−	0.135365i	$-0.956779\pi$
$967$		−	8.41879i		−	0.270730i	0.990796	−	0.135365i	$-0.0432207\pi$
$968$	0.709222			0.0227952
$969$	24.4194	+	7.23906i	0.784465	+	0.232552i
$970$	−32.3951			−1.04015
$971$			1.67928i			0.0538907i	0.999637	+	0.0269453i	$0.00857801\pi$
$971$			1.67928i			0.0538907i	−0.999637	+	0.0269453i	$0.991422\pi$
$972$	−4.74244	+	4.74244i	−0.152114	+	0.152114i
$973$	−22.0888			−0.708133
$974$	43.1456	−	43.1456i	1.38247	−	1.38247i
$975$	17.8974	+	17.8974i	0.573177	+	0.573177i
$976$	−14.5077	−	14.5077i	−0.464382	−	0.464382i
$977$		−	26.5779i		−	0.850303i	−0.905122	−	0.425151i	$-0.860221\pi$
$977$		−	26.5779i		−	0.850303i	0.905122	−	0.425151i	$-0.139779\pi$
$978$			12.0901i			0.386598i
$979$	−12.9574	−	12.9574i	−0.414121	−	0.414121i
$980$	56.5707	+	56.5707i	1.80708	+	1.80708i
$981$	−3.37809	+	3.37809i	−0.107854	+	0.107854i
$982$	29.4681			0.940364
$983$	6.79645	−	6.79645i	0.216773	−	0.216773i	−0.590364	−	0.807137i	$-0.701016\pi$
$983$	6.79645	−	6.79645i	0.216773	−	0.216773i	0.807137	+	0.590364i	$0.201016\pi$
$984$			8.94036i			0.285008i
$985$	−48.4306			−1.54313
$986$	33.5320	+	9.94047i	1.06788	+	0.316569i
$987$	42.1220			1.34076
$988$		−	17.7845i		−	0.565800i
$989$	41.7386	−	41.7386i	1.32721	−	1.32721i
$990$	2.46452			0.0783276
$991$	−28.1286	+	28.1286i	−0.893534	+	0.893534i	−0.994854	−	0.101320i	$-0.967694\pi$
$991$	−28.1286	+	28.1286i	−0.893534	+	0.893534i	0.101320	+	0.994854i	$0.467694\pi$
$992$	10.5836	+	10.5836i	0.336030	+	0.336030i
$993$	30.0956	+	30.0956i	0.955056	+	0.955056i
$994$		−	42.0766i		−	1.33459i
$995$			56.6081i			1.79460i
$996$	−28.0955	−	28.0955i	−0.890239	−	0.890239i
$997$	−43.4591	−	43.4591i	−1.37636	−	1.37636i	−0.850683	−	0.525680i	$-0.823811\pi$
$997$	−43.4591	−	43.4591i	−1.37636	−	1.37636i	−0.525680	−	0.850683i	$-0.676189\pi$
$998$	−39.0899	+	39.0899i	−1.23737	+	1.23737i
$999$	−11.8607			−0.375255

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.e.b.89.3	✓	28
17.8	even	8		3179.2.a.be.1.3		14
17.9	even	8		3179.2.a.bd.1.3		14
17.13	even	4	inner	187.2.e.b.166.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.3	✓	28	1.1	even	1	trivial
187.2.e.b.166.12	yes	28	17.13	even	4	inner
3179.2.a.bd.1.3		14	17.9	even	8
3179.2.a.be.1.3		14	17.8	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.90463i q^{2} +(-1.14033 + 1.14033i) q^{3} -1.62763 q^{4} +(-2.29152 + 2.29152i) q^{5} +(2.17192 + 2.17192i) q^{6} +(3.32922 + 3.32922i) q^{7} -0.709222i q^{8} +0.399285i q^{9} +O(q^{10})\)	\(q-1.90463i q^{2} +(-1.14033 + 1.14033i) q^{3} -1.62763 q^{4} +(-2.29152 + 2.29152i) q^{5} +(2.17192 + 2.17192i) q^{6} +(3.32922 + 3.32922i) q^{7} -0.709222i q^{8} +0.399285i q^{9} +(4.36451 + 4.36451i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(1.85604 - 1.85604i) q^{12} +2.85253 q^{13} +(6.34095 - 6.34095i) q^{14} -5.22619i q^{15} -4.60608 q^{16} +(-3.62388 + 1.96660i) q^{17} +0.760491 q^{18} +3.83050i q^{19} +(3.72975 - 3.72975i) q^{20} -7.59283 q^{21} +(-1.34678 + 1.34678i) q^{22} +(3.28150 + 3.28150i) q^{23} +(0.808748 + 0.808748i) q^{24} -5.50212i q^{25} -5.43302i q^{26} +(-3.87631 - 3.87631i) q^{27} +(-5.41875 - 5.41875i) q^{28} +(3.14919 - 3.14919i) q^{29} -9.95398 q^{30} +(1.43907 - 1.43907i) q^{31} +7.35445i q^{32} +1.61267 q^{33} +(3.74565 + 6.90216i) q^{34} -15.2579 q^{35} -0.649889i q^{36} +(1.52989 - 1.52989i) q^{37} +7.29570 q^{38} +(-3.25283 + 3.25283i) q^{39} +(1.62519 + 1.62519i) q^{40} +(5.52729 + 5.52729i) q^{41} +14.4616i q^{42} -12.7194i q^{43} +(1.15091 + 1.15091i) q^{44} +(-0.914968 - 0.914968i) q^{45} +(6.25006 - 6.25006i) q^{46} -5.54760 q^{47} +(5.25246 - 5.25246i) q^{48} +15.1674i q^{49} -10.4795 q^{50} +(1.88985 - 6.37500i) q^{51} -4.64287 q^{52} -4.51499i q^{53} +(-7.38296 + 7.38296i) q^{54} +3.24070 q^{55} +(2.36115 - 2.36115i) q^{56} +(-4.36804 - 4.36804i) q^{57} +(-5.99806 - 5.99806i) q^{58} -0.104183i q^{59} +8.50632i q^{60} +(3.14970 + 3.14970i) q^{61} +(-2.74091 - 2.74091i) q^{62} +(-1.32931 + 1.32931i) q^{63} +4.79539 q^{64} +(-6.53662 + 6.53662i) q^{65} -3.07155i q^{66} -2.20907 q^{67} +(5.89835 - 3.20090i) q^{68} -7.48400 q^{69} +29.0608i q^{70} +(3.31785 - 3.31785i) q^{71} +0.283181 q^{72} +(2.33617 - 2.33617i) q^{73} +(-2.91388 - 2.91388i) q^{74} +(6.27424 + 6.27424i) q^{75} -6.23465i q^{76} -4.70823i q^{77} +(6.19545 + 6.19545i) q^{78} +(-4.15365 - 4.15365i) q^{79} +(10.5549 - 10.5549i) q^{80} +7.64272 q^{81} +(10.5275 - 10.5275i) q^{82} -15.1373i q^{83} +12.3584 q^{84} +(3.79769 - 12.8107i) q^{85} -24.2257 q^{86} +7.18225i q^{87} +(-0.501495 + 0.501495i) q^{88} +18.3246 q^{89} +(-1.74268 + 1.74268i) q^{90} +(9.49669 + 9.49669i) q^{91} +(-5.34108 - 5.34108i) q^{92} +3.28205i q^{93} +10.5661i q^{94} +(-8.77765 - 8.77765i) q^{95} +(-8.38652 - 8.38652i) q^{96} +(-3.71120 + 3.71120i) q^{97} +28.8884 q^{98} +(0.282337 - 0.282337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Introduction

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