LMFDB - Embedded newform 189.2.u.a.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.279530 - 1.58529i) q^{2} +(-1.44281 + 0.958286i) q^{3} +(-0.555633 + 0.202234i) q^{4} +(0.230811 - 0.0840085i) q^{5} +(1.92247 + 2.01940i) q^{6} +(-1.31413 - 2.29631i) q^{7} +(-1.13383 - 1.96386i) q^{8} +(1.16338 - 2.76524i) q^{9} +O(q^{10})$	\(q+(-0.279530 - 1.58529i) q^{2} +(-1.44281 + 0.958286i) q^{3} +(-0.555633 + 0.202234i) q^{4} +(0.230811 - 0.0840085i) q^{5} +(1.92247 + 2.01940i) q^{6} +(-1.31413 - 2.29631i) q^{7} +(-1.13383 - 1.96386i) q^{8} +(1.16338 - 2.76524i) q^{9} +(-0.197697 - 0.342421i) q^{10} +(-4.84773 - 1.76443i) q^{11} +(0.607872 - 0.824240i) q^{12} +(4.55694 - 1.65859i) q^{13} +(-3.27299 + 2.72518i) q^{14} +(-0.252512 + 0.342391i) q^{15} +(-3.70226 + 3.10657i) q^{16} +(-0.800052 - 1.38573i) q^{17} +(-4.70892 - 1.07132i) q^{18} +(-1.01489 + 1.75785i) q^{19} +(-0.111257 + 0.0933558i) q^{20} +(4.09656 + 2.05382i) q^{21} +(-1.44205 + 8.17829i) q^{22} +(0.761889 - 4.32089i) q^{23} +(3.51784 + 1.74693i) q^{24} +(-3.78401 + 3.17516i) q^{25} +(-3.90315 - 6.76046i) q^{26} +(0.971367 + 5.10455i) q^{27} +(1.19457 + 1.01014i) q^{28} +(4.90485 + 1.78522i) q^{29} +(0.613375 + 0.304597i) q^{30} +(6.87843 - 2.50354i) q^{31} +(2.48544 + 2.08554i) q^{32} +(8.68517 - 2.09979i) q^{33} +(-1.97315 + 1.65567i) q^{34} +(-0.496227 - 0.419617i) q^{35} +(-0.0871845 + 1.77173i) q^{36} +7.97175 q^{37} +(3.07039 + 1.11753i) q^{38} +(-4.98537 + 6.75988i) q^{39} +(-0.426682 - 0.358029i) q^{40} +(-5.13780 + 1.87001i) q^{41} +(2.11079 - 7.06836i) q^{42} +(-1.25671 - 7.12716i) q^{43} +3.05039 q^{44} +(0.0362167 - 0.735983i) q^{45} -7.06285 q^{46} +(2.05603 + 0.748334i) q^{47} +(2.36466 - 8.02999i) q^{48} +(-3.54610 + 6.03533i) q^{49} +(6.09130 + 5.11121i) q^{50} +(2.48225 + 1.23266i) q^{51} +(-2.19656 + 1.84314i) q^{52} +(3.36601 - 5.83010i) q^{53} +(7.82069 - 2.96678i) q^{54} -1.26714 q^{55} +(-3.01962 + 5.18441i) q^{56} +(-0.220226 - 3.50879i) q^{57} +(1.45904 - 8.27464i) q^{58} +(9.52886 + 7.99566i) q^{59} +(0.0710608 - 0.241310i) q^{60} +(-3.15274 - 1.14750i) q^{61} +(-5.89158 - 10.2045i) q^{62} +(-7.87869 + 0.962425i) q^{63} +(-2.22153 + 3.84780i) q^{64} +(0.912458 - 0.765644i) q^{65} +(-5.75654 - 13.1816i) q^{66} +(-1.29472 + 7.34273i) q^{67} +(0.724777 + 0.608160i) q^{68} +(3.04139 + 6.96431i) q^{69} +(-0.526505 + 0.903961i) q^{70} +(-0.508002 + 0.879885i) q^{71} +(-6.74961 + 0.850619i) q^{72} +5.79634 q^{73} +(-2.22834 - 12.6376i) q^{74} +(2.41687 - 8.20730i) q^{75} +(0.208412 - 1.18196i) q^{76} +(2.31889 + 13.4506i) q^{77} +(12.1099 + 6.01369i) q^{78} +(-1.44495 - 8.19469i) q^{79} +(-0.593546 + 1.02805i) q^{80} +(-6.29311 - 6.43403i) q^{81} +(4.40068 + 7.62220i) q^{82} +(6.59880 + 2.40177i) q^{83} +(-2.69154 - 0.312703i) q^{84} +(-0.301074 - 0.252631i) q^{85} +(-10.9473 + 3.98451i) q^{86} +(-8.78749 + 2.12452i) q^{87} +(2.03143 + 11.5208i) q^{88} +(-7.78417 + 13.4826i) q^{89} +(-1.17687 + 0.148315i) q^{90} +(-9.79707 - 8.28455i) q^{91} +(0.450499 + 2.55491i) q^{92} +(-7.52512 + 10.2036i) q^{93} +(0.611607 - 3.46859i) q^{94} +(-0.0865749 + 0.490991i) q^{95} +(-5.58455 - 0.627255i) q^{96} +(-1.78818 - 10.1413i) q^{97} +(10.5590 + 3.93456i) q^{98} +(-10.5188 + 11.3525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.279530	−	1.58529i	−0.197658	−	1.12097i	−0.908583	−	0.417704i	$-0.862835\pi$
$2$	−0.279530	−	1.58529i	−0.197658	−	1.12097i	0.710925	−	0.703267i	$-0.248276\pi$
$3$	−1.44281	+	0.958286i	−0.833004	+	0.553267i
$3$	−1.44281	+	0.958286i	−0.833004	+	0.553267i
$4$	−0.555633	+	0.202234i	−0.277817	+	0.101117i
$5$	0.230811	−	0.0840085i	0.103222	−	0.0375697i	−0.289893	−	0.957059i	$-0.593620\pi$
$5$	0.230811	−	0.0840085i	0.103222	−	0.0375697i	0.393115	+	0.919489i	$0.371397\pi$
$6$	1.92247	+	2.01940i	0.784846	+	0.824417i
$7$	−1.31413	−	2.29631i	−0.496696	−	0.867924i
$7$	−1.31413	−	2.29631i	−0.496696	−	0.867924i
$8$	−1.13383	−	1.96386i	−0.400871	−	0.694328i
$9$	1.16338	−	2.76524i	0.387792	−	0.921747i
$10$	−0.197697	−	0.342421i	−0.0625172	−	0.108283i
$11$	−4.84773	−	1.76443i	−1.46165	−	0.531996i	−0.515828	−	0.856692i	$-0.672516\pi$
$11$	−4.84773	−	1.76443i	−1.46165	−	0.531996i	−0.945818	+	0.324696i	$0.894738\pi$
$12$	0.607872	−	0.824240i	0.175478	−	0.237937i
$13$	4.55694	−	1.65859i	1.26387	−	0.460010i	0.378803	−	0.925477i	$-0.376336\pi$
$13$	4.55694	−	1.65859i	1.26387	−	0.460010i	0.885065	+	0.465467i	$0.154114\pi$
$14$	−3.27299	+	2.72518i	−0.874743	+	0.728334i
$15$	−0.252512	+	0.342391i	−0.0651983	+	0.0884051i
$16$	−3.70226	+	3.10657i	−0.925565	+	0.776641i
$17$	−0.800052	−	1.38573i	−0.194041	−	0.336089i	0.752545	−	0.658541i	$-0.228826\pi$
$17$	−0.800052	−	1.38573i	−0.194041	−	0.336089i	−0.946586	+	0.322452i	$0.895493\pi$
$18$	−4.70892	−	1.07132i	−1.10990	−	0.252513i
$19$	−1.01489	+	1.75785i	−0.232832	+	0.403278i	−0.958641	−	0.284620i	$-0.908133\pi$
$19$	−1.01489	+	1.75785i	−0.232832	+	0.403278i	0.725808	+	0.687897i	$0.241466\pi$
$20$	−0.111257	+	0.0933558i	−0.0248778	+	0.0208750i
$21$	4.09656	+	2.05382i	0.893944	+	0.448179i
$22$	−1.44205	+	8.17829i	−0.307447	+	1.74362i
$23$	0.761889	−	4.32089i	0.158865	−	0.900967i	−0.796302	−	0.604899i	$-0.793213\pi$
$23$	0.761889	−	4.32089i	0.158865	−	0.900967i	0.955167	−	0.296068i	$-0.0956756\pi$
$24$	3.51784	+	1.74693i	0.718075	+	0.356590i
$25$	−3.78401	+	3.17516i	−0.756801	+	0.635032i
$26$	−3.90315	−	6.76046i	−0.765472	−	1.32584i
$27$	0.971367	+	5.10455i	0.186940	+	0.982371i
$28$	1.19457	+	1.01014i	0.225752	+	0.190899i
$29$	4.90485	+	1.78522i	0.910807	+	0.331507i	0.754575	−	0.656214i	$-0.227843\pi$
$29$	4.90485	+	1.78522i	0.910807	+	0.331507i	0.156232	+	0.987720i	$0.450065\pi$
$30$	0.613375	+	0.304597i	0.111987	+	0.0556115i
$31$	6.87843	−	2.50354i	1.23540	−	0.449650i	0.359958	−	0.932969i	$-0.382791\pi$
$31$	6.87843	−	2.50354i	1.23540	−	0.449650i	0.875444	+	0.483319i	$0.160569\pi$
$32$	2.48544	+	2.08554i	0.439369	+	0.368674i
$33$	8.68517	−	2.09979i	1.51189	−	0.365526i
$34$	−1.97315	+	1.65567i	−0.338393	+	0.283945i
$35$	−0.496227	−	0.419617i	−0.0838777	−	0.0709282i
$36$	−0.0871845	+	1.77173i	−0.0145307	+	0.295289i
$37$	7.97175			1.31055			0.655273	−	0.755392i	$-0.272553\pi$
$37$	7.97175			1.31055			0.655273	+	0.755392i	$0.272553\pi$
$38$	3.07039	+	1.11753i	0.498084	+	0.181288i
$39$	−4.98537	+	6.75988i	−0.798299	+	1.08245i
$40$	−0.426682	−	0.358029i	−0.0674644	−	0.0566094i
$41$	−5.13780	+	1.87001i	−0.802389	+	0.292046i	−0.710476	−	0.703721i	$-0.751520\pi$
$41$	−5.13780	+	1.87001i	−0.802389	+	0.292046i	−0.0919131	+	0.995767i	$0.529298\pi$
$42$	2.11079	−	7.06836i	0.325702	−	1.09067i
$43$	−1.25671	−	7.12716i	−0.191646	−	1.08688i	−0.917114	−	0.398625i	$-0.869488\pi$
$43$	−1.25671	−	7.12716i	−0.191646	−	1.08688i	0.725468	−	0.688256i	$-0.241624\pi$
$44$	3.05039			0.459863
$45$	0.0362167	−	0.735983i	0.00539886	−	0.109714i
$46$	−7.06285			−1.04136
$47$	2.05603	+	0.748334i	0.299903	+	0.109156i	0.487589	−	0.873073i	$-0.337877\pi$
$47$	2.05603	+	0.748334i	0.299903	+	0.109156i	−0.187686	+	0.982229i	$0.560099\pi$
$48$	2.36466	−	8.02999i	0.341310	−	1.15903i
$49$	−3.54610	+	6.03533i	−0.506586	+	0.862190i
$50$	6.09130	+	5.11121i	0.861440	+	0.722834i
$51$	2.48225	+	1.23266i	0.347584	+	0.172607i
$52$	−2.19656	+	1.84314i	−0.304609	+	0.255597i
$53$	3.36601	−	5.83010i	0.462357	−	0.800826i	−0.536721	−	0.843760i	$-0.680337\pi$
$53$	3.36601	−	5.83010i	0.462357	−	0.800826i	0.999078	+	0.0429338i	$0.0136705\pi$
$54$	7.82069	−	2.96678i	1.06426	−	0.403727i
$55$	−1.26714			−0.170861
$56$	−3.01962	+	5.18441i	−0.403514	+	0.692795i
$57$	−0.220226	−	3.50879i	−0.0291697	−	0.464750i
$58$	1.45904	−	8.27464i	0.191582	−	1.08651i
$59$	9.52886	+	7.99566i	1.24055	+	1.04095i	0.997481	+	0.0709378i	$0.0225992\pi$
$59$	9.52886	+	7.99566i	1.24055	+	1.04095i	0.243071	+	0.970009i	$0.421845\pi$
$60$	0.0710608	−	0.241310i	0.00917391	−	0.0311530i
$61$	−3.15274	−	1.14750i	−0.403667	−	0.146923i	0.132204	−	0.991223i	$-0.457795\pi$
$61$	−3.15274	−	1.14750i	−0.403667	−	0.146923i	−0.535871	+	0.844300i	$0.680017\pi$
$62$	−5.89158	−	10.2045i	−0.748231	−	1.29597i
$63$	−7.87869	+	0.962425i	−0.992621	+	0.121254i
$64$	−2.22153	+	3.84780i	−0.277691	+	0.480975i
$65$	0.912458	−	0.765644i	0.113177	−	0.0949664i
$66$	−5.75654	−	13.1816i	−0.708581	−	1.62254i
$67$	−1.29472	+	7.34273i	−0.158175	+	0.897058i	0.797649	+	0.603121i	$0.206077\pi$
$67$	−1.29472	+	7.34273i	−0.158175	+	0.897058i	−0.955825	+	0.293936i	$0.905035\pi$
$68$	0.724777	+	0.608160i	0.0878922	+	0.0737503i
$69$	3.04139	+	6.96431i	0.366140	+	0.838404i
$70$	−0.526505	+	0.903961i	−0.0629294	+	0.108044i
$71$	−0.508002	+	0.879885i	−0.0602887	+	0.104423i	−0.894594	−	0.446879i	$-0.852535\pi$
$71$	−0.508002	+	0.879885i	−0.0602887	+	0.104423i	0.834306	+	0.551302i	$0.185869\pi$
$72$	−6.74961	+	0.850619i	−0.795449	+	0.100246i
$73$	5.79634			0.678410			0.339205	−	0.940712i	$-0.389842\pi$
$73$	5.79634			0.678410			0.339205	+	0.940712i	$0.389842\pi$
$74$	−2.22834	−	12.6376i	−0.259040	−	1.46909i
$75$	2.41687	−	8.20730i	0.279077	−	0.947697i
$76$	0.208412	−	1.18196i	0.0239065	−	0.135580i
$77$	2.31889	+	13.4506i	0.264262	+	1.53284i
$78$	12.1099	+	6.01369i	1.37118	+	0.680917i
$79$	−1.44495	−	8.19469i	−0.162569	−	0.921975i	−0.951536	−	0.307539i	$-0.900495\pi$
$79$	−1.44495	−	8.19469i	−0.162569	−	0.921975i	0.788967	−	0.614436i	$-0.210616\pi$
$80$	−0.593546	+	1.02805i	−0.0663605	+	0.114940i
$81$	−6.29311	−	6.43403i	−0.699235	−	0.714892i
$82$	4.40068	+	7.62220i	0.485973	+	0.841731i
$83$	6.59880	+	2.40177i	0.724312	+	0.263628i	0.677755	−	0.735288i	$-0.262953\pi$
$83$	6.59880	+	2.40177i	0.724312	+	0.263628i	0.0465569	+	0.998916i	$0.485175\pi$
$84$	−2.69154	−	0.312703i	−0.293671	−	0.0341187i
$85$	−0.301074	−	0.252631i	−0.0326561	−	0.0274017i
$86$	−10.9473	+	3.98451i	−1.18048	+	0.429661i
$87$	−8.78749	+	2.12452i	−0.942118	+	0.227773i
$88$	2.03143	+	11.5208i	0.216551	+	1.22812i
$89$	−7.78417	+	13.4826i	−0.825120	+	1.42915i	0.0767068	+	0.997054i	$0.475559\pi$
$89$	−7.78417	+	13.4826i	−0.825120	+	1.42915i	−0.901827	+	0.432097i	$0.857774\pi$
$90$	−1.17687	+	0.148315i	−0.124053	+	0.0156338i
$91$	−9.79707	−	8.28455i	−1.02701	−	0.868457i
$92$	0.450499	+	2.55491i	0.0469678	+	0.266368i
$93$	−7.52512	+	10.2036i	−0.780319	+	1.05807i
$94$	0.611607	−	3.46859i	0.0630824	−	0.357758i
$95$	−0.0865749	+	0.490991i	−0.00888240	+	0.0503746i
$96$	−5.58455	−	0.627255i	−0.569971	−	0.0640190i
$97$	−1.78818	−	10.1413i	−0.181563	−	1.02969i	−0.930293	−	0.366818i	$-0.880447\pi$
$97$	−1.78818	−	10.1413i	−0.181563	−	1.02969i	0.748730	−	0.662875i	$-0.230664\pi$
$98$	10.5590	+	3.93456i	1.06662	+	0.397450i
$99$	−10.5188	+	11.3525i	−1.05718	+	1.14096i
$100$	1.46039	−	2.52948i	0.146039	−	0.252948i
$101$	−0.216381	−	1.22716i	−0.0215307	−	0.122107i	0.972148	−	0.234368i	$-0.0753019\pi$
$101$	−0.216381	−	1.22716i	−0.0215307	−	0.122107i	−0.993679	+	0.112261i	$0.964191\pi$
$102$	1.26027	−	4.27966i	0.124785	−	0.423749i
$103$	−5.49218	+	1.99899i	−0.541161	+	0.196966i	−0.598115	−	0.801410i	$-0.704083\pi$
$103$	−5.49218	+	1.99899i	−0.541161	+	0.196966i	0.0569541	+	0.998377i	$0.481861\pi$
$104$	−8.42404	−	7.06861i	−0.826045	−	0.693134i
$105$	1.11807	+	0.129898i	0.109113	+	0.0126767i
$106$	−10.1833	−	3.70643i	−0.989092	−	0.360000i
$107$	−0.697132	−	1.20747i	−0.0673943	−	0.116730i	0.830359	−	0.557228i	$-0.188135\pi$
$107$	−0.697132	−	1.20747i	−0.0673943	−	0.116730i	−0.897754	+	0.440498i	$0.854802\pi$
$108$	−1.57204	−	2.63981i	−0.151269	−	0.254016i
$109$	7.71790	−	13.3678i	0.739241	−	1.28040i	−0.213596	−	0.976922i	$-0.568518\pi$
$109$	7.71790	−	13.3678i	0.739241	−	1.28040i	0.952837	−	0.303481i	$-0.0981489\pi$
$110$	0.354204	+	2.00879i	0.0337720	+	0.191530i
$111$	−11.5017	+	7.63921i	−1.09169	+	0.725082i
$112$	11.9989	+	4.41910i	1.13379	+	0.417566i
$113$	1.58825	−	9.00739i	0.149410	−	0.847344i	−0.814310	−	0.580430i	$-0.802885\pi$
$113$	1.58825	−	9.00739i	0.149410	−	0.847344i	0.963720	−	0.266915i	$-0.0860042\pi$
$114$	−5.50090	+	1.32993i	−0.515206	+	0.124560i
$115$	−0.187139	−	1.06132i	−0.0174508	−	0.0989682i
$116$	−3.08633			−0.286558
$117$	0.715030	−	14.5306i	0.0661046	−	1.34335i
$118$	10.0119	−	17.3411i	0.921667	−	1.59637i
$119$	−2.13070	+	3.65821i	−0.195321	+	0.335347i
$120$	0.958714	+	0.107682i	0.0875182	+	0.00983002i
$121$	11.9608	+	10.0363i	1.08735	+	0.912393i
$122$	−0.937845	+	5.31878i	−0.0849085	+	0.481540i
$123$	5.62084	−	7.62154i	0.506814	−	0.687211i
$124$	−3.31558	+	2.78210i	−0.297748	+	0.249840i
$125$	−1.22071	+	2.11434i	−0.109184	+	0.189112i
$126$	3.72806	+	12.2210i	0.332122	+	1.08873i
$127$	−5.99018	−	10.3753i	−0.531543	−	0.920659i	−0.999322	−	0.0368140i	$-0.988279\pi$
$127$	−5.99018	−	10.3753i	−0.531543	−	0.920659i	0.467779	−	0.883845i	$-0.345054\pi$
$128$	12.8186	+	4.66558i	1.13301	+	0.412383i
$129$	8.64304	+	9.07881i	0.760978	+	0.799345i
$130$	−1.46883	−	1.23249i	−0.128825	−	0.108097i
$131$	2.70243	−	15.3262i	0.236112	−	1.33906i	−0.604147	−	0.796873i	$-0.706486\pi$
$131$	2.70243	−	15.3262i	0.236112	−	1.33906i	0.840259	−	0.542185i	$-0.182403\pi$
$132$	−4.40112	+	2.92315i	−0.383068	+	0.254427i
$133$	5.37027	+	0.0204650i	0.465661	+	0.00177454i
$134$	12.0023			1.03684
$135$	0.653028	+	1.09659i	0.0562037	+	0.0943791i
$136$	−1.81425	+	3.14238i	−0.155571	+	0.269456i
$137$	12.6174	−	10.5872i	1.07797	−	0.904527i	0.0822224	−	0.996614i	$-0.473798\pi$
$137$	12.6174	−	10.5872i	1.07797	−	0.904527i	0.995751	+	0.0920869i	$0.0293538\pi$
$138$	10.1903	−	6.76823i	0.867457	−	0.576150i
$139$	−9.40916	−	7.89523i	−0.798075	−	0.669664i	0.149655	−	0.988738i	$-0.452184\pi$
$139$	−9.40916	−	7.89523i	−0.798075	−	0.669664i	−0.947730	+	0.319074i	$0.896628\pi$
$140$	0.360581	+	0.132799i	0.0304746	+	0.0112236i
$141$	−3.68357	+	0.890565i	−0.310213	+	0.0749991i
$142$	1.53688	+	0.559377i	0.128972	+	0.0469419i
$143$	−25.0173			−2.09205
$144$	4.28328	+	13.8517i	0.356940	+	1.15431i
$145$	1.28207			0.106470
$146$	−1.62025	−	9.18890i	−0.134093	−	0.760479i
$147$	−0.667235	−	12.1060i	−0.0550326	−	0.998485i
$148$	−4.42936	+	1.61216i	−0.364092	+	0.132518i
$149$	2.57300	+	2.15900i	0.210788	+	0.176872i	0.742069	−	0.670324i	$-0.233845\pi$
$149$	2.57300	+	2.15900i	0.210788	+	0.176872i	−0.531281	+	0.847196i	$0.678289\pi$
$150$	−13.6866	−	1.53727i	−1.11750	−	0.125518i
$151$	9.11293	+	3.31683i	0.741600	+	0.269920i	0.685067	−	0.728481i	$-0.259773\pi$
$151$	9.11293	+	3.31683i	0.741600	+	0.269920i	0.0565331	+	0.998401i	$0.481995\pi$
$152$	4.60288			0.373343
$153$	−4.76264	+	0.600211i	−0.385037	+	0.0485242i
$154$	20.6750	−	7.43597i	1.66604	−	0.599208i
$155$	1.37730	−	1.15569i	0.110628	−	0.0928275i
$156$	1.40296	−	4.76422i	0.112327	−	0.381443i
$157$	−1.72819	−	1.45013i	−0.137925	−	0.115733i	0.571215	−	0.820800i	$-0.306472\pi$
$157$	−1.72819	−	1.45013i	−0.137925	−	0.115733i	−0.709140	+	0.705068i	$0.750917\pi$
$158$	−12.5871	+	4.58132i	−1.00137	+	0.364471i
$159$	0.730406	+	11.6373i	0.0579250	+	0.922898i
$160$	0.748872	+	0.272567i	0.0592035	+	0.0215483i
$161$	−10.9233	+	3.92869i	−0.860879	+	0.309624i
$162$	−8.44071	+	11.7749i	−0.663165	+	0.925126i
$163$	−0.843390	−	1.46079i	−0.0660594	−	0.114418i	0.831104	−	0.556117i	$-0.187709\pi$
$163$	−0.843390	−	1.46079i	−0.0660594	−	0.114418i	−0.897163	+	0.441699i	$0.854376\pi$
$164$	2.47655	−	2.07807i	0.193386	−	0.162270i
$165$	1.82824	−	1.21428i	0.142328	−	0.0945318i
$166$	1.96294	−	11.1324i	0.152354	−	0.864041i
$167$	−2.50098	+	14.1838i	−0.193532	+	1.09757i	0.720963	+	0.692974i	$0.243700\pi$
$167$	−2.50098	+	14.1838i	−0.193532	+	1.09757i	−0.914494	+	0.404598i	$0.867411\pi$
$168$	−0.611422	−	10.3737i	−0.0471722	−	0.800352i
$169$	8.05621	−	6.75996i	0.619708	−	0.519997i
$170$	−0.316336	+	0.547909i	−0.0242618	+	0.0420227i
$171$	3.68017	+	4.85146i	0.281429	+	0.371000i
$172$	2.13962	+	3.70593i	0.163145	+	0.282575i
$173$	1.35283	−	1.13516i	0.102854	−	0.0863048i	−0.589910	−	0.807469i	$-0.700837\pi$
$173$	1.35283	−	1.13516i	0.102854	−	0.0863048i	0.692765	+	0.721164i	$0.256393\pi$
$174$	5.82436	+	13.3369i	0.441544	+	1.01107i
$175$	12.2638	+	4.51667i	0.927060	+	0.341429i
$176$	23.4289	−	8.52742i	1.76602	−	0.642779i
$177$	−21.4104	−	2.40481i	−1.60931	−	0.180757i
$178$	23.5498	+	8.57141i	1.76513	+	0.642454i
$179$	9.33259	+	16.1645i	0.697550	+	1.20819i	0.969313	+	0.245829i	$0.0790600\pi$
$179$	9.33259	+	16.1645i	0.697550	+	1.20819i	−0.271763	+	0.962364i	$0.587607\pi$
$180$	0.128717	+	0.416261i	0.00959403	+	0.0310262i
$181$	3.45518	+	5.98454i	0.256821	+	0.444827i	0.965389	−	0.260816i	$-0.0839915\pi$
$181$	3.45518	+	5.98454i	0.256821	+	0.444827i	−0.708567	+	0.705643i	$0.750658\pi$
$182$	−10.3949	+	17.8470i	−0.770518	+	1.32291i
$183$	5.64843	−	1.36560i	0.417544	−	0.100948i
$184$	−9.34946	+	3.40292i	−0.689251	+	0.250867i
$185$	1.83997	−	0.669694i	0.135277	−	0.0492369i
$186$	18.2792	+	9.07731i	1.34030	+	0.665581i
$187$	1.43341	+	8.12929i	0.104822	+	0.594473i
$188$	−1.29374			−0.0943555
$189$	10.4451	−	8.93863i	0.759772	−	0.650190i
$190$	0.802565			0.0582242
$191$	0.731779	+	4.15013i	0.0529497	+	0.300293i	0.999769	−	0.0214718i	$-0.00683522\pi$
$191$	0.731779	+	4.15013i	0.0529497	+	0.300293i	−0.946820	+	0.321764i	$0.895724\pi$
$192$	−0.482060	−	7.68049i	−0.0347897	−	0.554291i
$193$	−16.5826	+	6.03556i	−1.19364	+	0.434449i	−0.861000	−	0.508606i	$-0.830161\pi$
$193$	−16.5826	+	6.03556i	−1.19364	+	0.434449i	−0.332639	+	0.943054i	$0.607939\pi$
$194$	−15.5771	+	5.66959i	−1.11837	+	0.407053i
$195$	−0.582795	+	1.97907i	−0.0417348	+	0.141724i
$196$	0.749783	−	4.07057i	0.0535560	−	0.290755i
$197$	−3.45583	−	5.98566i	−0.246217	−	0.426461i	0.716256	−	0.697838i	$-0.245854\pi$
$197$	−3.45583	−	5.98566i	−0.246217	−	0.426461i	−0.962473	+	0.271377i	$0.912521\pi$
$198$	20.9373	+	13.5021i	1.48795	+	0.959549i
$199$	−2.90529	−	5.03211i	−0.205950	−	0.356717i	0.744485	−	0.667639i	$-0.232695\pi$
$199$	−2.90529	−	5.03211i	−0.205950	−	0.356717i	−0.950435	+	0.310923i	$0.899362\pi$
$200$	10.5260	+	3.83115i	0.744299	+	0.270903i
$201$	−5.16841	−	11.8349i	−0.364551	−	0.834766i
$202$	−1.88492	+	0.686055i	−0.132622	+	0.0482706i
$203$	−2.34621	−	13.6091i	−0.164672	−	0.955170i
$204$	−1.62850	−	0.182913i	−0.114018	−	0.0128065i
$205$	−1.02877	+	0.863238i	−0.0718522	+	0.0602911i
$206$	4.70422	+	8.14794i	0.327758	+	0.567694i
$207$	−11.0619	−	7.13362i	−0.768858	−	0.495821i
$208$	−11.7185	+	20.2970i	−0.812529	+	1.40734i
$209$	8.02153	−	6.73086i	0.554861	−	0.465583i
$210$	−0.106608	−	1.80878i	−0.00735668	−	0.124818i
$211$	−1.52641	+	8.65668i	−0.105082	+	0.595950i	0.886105	+	0.463484i	$0.153401\pi$
$211$	−1.52641	+	8.65668i	−0.105082	+	0.595950i	−0.991187	+	0.132466i	$0.957710\pi$
$212$	−0.691223	+	3.92012i	−0.0474734	+	0.269235i
$213$	−0.110234	−	1.75631i	−0.00755308	−	0.120341i
$214$	−1.71932	+	1.44268i	−0.117530	+	0.0986197i
$215$	−0.888805	−	1.53946i	−0.0606160	−	0.104990i
$216$	8.92324	−	7.69533i	0.607149	−	0.523601i
$217$	−14.7881	−	12.5050i	−1.00388	−	0.848897i
$218$	−23.3493	−	8.49844i	−1.58141	−	0.575587i
$219$	−8.36299	+	5.55455i	−0.565119	+	0.375342i
$220$	0.704065	−	0.256259i	0.0474680	−	0.0172770i
$221$	−5.94415	−	4.98774i	−0.399847	−	0.335511i
$222$	15.3255	+	16.0981i	1.02858	+	1.08044i
$223$	−7.61933	+	6.39338i	−0.510228	+	0.428132i	−0.861210	−	0.508250i	$-0.830293\pi$
$223$	−7.61933	+	6.39338i	−0.510228	+	0.428132i	0.350981	+	0.936383i	$0.385848\pi$
$224$	1.52283	−	8.44803i	0.101749	−	0.564458i
$225$	4.37786	+	14.1576i	0.291857	+	0.943839i
$226$	−14.7233			−0.979381
$227$	18.4448	+	6.71335i	1.22422	+	0.445581i	0.871616	−	0.490190i	$-0.163073\pi$
$227$	18.4448	+	6.71335i	1.22422	+	0.445581i	0.352608	+	0.935771i	$0.385295\pi$
$228$	0.831961	+	1.90506i	0.0550979	+	0.126166i
$229$	7.22389	+	6.06156i	0.477368	+	0.400559i	0.849474	−	0.527631i	$-0.176920\pi$
$229$	7.22389	+	6.06156i	0.477368	+	0.400559i	−0.372106	+	0.928190i	$0.621364\pi$
$230$	−1.63019	+	0.593339i	−0.107491	+	0.0391236i
$231$	−16.2352	−	17.1845i	−1.06820	−	1.13065i
$232$	−2.05536	−	11.6566i	−0.134941	−	0.765290i
$233$	10.4888			0.687145			0.343572	−	0.939126i	$-0.388363\pi$
$233$	10.4888			0.687145			0.343572	+	0.939126i	$0.388363\pi$
$234$	−23.2351	+	2.92821i	−1.51893	+	0.191423i
$235$	0.537422			0.0350575
$236$	−6.91154	−	2.51560i	−0.449903	−	0.163751i
$237$	9.93763	+	10.4387i	0.645519	+	0.678065i
$238$	6.39493	+	2.35520i	0.414521	+	0.152665i
$239$	5.79830	+	4.86535i	0.375061	+	0.314714i	0.810760	−	0.585379i	$-0.199054\pi$
$239$	5.79830	+	4.86535i	0.375061	+	0.314714i	−0.435699	+	0.900093i	$0.643499\pi$
$240$	−0.128796	−	2.05207i	−0.00831377	−	0.132460i
$241$	7.18643	−	6.03013i	0.462919	−	0.388435i	−0.381285	−	0.924458i	$-0.624518\pi$
$241$	7.18643	−	6.03013i	0.462919	−	0.388435i	0.844204	+	0.536023i	$0.180074\pi$
$242$	12.5671	−	21.7669i	0.807844	−	1.39923i
$243$	15.2454	+	3.25245i	0.977992	+	0.208645i
$244$	1.98383			0.127002
$245$	−0.311462	+	1.69093i	−0.0198986	+	0.108029i
$246$	−13.6536	−	6.78024i	−0.870520	−	0.432292i
$247$	−1.70926	+	9.69369i	−0.108758	+	0.616795i
$248$	−12.7156	−	10.6696i	−0.807441	−	0.677523i
$249$	−11.8224	+	2.85825i	−0.749212	+	0.181135i
$250$	3.69307	+	1.34417i	0.233570	+	0.0850126i
$251$	10.5090	+	18.2021i	0.663322	+	1.14891i	0.979737	+	0.200287i	$0.0641873\pi$
$251$	10.5090	+	18.2021i	0.663322	+	1.14891i	−0.316415	+	0.948621i	$0.602479\pi$
$252$	4.18302	−	2.12809i	0.263506	−	0.134057i
$253$	−11.3173	+	19.6022i	−0.711515	+	1.23238i
$254$	−14.7735	+	12.3964i	−0.926970	+	0.777820i
$255$	0.676485	+	0.0759826i	0.0423631	+	0.00475822i
$256$	2.27008	−	12.8743i	0.141880	−	0.804641i
$257$	−18.8715	−	15.8350i	−1.17717	−	0.987762i	−0.999994	−	0.00358315i	$-0.998859\pi$
$257$	−18.8715	−	15.8350i	−1.17717	−	0.987762i	−0.177176	−	0.984179i	$-0.556696\pi$
$258$	11.9766	−	16.2396i	0.745630	−	1.01103i
$259$	−10.4759	−	18.3056i	−0.650944	−	1.13746i
$260$	−0.352153	+	0.609947i	−0.0218396	+	0.0378273i
$261$	10.6427	−	11.4862i	0.658769	−	0.710978i
$262$	−25.0520			−1.54772
$263$	−0.272526	−	1.54557i	−0.0168047	−	0.0953042i	0.975252	−	0.221097i	$-0.0709637\pi$
$263$	−0.272526	−	1.54557i	−0.0168047	−	0.0953042i	−0.992057	+	0.125793i	$0.959853\pi$
$264$	−13.9712	−	14.6756i	−0.859868	−	0.903222i
$265$	0.287136	−	1.62843i	0.0176386	−	0.100034i
$266$	−1.46871	−	8.51917i	−0.0900523	−	0.522344i
$267$	−1.68912	−	26.9122i	−0.103373	−	1.64700i
$268$	−0.765559	−	4.34170i	−0.0467640	−	0.265212i
$269$	2.97432	−	5.15166i	0.181347	−	0.314103i	−0.760992	−	0.648761i	$-0.775288\pi$
$269$	2.97432	−	5.15166i	0.181347	−	0.314103i	0.942340	+	0.334658i	$0.108621\pi$
$270$	1.55587	−	1.34177i	0.0946872	−	0.0816575i
$271$	5.09086	+	8.81763i	0.309248	+	0.535633i	0.978198	−	0.207674i	$-0.0665895\pi$
$271$	5.09086	+	8.81763i	0.309248	+	0.535633i	−0.668950	+	0.743307i	$0.733256\pi$
$272$	7.26687	+	2.64492i	0.440619	+	0.160372i
$273$	22.0742	+	2.56459i	1.33599	+	0.155216i
$274$	−20.3108	−	17.0428i	−1.22702	−	1.02959i
$275$	23.9462	−	8.71570i	1.44401	−	0.525577i
$276$	−3.09832	−	3.25453i	−0.186497	−	0.195900i
$277$	3.13289	+	17.7675i	0.188237	+	1.06755i	0.921725	+	0.387843i	$0.126780\pi$
$277$	3.13289	+	17.7675i	0.188237	+	1.06755i	−0.733488	+	0.679702i	$0.762109\pi$
$278$	−9.88611	+	17.1232i	−0.592929	+	1.02698i
$279$	1.07930	−	21.9331i	0.0646157	−	1.31310i
$280$	−0.261428	+	1.45029i	−0.0156233	+	0.0866717i
$281$	−1.12946	−	6.40548i	−0.0673779	−	0.382119i	−0.999786	−	0.0207105i	$-0.993407\pi$
$281$	−1.12946	−	6.40548i	−0.0673779	−	0.382119i	0.932408	−	0.361408i	$-0.117704\pi$
$282$	2.44148	+	5.59060i	0.145388	+	0.332915i
$283$	2.14044	−	12.1391i	0.127236	−	0.721592i	−0.852718	−	0.522371i	$-0.825048\pi$
$283$	2.14044	−	12.1391i	0.127236	−	0.721592i	0.979955	−	0.199221i	$-0.0638412\pi$
$284$	0.104320	−	0.591628i	0.00619025	−	0.0351067i
$285$	−0.345599	−	0.791368i	−0.0204715	−	0.0468766i
$286$	6.99309	+	39.6598i	0.413510	+	2.34513i
$287$	11.0459	+	9.34055i	0.652017	+	0.551355i
$288$	8.65852	−	4.44659i	0.510208	−	0.262018i
$289$	7.21983	−	12.5051i	0.424696	−	0.735595i
$290$	−0.358377	−	2.03245i	−0.0210446	−	0.119350i
$291$	12.2983	+	12.9183i	0.720937	+	0.757286i
$292$	−3.22064	+	1.17222i	−0.188474	+	0.0685988i
$293$	2.38551	+	2.00168i	0.139363	+	0.116939i	0.709804	−	0.704399i	$-0.248783\pi$
$293$	2.38551	+	2.00168i	0.139363	+	0.116939i	−0.570441	+	0.821338i	$0.693228\pi$
$294$	−19.0050	+	4.44175i	−1.10840	+	0.259048i
$295$	2.87107	+	1.04499i	0.167160	+	0.0608414i
$296$	−9.03863	−	15.6554i	−0.525360	−	0.909950i
$297$	4.29770	−	26.4594i	0.249378	−	1.53533i
$298$	2.70342	−	4.68246i	0.156605	−	0.271248i
$299$	−3.69470	−	20.9537i	−0.213670	−	1.21178i
$300$	0.316898	+	5.04902i	0.0182961	+	0.291505i
$301$	−14.7147	+	12.2518i	−0.848141	+	0.706184i
$302$	2.71082	−	15.3738i	0.155990	−	0.884664i
$303$	1.48816	+	1.56319i	0.0854927	+	0.0898032i
$304$	−1.70347	−	9.66084i	−0.0977005	−	0.554087i
$305$	−0.824089			−0.0471872
$306$	2.28281	+	7.38241i	0.130500	+	0.422024i
$307$	−8.70368	+	15.0752i	−0.496745	+	0.860388i	−0.999993	−	0.00375447i	$-0.998805\pi$
$307$	−8.70368	+	15.0752i	−0.496745	+	0.860388i	0.503248	+	0.864142i	$0.332138\pi$
$308$	−4.00862	−	7.00465i	−0.228412	−	0.399127i
$309$	6.00854	−	8.14724i	0.341814	−	0.463480i
$310$	−2.21711	−	1.86038i	−0.125923	−	0.105662i
$311$	−4.50894	+	25.5715i	−0.255679	+	1.45003i	0.538646	+	0.842532i	$0.318936\pi$
$311$	−4.50894	+	25.5715i	−0.255679	+	1.45003i	−0.794325	+	0.607493i	$0.792175\pi$
$312$	18.9280	+	2.12599i	1.07159	+	0.120360i
$313$	−20.1564	+	16.9132i	−1.13931	+	0.955991i	−0.999416	−	0.0341761i	$-0.989119\pi$
$313$	−20.1564	+	16.9132i	−1.13931	+	0.955991i	−0.139890	+	0.990167i	$0.544675\pi$
$314$	−1.81580	+	3.14505i	−0.102471	+	0.177485i
$315$	−1.73764	+	0.884016i	−0.0979049	+	0.0498086i
$316$	2.46010	+	4.26102i	0.138392	+	0.239701i
$317$	2.51228	+	0.914394i	0.141104	+	0.0513575i	0.411607	−	0.911362i	$-0.364968\pi$
$317$	2.51228	+	0.914394i	0.141104	+	0.0513575i	−0.270503	+	0.962719i	$0.587190\pi$
$318$	18.2444	−	4.41088i	1.02309	−	0.247350i
$319$	−20.6275	−	17.3085i	−1.15492	−	0.969091i
$320$	−0.189506	+	1.07474i	−0.0105937	+	0.0600800i
$321$	2.16292	+	1.07409i	0.120723	+	0.0599498i
$322$	9.28153	+	16.2185i	0.517239	+	0.903822i
$323$	3.24787			0.180716
$324$	4.79784	+	2.30228i	0.266547	+	0.127904i
$325$	−11.9772	+	20.7451i	−0.664376	+	1.15073i
$326$	−2.08003	+	1.74536i	−0.115202	+	0.0966663i
$327$	1.67474	+	26.6831i	0.0926135	+	1.47558i
$328$	9.49783	+	7.96962i	0.524430	+	0.440049i
$329$	−0.983492	−	5.70470i	−0.0542217	−	0.314510i
$330$	−2.43604	−	2.55886i	−0.134100	−	0.140861i
$331$	−19.3284	−	7.03494i	−1.06238	−	0.386676i	−0.249059	−	0.968488i	$-0.580121\pi$
$331$	−19.3284	−	7.03494i	−1.06238	−	0.386676i	−0.813323	+	0.581813i	$0.802344\pi$
$332$	−4.15223			−0.227883
$333$	9.27413	−	22.0438i	0.508219	−	1.20799i
$334$	23.1845			1.26860
$335$	0.318015	+	1.80356i	0.0173750	+	0.0985387i
$336$	−21.5469	+	5.12249i	−1.17548	+	0.279455i
$337$	−26.6331	+	9.69364i	−1.45079	+	0.528046i	−0.942813	−	0.333322i	$-0.891830\pi$
$337$	−26.6331	+	9.69364i	−1.45079	+	0.528046i	−0.507982	+	0.861368i	$0.669608\pi$
$338$	−12.9685	−	10.8818i	−0.705392	−	0.591894i
$339$	6.34013	+	14.5179i	0.344349	+	0.788505i
$340$	0.218378	+	0.0794829i	0.0118432	+	0.00431057i
$341$	−37.7621			−2.04493
$342$	6.66227	−	7.19027i	0.360254	−	0.388805i
$343$	18.5190	+	0.211725i	0.999935	+	0.0114321i
$344$	−12.5718	+	10.5490i	−0.677827	+	0.568764i
$345$	1.28705	+	1.35194i	0.0692924	+	0.0727860i
$346$	−2.17772	−	1.82733i	−0.117075	−	0.0982377i
$347$	−3.24503	+	1.18110i	−0.174203	+	0.0634045i	−0.427649	−	0.903945i	$-0.640658\pi$
$347$	−3.24503	+	1.18110i	−0.174203	+	0.0634045i	0.253446	+	0.967349i	$0.418436\pi$
$348$	4.45297	−	2.95758i	0.238704	−	0.158543i
$349$	13.4023	+	4.87804i	0.717409	+	0.261116i	0.674826	−	0.737977i	$-0.264219\pi$
$349$	13.4023	+	4.87804i	0.717409	+	0.261116i	0.0425837	+	0.999093i	$0.486441\pi$
$350$	3.73214	−	20.7043i	0.199491	−	1.10669i
$351$	12.8928	+	21.6500i	0.688168	+	1.15559i
$352$	−8.36899	−	14.4955i	−0.446069	−	0.772614i
$353$	−18.5879	+	15.5971i	−0.989332	+	0.830148i	−0.985471	−	0.169844i	$-0.945674\pi$
$353$	−18.5879	+	15.5971i	−0.989332	+	0.830148i	−0.00386143	+	0.999993i	$0.501229\pi$
$354$	2.17252	+	34.6140i	0.115468	+	1.83971i
$355$	−0.0433348	+	0.245764i	−0.00229997	+	0.0130438i
$356$	1.59851	−	9.06559i	0.0847208	−	0.480475i
$357$	−0.431430	−	7.31990i	−0.0228337	−	0.387410i
$358$	23.0168	−	19.3134i	1.21647	−	1.02074i
$359$	−2.27027	+	3.93223i	−0.119820	+	0.207535i	−0.919696	−	0.392630i	$-0.871565\pi$
$359$	−2.27027	+	3.93223i	−0.119820	+	0.207535i	0.799876	+	0.600165i	$0.204899\pi$
$360$	−1.48643	+	0.763357i	−0.0783416	+	0.0402325i
$361$	7.43998	+	12.8864i	0.391578	+	0.678233i
$362$	8.52143	−	7.15033i	0.447876	−	0.375813i
$363$	−26.8748	−	3.01857i	−1.41056	−	0.158434i
$364$	7.11899	+	2.62187i	0.373137	+	0.137423i
$365$	1.33786	−	0.486942i	0.0700269	−	0.0254877i
$366$	−3.74379	−	8.57269i	−0.195691	−	0.448102i
$367$	−8.69204	−	3.16364i	−0.453721	−	0.165141i	0.105043	−	0.994468i	$-0.466502\pi$
$367$	−8.69204	−	3.16364i	−0.453721	−	0.165141i	−0.558764	+	0.829327i	$0.688724\pi$
$368$	10.6024	+	18.3639i	0.552689	+	0.957285i
$369$	−0.806173	+	16.3828i	−0.0419677	+	0.852853i
$370$	−1.57599	−	2.72969i	−0.0819318	−	0.141910i
$371$	−17.8111	−	0.0678745i	−0.924708	−	0.00352387i
$372$	2.11769	−	7.19131i	0.109797	−	0.372852i
$373$	35.7808	−	13.0231i	1.85266	−	0.674313i	0.868856	−	0.495064i	$-0.164855\pi$
$373$	35.7808	−	13.0231i	1.85266	−	0.674313i	0.983804	−	0.179249i	$-0.0573667\pi$
$374$	12.4866	−	4.54476i	0.645668	−	0.235004i
$375$	−0.264888	−	4.22037i	−0.0136788	−	0.217939i
$376$	−0.861575	−	4.88623i	−0.0444323	−	0.251988i
$377$	25.3120			1.30364
$378$	−17.0901	−	14.0600i	−0.879019	−	0.723168i
$379$	31.7811			1.63248			0.816242	−	0.577710i	$-0.196054\pi$
$379$	31.7811			1.63248			0.816242	+	0.577710i	$0.196054\pi$
$380$	−0.0511911	−	0.290319i	−0.00262605	−	0.0148931i
$381$	18.5852	+	9.22924i	0.952148	+	0.472828i
$382$	6.37461	−	2.32017i	0.326154	−	0.118710i
$383$	35.5306	−	12.9321i	1.81553	−	0.660799i	0.819368	−	0.573268i	$-0.194325\pi$
$383$	35.5306	−	12.9321i	1.81553	−	0.660799i	0.996162	−	0.0875309i	$-0.0278976\pi$
$384$	−22.9657	+	5.55234i	−1.17196	+	0.283342i
$385$	1.66519	+	2.90975i	0.0848661	+	0.148295i
$386$	14.2034	+	24.6011i	0.722936	+	1.25216i
$387$	−21.1703	−	4.81645i	−1.07615	−	0.244834i
$388$	3.04449	+	5.27321i	0.154560	+	0.267707i
$389$	−33.5247	−	12.2020i	−1.69977	−	0.618666i	−0.703971	−	0.710229i	$-0.748591\pi$
$389$	−33.5247	−	12.2020i	−1.69977	−	0.618666i	−0.995799	+	0.0915636i	$0.970814\pi$
$390$	3.30032	+	0.370691i	0.167118	+	0.0187707i
$391$	−6.59714	+	2.40116i	−0.333632	+	0.121432i
$392$	15.8732	+	0.120981i	0.801718	+	0.00611045i
$393$	10.7878	+	24.7025i	0.544174	+	1.24607i
$394$	−8.52303	+	7.15167i	−0.429384	+	0.360296i
$395$	−1.02193	−	1.77004i	−0.0514191	−	0.0890604i
$396$	3.54875	−	8.43506i	0.178331	−	0.423878i
$397$	−17.0510	+	29.5331i	−0.855763	+	1.48223i	0.0201719	+	0.999797i	$0.493579\pi$
$397$	−17.0510	+	29.5331i	−0.855763	+	1.48223i	−0.875935	+	0.482429i	$0.839755\pi$
$398$	−7.16525	+	6.01236i	−0.359161	+	0.301372i
$399$	−7.76787	+	5.11673i	−0.388880	+	0.256157i
$400$	4.14554	−	23.5105i	0.207277	−	1.17553i
$401$	−0.0515308	+	0.292246i	−0.00257333	+	0.0145941i	−0.986067	−	0.166346i	$-0.946803\pi$
$401$	−0.0515308	+	0.292246i	−0.00257333	+	0.0145941i	0.983494	+	0.180940i	$0.0579141\pi$
$402$	−17.3170	+	11.5016i	−0.863693	+	0.573650i
$403$	27.1922	−	22.8170i	1.35454	−	1.13660i
$404$	0.368401	+	0.638090i	0.0183286	+	0.0317461i
$405$	−1.99304	−	0.956372i	−0.0990348	−	0.0475225i
$406$	−20.9185	+	7.52358i	−1.03817	+	0.373389i
$407$	−38.6449	−	14.0656i	−1.91556	−	0.697206i
$408$	−0.393683	−	6.27241i	−0.0194902	−	0.310531i
$409$	26.9921	−	9.82433i	1.33468	−	0.485782i	0.426544	−	0.904467i	$-0.359731\pi$
$409$	26.9921	−	9.82433i	1.33468	−	0.485782i	0.908132	+	0.418685i	$0.137509\pi$
$410$	1.65606	+	1.38960i	0.0817868	+	0.0686273i
$411$	−8.05881	+	27.3663i	−0.397512	+	1.34988i
$412$	2.64737	−	2.22141i	0.130427	−	0.109441i
$413$	5.83833	−	32.3886i	0.287286	−	1.59374i
$414$	−8.21674	+	19.5305i	−0.403831	+	0.959870i
$415$	1.72485			0.0846694
$416$	14.7851	+	5.38133i	0.724898	+	0.263841i
$417$	21.1415	+	2.37460i	1.03530	+	0.116285i
$418$	−12.9126	−	10.8350i	−0.631578	−	0.529957i
$419$	19.7106	−	7.17406i	0.962925	−	0.350476i	0.187746	−	0.982218i	$-0.439882\pi$
$419$	19.7106	−	7.17406i	0.962925	−	0.350476i	0.775179	+	0.631742i	$0.217660\pi$
$420$	−0.647508	+	0.153937i	−0.0315951	+	0.00751133i
$421$	−4.09657	−	23.2328i	−0.199655	−	1.13230i	−0.905632	−	0.424064i	$-0.860603\pi$
$421$	−4.09657	−	23.2328i	−0.199655	−	1.13230i	0.705977	−	0.708234i	$-0.250508\pi$
$422$	14.1500			0.688814
$423$	4.46126	−	4.81483i	0.216914	−	0.234105i
$424$	−15.2660			−0.741381
$425$	7.42732	+	2.70332i	0.360278	+	0.131130i
$426$	−2.75346	+	0.665695i	−0.133405	+	0.0322530i
$427$	1.50810	+	8.74765i	0.0729820	+	0.423329i
$428$	0.631540	+	0.529925i	0.0305266	+	0.0256149i
$429$	36.0951	−	23.9737i	1.74269	−	1.15746i
$430$	−2.19204	+	1.83934i	−0.105710	+	0.0887009i
$431$	−10.1733	+	17.6207i	−0.490031	+	0.848759i	−0.999934	−	0.0114729i	$-0.996348\pi$
$431$	−10.1733	+	17.6207i	−0.490031	+	0.848759i	0.509903	+	0.860232i	$0.329681\pi$
$432$	−19.4539	−	15.8808i	−0.935975	−	0.764064i
$433$	−29.6631			−1.42552			−0.712758	−	0.701410i	$-0.752554\pi$
$433$	−29.6631			−1.42552			−0.712758	+	0.701410i	$0.752554\pi$
$434$	−15.6904	+	26.9390i	−0.753164	+	1.29311i
$435$	−1.84978	+	1.22859i	−0.0886899	+	0.0589063i
$436$	−1.58490	+	8.98841i	−0.0759029	+	0.430467i
$437$	6.82222	+	5.72452i	0.326351	+	0.273841i
$438$	11.1433	+	11.7051i	0.532448	+	0.559293i
$439$	0.909155	+	0.330905i	0.0433916	+	0.0157933i	0.363625	−	0.931546i	$-0.381539\pi$
$439$	0.909155	+	0.330905i	0.0433916	+	0.0157933i	−0.320233	+	0.947339i	$0.603761\pi$
$440$	1.43673	+	2.48848i	0.0684932	+	0.118634i
$441$	12.5637	+	16.8272i	0.598271	+	0.801294i
$442$	−6.24546	+	10.8174i	−0.297066	+	0.514533i
$443$	−1.65088	+	1.38526i	−0.0784358	+	0.0658155i	−0.681163	−	0.732132i	$-0.738525\pi$
$443$	−1.65088	+	1.38526i	−0.0784358	+	0.0658155i	0.602727	+	0.797948i	$0.294081\pi$
$444$	4.84580	−	6.57063i	0.229972	−	0.311828i
$445$	−0.664025	+	3.76587i	−0.0314778	+	0.178519i
$446$	12.2652	+	10.2917i	0.580775	+	0.487328i
$447$	−5.78127	−	0.649351i	−0.273445	−	0.0307132i
$448$	11.7551	+	0.0447964i	0.555378	+	0.00211643i
$449$	0.802022	−	1.38914i	0.0378498	−	0.0655577i	−0.846480	−	0.532421i	$-0.821282\pi$
$449$	0.802022	−	1.38914i	0.0378498	−	0.0655577i	0.884330	+	0.466863i	$0.154616\pi$
$450$	21.2202	−	10.8977i	1.00033	−	0.513721i
$451$	28.2062			1.32818
$452$	0.939118	+	5.32600i	0.0441724	+	0.250514i
$453$	−16.3267	+	3.94725i	−0.767093	+	0.185458i
$454$	5.48676	−	31.1170i	0.257507	−	1.46039i
$455$	−2.95725	−	1.08913i	−0.138638	−	0.0510593i
$456$	−6.64106	+	4.41087i	−0.310996	+	0.206558i
$457$	5.25692	+	29.8135i	0.245908	+	1.39461i	0.818374	+	0.574686i	$0.194876\pi$
$457$	5.25692	+	29.8135i	0.245908	+	1.39461i	−0.572466	+	0.819929i	$0.694013\pi$
$458$	7.59006	−	13.1464i	0.354660	−	0.614289i
$459$	6.29639	−	5.42996i	0.293890	−	0.253449i
$460$	0.318614	+	0.551856i	0.0148555	+	0.0257304i
$461$	11.1051	+	4.04192i	0.517216	+	0.188251i	0.587421	−	0.809281i	$-0.300143\pi$
$461$	11.1051	+	4.04192i	0.517216	+	0.188251i	−0.0702054	+	0.997533i	$0.522365\pi$
$462$	−22.7042	+	30.5412i	−1.05629	+	1.42090i
$463$	27.5236	+	23.0951i	1.27913	+	1.07332i	0.993363	+	0.115019i	$0.0366930\pi$
$463$	27.5236	+	23.0951i	1.27913	+	1.07332i	0.285768	+	0.958299i	$0.407751\pi$
$464$	−23.7049	+	8.62788i	−1.10047	+	0.400539i
$465$	−0.879693	+	2.98729i	−0.0407948	+	0.138532i
$466$	−2.93194	−	16.6278i	−0.135819	−	0.770270i
$467$	−1.42224	+	2.46339i	−0.0658134	+	0.113992i	−0.897055	−	0.441920i	$-0.854298\pi$
$467$	−1.42224	+	2.46339i	−0.0658134	+	0.113992i	0.831241	+	0.555912i	$0.187631\pi$
$468$	2.54129	+	8.21829i	0.117471	+	0.379890i
$469$	18.5627	−	6.67625i	0.857144	−	0.308281i
$470$	−0.150226	−	0.851971i	−0.00692939	−	0.0392985i
$471$	3.88309	+	0.436147i	0.178923	+	0.0200966i
$472$	4.89820	−	27.7791i	0.225458	−	1.27863i
$473$	−6.48318	+	36.7679i	−0.298097	+	1.69059i
$474$	13.7705	−	18.6720i	0.632500	−	0.857633i
$475$	−1.74108	−	9.87414i	−0.0798861	−	0.453057i
$476$	0.444071	−	2.46352i	0.0203540	−	0.112915i
$477$	−12.2057	−	16.0904i	−0.558861	−	0.736730i
$478$	6.09221	−	10.5520i	0.278651	−	0.482638i
$479$	−5.99052	−	33.9740i	−0.273714	−	1.55231i	−0.743017	−	0.669272i	$-0.766606\pi$
$479$	−5.99052	−	33.9740i	−0.273714	−	1.55231i	0.469303	−	0.883037i	$-0.344505\pi$
$480$	−1.34167	+	0.324372i	−0.0612388	+	0.0148055i
$481$	36.3268	−	13.2219i	1.65636	−	0.602865i
$482$	−11.5684	−	9.70700i	−0.526924	−	0.442142i
$483$	11.9954	−	16.1360i	0.545811	−	0.734214i
$484$	−8.67551	−	3.15763i	−0.394341	−	0.143529i
$485$	−1.26469	−	2.19051i	−0.0574266	−	0.0994657i
$486$	0.894541	−	25.0776i	0.0405772	−	1.13754i
$487$	4.94964	−	8.57303i	0.224290	−	0.388481i	−0.731816	−	0.681502i	$-0.761327\pi$
$487$	4.94964	−	8.57303i	0.224290	−	0.388481i	0.956106	+	0.293021i	$0.0946605\pi$
$488$	1.32115	+	7.49261i	0.0598056	+	0.339174i
$489$	2.61671	+	1.29943i	0.118332	+	0.0587624i
$490$	2.76768	+	0.0210944i	0.125031	+	0.000952948i
$491$	2.63401	−	14.9382i	0.118871	−	0.674152i	−0.865889	−	0.500236i	$-0.833247\pi$
$491$	2.63401	−	14.9382i	0.118871	−	0.674152i	0.984760	−	0.173916i	$-0.0556422\pi$
$492$	−1.58179	+	5.37150i	−0.0713128	+	0.242166i
$493$	−1.45030	−	8.22507i	−0.0653183	−	0.370438i
$494$	15.8451			0.712906
$495$	−1.47416	+	3.50395i	−0.0662586	+	0.157491i
$496$	−17.6883	+	30.6371i	−0.794229	+	1.37564i
$497$	2.68807	+	0.0102437i	0.120577	+	0.000459492i
$498$	7.83588	+	17.9429i	0.351134	+	0.804042i
$499$	−15.6060	−	13.0950i	−0.698619	−	0.586211i	0.222761	−	0.974873i	$-0.428493\pi$
$499$	−15.6060	−	13.0950i	−0.698619	−	0.586211i	−0.921380	+	0.388662i	$0.872937\pi$
$500$	0.250678	−	1.42166i	0.0112107	−	0.0635788i
$501$	−9.98367	−	22.8611i	−0.446037	−	1.02136i
$502$	25.9181	−	21.7479i	1.15678	−	0.970655i
$503$	6.10125	−	10.5677i	0.272041	−	0.471189i	−0.697343	−	0.716737i	$-0.745635\pi$
$503$	6.10125	−	10.5677i	0.272041	−	0.471189i	0.969384	+	0.245548i	$0.0789680\pi$
$504$	10.8232	+	14.3814i	0.482103	+	0.640598i
$505$	−0.153035	−	0.265064i	−0.00680996	−	0.0117952i
$506$	34.2388	+	12.4619i	1.52210	+	0.553999i
$507$	−5.14556	+	17.4735i	−0.228522	+	0.776023i
$508$	5.42658	+	4.55344i	0.240766	+	0.202026i
$509$	−3.98485	+	22.5992i	−0.176625	+	1.00169i	0.759626	+	0.650360i	$0.225382\pi$
$509$	−3.98485	+	22.5992i	−0.176625	+	1.00169i	−0.936251	+	0.351331i	$0.885729\pi$
$510$	−0.0686432	−	1.09367i	−0.00303957	−	0.0484284i
$511$	−7.61717	−	13.3102i	−0.336964	−	0.588809i
$512$	6.23845			0.275703
$513$	−9.95885	−	3.47306i	−0.439694	−	0.153339i
$514$	−19.8280	+	34.3432i	−0.874577	+	1.51481i
$515$	−1.09973	+	0.922780i	−0.0484597	+	0.0406625i
$516$	−6.63840	−	3.29657i	−0.292239	−	0.145123i
$517$	−8.64671	−	7.25545i	−0.380282	−	0.319094i
$518$	−26.0914	+	21.7244i	−1.14639	+	0.954516i
$519$	−0.864066	+	2.93422i	−0.0379283	+	0.128798i
$520$	−2.53819	−	0.923825i	−0.111307	−	0.0405124i
$521$	−29.0781			−1.27393			−0.636967	−	0.770891i	$-0.719811\pi$
$521$	−29.0781			−1.27393			−0.636967	+	0.770891i	$0.719811\pi$
$522$	−21.1840	−	13.6611i	−0.927197	−	0.597931i
$523$	27.7925			1.21528			0.607641	−	0.794212i	$-0.292116\pi$
$523$	27.7925			1.21528			0.607641	+	0.794212i	$0.292116\pi$
$524$	1.59792	+	9.06228i	0.0698056	+	0.395887i
$525$	−22.0226	+	5.23559i	−0.961146	+	0.228500i
$526$	−2.37401	+	0.864068i	−0.103512	+	0.0376752i
$527$	−8.97234	−	7.52869i	−0.390841	−	0.327955i
$528$	−25.6316	+	34.7550i	−1.11547	+	1.51252i
$529$	3.52333	+	1.28239i	0.153188	+	0.0557560i
$530$	−2.66180			−0.115621
$531$	33.1956	−	17.0476i	1.44056	−	0.739804i
$532$	−2.98804	+	1.07468i	−0.129548	+	0.0465933i
$533$	−20.3111	+	17.0430i	−0.879770	+	0.738215i
$534$	−42.1916	+	10.2005i	−1.82581	+	0.441420i
$535$	−0.262344	−	0.220132i	−0.0113421	−	0.00951715i
$536$	15.8881	−	5.78279i	0.686260	−	0.249778i
$537$	−28.9553	−	14.3790i	−1.24952	−	0.620498i
$538$	−8.99831	−	3.27512i	−0.387945	−	0.141200i
$539$	27.8395	−	23.0008i	1.19913	−	0.990715i
$540$	−0.584611	−	0.477235i	−0.0251577	−	0.0205369i
$541$	12.1578	+	21.0579i	0.522704	+	0.905350i	0.999651	+	0.0264179i	$0.00841006\pi$
$541$	12.1578	+	21.0579i	0.522704	+	0.905350i	−0.476947	+	0.878932i	$0.658257\pi$
$542$	12.5555	−	10.5353i	0.539304	−	0.452530i
$543$	−10.7200	−	5.32348i	−0.460041	−	0.228452i
$544$	0.901506	−	5.11270i	0.0386518	−	0.219205i
$545$	0.658372	−	3.73381i	0.0282015	−	0.159939i
$546$	−2.10478	−	35.7110i	−0.0900764	−	1.52829i
$547$	3.22077	−	2.70254i	0.137710	−	0.115552i	−0.571331	−	0.820720i	$-0.693573\pi$
$547$	3.22077	−	2.70254i	0.137710	−	0.115552i	0.709041	+	0.705167i	$0.249128\pi$
$548$	−4.86952	+	8.43426i	−0.208016	+	0.360294i
$549$	−6.84095	+	7.38311i	−0.291964	+	0.315103i
$550$	−20.5106	−	35.5255i	−0.874576	−	1.51481i
$551$	−8.11603	+	6.81016i	−0.345755	+	0.290123i
$552$	10.2285	−	13.8692i	0.435353	−	0.590313i
$553$	−16.9187	+	14.0870i	−0.719457	+	0.599039i
$554$	27.2910	−	9.93310i	1.15948	−	0.422017i
$555$	−2.01296	+	2.72946i	−0.0854454	+	0.115859i
$556$	6.82472	+	2.48400i	0.289433	+	0.105345i
$557$	−6.63331	−	11.4892i	−0.281062	−	0.486814i	0.690584	−	0.723252i	$-0.257353\pi$
$557$	−6.63331	−	11.4892i	−0.281062	−	0.486814i	−0.971647	+	0.236438i	$0.924020\pi$
$558$	−35.0721	+	4.41995i	−1.48472	+	0.187111i
$559$	−17.5478	−	30.3937i	−0.742192	−	1.28551i
$560$	3.14073	+	0.0119687i	0.132720	+	0.000505769i
$561$	−9.85833	−	10.3554i	−0.416219	−	0.437204i
$562$	−9.83885	+	3.58105i	−0.415027	+	0.151057i
$563$	−17.1364	+	6.23715i	−0.722214	+	0.262864i	−0.676865	−	0.736107i	$-0.736662\pi$
$563$	−17.1364	+	6.23715i	−0.722214	+	0.262864i	−0.0453487	+	0.998971i	$0.514440\pi$
$564$	1.86661	−	1.23977i	0.0785985	−	0.0522037i
$565$	−0.390112	−	2.21244i	−0.0164121	−	0.0930779i
$566$	−19.8423			−0.834033
$567$	−6.50454	+	22.9061i	−0.273165	+	0.961967i
$568$	2.30396			0.0966718
$569$	4.96317	+	28.1475i	0.208067	+	1.18001i	0.892540	+	0.450968i	$0.148921\pi$
$569$	4.96317	+	28.1475i	0.208067	+	1.18001i	−0.684473	+	0.729038i	$0.739968\pi$
$570$	−1.15794	+	0.769087i	−0.0485010	+	0.0322135i
$571$	−15.5965	+	5.67666i	−0.652693	+	0.237561i	−0.647079	−	0.762423i	$-0.724009\pi$
$571$	−15.5965	+	5.67666i	−0.652693	+	0.237561i	−0.00561479	+	0.999984i	$0.501787\pi$
$572$	13.9004	−	5.05935i	0.581207	−	0.211542i
$573$	−5.03282	−	5.28657i	−0.210249	−	0.220850i
$574$	11.7199	−	20.1219i	0.489178	−	0.839873i
$575$	10.8365	+	18.7694i	0.451914	+	0.782737i
$576$	8.05562	+	10.6195i	0.335651	+	0.442479i
$577$	−10.3149	−	17.8659i	−0.429415	−	0.743768i	0.567407	−	0.823438i	$-0.307947\pi$
$577$	−10.3149	−	17.8659i	−0.429415	−	0.743768i	−0.996821	+	0.0796698i	$0.974613\pi$
$578$	−21.8424	−	7.95000i	−0.908526	−	0.330676i
$579$	18.1416	−	24.5990i	0.753940	−	1.02230i
$580$	−0.712359	+	0.259278i	−0.0295791	+	0.0107659i
$581$	−3.15650	−	18.3091i	−0.130954	−	0.759591i
$582$	17.0416	−	23.1074i	0.706397	−	0.957833i
$583$	−26.6043	+	22.3237i	−1.10184	+	0.924553i
$584$	−6.57208	−	11.3832i	−0.271955	−	0.471039i
$585$	−1.05566	−	3.41390i	−0.0436460	−	0.141147i
$586$	2.50642	−	4.34125i	0.103539	−	0.179336i
$587$	−5.41973	+	4.54769i	−0.223696	+	0.187703i	−0.747747	−	0.663983i	$-0.768865\pi$
$587$	−5.41973	+	4.54769i	−0.223696	+	0.187703i	0.524051	+	0.851687i	$0.324420\pi$
$588$	2.81898	+	6.59155i	0.116253	+	0.271831i
$589$	−2.58002	+	14.6320i	−0.106308	+	0.602903i
$590$	0.854057	−	4.84360i	0.0351610	−	0.199408i
$591$	10.7221	+	5.32448i	0.441047	+	0.219020i
$592$	−29.5135	+	24.7647i	−1.21300	+	1.01782i
$593$	2.82966	+	4.90111i	0.116200	+	0.201265i	0.918259	−	0.395981i	$-0.129595\pi$
$593$	2.82966	+	4.90111i	0.116200	+	0.201265i	−0.802059	+	0.597245i	$0.796262\pi$
$594$	−43.1473	+	0.583088i	−1.77035	+	0.0239244i
$595$	−0.184468	+	1.02335i	−0.00756247	+	0.0419534i
$596$	−1.86626	−	0.679265i	−0.0764452	−	0.0278238i
$597$	9.01396	+	4.47625i	0.368917	+	0.183201i
$598$	−32.1850	+	11.7144i	−1.31614	+	0.479036i
$599$	−9.79402	−	8.21816i	−0.400173	−	0.335785i	0.420388	−	0.907345i	$-0.361894\pi$
$599$	−9.79402	−	8.21816i	−0.400173	−	0.335785i	−0.820560	+	0.571560i	$0.806339\pi$
$600$	−18.8583	+	4.55931i	−0.769886	+	0.186133i
$601$	−27.4619	+	23.0433i	−1.12019	+	0.939954i	−0.998614	−	0.0526274i	$-0.983240\pi$
$601$	−27.4619	+	23.0433i	−1.12019	+	0.939954i	−0.121580	+	0.992582i	$0.538796\pi$
$602$	23.5360	+	19.9023i	0.959254	+	0.811159i
$603$	18.7982	+	12.1226i	0.765521	+	0.493669i
$604$	−5.73422			−0.233322
$605$	3.60383	+	1.31169i	0.146517	+	0.0533277i
$606$	2.06214	−	2.79614i	0.0837685	−	0.113585i
$607$	−31.8737	−	26.7452i	−1.29371	−	1.08556i	−0.991195	−	0.132412i	$-0.957728\pi$
$607$	−31.8737	−	26.7452i	−1.29371	−	1.08556i	−0.302519	−	0.953143i	$-0.597828\pi$
$608$	−6.18851	+	2.25243i	−0.250977	+	0.0913483i
$609$	16.4265	+	17.3869i	0.665636	+	0.704553i
$610$	0.230358	+	1.30642i	0.00932690	+	0.0528955i
$611$	10.6104			0.429250
$612$	2.52490	−	1.29666i	0.102063	−	0.0524146i
$613$	16.6078			0.670782			0.335391	−	0.942079i	$-0.391132\pi$
$613$	16.6078			0.670782			0.335391	+	0.942079i	$0.391132\pi$
$614$	26.3316	+	9.58391i	1.06266	+	0.386775i
$615$	0.657081	−	2.23134i	0.0264961	−	0.0899762i
$616$	23.7858	−	19.8047i	0.958359	−	0.797955i
$617$	13.0354	+	10.9380i	0.524785	+	0.440347i	0.866296	−	0.499531i	$-0.166494\pi$
$617$	13.0354	+	10.9380i	0.524785	+	0.440347i	−0.341511	+	0.939878i	$0.610939\pi$
$618$	−14.5953	−	7.24791i	−0.587110	−	0.291554i
$619$	8.97501	−	7.53093i	0.360736	−	0.302694i	−0.444348	−	0.895854i	$-0.646565\pi$
$619$	8.97501	−	7.53093i	0.360736	−	0.302694i	0.805084	+	0.593161i	$0.202120\pi$
$620$	−0.531554	+	0.920678i	−0.0213477	+	0.0369753i
$621$	22.7963	−	0.308066i	0.914783	−	0.0123623i
$622$	41.7987			1.67597
$623$	41.1897	+	0.156965i	1.65023	+	0.00628868i
$624$	−2.54284	−	40.5142i	−0.101795	−	1.62187i
$625$	4.18469	−	23.7326i	0.167388	−	0.949302i
$626$	32.4467	+	27.2260i	1.29683	+	1.08817i
$627$	−5.12342	+	17.3982i	−0.204609	+	0.694819i
$628$	1.25351	+	0.456239i	0.0500204	+	0.0182059i
$629$	−6.37781	−	11.0467i	−0.254300	−	0.440461i
$630$	1.88715	+	2.50756i	0.0751857	+	0.0999036i
$631$	−3.25090	+	5.63073i	−0.129416	+	0.224156i	−0.923451	−	0.383717i	$-0.874644\pi$
$631$	−3.25090	+	5.63073i	−0.129416	+	0.224156i	0.794034	+	0.607873i	$0.207977\pi$
$632$	−14.4549	+	12.1291i	−0.574984	+	0.482469i
$633$	−6.09327	−	13.9526i	−0.242186	−	0.554567i
$634$	0.747326	−	4.23830i	0.0296801	−	0.168324i
$635$	−2.25422	−	1.89151i	−0.0894559	−	0.0750624i
$636$	−2.75930	−	6.31836i	−0.109413	−	0.250539i
$637$	−6.14924	+	33.3842i	−0.243642	+	1.32273i
$638$	−21.6731	+	37.5389i	−0.858046	+	1.48618i
$639$	1.84210	+	2.42838i	0.0728722	+	0.0960653i
$640$	3.35062			0.132445
$641$	1.73512	+	9.84038i	0.0685333	+	0.388672i	0.999710	+	0.0241022i	$0.00767271\pi$
$641$	1.73512	+	9.84038i	0.0685333	+	0.388672i	−0.931176	+	0.364569i	$0.881216\pi$
$642$	1.09814	−	3.72911i	0.0433403	−	0.147176i
$643$	−2.03715	+	11.5532i	−0.0803373	+	0.455615i	0.917928	+	0.396746i	$0.129861\pi$
$643$	−2.03715	+	11.5532i	−0.0803373	+	0.455615i	−0.998266	+	0.0588693i	$0.981250\pi$
$644$	5.27485	−	4.39198i	0.207858	−	0.173068i
$645$	2.75761	+	1.36941i	0.108581	+	0.0539203i
$646$	−0.907877	−	5.14883i	−0.0357199	−	0.202578i
$647$	−12.6777	+	21.9584i	−0.498411	+	0.863274i	−0.999998	−	0.00183352i	$-0.999416\pi$
$647$	−12.6777	+	21.9584i	−0.498411	+	0.863274i	0.501587	+	0.865107i	$0.332750\pi$
$648$	−5.50016	+	19.6539i	−0.216067	+	0.772078i
$649$	−32.0856	−	55.5738i	−1.25947	−	2.18146i
$650$	36.2351	+	13.1885i	1.42126	+	0.517295i
$651$	33.3197	+	3.87110i	1.30590	+	0.151720i
$652$	0.764037	+	0.641103i	0.0299220	+	0.0251075i
$653$	−24.3880	+	8.87651i	−0.954376	+	0.347365i	−0.771827	−	0.635832i	$-0.780657\pi$
$653$	−24.3880	+	8.87651i	−0.954376	+	0.347365i	−0.182549	+	0.983197i	$0.558435\pi$
$654$	41.8324	−	10.1137i	1.63578	−	0.395476i
$655$	−0.663782	−	3.76450i	−0.0259361	−	0.147091i
$656$	13.2122	−	22.8842i	0.515849	−	0.893476i
$657$	6.74332	−	16.0283i	0.263082	−	0.625323i
$658$	−8.76871	+	3.15376i	−0.341840	+	0.122946i
$659$	0.938027	+	5.31981i	0.0365403	+	0.207230i	0.997612	−	0.0690691i	$-0.0220029\pi$
$659$	0.938027	+	5.31981i	0.0365403	+	0.207230i	−0.961072	+	0.276300i	$0.910892\pi$
$660$	−0.770260	+	1.04443i	−0.0299823	+	0.0406543i
$661$	−1.04141	+	5.90614i	−0.0405062	+	0.229722i	−0.998340	−	0.0576020i	$-0.981655\pi$
$661$	−1.04141	+	5.90614i	−0.0405062	+	0.229722i	0.957833	+	0.287324i	$0.0927657\pi$
$662$	−5.74960	+	32.6076i	−0.223464	+	1.26733i
$663$	13.3559	+	1.50013i	0.518701	+	0.0582604i
$664$	−2.76521	−	15.6823i	−0.107311	−	0.608591i
$665$	1.24124	−	0.446425i	0.0481332	−	0.0173116i
$666$	−37.5383	−	8.54032i	−1.45458	−	0.330931i
$667$	11.4507	−	19.8332i	0.443372	−	0.767943i
$668$	−1.47881	−	8.38675i	−0.0572169	−	0.324493i
$669$	4.86653	−	16.5259i	0.188151	−	0.638928i
$670$	2.77027	−	1.00830i	0.107025	−	0.0389539i
$671$	13.2590	+	11.1256i	0.511856	+	0.429498i
$672$	5.89848	+	13.6482i	0.227539	+	0.526490i
$673$	11.3701	+	4.13838i	0.438285	+	0.159523i	0.551732	−	0.834021i	$-0.313967\pi$
$673$	11.3701	+	4.13838i	0.438285	+	0.159523i	−0.113447	+	0.993544i	$0.536189\pi$
$674$	22.8120	+	39.5115i	0.878685	+	1.52193i
$675$	−19.8834	−	16.2314i	−0.765313	−	0.624747i
$676$	−3.10920	+	5.38529i	−0.119585	+	0.207127i
$677$	−7.27638	−	41.2664i	−0.279654	−	1.58600i	−0.723779	−	0.690032i	$-0.757597\pi$
$677$	−7.27638	−	41.2664i	−0.279654	−	1.58600i	0.444125	−	0.895965i	$-0.353515\pi$
$678$	21.2429	−	14.1092i	0.815829	−	0.541859i
$679$	−20.9377	+	17.4333i	−0.803514	+	0.669027i
$680$	−0.154764	+	0.877709i	−0.00593492	+	0.0336586i
$681$	−33.0456	+	7.98932i	−1.26631	+	0.306151i
$682$	10.5556	+	59.8640i	0.404197	+	2.29231i
$683$	−8.33047			−0.318757			−0.159378	−	0.987218i	$-0.550949\pi$
$683$	−8.33047			−0.318757			−0.159378	+	0.987218i	$0.550949\pi$
$684$	−3.02595	−	1.95138i	−0.115700	−	0.0746127i
$685$	2.02281	−	3.50362i	0.0772878	−	0.133866i
$686$	−4.84098	−	29.4173i	−0.184830	−	1.12316i
$687$	−16.2314	−	1.82310i	−0.619265	−	0.0695557i
$688$	26.7936	+	22.4825i	1.02150	+	0.857139i
$689$	5.66896	−	32.1503i	0.215970	−	1.22483i
$690$	1.78345	−	2.41826i	0.0678949	−	0.0920615i
$691$	28.1849	−	23.6500i	1.07221	−	0.899687i	0.0769548	−	0.997035i	$-0.475480\pi$
$691$	28.1849	−	23.6500i	1.07221	−	0.899687i	0.995250	+	0.0973475i	$0.0310358\pi$
$692$	−0.522111	+	0.904323i	−0.0198477	+	0.0343772i
$693$	39.8919	+	9.23582i	1.51537	+	0.350840i
$694$	2.77947	+	4.81418i	0.105507	+	0.182744i
$695$	−2.83501	−	1.03186i	−0.107538	−	0.0391406i
$696$	14.1358	+	14.8485i	0.535816	+	0.562831i
$697$	6.70183	+	5.62351i	0.253850	+	0.213005i
$698$	3.98678	−	22.6102i	0.150902	−	0.855807i
$699$	−15.1333	+	10.0513i	−0.572394	+	0.380174i
$700$	−7.72762	−	0.0294484i	−0.292077	−	0.00111304i
$701$	−51.6323			−1.95013			−0.975063	−	0.221930i	$-0.928764\pi$
$701$	−51.6323			−1.95013			−0.975063	+	0.221930i	$0.928764\pi$
$702$	30.7177	−	26.4907i	1.15937	−	0.999829i
$703$	−8.09047	+	14.0131i	−0.305138	+	0.528514i
$704$	17.5586	−	14.7334i	0.661763	−	0.555285i
$705$	−0.775395	+	0.515004i	−0.0292031	+	0.0193962i
$706$	29.9218	+	25.1074i	1.12612	+	0.944929i
$707$	−2.53358	+	2.10953i	−0.0952852	+	0.0793370i
$708$	12.3827	−	2.99372i	0.465369	−	0.112511i
$709$	8.18015	+	2.97733i	0.307212	+	0.111816i	0.491026	−	0.871145i	$-0.336622\pi$
$709$	8.18015	+	2.97733i	0.307212	+	0.111816i	−0.183814	+	0.982961i	$0.558844\pi$
$710$	0.401721			0.0150763
$711$	−24.3413	−	5.53788i	−0.912871	−	0.207687i
$712$	35.3038			1.32307
$713$	−5.57693	−	31.6283i	−0.208858	−	1.18449i
$714$	−11.4836	+	2.73007i	−0.429762	+	0.102170i
$715$	−5.77428	+	2.10167i	−0.215946	+	0.0785979i
$716$	−8.45451	−	7.09417i	−0.315960	−	0.265122i
$717$	−13.0282	−	1.46333i	−0.486548	−	0.0546489i
$718$	6.86835	+	2.49987i	0.256324	+	0.0932945i
$719$	37.2254			1.38827			0.694137	−	0.719843i	$-0.255786\pi$
$719$	37.2254			1.38827			0.694137	+	0.719843i	$0.255786\pi$
$720$	2.15230	+	2.83731i	0.0802113	+	0.105740i
$721$	11.8078	+	9.98482i	0.439744	+	0.371854i
$722$	18.3491	−	15.3967i	0.682882	−	0.573006i
$723$	−4.59003	+	15.5870i	−0.170705	+	0.579685i
$724$	−3.13009	−	2.62645i	−0.116329	−	0.0976114i
$725$	−24.2283	+	8.81839i	−0.899817	+	0.327507i
$726$	2.72699	+	43.4482i	0.101208	+	1.61252i
$727$	−13.2093	−	4.80779i	−0.489905	−	0.178311i	0.0852428	−	0.996360i	$-0.472833\pi$
$727$	−13.2093	−	4.80779i	−0.489905	−	0.178311i	−0.575148	+	0.818049i	$0.695056\pi$
$728$	−5.16141	+	28.6333i	−0.191295	+	1.06122i
$729$	−25.1129	+	9.91679i	−0.930107	+	0.367288i
$730$	−1.14592	−	1.98479i	−0.0424123	−	0.0734603i
$731$	−8.87089	+	7.44356i	−0.328102	+	0.275310i
$732$	−2.86228	+	1.90108i	−0.105793	+	0.0702658i
$733$	−3.26371	+	18.5094i	−0.120548	+	0.683661i	0.863305	+	0.504682i	$0.168390\pi$
$733$	−3.26371	+	18.5094i	−0.120548	+	0.683661i	−0.983853	+	0.178978i	$0.942721\pi$
$734$	−2.58562	+	14.6638i	−0.0954369	+	0.541250i
$735$	−1.17101	−	2.73815i	−0.0431934	−	0.100998i
$736$	10.9050	−	9.15038i	0.401964	−	0.337288i
$737$	19.2322	−	33.3112i	0.708428	−	1.22703i
$738$	26.1968	−	3.30146i	0.964319	−	0.121528i
$739$	8.36238	+	14.4841i	0.307615	+	0.532805i	0.977840	−	0.209353i	$-0.0671357\pi$
$739$	8.36238	+	14.4841i	0.307615	+	0.532805i	−0.670225	+	0.742158i	$0.733802\pi$
$740$	−0.886913	+	0.744209i	−0.0326036	+	0.0273577i
$741$	−6.82320	−	15.6241i	−0.250657	−	0.573965i
$742$	4.87114	+	28.2548i	0.178825	+	1.03727i
$743$	−6.60496	+	2.40401i	−0.242313	+	0.0881945i	−0.460322	−	0.887752i	$-0.652266\pi$
$743$	−6.60496	+	2.40401i	−0.242313	+	0.0881945i	0.218009	+	0.975947i	$0.430044\pi$
$744$	28.5707	+	3.20905i	1.04745	+	0.117650i
$745$	0.775251	+	0.282168i	0.0284030	+	0.0103379i
$746$	−30.6473	−	53.0827i	−1.12208	−	1.94350i
$747$	14.3183	−	15.4531i	0.523881	−	0.565400i
$748$	−2.44047	−	4.22702i	−0.0892324	−	0.154555i
$749$	−1.85660	+	3.18761i	−0.0678386	+	0.116473i
$750$	−6.61648	+	1.59965i	−0.241600	+	0.0584108i
$751$	8.78339	−	3.19689i	0.320510	−	0.116656i	−0.176755	−	0.984255i	$-0.556560\pi$
$751$	8.78339	−	3.19689i	0.320510	−	0.116656i	0.497265	+	0.867599i	$0.334338\pi$
$752$	−9.93671	+	3.61667i	−0.362355	+	0.131886i
$753$	−32.6053	−	16.1915i	−1.18820	−	0.590051i
$754$	−7.07547	−	40.1270i	−0.257674	−	1.46134i
$755$	2.38201			0.0866903
$756$	−3.99597	+	7.07896i	−0.145332	+	0.257459i
$757$	34.6375			1.25892			0.629461	−	0.777032i	$-0.283276\pi$
$757$	34.6375			1.25892			0.629461	+	0.777032i	$0.283276\pi$
$758$	−8.88376	−	50.3823i	−0.322673	−	1.82997i
$759$	−2.45580	−	39.1274i	−0.0891400	−	1.42024i
$760$	1.06240	−	0.386681i	0.0385372	−	0.0140264i
$761$	12.5940	−	4.58385i	0.456533	−	0.166165i	−0.103509	−	0.994629i	$-0.533007\pi$
$761$	12.5940	−	4.58385i	0.456533	−	0.166165i	0.560042	+	0.828464i	$0.310785\pi$
$762$	9.43593	−	32.0428i	0.341828	−	1.16079i
$763$	−40.8390	−	0.155629i	−1.47847	−	0.00563415i
$764$	−1.24590	−	2.15796i	−0.0450750	−	0.0780721i
$765$	−1.04885	+	0.538638i	−0.0379212	+	0.0194745i
$766$	−30.4330	−	52.7115i	−1.09959	−	1.90455i
$767$	56.6840	+	20.6313i	2.04674	+	0.744952i
$768$	9.06194	+	20.7504i	0.326995	+	0.748767i
$769$	35.9631	−	13.0895i	1.29686	−	0.472020i	0.400890	−	0.916126i	$-0.368701\pi$
$769$	35.9631	−	13.0895i	1.29686	−	0.472020i	0.895974	+	0.444106i	$0.146479\pi$
$770$	4.14734	−	3.45318i	0.149460	−	0.124444i
$771$	42.4023	+	4.76262i	1.52708	+	0.171522i
$772$	7.99322	−	6.70711i	0.287682	−	0.241394i
$773$	−3.99713	−	6.92324i	−0.143767	−	0.249012i	0.785145	−	0.619312i	$-0.212588\pi$
$773$	−3.99713	−	6.92324i	−0.143767	−	0.249012i	−0.928912	+	0.370300i	$0.879255\pi$
$774$	−1.71775	+	34.9075i	−0.0617433	+	1.25473i
$775$	−18.0789	+	31.3135i	−0.649412	+	1.12481i
$776$	−17.8885	+	15.0103i	−0.642161	+	0.538837i
$777$	32.6568	+	16.3725i	1.17156	+	0.587360i
$778$	−9.97258	+	56.5573i	−0.357534	+	2.02768i
$779$	1.92713	−	10.9293i	0.0690467	−	0.391583i
$780$	−0.0764153	−	1.21750i	−0.00273611	−	0.0435934i
$781$	4.01515	−	3.36911i	0.143673	−	0.120556i
$782$	5.65065	+	9.78721i	0.202067	+	0.349990i
$783$	−4.34833	+	26.7711i	−0.155397	+	0.956723i
$784$	−5.62055	−	33.3605i	−0.200734	−	1.19145i
$785$	−0.520710	−	0.189523i	−0.0185849	−	0.00676437i
$786$	36.1451	−	24.0070i	1.28925	−	0.856300i
$787$	4.41835	−	1.60815i	0.157497	−	0.0573243i	−0.262068	−	0.965049i	$-0.584405\pi$
$787$	4.41835	−	1.60815i	0.157497	−	0.0573243i	0.419566	+	0.907725i	$0.362182\pi$
$788$	3.13067	+	2.62695i	0.111526	+	0.0935811i
$789$	1.87430	+	1.96880i	0.0667270	+	0.0700913i
$790$	−2.52037	+	2.11484i	−0.0896709	+	0.0752428i
$791$	−22.7710	+	8.18982i	−0.809642	+	0.291196i
$792$	34.2212	+	7.78565i	1.21600	+	0.276651i
$793$	−16.2701			−0.577768
$794$	51.5849	+	18.7754i	1.83068	+	0.666313i
$795$	1.14622	+	2.62466i	0.0406522	+	0.0930872i
$796$	2.63194	+	2.20846i	0.0932865	+	0.0782767i
$797$	−36.5725	+	13.3113i	−1.29546	+	0.471510i	−0.895517	−	0.445028i	$-0.853194\pi$
$797$	−36.5725	+	13.3113i	−1.29546	+	0.471510i	−0.399947	+	0.916538i	$0.630971\pi$
$798$	10.2829	+	10.8841i	0.364010	+	0.385292i
$799$	−0.607942	−	3.44781i	−0.0215075	−	0.121975i
$800$	−16.0268			−0.566634
$801$	28.2267	+	37.2104i	0.997340	+	1.31477i
$802$	0.477700			0.0168682
$803$	−28.0991	−	10.2272i	−0.991596	−	0.360912i
$804$	5.26515	+	5.53061i	0.185687	+	0.195049i
$805$	−2.19119	+	1.82444i	−0.0772292	+	0.0643031i
$806$	−43.7727	−	36.7296i	−1.54183	−	1.29375i
$807$	0.645410	+	10.2831i	0.0227195	+	0.361982i
$808$	−2.16462	+	1.81633i	−0.0761511	+	0.0638984i
$809$	−16.0261	+	27.7580i	−0.563448	+	0.975920i	0.433744	+	0.901036i	$0.357192\pi$
$809$	−16.0261	+	27.7580i	−0.563448	+	0.975920i	−0.997192	+	0.0748842i	$0.976141\pi$
$810$	−0.959017	+	3.42688i	−0.0336964	+	0.120408i
$811$	42.8701			1.50537			0.752686	−	0.658380i	$-0.228758\pi$
$811$	42.8701			1.50537			0.752686	+	0.658380i	$0.228758\pi$
$812$	4.05585	+	7.08717i	0.142332	+	0.248711i
$813$	−15.7949	−	7.84362i	−0.553952	−	0.275088i
$814$	−11.4957	+	65.1953i	−0.402924	+	2.28509i
$815$	−0.317383	−	0.266316i	−0.0111174	−	0.00932865i
$816$	−13.0193	+	3.14763i	−0.455766	+	0.110189i
$817$	13.8039	+	5.02420i	0.482936	+	0.175774i
$818$	−23.1196	−	40.0443i	−0.808357	−	1.40011i
$819$	−34.3064	+	17.4532i	−1.19876	+	0.609865i
$820$	0.397041	−	0.687695i	0.0138653	−	0.0240153i
$821$	−17.0593	+	14.3145i	−0.595375	+	0.499579i	−0.889955	−	0.456048i	$-0.849265\pi$
$821$	−17.0593	+	14.3145i	−0.595375	+	0.499579i	0.294581	+	0.955627i	$0.404820\pi$
$822$	45.6363	+	5.12586i	1.59175	+	0.178785i
$823$	2.13865	−	12.1289i	0.0745485	−	0.422786i	−0.924578	−	0.380993i	$-0.875582\pi$
$823$	2.13865	−	12.1289i	0.0745485	−	0.422786i	0.999126	−	0.0417924i	$-0.0133068\pi$
$824$	10.1529	+	8.51933i	0.353695	+	0.296785i
$825$	−26.1976	+	35.5224i	−0.912082	+	1.23673i
$826$	−52.9774	−	0.201886i	−1.84332	−	0.00702452i
$827$	6.06462	−	10.5042i	0.210888	−	0.365268i	−0.741105	−	0.671389i	$-0.765698\pi$
$827$	6.06462	−	10.5042i	0.210888	−	0.365268i	0.951993	+	0.306121i	$0.0990312\pi$
$828$	7.58904	+	1.72658i	0.263737	+	0.0600028i
$829$	−35.2246			−1.22340			−0.611700	−	0.791089i	$-0.709514\pi$
$829$	−35.2246			−1.22340			−0.611700	+	0.791089i	$0.709514\pi$
$830$	−0.482146	−	2.73439i	−0.0167355	−	0.0949120i
$831$	−21.5465	−	22.6328i	−0.747440	−	0.785124i
$832$	−3.74145	+	21.2188i	−0.129711	+	0.735629i
$833$	11.2004	+	0.0853661i	0.388071	+	0.00295776i
$834$	−2.14523	−	34.1792i	−0.0742833	−	1.18353i
$835$	0.614302	+	3.48388i	0.0212588	+	0.120565i
$836$	−3.09582	+	5.36211i	−0.107071	+	0.185453i
$837$	19.4609	+	32.6794i	0.672669	+	1.12957i
$838$	−16.8827	−	29.2417i	−0.583203	−	1.01014i
$839$	−13.6226	−	4.95823i	−0.470305	−	0.171177i	0.0959854	−	0.995383i	$-0.469400\pi$
$839$	−13.6226	−	4.95823i	−0.470305	−	0.171177i	−0.566291	+	0.824206i	$0.691622\pi$
$840$	−1.01261	−	2.34302i	−0.0349382	−	0.0808417i
$841$	−1.34478	−	1.12840i	−0.0463716	−	0.0389104i
$842$	−35.6857	+	12.9885i	−1.22981	+	0.447615i
$843$	7.76787	+	8.15952i	0.267540	+	0.281029i
$844$	−0.902552	−	5.11863i	−0.0310671	−	0.176190i
$845$	1.29157	−	2.23707i	0.0444314	−	0.0769574i
$846$	−8.87997	−	5.72652i	−0.305300	−	0.196882i
$847$	7.32840	−	40.6549i	0.251807	−	1.39692i
$848$	5.64974	+	32.0413i	0.194013	+	1.10030i
$849$	8.54444	+	19.5655i	0.293245	+	0.671485i
$850$	2.20940	−	12.5301i	0.0757818	−	0.429780i
$851$	6.07359	−	34.4450i	0.208200	−	1.18076i
$852$	0.416435	+	0.953573i	0.0142668	+	0.0326689i
$853$	−0.496485	−	2.81571i	−0.0169993	−	0.0964079i	0.975128	−	0.221644i	$-0.0711423\pi$
$853$	−0.496485	−	2.81571i	−0.0169993	−	0.0964079i	−0.992127	+	0.125236i	$0.960031\pi$
$854$	13.4460	−	4.83601i	0.460114	−	0.165485i
$855$	1.25699	+	0.810607i	0.0429881	+	0.0277222i
$856$	−1.58086	+	2.73813i	−0.0540327	+	0.0935875i
$857$	−8.65112	−	49.0629i	−0.295516	−	1.67596i	−0.665096	−	0.746758i	$-0.731609\pi$
$857$	−8.65112	−	49.0629i	−0.295516	−	1.67596i	0.369579	−	0.929199i	$-0.379502\pi$
$858$	−48.0951	−	50.5200i	−1.64194	−	1.72472i
$859$	−30.7421	+	11.1892i	−1.04891	+	0.381771i	−0.808250	−	0.588839i	$-0.799585\pi$
$859$	−30.7421	+	11.1892i	−1.04891	+	0.381771i	−0.240657	+	0.970610i	$0.577363\pi$
$860$	0.805179	+	0.675626i	0.0274564	+	0.0230386i
$861$	−24.8880	−	2.89149i	−0.848180	−	0.0985417i
$862$	30.7777	+	11.2022i	1.04829	+	0.381548i
$863$	−17.4245	−	30.1802i	−0.593138	−	1.02735i	−0.993807	−	0.111123i	$-0.964555\pi$
$863$	−17.4245	−	30.1802i	−0.593138	−	1.02735i	0.400668	−	0.916223i	$-0.368778\pi$
$864$	−8.23145	+	14.7129i	−0.280039	+	0.500543i
$865$	0.216886	−	0.375658i	0.00737436	−	0.0127728i
$866$	8.29172	+	47.0247i	0.281764	+	1.59796i
$867$	1.56667	+	24.9611i	0.0532067	+	0.847724i
$868$	10.7457	+	3.95755i	0.364733	+	0.134328i
$869$	−7.45426	+	42.2752i	−0.252868	+	1.43409i
$870$	2.46474	+	2.58901i	0.0835625	+	0.0877756i
$871$	6.27862	+	35.6078i	0.212743	+	1.20652i
$872$	−35.0033			−1.18536
$873$	−30.1235	−	6.85338i	−1.01952	−	0.231952i
$874$	7.16803	−	12.4154i	0.242462	−	0.419957i
$875$	6.45936	+	0.0246153i	0.218366	+	0.000832149i
$876$	3.52344	−	4.77757i	0.119046	−	0.161419i
$877$	−8.01545	−	6.72576i	−0.270663	−	0.227113i	0.497346	−	0.867552i	$-0.334308\pi$
$877$	−8.01545	−	6.72576i	−0.270663	−	0.227113i	−0.768009	+	0.640439i	$0.778752\pi$
$878$	0.270446	−	1.53378i	0.00912711	−	0.0517624i
$879$	−5.36000	−	0.602034i	−0.180788	−	0.0203061i
$880$	4.69128	−	3.93645i	0.158143	−	0.132698i
$881$	1.08469	−	1.87874i	0.0365443	−	0.0632965i	−0.847175	−	0.531314i	$-0.821698\pi$
$881$	1.08469	−	1.87874i	0.0365443	−	0.0632965i	0.883719	+	0.468018i	$0.155032\pi$
$882$	23.1641	−	24.6208i	0.779975	−	0.829026i
$883$	21.1805	+	36.6856i	0.712779	+	1.23457i	0.963810	+	0.266590i	$0.0858971\pi$
$883$	21.1805	+	36.6856i	0.712779	+	1.23457i	−0.251031	+	0.967979i	$0.580770\pi$
$884$	4.31146	+	1.56924i	0.145010	+	0.0527793i
$885$	−5.14380	+	1.24360i	−0.172907	+	0.0418031i
$886$	2.65751	+	2.22991i	0.0892807	+	0.0749154i
$887$	−7.77661	+	44.1034i	−0.261113	+	1.48085i	0.518766	+	0.854916i	$0.326392\pi$
$887$	−7.77661	+	44.1034i	−0.261113	+	1.48085i	−0.779879	+	0.625930i	$0.784720\pi$
$888$	28.0433	+	13.9261i	0.941072	+	0.467328i
$889$	−15.9530	+	27.3899i	−0.535048	+	0.918627i
$890$	6.15563			0.206337
$891$	19.1549	+	42.2942i	0.641715	+	1.41691i
$892$	2.94060	−	5.09326i	0.0984584	−	0.170535i
$893$	−3.40211	+	2.85471i	−0.113847	+	0.0955291i
$894$	0.586627	+	9.34653i	0.0196198	+	0.312595i
$895$	3.51203	+	2.94694i	0.117394	+	0.0985053i
$896$	−6.13170	−	35.5666i	−0.204846	−	1.18820i
$897$	25.4104	+	26.6915i	0.848427	+	0.891204i
$898$	−2.42639	−	0.883133i	−0.0809697	−	0.0294705i
$899$	38.2070			1.27427
$900$	−5.29563	−	6.98107i	−0.176521	−	0.232702i
$901$	−10.7719			−0.358865
$902$	−7.88447	−	44.7151i	−0.262524	−	1.48885i
$903$	9.48967	−	31.7779i	0.315796	−	1.05750i
$904$	−19.4900	+	7.09379i	−0.648229	+	0.235936i
$905$	1.30025	+	1.09104i	0.0432217	+	0.0362673i
$906$	10.8213	+	24.7792i	0.359515	+	0.823233i
$907$	21.4579	+	7.81004i	0.712498	+	0.259328i	0.672738	−	0.739881i	$-0.265118\pi$
$907$	21.4579	+	7.81004i	0.712498	+	0.259328i	0.0397604	+	0.999209i	$0.487341\pi$
$908$	−11.6062			−0.385165
$909$	−3.64512	−	0.829299i	−0.120901	−	0.0275061i
$910$	−0.899952	+	4.99255i	−0.0298331	+	0.165502i
$911$	32.3047	−	27.1069i	1.07030	−	0.898090i	0.0752226	−	0.997167i	$-0.476033\pi$
$911$	32.3047	−	27.1069i	1.07030	−	0.898090i	0.995080	+	0.0990764i	$0.0315888\pi$
$912$	11.7156	+	12.3063i	0.387943	+	0.407502i
$913$	−27.7515	−	23.2862i	−0.918439	−	0.770662i
$914$	45.7936	−	16.6675i	1.51472	−	0.551312i
$915$	1.18900	−	0.789713i	0.0393071	−	0.0261071i
$916$	−5.23968	−	1.90709i	−0.173124	−	0.0630120i
$917$	−38.7452	+	13.9351i	−1.27948	+	0.460178i
$918$	−10.3681	−	8.46379i	−0.342199	−	0.279347i
$919$	9.59973	+	16.6272i	0.316666	+	0.548481i	0.979790	−	0.200028i	$-0.0641033\pi$
$919$	9.59973	+	16.6272i	0.316666	+	0.548481i	−0.663124	+	0.748509i	$0.730770\pi$
$920$	−1.87209	+	1.57087i	−0.0617209	+	0.0517900i
$921$	−1.88865	−	30.0912i	−0.0622332	−	0.991539i
$922$	3.30343	−	18.7347i	0.108793	−	0.616993i
$923$	−0.855565	+	4.85215i	−0.0281613	+	0.159710i
$924$	12.4961	+	6.26494i	0.411092	+	0.206101i
$925$	−30.1651	+	25.3115i	−0.991823	+	0.832239i
$926$	28.9188	−	50.0888i	0.950329	−	1.64602i
$927$	−0.861779	+	17.5128i	−0.0283045	+	0.575195i
$928$	8.46759	+	14.6663i	0.277962	+	0.481445i
$929$	30.1349	−	25.2862i	0.988695	−	0.829613i	0.00331649	−	0.999995i	$-0.498944\pi$
$929$	30.1349	−	25.2862i	0.988695	−	0.829613i	0.985378	+	0.170381i	$0.0544999\pi$
$930$	4.98163	+	0.559535i	0.163354	+	0.0183479i
$931$	−7.01026	−	12.3587i	−0.229752	−	0.405040i
$932$	−5.82793	+	2.12119i	−0.190900	+	0.0694820i
$933$	−17.9993	−	41.2155i	−0.589269	−	1.34934i
$934$	4.30275	+	1.56607i	0.140790	+	0.0512435i
$935$	1.01378	+	1.75592i	0.0331541	+	0.0574246i
$936$	−29.3467	+	15.0711i	−0.959228	+	0.492613i
$937$	−20.5733	−	35.6340i	−0.672100	−	1.16411i	−0.977307	−	0.211826i	$-0.932059\pi$
$937$	−20.5733	−	35.6340i	−0.672100	−	1.16411i	0.305207	−	0.952286i	$-0.401274\pi$
$938$	−15.7726	−	27.5610i	−0.514995	−	0.899900i
$939$	12.8740	−	43.7180i	0.420128	−	1.42668i
$940$	−0.298609	+	0.108685i	−0.00973956	+	0.00354491i
$941$	3.22718	−	1.17460i	0.105203	−	0.0382908i	−0.288882	−	0.957365i	$-0.593284\pi$
$941$	3.22718	−	1.17460i	0.105203	−	0.0382908i	0.394085	+	0.919074i	$0.371061\pi$
$942$	−0.394018	−	6.27775i	−0.0128378	−	0.204540i
$943$	4.16565	+	23.6246i	0.135652	+	0.769323i
$944$	−60.1174			−1.95665
$945$	1.65994	−	2.94062i	0.0539977	−	0.0956583i
$946$	60.1002			1.95403
$947$	−6.02438	−	34.1660i	−0.195766	−	1.11024i	−0.911324	−	0.411691i	$-0.864938\pi$
$947$	−6.02438	−	34.1660i	−0.195766	−	1.11024i	0.715557	−	0.698554i	$-0.246173\pi$
$948$	−7.63273	−	3.79035i	−0.247900	−	0.123105i
$949$	26.4136	−	9.61376i	0.857421	−	0.312076i
$950$	−15.1667	+	5.52024i	−0.492074	+	0.179100i
$951$	−4.50098	+	1.08819i	−0.145954	+	0.0352869i
$952$	9.60005	+	0.0365838i	0.311139	+	0.00118569i
$953$	2.32892	+	4.03381i	0.0754411	+	0.130668i	0.901278	−	0.433241i	$-0.142630\pi$
$953$	2.32892	+	4.03381i	0.0754411	+	0.130668i	−0.825837	+	0.563909i	$0.809297\pi$
$954$	−22.0962	+	23.8474i	−0.715391	+	0.772087i
$955$	0.517549	+	0.896421i	0.0167475	+	0.0290075i
$956$	−4.20567	−	1.53074i	−0.136021	−	0.0495076i
$957$	46.3480	+	5.20579i	1.49822	+	0.168279i
$958$	−52.1842	+	18.9935i	−1.68599	+	0.613651i
$959$	−40.8925	−	15.0604i	−1.32049	−	0.486324i
$960$	−0.756491	−	1.73225i	−0.0244156	−	0.0559080i
$961$	17.2977	−	14.5145i	0.557989	−	0.468209i
$962$	−31.1150	−	53.8927i	−1.00319	−	1.73757i
$963$	−4.14996	+	0.522999i	−0.133731	+	0.0168534i
$964$	−2.77352	+	4.80388i	−0.0893291	+	0.154723i
$965$	−3.32041	+	2.78615i	−0.106888	+	0.0896894i
$966$	−28.9334	−	14.5058i	−0.930917	−	0.466716i
$967$	4.09834	−	23.2428i	0.131794	−	0.747439i	−0.845245	−	0.534378i	$-0.820546\pi$
$967$	4.09834	−	23.2428i	0.131794	−	0.747439i	0.977039	−	0.213060i	$-0.0683431\pi$
$968$	6.14832	−	34.8689i	0.197614	−	1.12073i
$969$	−4.68604	+	3.11239i	−0.150537	+	0.0999843i
$970$	−3.11908	+	2.61721i	−0.100147	+	0.0840337i
$971$	23.5907	+	40.8602i	0.757060	+	1.31127i	0.944344	+	0.328961i	$0.106698\pi$
$971$	23.5907	+	40.8602i	0.757060	+	1.31127i	−0.187283	+	0.982306i	$0.559968\pi$
$972$	−9.12859	+	1.27597i	−0.292800	+	0.0409266i
$973$	−5.76500	+	31.9818i	−0.184817	+	1.02529i
$974$	−14.9743	−	5.45022i	−0.479809	−	0.174636i
$975$	−2.59899	−	41.4088i	−0.0832343	−	1.32614i
$976$	15.2371	−	5.54584i	0.487726	−	0.177518i
$977$	−9.46089	−	7.93863i	−0.302681	−	0.253979i	0.478778	−	0.877936i	$-0.341080\pi$
$977$	−9.46089	−	7.93863i	−0.302681	−	0.253979i	−0.781459	+	0.623957i	$0.785524\pi$
$978$	1.32853	−	4.51148i	0.0424819	−	0.144261i
$979$	61.5247	−	51.6253i	1.96634	−	1.64995i
$980$	−0.168904	−	1.00252i	−0.00539543	−	0.0320244i
$981$	−27.9864	−	36.8936i	−0.893536	−	1.17792i
$982$	−24.4177			−0.779201
$983$	−21.5950	−	7.85993i	−0.688773	−	0.250693i	−0.0261629	−	0.999658i	$-0.508329\pi$
$983$	−21.5950	−	7.85993i	−0.688773	−	0.250693i	−0.662610	+	0.748965i	$0.730551\pi$
$984$	−21.3407	−	2.39698i	−0.680317	−	0.0764130i
$985$	−1.30049	−	1.09124i	−0.0414371	−	0.0347698i
$986$	−12.6337	+	4.59831i	−0.402340	+	0.146440i
$987$	6.88572	+	7.28831i	0.219175	+	0.231989i
$988$	−1.01067	−	5.73181i	−0.0321538	−	0.182353i
$989$	−31.7531			−1.00969
$990$	5.96686	+	1.35752i	0.189639	+	0.0431447i
$991$	−35.4288			−1.12543			−0.562716	−	0.826650i	$-0.690244\pi$
$991$	−35.4288			−1.12543			−0.562716	+	0.826650i	$0.690244\pi$
$992$	22.3172	+	8.12279i	0.708571	+	0.257899i
$993$	34.6285	−	8.37203i	1.09890	−	0.265678i
$994$	−0.735158	−	4.26425i	−0.0233178	−	0.135254i
$995$	−1.09331	−	0.917399i	−0.0346604	−	0.0290835i
$996$	5.99086	−	3.97902i	0.189828	−	0.126080i
$997$	−20.2704	+	17.0089i	−0.641969	+	0.538676i	−0.904622	−	0.426214i	$-0.859847\pi$
$997$	−20.2704	+	17.0089i	−0.641969	+	0.538676i	0.262653	+	0.964890i	$0.415403\pi$
$998$	−16.3970	+	28.4005i	−0.519039	+	0.899001i
$999$	7.74349	+	40.6922i	0.244993	+	1.28744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.6	✓	132
3.2	odd	2		567.2.u.a.550.17		132
7.2	even	3		189.2.w.a.58.6	yes	132
21.2	odd	6		567.2.w.a.226.17		132
27.7	even	9		189.2.w.a.88.6	yes	132
27.20	odd	18		567.2.w.a.424.17		132
189.128	odd	18		567.2.u.a.100.17		132
189.142	even	9	inner	189.2.u.a.142.6	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.6	✓	132	1.1	even	1	trivial
189.2.u.a.142.6	yes	132	189.142	even	9	inner
189.2.w.a.58.6	yes	132	7.2	even	3
189.2.w.a.88.6	yes	132	27.7	even	9
567.2.u.a.100.17		132	189.128	odd	18
567.2.u.a.550.17		132	3.2	odd	2
567.2.w.a.226.17		132	21.2	odd	6
567.2.w.a.424.17		132	27.20	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.279530 - 1.58529i) q^{2} +(-1.44281 + 0.958286i) q^{3} +(-0.555633 + 0.202234i) q^{4} +(0.230811 - 0.0840085i) q^{5} +(1.92247 + 2.01940i) q^{6} +(-1.31413 - 2.29631i) q^{7} +(-1.13383 - 1.96386i) q^{8} +(1.16338 - 2.76524i) q^{9} +O(q^{10})\)	\(q+(-0.279530 - 1.58529i) q^{2} +(-1.44281 + 0.958286i) q^{3} +(-0.555633 + 0.202234i) q^{4} +(0.230811 - 0.0840085i) q^{5} +(1.92247 + 2.01940i) q^{6} +(-1.31413 - 2.29631i) q^{7} +(-1.13383 - 1.96386i) q^{8} +(1.16338 - 2.76524i) q^{9} +(-0.197697 - 0.342421i) q^{10} +(-4.84773 - 1.76443i) q^{11} +(0.607872 - 0.824240i) q^{12} +(4.55694 - 1.65859i) q^{13} +(-3.27299 + 2.72518i) q^{14} +(-0.252512 + 0.342391i) q^{15} +(-3.70226 + 3.10657i) q^{16} +(-0.800052 - 1.38573i) q^{17} +(-4.70892 - 1.07132i) q^{18} +(-1.01489 + 1.75785i) q^{19} +(-0.111257 + 0.0933558i) q^{20} +(4.09656 + 2.05382i) q^{21} +(-1.44205 + 8.17829i) q^{22} +(0.761889 - 4.32089i) q^{23} +(3.51784 + 1.74693i) q^{24} +(-3.78401 + 3.17516i) q^{25} +(-3.90315 - 6.76046i) q^{26} +(0.971367 + 5.10455i) q^{27} +(1.19457 + 1.01014i) q^{28} +(4.90485 + 1.78522i) q^{29} +(0.613375 + 0.304597i) q^{30} +(6.87843 - 2.50354i) q^{31} +(2.48544 + 2.08554i) q^{32} +(8.68517 - 2.09979i) q^{33} +(-1.97315 + 1.65567i) q^{34} +(-0.496227 - 0.419617i) q^{35} +(-0.0871845 + 1.77173i) q^{36} +7.97175 q^{37} +(3.07039 + 1.11753i) q^{38} +(-4.98537 + 6.75988i) q^{39} +(-0.426682 - 0.358029i) q^{40} +(-5.13780 + 1.87001i) q^{41} +(2.11079 - 7.06836i) q^{42} +(-1.25671 - 7.12716i) q^{43} +3.05039 q^{44} +(0.0362167 - 0.735983i) q^{45} -7.06285 q^{46} +(2.05603 + 0.748334i) q^{47} +(2.36466 - 8.02999i) q^{48} +(-3.54610 + 6.03533i) q^{49} +(6.09130 + 5.11121i) q^{50} +(2.48225 + 1.23266i) q^{51} +(-2.19656 + 1.84314i) q^{52} +(3.36601 - 5.83010i) q^{53} +(7.82069 - 2.96678i) q^{54} -1.26714 q^{55} +(-3.01962 + 5.18441i) q^{56} +(-0.220226 - 3.50879i) q^{57} +(1.45904 - 8.27464i) q^{58} +(9.52886 + 7.99566i) q^{59} +(0.0710608 - 0.241310i) q^{60} +(-3.15274 - 1.14750i) q^{61} +(-5.89158 - 10.2045i) q^{62} +(-7.87869 + 0.962425i) q^{63} +(-2.22153 + 3.84780i) q^{64} +(0.912458 - 0.765644i) q^{65} +(-5.75654 - 13.1816i) q^{66} +(-1.29472 + 7.34273i) q^{67} +(0.724777 + 0.608160i) q^{68} +(3.04139 + 6.96431i) q^{69} +(-0.526505 + 0.903961i) q^{70} +(-0.508002 + 0.879885i) q^{71} +(-6.74961 + 0.850619i) q^{72} +5.79634 q^{73} +(-2.22834 - 12.6376i) q^{74} +(2.41687 - 8.20730i) q^{75} +(0.208412 - 1.18196i) q^{76} +(2.31889 + 13.4506i) q^{77} +(12.1099 + 6.01369i) q^{78} +(-1.44495 - 8.19469i) q^{79} +(-0.593546 + 1.02805i) q^{80} +(-6.29311 - 6.43403i) q^{81} +(4.40068 + 7.62220i) q^{82} +(6.59880 + 2.40177i) q^{83} +(-2.69154 - 0.312703i) q^{84} +(-0.301074 - 0.252631i) q^{85} +(-10.9473 + 3.98451i) q^{86} +(-8.78749 + 2.12452i) q^{87} +(2.03143 + 11.5208i) q^{88} +(-7.78417 + 13.4826i) q^{89} +(-1.17687 + 0.148315i) q^{90} +(-9.79707 - 8.28455i) q^{91} +(0.450499 + 2.55491i) q^{92} +(-7.52512 + 10.2036i) q^{93} +(0.611607 - 3.46859i) q^{94} +(-0.0865749 + 0.490991i) q^{95} +(-5.58455 - 0.627255i) q^{96} +(-1.78818 - 10.1413i) q^{97} +(10.5590 + 3.93456i) q^{98} +(-10.5188 + 11.3525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

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