LMFDB - Embedded newform 189.2.v.a.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(22,189)]

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([14, 0]))

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

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

chi := DirichletCharacter("189.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.v (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:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.5
Character	$\chi$	$=$	189.43
Dual form			189.2.v.a.22.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.731503 + 0.613803i) q^{2} +(-1.57520 + 0.720230i) q^{3} +(-0.188955 - 1.07162i) q^{4} +(-3.78665 - 1.37823i) q^{5} +(-1.59435 - 0.440016i) q^{6} +(0.173648 - 0.984808i) q^{7} +(1.47445 - 2.55382i) q^{8} +(1.96254 - 2.26902i) q^{9} +O(q^{10})$	\(q+(0.731503 + 0.613803i) q^{2} +(-1.57520 + 0.720230i) q^{3} +(-0.188955 - 1.07162i) q^{4} +(-3.78665 - 1.37823i) q^{5} +(-1.59435 - 0.440016i) q^{6} +(0.173648 - 0.984808i) q^{7} +(1.47445 - 2.55382i) q^{8} +(1.96254 - 2.26902i) q^{9} +(-1.92398 - 3.33244i) q^{10} +(-3.90983 + 1.42306i) q^{11} +(1.06945 + 1.55193i) q^{12} +(0.402272 - 0.337546i) q^{13} +(0.731503 - 0.613803i) q^{14} +(6.95740 - 0.556267i) q^{15} +(0.601058 - 0.218767i) q^{16} +(-1.49397 - 2.58763i) q^{17} +(2.82833 - 0.455179i) q^{18} +(-1.44865 + 2.50914i) q^{19} +(-0.761427 + 4.31827i) q^{20} +(0.435756 + 1.67634i) q^{21} +(-3.73353 - 1.35889i) q^{22} +(-0.299868 - 1.70064i) q^{23} +(-0.483222 + 5.08474i) q^{24} +(8.60901 + 7.22382i) q^{25} +0.501450 q^{26} +(-1.45719 + 4.98765i) q^{27} -1.08815 q^{28} +(0.978952 + 0.821438i) q^{29} +(5.43079 + 3.86356i) q^{30} +(-1.14367 - 6.48610i) q^{31} +(-4.96817 - 1.80826i) q^{32} +(5.13385 - 5.05759i) q^{33} +(0.495454 - 2.80986i) q^{34} +(-2.01484 + 3.48980i) q^{35} +(-2.80235 - 1.67435i) q^{36} +(-2.51013 - 4.34766i) q^{37} +(-2.59981 + 0.946255i) q^{38} +(-0.390550 + 0.821433i) q^{39} +(-9.10299 + 7.63831i) q^{40} +(7.74629 - 6.49991i) q^{41} +(-0.710187 + 1.49372i) q^{42} +(5.92226 - 2.15553i) q^{43} +(2.26376 + 3.92095i) q^{44} +(-10.5587 + 5.88716i) q^{45} +(0.824503 - 1.42808i) q^{46} +(-1.47781 + 8.38105i) q^{47} +(-0.789226 + 0.777503i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(1.86351 + 10.5685i) q^{50} +(4.21699 + 3.00004i) q^{51} +(-0.437732 - 0.367301i) q^{52} -10.6125 q^{53} +(-4.12737 + 2.75405i) q^{54} +16.7665 q^{55} +(-2.25899 - 1.89552i) q^{56} +(0.474767 - 4.99577i) q^{57} +(0.211904 + 1.20177i) q^{58} +(12.4329 + 4.52520i) q^{59} +(-1.91074 - 7.35056i) q^{60} +(1.79378 - 10.1730i) q^{61} +(3.14459 - 5.44659i) q^{62} +(-1.89376 - 2.32673i) q^{63} +(-3.16394 - 5.48010i) q^{64} +(-1.98848 + 0.723748i) q^{65} +(6.85979 - 0.548464i) q^{66} +(2.09084 - 1.75442i) q^{67} +(-2.49066 + 2.08991i) q^{68} +(1.69720 + 2.46288i) q^{69} +(-3.61591 + 1.31608i) q^{70} +(-0.743219 - 1.28729i) q^{71} +(-2.90100 - 8.35753i) q^{72} +(-1.01768 + 1.76267i) q^{73} +(0.832449 - 4.72105i) q^{74} +(-18.7638 - 5.17853i) q^{75} +(2.96257 + 1.07829i) q^{76} +(0.722508 + 4.09754i) q^{77} +(-0.789887 + 0.361159i) q^{78} +(3.06523 + 2.57203i) q^{79} -2.57751 q^{80} +(-1.29689 - 8.90607i) q^{81} +9.65610 q^{82} +(-3.89731 - 3.27024i) q^{83} +(1.71406 - 0.783717i) q^{84} +(2.09079 + 11.8575i) q^{85} +(5.65522 + 2.05833i) q^{86} +(-2.13367 - 0.588863i) q^{87} +(-2.13060 + 12.0833i) q^{88} +(5.12426 - 8.87547i) q^{89} +(-11.3373 - 2.17448i) q^{90} +(-0.262564 - 0.454775i) q^{91} +(-1.76577 + 0.642689i) q^{92} +(6.47301 + 9.39323i) q^{93} +(-6.22534 + 5.22368i) q^{94} +(8.94372 - 7.50467i) q^{95} +(9.12824 - 0.729834i) q^{96} +(-11.3317 + 4.12439i) q^{97} +(-0.477454 - 0.826975i) q^{98} +(-4.44424 + 11.6643i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9}+O(q^{10}) $ 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9	$ 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9} - 6 q^{11} + 24 q^{12} - 9 q^{13} - 9 q^{15} - 30 q^{17} - 27 q^{18} - 12 q^{20} - 3 q^{21} - 9 q^{22} - 12 q^{23} + 36 q^{24} + 27 q^{25} + 18 q^{26} + 63 q^{27} + 54 q^{28} + 6 q^{29} - 72 q^{30} - 9 q^{31} - 9 q^{32} - 36 q^{33} - 9 q^{34} - 12 q^{35} + 54 q^{38} + 12 q^{39} - 45 q^{40} - 15 q^{41} - 18 q^{42} - 9 q^{43} - 42 q^{44} - 9 q^{45} - 45 q^{47} - 93 q^{48} + 18 q^{50} + 72 q^{51} - 63 q^{52} + 132 q^{53} + 54 q^{54} - 9 q^{56} + 3 q^{57} - 27 q^{58} - 9 q^{60} - 36 q^{62} - 9 q^{63} - 27 q^{64} + 66 q^{65} + 153 q^{66} + 45 q^{67} + 87 q^{68} - 72 q^{71} - 45 q^{72} - 72 q^{74} - 39 q^{75} + 54 q^{76} + 3 q^{77} - 54 q^{78} - 36 q^{79} + 42 q^{80} + 27 q^{81} + 24 q^{83} - 12 q^{84} + 18 q^{85} - 90 q^{86} - 99 q^{87} + 54 q^{88} - 42 q^{89} - 9 q^{90} + 87 q^{92} + 93 q^{93} - 90 q^{94} + 12 q^{95} + 108 q^{96} - 18 q^{97} - 9 q^{98} - 117 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9 - 6 * q^11 + 24 * q^12 - 9 * q^13 - 9 * q^15 - 30 * q^17 - 27 * q^18 - 12 * q^20 - 3 * q^21 - 9 * q^22 - 12 * q^23 + 36 * q^24 + 27 * q^25 + 18 * q^26 + 63 * q^27 + 54 * q^28 + 6 * q^29 - 72 * q^30 - 9 * q^31 - 9 * q^32 - 36 * q^33 - 9 * q^34 - 12 * q^35 + 54 * q^38 + 12 * q^39 - 45 * q^40 - 15 * q^41 - 18 * q^42 - 9 * q^43 - 42 * q^44 - 9 * q^45 - 45 * q^47 - 93 * q^48 + 18 * q^50 + 72 * q^51 - 63 * q^52 + 132 * q^53 + 54 * q^54 - 9 * q^56 + 3 * q^57 - 27 * q^58 - 9 * q^60 - 36 * q^62 - 9 * q^63 - 27 * q^64 + 66 * q^65 + 153 * q^66 + 45 * q^67 + 87 * q^68 - 72 * q^71 - 45 * q^72 - 72 * q^74 - 39 * q^75 + 54 * q^76 + 3 * q^77 - 54 * q^78 - 36 * q^79 + 42 * q^80 + 27 * q^81 + 24 * q^83 - 12 * q^84 + 18 * q^85 - 90 * q^86 - 99 * q^87 + 54 * q^88 - 42 * q^89 - 9 * q^90 + 87 * q^92 + 93 * q^93 - 90 * q^94 + 12 * q^95 + 108 * q^96 - 18 * q^97 - 9 * q^98 - 117 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.731503	+	0.613803i	0.517250	+	0.434025i	0.863672	−	0.504054i	$-0.168159\pi$
$2$	0.731503	+	0.613803i	0.517250	+	0.434025i	−0.346422	+	0.938079i	$0.612603\pi$
$3$	−1.57520	+	0.720230i	−0.909445	+	0.415825i
$3$	−1.57520	+	0.720230i	−0.909445	+	0.415825i
$4$	−0.188955	−	1.07162i	−0.0944776	−	0.535809i
$5$	−3.78665	−	1.37823i	−1.69344	−	0.616363i	−0.698391	−	0.715716i	$-0.746100\pi$
$5$	−3.78665	−	1.37823i	−1.69344	−	0.616363i	−0.995052	+	0.0993536i	$0.968323\pi$
$6$	−1.59435	−	0.440016i	−0.650889	−	0.179636i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$8$	1.47445	−	2.55382i	0.521297	−	0.902913i
$9$	1.96254	−	2.26902i	0.654180	−	0.756339i
$10$	−1.92398	−	3.33244i	−0.608417	−	1.05381i
$11$	−3.90983	+	1.42306i	−1.17886	+	0.429069i	−0.855799	−	0.517309i	$-0.826934\pi$
$11$	−3.90983	+	1.42306i	−1.17886	+	0.429069i	−0.323060	+	0.946379i	$0.604712\pi$
$12$	1.06945	+	1.55193i	0.308725	+	0.448003i
$13$	0.402272	−	0.337546i	0.111570	−	0.0936185i	−0.585296	−	0.810820i	$-0.699022\pi$
$13$	0.402272	−	0.337546i	0.111570	−	0.0936185i	0.696866	+	0.717201i	$0.254577\pi$
$14$	0.731503	−	0.613803i	0.195502	−	0.164046i
$15$	6.95740	−	0.556267i	1.79639	−	0.143628i
$16$	0.601058	−	0.218767i	0.150264	−	0.0546918i
$17$	−1.49397	−	2.58763i	−0.362340	−	0.627592i	0.626005	−	0.779819i	$-0.284689\pi$
$17$	−1.49397	−	2.58763i	−0.362340	−	0.627592i	−0.988346	+	0.152227i	$0.951356\pi$
$18$	2.82833	−	0.455179i	0.666644	−	0.107287i
$19$	−1.44865	+	2.50914i	−0.332344	+	0.575636i	−0.982971	−	0.183761i	$-0.941173\pi$
$19$	−1.44865	+	2.50914i	−0.332344	+	0.575636i	0.650627	+	0.759397i	$0.274506\pi$
$20$	−0.761427	+	4.31827i	−0.170260	+	0.965594i
$21$	0.435756	+	1.67634i	0.0950898	+	0.365807i
$22$	−3.73353	−	1.35889i	−0.795992	−	0.289717i
$23$	−0.299868	−	1.70064i	−0.0625269	−	0.354608i	−0.999979	−	0.00649317i	$-0.997933\pi$
$23$	−0.299868	−	1.70064i	−0.0625269	−	0.354608i	0.937452	−	0.348115i	$-0.113178\pi$
$24$	−0.483222	+	5.08474i	−0.0986372	+	1.03792i
$25$	8.60901	+	7.22382i	1.72180	+	1.44476i
$26$	0.501450			0.0983425
$27$	−1.45719	+	4.98765i	−0.280435	+	0.959873i
$28$	−1.08815			−0.205641
$29$	0.978952	+	0.821438i	0.181787	+	0.152537i	0.729140	−	0.684364i	$-0.239920\pi$
$29$	0.978952	+	0.821438i	0.181787	+	0.152537i	−0.547353	+	0.836902i	$0.684365\pi$
$30$	5.43079	+	3.86356i	0.991522	+	0.705387i
$31$	−1.14367	−	6.48610i	−0.205410	−	1.16494i	−0.896793	−	0.442450i	$-0.854109\pi$
$31$	−1.14367	−	6.48610i	−0.205410	−	1.16494i	0.691383	−	0.722488i	$-0.257002\pi$
$32$	−4.96817	−	1.80826i	−0.878256	−	0.319659i
$33$	5.13385	−	5.05759i	0.893689	−	0.880414i
$34$	0.495454	−	2.80986i	0.0849697	−	0.481887i
$35$	−2.01484	+	3.48980i	−0.340570	+	0.589884i
$36$	−2.80235	−	1.67435i	−0.467059	−	0.279058i
$37$	−2.51013	−	4.34766i	−0.412662	−	0.714752i	0.582518	−	0.812818i	$-0.302068\pi$
$37$	−2.51013	−	4.34766i	−0.412662	−	0.714752i	−0.995180	+	0.0980662i	$0.968734\pi$
$38$	−2.59981	+	0.946255i	−0.421745	+	0.153503i
$39$	−0.390550	+	0.821433i	−0.0625380	+	0.131535i
$40$	−9.10299	+	7.63831i	−1.43931	+	1.20772i
$41$	7.74629	−	6.49991i	1.20977	−	1.01512i	0.210472	−	0.977600i	$-0.432500\pi$
$41$	7.74629	−	6.49991i	1.20977	−	1.01512i	0.999296	−	0.0375159i	$-0.0119445\pi$
$42$	−0.710187	+	1.49372i	−0.109584	+	0.230485i
$43$	5.92226	−	2.15553i	0.903137	−	0.328715i	0.151628	−	0.988438i	$-0.451549\pi$
$43$	5.92226	−	2.15553i	0.903137	−	0.328715i	0.751509	+	0.659723i	$0.229326\pi$
$44$	2.26376	+	3.92095i	0.341275	+	0.591106i
$45$	−10.5587	+	5.88716i	−1.57400	+	0.877606i
$46$	0.824503	−	1.42808i	0.121566	−	0.210559i
$47$	−1.47781	+	8.38105i	−0.215560	+	1.22250i	0.664372	+	0.747402i	$0.268699\pi$
$47$	−1.47781	+	8.38105i	−0.215560	+	1.22250i	−0.879932	+	0.475100i	$0.842412\pi$
$48$	−0.789226	+	0.777503i	−0.113915	+	0.112223i
$49$	−0.939693	−	0.342020i	−0.134242	−	0.0488600i
$50$	1.86351	+	10.5685i	0.263540	+	1.49461i
$51$	4.21699	+	3.00004i	0.590497	+	0.420090i
$52$	−0.437732	−	0.367301i	−0.0607025	−	0.0509355i
$53$	−10.6125			−1.45774			−0.728870	−	0.684652i	$-0.759954\pi$
$53$	−10.6125			−1.45774			−0.728870	+	0.684652i	$0.759954\pi$
$54$	−4.12737	+	2.75405i	−0.561664	+	0.374779i
$55$	16.7665			2.26079
$56$	−2.25899	−	1.89552i	−0.301870	−	0.253299i
$57$	0.474767	−	4.99577i	0.0628845	−	0.661706i
$58$	0.211904	+	1.20177i	0.0278244	+	0.157800i
$59$	12.4329	+	4.52520i	1.61862	+	0.589130i	0.983119	−	0.182967i	$-0.0585703\pi$
$59$	12.4329	+	4.52520i	1.61862	+	0.589130i	0.635504	+	0.772098i	$0.280792\pi$
$60$	−1.91074	−	7.35056i	−0.246676	−	0.948953i
$61$	1.79378	−	10.1730i	0.229670	−	1.30253i	−0.623882	−	0.781518i	$-0.714446\pi$
$61$	1.79378	−	10.1730i	0.229670	−	1.30253i	0.853553	−	0.521007i	$-0.174443\pi$
$62$	3.14459	−	5.44659i	0.399363	−	0.691718i
$63$	−1.89376	−	2.32673i	−0.238591	−	0.293141i
$64$	−3.16394	−	5.48010i	−0.395492	−	0.685013i
$65$	−1.98848	+	0.723748i	−0.246641	+	0.0897699i
$66$	6.85979	−	0.548464i	0.844382	−	0.0675112i
$67$	2.09084	−	1.75442i	0.255436	−	0.214337i	−0.506073	−	0.862491i	$-0.668903\pi$
$67$	2.09084	−	1.75442i	0.255436	−	0.214337i	0.761509	+	0.648154i	$0.224459\pi$
$68$	−2.49066	+	2.08991i	−0.302036	+	0.253439i
$69$	1.69720	+	2.46288i	0.204319	+	0.296496i
$70$	−3.61591	+	1.31608i	−0.432184	+	0.157302i
$71$	−0.743219	−	1.28729i	−0.0882039	−	0.152774i	0.818548	−	0.574438i	$-0.194779\pi$
$71$	−0.743219	−	1.28729i	−0.0882039	−	0.152774i	−0.906752	+	0.421664i	$0.861446\pi$
$72$	−2.90100	−	8.35753i	−0.341887	−	0.984944i
$73$	−1.01768	+	1.76267i	−0.119110	+	0.206305i	−0.919415	−	0.393288i	$-0.871338\pi$
$73$	−1.01768	+	1.76267i	−0.119110	+	0.206305i	0.800305	+	0.599593i	$0.204671\pi$
$74$	0.832449	−	4.72105i	0.0967702	−	0.548811i
$75$	−18.7638	−	5.17853i	−2.16665	−	0.597965i
$76$	2.96257	+	1.07829i	0.339830	+	0.123688i
$77$	0.722508	+	4.09754i	0.0823374	+	0.466959i
$78$	−0.789887	+	0.361159i	−0.0894370	+	0.0408932i
$79$	3.06523	+	2.57203i	0.344865	+	0.289376i	0.798724	−	0.601697i	$-0.205509\pi$
$79$	3.06523	+	2.57203i	0.344865	+	0.289376i	−0.453859	+	0.891073i	$0.649953\pi$
$80$	−2.57751			−0.288174
$81$	−1.29689	−	8.90607i	−0.144098	−	0.989563i
$82$	9.65610			1.06634
$83$	−3.89731	−	3.27024i	−0.427786	−	0.358955i	0.403330	−	0.915055i	$-0.367853\pi$
$83$	−3.89731	−	3.27024i	−0.427786	−	0.358955i	−0.831116	+	0.556100i	$0.812297\pi$
$84$	1.71406	−	0.783717i	0.187019	−	0.0855106i
$85$	2.09079	+	11.8575i	0.226778	+	1.28612i
$86$	5.65522	+	2.05833i	0.609818	+	0.221956i
$87$	−2.13367	−	0.588863i	−0.228754	−	0.0631327i
$88$	−2.13060	+	12.0833i	−0.227123	+	1.28808i
$89$	5.12426	−	8.87547i	0.543170	−	0.940798i	−0.455550	−	0.890210i	$-0.650557\pi$
$89$	5.12426	−	8.87547i	0.543170	−	0.940798i	0.998720	−	0.0505877i	$-0.0161094\pi$
$90$	−11.3373	−	2.17448i	−1.19505	−	0.229211i
$91$	−0.262564	−	0.454775i	−0.0275242	−	0.0476734i
$92$	−1.76577	+	0.642689i	−0.184095	+	0.0670049i
$93$	6.47301	+	9.39323i	0.671219	+	0.974033i
$94$	−6.22534	+	5.22368i	−0.642094	+	0.538781i
$95$	8.94372	−	7.50467i	0.917606	−	0.769963i
$96$	9.12824	−	0.729834i	0.931647	−	0.0744884i
$97$	−11.3317	+	4.12439i	−1.15056	+	0.418768i	−0.845715	−	0.533635i	$-0.820826\pi$
$97$	−11.3317	+	4.12439i	−1.15056	+	0.418768i	−0.304841	+	0.952403i	$0.598603\pi$
$98$	−0.477454	−	0.826975i	−0.0482302	−	0.0835371i
$99$	−4.44424	+	11.6643i	−0.446663	+	1.17231i
$100$	6.11446	−	10.5905i	0.611446	−	1.05905i
$101$	1.91797	−	10.8773i	0.190845	−	1.08233i	−0.727368	−	0.686247i	$-0.759257\pi$
$101$	1.91797	−	10.8773i	0.190845	−	1.08233i	0.918213	−	0.396087i	$-0.129632\pi$
$102$	1.24330	+	4.78294i	0.123105	+	0.473582i
$103$	−12.9847	−	4.72605i	−1.27942	−	0.465672i	−0.389181	−	0.921161i	$-0.627242\pi$
$103$	−12.9847	−	4.72605i	−1.27942	−	0.465672i	−0.890241	+	0.455490i	$0.849464\pi$
$104$	−0.268903	−	1.52503i	−0.0263681	−	0.149541i
$105$	0.660323	−	6.94829i	0.0644409	−	0.678084i
$106$	−7.76308	−	6.51400i	−0.754017	−	0.632695i
$107$	8.62687			0.833991			0.416996	−	0.908908i	$-0.363083\pi$
$107$	8.62687			0.833991			0.416996	+	0.908908i	$0.363083\pi$
$108$	5.62019	+	0.619105i	0.540803	+	0.0595734i
$109$	−15.8137			−1.51468			−0.757339	−	0.653022i	$-0.773501\pi$
$109$	−15.8137			−1.51468			−0.757339	+	0.653022i	$0.773501\pi$
$110$	12.2647	+	10.2913i	1.16940	+	0.981240i
$111$	7.08528	+	5.04059i	0.672505	+	0.478432i
$112$	−0.111071	−	0.629915i	−0.0104952	−	0.0595214i
$113$	−7.59508	−	2.76438i	−0.714485	−	0.260051i	−0.0409026	−	0.999163i	$-0.513023\pi$
$113$	−7.59508	−	2.76438i	−0.714485	−	0.260051i	−0.673583	+	0.739112i	$0.735246\pi$
$114$	3.41372	−	3.36301i	0.319724	−	0.314974i
$115$	−1.20837	+	6.85302i	−0.112681	+	0.639047i
$116$	0.695290	−	1.20428i	0.0645560	−	0.111814i
$117$	0.0235757	−	1.57521i	0.00217957	−	0.145628i
$118$	6.31710	+	10.9415i	0.581536	+	1.00725i
$119$	−2.80774	+	1.02193i	−0.257385	+	0.0936806i
$120$	8.83773	−	18.5881i	0.806770	−	1.69686i
$121$	4.83519	−	4.05720i	0.439563	−	0.368837i
$122$	7.55641	−	6.34058i	0.684125	−	0.574049i
$123$	−7.52057	+	15.8178i	−0.678107	+	1.42624i
$124$	−6.73452	+	2.45116i	−0.604778	+	0.220121i
$125$	−12.5691	−	21.7703i	−1.12421	−	1.94719i
$126$	0.0428707	−	2.86441i	0.00381922	−	0.255182i
$127$	−1.29622	+	2.24512i	−0.115021	+	0.199222i	−0.917788	−	0.397070i	$-0.870027\pi$
$127$	−1.29622	+	2.24512i	−0.115021	+	0.199222i	0.802767	+	0.596293i	$0.203360\pi$
$128$	−0.786883	+	4.46263i	−0.0695513	+	0.394445i
$129$	−7.77630	+	7.66079i	−0.684665	+	0.674495i
$130$	−1.89882	−	0.691113i	−0.166537	−	0.0606147i
$131$	−0.180227	−	1.02212i	−0.0157465	−	0.0893027i	0.975922	−	0.218121i	$-0.0699927\pi$
$131$	−0.180227	−	1.02212i	−0.0157465	−	0.0893027i	−0.991668	+	0.128818i	$0.958882\pi$
$132$	−6.38987	−	4.54587i	−0.556167	−	0.395667i
$133$	2.21947	+	1.86235i	0.192452	+	0.161486i
$134$	2.60632			0.225152
$135$	12.3920	−	16.8782i	1.06653	−	1.45264i
$136$	−8.81113			−0.755548
$137$	−2.68053	−	2.24923i	−0.229013	−	0.192165i	0.521060	−	0.853520i	$-0.325537\pi$
$137$	−2.68053	−	2.24923i	−0.229013	−	0.192165i	−0.750072	+	0.661356i	$0.769981\pi$
$138$	−0.270215	+	2.84335i	−0.0230022	+	0.242042i
$139$	2.13974	+	12.1351i	0.181490	+	1.02928i	0.930382	+	0.366590i	$0.119475\pi$
$139$	2.13974	+	12.1351i	0.181490	+	1.02928i	−0.748892	+	0.662692i	$0.769414\pi$
$140$	4.12045	+	1.49972i	0.348241	+	0.126749i
$141$	−3.70843	−	14.2662i	−0.312307	−	1.20143i
$142$	0.246478	−	1.39785i	0.0206840	−	0.117305i
$143$	−1.09247	+	1.89221i	−0.0913566	+	0.158234i
$144$	0.683212	−	1.79315i	0.0569344	−	0.149429i
$145$	−2.57482	−	4.45972i	−0.213827	−	0.370360i
$146$	−1.82637	+	0.664744i	−0.151151	+	0.0550146i
$147$	1.72654	−	0.138043i	0.142403	−	0.0113856i
$148$	−4.18473	+	3.51141i	−0.343983	+	0.288636i
$149$	9.04012	−	7.58556i	0.740595	−	0.621433i	−0.192402	−	0.981316i	$-0.561628\pi$
$149$	9.04012	−	7.58556i	0.740595	−	0.621433i	0.932997	+	0.359883i	$0.117183\pi$
$150$	−10.5471	−	15.3054i	−0.861170	−	1.24968i
$151$	18.5755	−	6.76092i	1.51165	−	0.550195i	0.552603	−	0.833444i	$-0.313634\pi$
$151$	18.5755	−	6.76092i	1.51165	−	0.550195i	0.959046	+	0.283249i	$0.0914123\pi$
$152$	4.27193	+	7.39921i	0.346500	+	0.600155i
$153$	−8.80335	−	1.68848i	−0.711708	−	0.136506i
$154$	−1.98657	+	3.44084i	−0.160082	+	0.277271i
$155$	−4.60864	+	26.1369i	−0.370175	+	2.09936i
$156$	0.954059	+	0.263306i	0.0763858	+	0.0210814i
$157$	12.8719	+	4.68501i	1.02729	+	0.373904i	0.800050	−	0.599934i	$-0.204806\pi$
$157$	12.8719	+	4.68501i	1.02729	+	0.373904i	0.227244	+	0.973838i	$0.427029\pi$
$158$	0.663500	+	3.76289i	0.0527852	+	0.299360i
$159$	16.7169	−	7.64345i	1.32573	−	0.606165i
$160$	16.3205	+	13.6945i	1.29025	+	1.08265i
$161$	−1.72687			−0.136097
$162$	4.51790	−	7.31085i	0.354960	−	0.574394i
$163$	−20.4893			−1.60485			−0.802423	−	0.596755i	$-0.796456\pi$
$163$	−20.4893			−1.60485			−0.802423	+	0.596755i	$0.796456\pi$
$164$	−8.42913	−	7.07288i	−0.658204	−	0.552299i
$165$	−26.4106	+	12.0757i	−2.05607	+	0.940094i
$166$	−0.843614	−	4.78437i	−0.0654771	−	0.371339i
$167$	−11.8892	−	4.32732i	−0.920016	−	0.334858i	−0.161771	−	0.986828i	$-0.551721\pi$
$167$	−11.8892	−	4.32732i	−0.920016	−	0.334858i	−0.758245	+	0.651970i	$0.773943\pi$
$168$	4.92358	+	1.35884i	0.379862	+	0.104836i
$169$	−2.20954	+	12.5309i	−0.169965	+	0.963918i
$170$	−5.74874	+	9.95712i	−0.440909	+	0.763676i
$171$	2.85025	+	8.21131i	0.217964	+	0.627934i
$172$	−3.42894	−	5.93911i	−0.261455	−	0.452853i
$173$	12.0873	−	4.39941i	0.918979	−	0.334481i	0.161147	−	0.986930i	$-0.448481\pi$
$173$	12.0873	−	4.39941i	0.918979	−	0.334481i	0.757832	+	0.652449i	$0.226259\pi$
$174$	−1.19934	−	1.74041i	−0.0909218	−	0.131940i
$175$	8.60901	−	7.22382i	0.650780	−	0.546069i
$176$	−2.03872	+	1.71069i	−0.153674	+	0.128948i
$177$	−22.8435	+	1.82642i	−1.71702	+	0.137282i
$178$	9.19620	−	3.34714i	0.689284	−	0.250879i
$179$	8.24968	+	14.2889i	0.616610	+	1.06800i	0.990100	+	0.140366i	$0.0448279\pi$
$179$	8.24968	+	14.2889i	0.616610	+	1.06800i	−0.373489	+	0.927634i	$0.621839\pi$
$180$	8.30390	+	10.2025i	0.618936	+	0.760447i
$181$	−1.08979	+	1.88756i	−0.0810032	+	0.140302i	−0.903681	−	0.428206i	$-0.859146\pi$
$181$	−1.08979	+	1.88756i	−0.0810032	+	0.140302i	0.822678	+	0.568508i	$0.192479\pi$
$182$	0.0870759	−	0.493832i	0.00645450	−	0.0366053i
$183$	4.50136	+	17.3166i	0.332750	+	1.28008i
$184$	−4.78527	−	1.74170i	−0.352775	−	0.128400i
$185$	3.51290	+	19.9226i	0.258273	+	1.46474i
$186$	−1.03058	+	10.8443i	−0.0755656	+	0.795144i
$187$	9.52352	+	7.99118i	0.696429	+	0.584373i
$188$	9.26052			0.675393
$189$	4.65883	+	2.30114i	0.338880	+	0.167384i
$190$	11.1487			0.808815
$191$	12.0821	+	10.1381i	0.874229	+	0.733565i	0.964984	−	0.262308i	$-0.0844837\pi$
$191$	12.0821	+	10.1381i	0.874229	+	0.733565i	−0.0907554	+	0.995873i	$0.528928\pi$
$192$	8.93078	+	6.35352i	0.644524	+	0.458526i
$193$	1.52376	+	8.64167i	0.109683	+	0.622041i	0.989246	+	0.146260i	$0.0467235\pi$
$193$	1.52376	+	8.64167i	0.109683	+	0.622041i	−0.879564	+	0.475781i	$0.842165\pi$
$194$	−10.8207	−	3.93841i	−0.776881	−	0.282762i
$195$	2.61100	−	2.57221i	0.186978	−	0.184200i
$196$	−0.188955	+	1.07162i	−0.0134968	+	0.0765441i
$197$	4.91970	−	8.52117i	0.350514	−	0.607108i	−0.635826	−	0.771833i	$-0.719340\pi$
$197$	4.91970	−	8.52117i	0.350514	−	0.607108i	0.986340	+	0.164725i	$0.0526736\pi$
$198$	−10.4106	+	5.80457i	−0.739846	+	0.412513i
$199$	9.74282	+	16.8751i	0.690650	+	1.19624i	0.971625	+	0.236526i	$0.0760089\pi$
$199$	9.74282	+	16.8751i	0.690650	+	1.19624i	−0.280975	+	0.959715i	$0.590658\pi$
$200$	31.1419	−	11.3347i	2.20207	−	0.801486i
$201$	−2.02991	+	4.26946i	−0.143179	+	0.301144i
$202$	8.07953	−	6.77953i	0.568474	−	0.477006i
$203$	0.978952	−	0.821438i	0.0687089	−	0.0576536i
$204$	2.41808	−	5.08588i	0.169299	−	0.356083i
$205$	−38.2909	+	13.9368i	−2.67435	+	0.973385i
$206$	−6.59749	−	11.4272i	−0.459669	−	0.796170i
$207$	−4.44728	−	2.65716i	−0.309108	−	0.184686i
$208$	0.167945	−	0.290889i	0.0116449	−	0.0201695i
$209$	2.09333	−	11.8718i	0.144798	−	0.821193i
$210$	4.74791	−	4.67739i	0.327637	−	0.322770i
$211$	−11.4983	−	4.18503i	−0.791574	−	0.288109i	−0.0855838	−	0.996331i	$-0.527276\pi$
$211$	−11.4983	−	4.18503i	−0.791574	−	0.288109i	−0.705990	+	0.708222i	$0.749498\pi$
$212$	2.00529	+	11.3726i	0.137724	+	0.781070i
$213$	2.09787	+	1.49246i	0.143744	+	0.102262i
$214$	6.31058	+	5.29521i	0.431382	+	0.361973i
$215$	−25.3964			−1.73202
$216$	10.5890	+	11.0754i	0.720491	+	0.753588i
$217$	−6.58616			−0.447098
$218$	−11.5678	−	9.70651i	−0.783468	−	0.657408i
$219$	0.333524	−	3.50953i	0.0225375	−	0.237152i
$220$	−3.16811	−	17.9673i	−0.213594	−	1.21135i
$221$	−1.47443	−	0.536647i	−0.0991806	−	0.0360988i
$222$	2.08896	+	8.03618i	0.140202	+	0.539353i
$223$	3.06689	−	17.3932i	0.205374	−	1.16474i	−0.691475	−	0.722400i	$-0.743039\pi$
$223$	3.06689	−	17.3932i	0.205374	−	1.16474i	0.896849	−	0.442336i	$-0.145850\pi$
$224$	−2.64351	+	4.57869i	−0.176627	+	0.305926i
$225$	33.2865	−	5.35698i	2.21910	−	0.357132i
$226$	−3.85903	−	6.68404i	−0.256699	−	0.444616i
$227$	−12.2133	+	4.44528i	−0.810626	+	0.295044i	−0.713883	−	0.700265i	$-0.753065\pi$
$227$	−12.2133	+	4.44528i	−0.810626	+	0.295044i	−0.0967438	+	0.995309i	$0.530843\pi$
$228$	−5.44327	+	0.435208i	−0.360489	+	0.0288223i
$229$	6.30393	−	5.28962i	0.416575	−	0.349548i	−0.410283	−	0.911958i	$-0.634570\pi$
$229$	6.30393	−	5.28962i	0.416575	−	0.349548i	0.826859	+	0.562410i	$0.190126\pi$
$230$	−5.09033	+	4.27130i	−0.335647	+	0.281641i
$231$	−4.08927	−	5.93410i	−0.269054	−	0.390435i
$232$	3.54122	−	1.28890i	0.232493	−	0.0846204i
$233$	2.31536	+	4.01032i	0.151684	+	0.262725i	0.931847	−	0.362852i	$-0.118197\pi$
$233$	2.31536	+	4.01032i	0.151684	+	0.262725i	−0.780163	+	0.625577i	$0.784864\pi$
$234$	0.984115	−	1.13780i	0.0643336	−	0.0743803i
$235$	17.1469	−	29.6994i	1.11854	−	1.93737i
$236$	2.50003	−	14.1784i	0.162738	−	0.922932i
$237$	−6.68081	−	1.84381i	−0.433965	−	0.119768i
$238$	−2.68114	−	0.975854i	−0.173792	−	0.0632552i
$239$	0.763043	+	4.32743i	0.0493571	+	0.279918i	0.999490	−	0.0319265i	$-0.0101643\pi$
$239$	0.763043	+	4.32743i	0.0493571	+	0.279918i	−0.950133	+	0.311845i	$0.899053\pi$
$240$	4.06010	−	1.85640i	0.262079	−	0.119830i
$241$	−3.27879	−	2.75123i	−0.211205	−	0.177222i	0.531048	−	0.847342i	$-0.321798\pi$
$241$	−3.27879	−	2.75123i	−0.211205	−	0.177222i	−0.742253	+	0.670120i	$0.766243\pi$
$242$	6.02728			0.387448
$243$	8.45728	+	13.0948i	0.542534	+	0.840034i
$244$	−11.2406			−0.719603
$245$	3.08691	+	2.59022i	0.197215	+	0.165483i
$246$	−15.2103	+	6.95461i	−0.969776	+	0.443410i
$247$	0.264199	+	1.49835i	0.0168106	+	0.0953374i
$248$	−18.2506	−	6.64269i	−1.15892	−	0.421811i
$249$	8.49439	+	2.34433i	0.538310	+	0.148566i
$250$	4.16836	−	23.6400i	0.263631	−	1.49512i
$251$	1.21897	−	2.11132i	0.0769407	−	0.133265i	−0.824988	−	0.565150i	$-0.808818\pi$
$251$	1.21897	−	2.11132i	0.0769407	−	0.133265i	0.901929	+	0.431885i	$0.142151\pi$
$252$	−2.13554	+	2.46903i	−0.134526	+	0.155534i
$253$	3.59255	+	6.22248i	0.225862	+	0.391204i
$254$	−2.32625	+	0.846686i	−0.145962	+	0.0531258i
$255$	−11.8335	−	17.1721i	−0.741045	−	1.07536i
$256$	−13.0097	+	10.9164i	−0.813104	+	0.682275i
$257$	4.71050	−	3.95258i	0.293833	−	0.246555i	−0.483939	−	0.875102i	$-0.660794\pi$
$257$	4.71050	−	3.95258i	0.293833	−	0.246555i	0.777772	+	0.628547i	$0.216350\pi$
$258$	−10.3906	+	0.830764i	−0.646891	+	0.0517211i
$259$	−4.71749	+	1.71703i	−0.293131	+	0.106691i
$260$	1.15132	+	1.99414i	0.0714015	+	0.123671i
$261$	3.78509	−	0.609155i	0.234291	−	0.0377058i
$262$	0.495542	−	0.858305i	0.0306147	−	0.0530262i
$263$	3.30355	−	18.7354i	0.203706	−	1.15527i	−0.695757	−	0.718277i	$-0.744931\pi$
$263$	3.30355	−	18.7354i	0.203706	−	1.15527i	0.899463	−	0.436996i	$-0.143958\pi$
$264$	−5.34658	−	20.5681i	−0.329059	−	1.26588i
$265$	40.1859	+	14.6265i	2.46860	+	0.898497i
$266$	0.480426	+	2.72463i	0.0294568	+	0.167058i
$267$	−1.67937	+	17.6713i	−0.102776	+	1.08147i
$268$	−2.27514	−	1.90907i	−0.138977	−	0.116615i
$269$	19.8948			1.21301			0.606505	−	0.795080i	$-0.292571\pi$
$269$	19.8948			1.21301			0.606505	+	0.795080i	$0.292571\pi$
$270$	19.4246	−	4.74017i	1.18215	−	0.288478i
$271$	−5.49656			−0.333892			−0.166946	−	0.985966i	$-0.553391\pi$
$271$	−5.49656			−0.333892			−0.166946	+	0.985966i	$0.553391\pi$
$272$	−1.46405	−	1.22848i	−0.0887710	−	0.0744877i
$273$	0.741135	+	0.527257i	0.0448555	+	0.0319110i
$274$	−0.580227	−	3.29063i	−0.0350528	−	0.198794i
$275$	−43.9397	−	15.9928i	−2.64967	−	0.964399i
$276$	2.31857	−	2.28413i	0.139562	−	0.137488i
$277$	1.42916	−	8.10515i	0.0858697	−	0.486991i	−0.911296	−	0.411752i	$-0.864917\pi$
$277$	1.42916	−	8.10515i	0.0858697	−	0.486991i	0.997166	−	0.0752391i	$-0.0239720\pi$
$278$	−5.88332	+	10.1902i	−0.352858	+	0.611168i
$279$	−16.9616	−	10.1342i	−1.01546	−	0.606719i
$280$	5.94155	+	10.2911i	0.355076	+	0.615009i
$281$	−19.2111	+	6.99226i	−1.14604	+	0.417123i	−0.844090	−	0.536201i	$-0.819859\pi$
$281$	−19.2111	+	6.99226i	−1.14604	+	0.417123i	−0.301947	+	0.953325i	$0.597637\pi$
$282$	6.04393	−	12.7120i	0.359911	−	0.756990i
$283$	10.2575	−	8.60709i	0.609747	−	0.511638i	−0.284815	−	0.958582i	$-0.591932\pi$
$283$	10.2575	−	8.60709i	0.609747	−	0.511638i	0.894562	+	0.446944i	$0.147488\pi$
$284$	−1.23905	+	1.03969i	−0.0735242	+	0.0616941i
$285$	−8.68310	+	18.2629i	−0.514343	+	1.08180i
$286$	−1.96059	+	0.713595i	−0.115932	+	0.0421957i
$287$	−5.05603	−	8.75731i	−0.298448	−	0.516928i
$288$	−13.8532	+	7.72407i	−0.816308	+	0.455145i
$289$	4.03612	−	6.99076i	0.237419	−	0.411221i
$290$	0.853904	−	4.84273i	0.0501430	−	0.284375i
$291$	14.8792	−	14.6582i	0.872233	−	0.859276i
$292$	2.08121	+	0.757498i	0.121793	+	0.0443292i
$293$	0.775443	+	4.39776i	0.0453019	+	0.256920i	0.999044	−	0.0437047i	$-0.0139161\pi$
$293$	0.775443	+	4.39776i	0.0453019	+	0.256920i	−0.953743	+	0.300624i	$0.902805\pi$
$294$	1.34770	+	0.958778i	0.0785995	+	0.0559171i
$295$	−40.8422	−	34.2707i	−2.37793	−	1.99532i
$296$	−14.8042			−0.860478
$297$	−1.40038	−	21.5745i	−0.0812583	−	1.25188i
$298$	11.2689			0.652790
$299$	−0.694673	−	0.582900i	−0.0401740	−	0.0337100i
$300$	−2.00389	+	21.0861i	−0.115695	+	1.21741i
$301$	−1.09439	−	6.20659i	−0.0630796	−	0.357742i
$302$	17.7379	+	6.45606i	1.02070	+	0.371504i
$303$	4.81298	+	18.5154i	0.276499	+	1.06368i
$304$	−0.321807	+	1.82506i	−0.0184569	+	0.104674i
$305$	−20.8132	+	36.0496i	−1.19176	+	2.06419i
$306$	−5.40327	−	6.63865i	−0.308885	−	0.379506i
$307$	2.01673	+	3.49307i	0.115101	+	0.199360i	0.917820	−	0.396997i	$-0.129948\pi$
$307$	2.01673	+	3.49307i	0.115101	+	0.199360i	−0.802719	+	0.596357i	$0.796614\pi$
$308$	4.25448	−	1.54850i	0.242422	−	0.0882342i
$309$	23.8574	−	1.90748i	1.35720	−	0.108513i
$310$	−19.4141	+	16.2904i	−1.10265	+	0.925232i
$311$	12.6142	−	10.5846i	0.715284	−	0.600195i	−0.210792	−	0.977531i	$-0.567604\pi$
$311$	12.6142	−	10.5846i	0.715284	−	0.600195i	0.926076	+	0.377336i	$0.123160\pi$
$312$	1.52195	+	2.20856i	0.0861633	+	0.125035i
$313$	−3.97424	+	1.44651i	−0.224637	+	0.0817613i	−0.451887	−	0.892075i	$-0.649249\pi$
$313$	−3.97424	+	1.44651i	−0.224637	+	0.0817613i	0.227250	+	0.973837i	$0.427027\pi$
$314$	6.54019	+	11.3279i	0.369084	+	0.639273i
$315$	3.96422	+	11.4206i	0.223359	+	0.643476i
$316$	2.17704	−	3.77075i	0.122468	−	0.212121i
$317$	−1.85839	+	10.5395i	−0.104378	+	0.591956i	0.887089	+	0.461598i	$0.152724\pi$
$317$	−1.85839	+	10.5395i	−0.104378	+	0.591956i	−0.991467	+	0.130358i	$0.958387\pi$
$318$	16.9200	+	4.66968i	0.948827	+	0.261863i
$319$	−4.99649	−	1.81857i	−0.279750	−	0.101821i
$320$	4.42790	+	25.1119i	0.247527	+	1.40380i
$321$	−13.5891	+	6.21333i	−0.758469	+	0.346794i
$322$	−1.26321	−	1.05996i	−0.0703961	−	0.0590693i
$323$	8.65697			0.481686
$324$	−9.29885	+	3.07261i	−0.516603	+	0.170701i
$325$	5.90154			0.327358
$326$	−14.9880	−	12.5764i	−0.830108	−	0.696543i
$327$	24.9098	−	11.3895i	1.37752	−	0.629841i
$328$	−5.17810	−	29.3665i	−0.285913	−	1.62149i
$329$	7.99710	+	2.91071i	0.440895	+	0.160473i
$330$	−26.7316	−	7.37753i	−1.47152	−	0.406119i
$331$	2.65088	−	15.0339i	0.145706	−	0.826338i	−0.821092	−	0.570796i	$-0.806635\pi$
$331$	2.65088	−	15.0339i	0.145706	−	0.826338i	0.966798	−	0.255542i	$-0.0822541\pi$
$332$	−2.76802	+	4.79436i	−0.151915	+	0.263125i
$333$	−14.7911	−	2.83694i	−0.810550	−	0.155463i
$334$	−6.04087	−	10.4631i	−0.330542	−	0.572515i
$335$	−10.3353	+	3.76173i	−0.564676	+	0.205525i
$336$	0.628643	+	0.912248i	0.0342953	+	0.0497672i
$337$	24.0827	−	20.2078i	1.31187	−	1.10079i	0.323909	−	0.946088i	$-0.395003\pi$
$337$	24.0827	−	20.2078i	1.31187	−	1.10079i	0.987961	−	0.154702i	$-0.0494417\pi$
$338$	−9.30781	+	7.81018i	−0.506278	+	0.424818i
$339$	13.9548	−	1.11573i	0.757921	−	0.0605983i
$340$	12.3116	−	4.48107i	0.667692	−	0.243020i
$341$	13.7017	+	23.7320i	0.741989	+	1.28516i
$342$	−2.95516	+	7.75608i	−0.159797	+	0.419401i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	3.22725	−	18.3026i	0.174002	−	0.986812i
$345$	−3.03231	−	11.6652i	−0.163254	−	0.628034i
$346$	11.5423	+	4.20104i	0.620515	+	0.225849i
$347$	−4.98575	−	28.2756i	−0.267649	−	1.51791i	−0.761384	−	0.648301i	$-0.775480\pi$
$347$	−4.98575	−	28.2756i	−0.267649	−	1.51791i	0.493735	−	0.869613i	$-0.335631\pi$
$348$	−0.227867	+	2.39775i	−0.0122150	+	0.128533i
$349$	−26.3086	−	22.0755i	−1.40827	−	1.18168i	−0.957287	−	0.289141i	$-0.906630\pi$
$349$	−26.3086	−	22.0755i	−1.40827	−	1.18168i	−0.450979	−	0.892535i	$-0.648925\pi$
$350$	10.7315			0.573624
$351$	1.09738	+	2.49826i	0.0585736	+	0.133347i
$352$	21.9980			1.17250
$353$	17.0574	+	14.3129i	0.907874	+	0.761796i	0.971713	−	0.236164i	$-0.0758902\pi$
$353$	17.0574	+	14.3129i	0.907874	+	0.761796i	−0.0638396	+	0.997960i	$0.520335\pi$
$354$	−17.8311	−	12.6854i	−0.947714	−	0.674221i
$355$	1.04013	+	5.89886i	0.0552043	+	0.313079i
$356$	−10.4794	−	3.81418i	−0.555405	−	0.202151i
$357$	3.68674	−	3.63197i	0.195123	−	0.192224i
$358$	−2.73590	+	15.5160i	−0.144597	+	0.820048i
$359$	0.477605	−	0.827236i	0.0252070	−	0.0436598i	−0.853147	−	0.521671i	$-0.825309\pi$
$359$	0.477605	−	0.827236i	0.0252070	−	0.0436598i	0.878354	+	0.478011i	$0.158642\pi$
$360$	−0.533493	+	35.6453i	−0.0281175	+	1.87867i
$361$	5.30281	+	9.18473i	0.279095	+	0.483407i
$362$	−1.95577	+	0.711844i	−0.102793	+	0.0374137i
$363$	−4.69429	+	9.87337i	−0.246386	+	0.518218i
$364$	−0.437732	+	0.367301i	−0.0229434	+	0.0192518i
$365$	6.28297	−	5.27204i	0.328866	−	0.275951i
$366$	−7.33621	+	15.4301i	−0.383470	+	0.806542i
$367$	7.54882	−	2.74755i	0.394045	−	0.143421i	−0.137395	−	0.990516i	$-0.543873\pi$
$367$	7.54882	−	2.74755i	0.394045	−	0.143421i	0.531441	+	0.847096i	$0.321651\pi$
$368$	−0.552282	−	0.956581i	−0.0287897	−	0.0498652i
$369$	0.453982	−	30.3328i	0.0236334	−	1.57906i
$370$	−9.65889	+	16.7297i	−0.502142	+	0.869735i
$371$	−1.84284	+	10.4513i	−0.0956757	+	0.542604i
$372$	8.84285	−	8.71149i	0.458480	−	0.451670i
$373$	9.03262	+	3.28761i	0.467692	+	0.170226i	0.565106	−	0.825018i	$-0.308835\pi$
$373$	9.03262	+	3.28761i	0.467692	+	0.170226i	−0.0974148	+	0.995244i	$0.531057\pi$
$374$	2.06146	+	11.6911i	0.106596	+	0.604534i
$375$	35.4785	+	25.2400i	1.83210	+	1.30339i
$376$	19.2248	+	16.1315i	0.991442	+	0.831918i
$377$	0.671078			0.0345623
$378$	1.99550	+	4.54290i	0.102637	+	0.233662i
$379$	−23.3222			−1.19798			−0.598990	−	0.800757i	$-0.704431\pi$
$379$	−23.3222			−1.19798			−0.598990	+	0.800757i	$0.704431\pi$
$380$	−9.73210	−	8.16620i	−0.499246	−	0.418917i
$381$	0.424811	−	4.47010i	0.0217637	−	0.229010i
$382$	2.61529	+	14.8320i	0.133810	+	0.758874i
$383$	3.61550	+	1.31594i	0.184744	+	0.0672412i	0.432735	−	0.901521i	$-0.357548\pi$
$383$	3.61550	+	1.31594i	0.184744	+	0.0672412i	−0.247992	+	0.968762i	$0.579771\pi$
$384$	−1.97462	−	7.59630i	−0.100767	−	0.387647i
$385$	2.91147	−	16.5118i	0.148382	−	0.841517i
$386$	−4.18965	+	7.25669i	−0.213248	+	0.369356i
$387$	6.73174	−	17.6680i	0.342194	−	0.898116i
$388$	6.56094	+	11.3639i	0.333081	+	0.576914i
$389$	20.4292	−	7.43562i	1.03580	−	0.377001i	0.232515	−	0.972593i	$-0.425305\pi$
$389$	20.4292	−	7.43562i	1.03580	−	0.377001i	0.803287	+	0.595592i	$0.203082\pi$
$390$	3.48879	−	0.278940i	0.176662	−	0.0141247i
$391$	−3.95263	+	3.31665i	−0.199893	+	0.167730i
$392$	−2.25899	+	1.89552i	−0.114096	+	0.0957381i
$393$	1.02005	+	1.48024i	0.0514548	+	0.0746681i
$394$	8.82909	−	3.21353i	0.444803	−	0.161895i
$395$	−8.06210	−	13.9640i	−0.405649	−	0.702604i
$396$	13.3394	+	2.55850i	0.670331	+	0.128569i
$397$	−8.65531	+	14.9914i	−0.434398	+	0.752399i	−0.997246	−	0.0741612i	$-0.976372\pi$
$397$	−8.65531	+	14.9914i	−0.434398	+	0.752399i	0.562849	+	0.826560i	$0.309705\pi$
$398$	−3.23107	+	18.3243i	−0.161959	+	0.918515i
$399$	−4.83743	−	1.33506i	−0.242175	−	0.0668367i
$400$	6.75485	+	2.45856i	0.337742	+	0.122928i
$401$	−0.230337	−	1.30631i	−0.0115025	−	0.0652339i	0.978516	−	0.206170i	$-0.0660999\pi$
$401$	−0.230337	−	1.30631i	−0.0115025	−	0.0652339i	−0.990019	+	0.140936i	$0.954989\pi$
$402$	−4.10549	+	1.87715i	−0.204763	+	0.0936238i
$403$	−2.64943	−	2.22313i	−0.131977	−	0.110742i
$404$	−12.0187			−0.597955
$405$	−7.36375	+	35.5116i	−0.365908	+	1.76459i
$406$	1.22031			0.0605628
$407$	16.0012	+	13.4266i	0.793148	+	0.665530i
$408$	13.8793	−	6.34603i	0.687129	−	0.314176i
$409$	2.25387	+	12.7824i	0.111447	+	0.632047i	0.988448	+	0.151559i	$0.0484293\pi$
$409$	2.25387	+	12.7824i	0.111447	+	0.632047i	−0.877001	+	0.480488i	$0.840460\pi$
$410$	−36.5643	−	13.3083i	−1.80578	−	0.657251i
$411$	5.84234	+	1.61240i	0.288181	+	0.0795339i
$412$	−2.61099	+	14.8077i	−0.128634	+	0.729521i
$413$	6.61540	−	11.4582i	0.325522	−	0.563821i
$414$	−1.62222	−	4.67348i	−0.0797279	−	0.229689i
$415$	10.2506	+	17.7546i	0.503184	+	0.871541i
$416$	−2.60893	+	0.949572i	−0.127913	+	0.0465566i
$417$	−12.1106	−	17.5741i	−0.593056	−	0.860607i
$418$	8.81825	−	7.39939i	0.431315	−	0.361916i
$419$	6.14231	−	5.15401i	0.300071	−	0.251790i	−0.480303	−	0.877103i	$-0.659473\pi$
$419$	6.14231	−	5.15401i	0.300071	−	0.251790i	0.780374	+	0.625313i	$0.215029\pi$
$420$	−7.57069	+	0.605302i	−0.369412	+	0.0295357i
$421$	29.3637	−	10.6875i	1.43110	−	0.520878i	0.493854	−	0.869545i	$-0.335588\pi$
$421$	29.3637	−	10.6875i	1.43110	−	0.520878i	0.937247	+	0.348667i	$0.113366\pi$
$422$	−5.84223	−	10.1190i	−0.284395	−	0.492587i
$423$	16.1165	+	19.8013i	0.783611	+	0.962772i
$424$	−15.6476	+	27.1025i	−0.759916	+	1.31621i
$425$	5.83097	−	33.0691i	0.282844	−	1.60409i
$426$	0.618518	+	2.37942i	0.0299673	+	0.115283i
$427$	−9.70701	−	3.53306i	−0.469755	−	0.170977i
$428$	−1.63009	−	9.24471i	−0.0787935	−	0.446860i
$429$	0.358034	−	3.76744i	0.0172861	−	0.181894i
$430$	−18.5775	−	15.5884i	−0.895887	−	0.751739i
$431$	0.875234			0.0421585			0.0210793	−	0.999778i	$-0.493290\pi$
$431$	0.875234			0.0421585			0.0210793	+	0.999778i	$0.493290\pi$
$432$	0.215280	+	3.31665i	0.0103577	+	0.159572i
$433$	−3.75223			−0.180321			−0.0901604	−	0.995927i	$-0.528738\pi$
$433$	−3.75223			−0.180321			−0.0901604	+	0.995927i	$0.528738\pi$
$434$	−4.81779	−	4.04261i	−0.231261	−	0.194051i
$435$	7.26789	+	5.17051i	0.348469	+	0.247907i
$436$	2.98808	+	16.9462i	0.143103	+	0.811578i
$437$	4.70155	+	1.71122i	0.224906	+	0.0818589i
$438$	2.39814	−	2.36251i	0.114587	−	0.112885i
$439$	−6.59712	+	37.4142i	−0.314864	+	1.78568i	0.258120	+	0.966113i	$0.416897\pi$
$439$	−6.59712	+	37.4142i	−0.314864	+	1.78568i	−0.572983	+	0.819567i	$0.694214\pi$
$440$	24.7214	−	42.8186i	1.17854	−	2.04130i
$441$	−2.62023	+	1.46095i	−0.124773	+	0.0695691i
$442$	−0.749151	−	1.29757i	−0.0356335	−	0.0617190i
$443$	−7.02357	+	2.55637i	−0.333700	+	0.121457i	−0.503436	−	0.864033i	$-0.667931\pi$
$443$	−7.02357	+	2.55637i	−0.333700	+	0.121457i	0.169736	+	0.985490i	$0.445709\pi$
$444$	4.06279	−	8.54516i	0.192812	−	0.405535i
$445$	−31.6362	+	26.5459i	−1.49970	+	1.25840i
$446$	12.9195	−	10.8407i	0.611754	−	0.513323i
$447$	−8.77669	+	18.4598i	−0.415123	+	0.873117i
$448$	−5.94626	+	2.16426i	−0.280934	+	0.102252i
$449$	6.38762	+	11.0637i	0.301450	+	0.522127i	0.976465	−	0.215677i	$-0.0691959\pi$
$449$	6.38762	+	11.0637i	0.301450	+	0.522127i	−0.675014	+	0.737805i	$0.735863\pi$
$450$	27.6373	+	16.5127i	1.30283	+	0.778417i
$451$	−21.0369	+	36.4370i	−0.990590	+	1.71575i
$452$	−1.52723	+	8.66137i	−0.0718350	+	0.407397i
$453$	−24.3907	+	24.0284i	−1.14598	+	1.12895i
$454$	−11.6626	−	4.24484i	−0.547353	−	0.199220i
$455$	0.367457	+	2.08395i	0.0172266	+	0.0976971i
$456$	−12.0583	−	8.57849i	−0.564682	−	0.401725i
$457$	−8.38088	−	7.03239i	−0.392041	−	0.328962i	0.425367	−	0.905021i	$-0.360145\pi$
$457$	−8.38088	−	7.03239i	−0.392041	−	0.328962i	−0.817408	+	0.576060i	$0.804590\pi$
$458$	7.85813			0.367186
$459$	15.0832	−	3.68073i	0.704022	−	0.171802i
$460$	7.57215			0.353053
$461$	−16.2100	−	13.6018i	−0.754973	−	0.633497i	0.181840	−	0.983328i	$-0.441795\pi$
$461$	−16.2100	−	13.6018i	−0.754973	−	0.633497i	−0.936813	+	0.349831i	$0.886239\pi$
$462$	0.651059	−	6.85082i	0.0302900	−	0.318729i
$463$	−4.14357	−	23.4994i	−0.192568	−	1.09211i	−0.915840	−	0.401544i	$-0.868474\pi$
$463$	−4.14357	−	23.4994i	−0.192568	−	1.09211i	0.723272	−	0.690564i	$-0.242638\pi$
$464$	0.768110	+	0.279569i	0.0356586	+	0.0129787i
$465$	−11.5650	−	44.4902i	−0.536314	−	2.06318i
$466$	−0.767857	+	4.35473i	−0.0355703	+	0.201729i
$467$	−4.79553	+	8.30609i	−0.221910	+	0.384360i	−0.955388	−	0.295353i	$-0.904563\pi$
$467$	−4.79553	+	8.30609i	−0.221910	+	0.384360i	0.733478	+	0.679714i	$0.237896\pi$
$468$	−1.69248	+	0.272380i	−0.0782348	+	0.0125908i
$469$	−1.36470	−	2.36373i	−0.0630159	−	0.109147i
$470$	30.7726	−	11.2003i	1.41943	−	0.516632i
$471$	−23.6502	+	1.89092i	−1.08974	+	0.0871288i
$472$	29.8882	−	25.0792i	1.37572	−	1.15436i
$473$	−20.0876	+	16.8555i	−0.923629	+	0.775017i
$474$	−3.75530	−	5.44945i	−0.172486	−	0.250302i
$475$	−30.5970	+	11.1364i	−1.40389	+	0.510974i
$476$	1.62566	+	2.81573i	0.0745120	+	0.129059i
$477$	−20.8275	+	24.0800i	−0.953624	+	1.10255i
$478$	−2.09802	+	3.63388i	−0.0959614	+	0.166210i
$479$	−0.386092	+	2.18964i	−0.0176410	+	0.100047i	−0.992357	−	0.123400i	$-0.960620\pi$
$479$	−0.386092	+	2.18964i	−0.0176410	+	0.100047i	0.974716	+	0.223448i	$0.0717311\pi$
$480$	−35.5714	−	9.81718i	−1.62360	−	0.448091i
$481$	−2.47729	−	0.901661i	−0.112955	−	0.0411122i
$482$	−0.709727	−	4.02506i	−0.0323272	−	0.183336i
$483$	2.72018	−	1.24375i	0.123772	−	0.0565924i
$484$	−5.26141	−	4.41484i	−0.239155	−	0.200675i
$485$	48.5934			2.20651
$486$	−1.85113	+	14.7700i	−0.0839691	+	0.669981i
$487$	12.6488			0.573172			0.286586	−	0.958054i	$-0.407480\pi$
$487$	12.6488			0.573172			0.286586	+	0.958054i	$0.407480\pi$
$488$	−23.3353	−	19.5807i	−1.05634	−	0.886375i
$489$	32.2749	−	14.7570i	1.45952	−	0.667335i
$490$	0.668193	+	3.78951i	0.0301859	+	0.171193i
$491$	−18.2787	−	6.65291i	−0.824908	−	0.300242i	−0.105140	−	0.994457i	$-0.533529\pi$
$491$	−18.2787	−	6.65291i	−0.824908	−	0.300242i	−0.719767	+	0.694216i	$0.755751\pi$
$492$	18.3717	+	5.07032i	0.828260	+	0.228588i
$493$	0.663054	−	3.76037i	0.0298624	−	0.169358i
$494$	−0.726427	+	1.25821i	−0.0326835	+	0.0566095i
$495$	32.9049	−	38.0435i	1.47896	−	1.70993i
$496$	−2.10636	−	3.64832i	−0.0945784	−	0.163815i
$497$	−1.39679	+	0.508392i	−0.0626548	+	0.0228045i
$498$	4.77471	+	6.92877i	0.213960	+	0.310485i
$499$	8.43660	−	7.07915i	0.377674	−	0.316906i	−0.434114	−	0.900858i	$-0.642939\pi$
$499$	8.43660	−	7.07915i	0.377674	−	0.316906i	0.811789	+	0.583951i	$0.198494\pi$
$500$	−20.9544	+	17.5829i	−0.937111	+	0.786330i
$501$	21.8446	−	1.74655i	0.975946	−	0.0780302i
$502$	2.18761	−	0.796227i	0.0976380	−	0.0355373i
$503$	9.36478	+	16.2203i	0.417555	+	0.723226i	0.995693	−	0.0927129i	$-0.0295539\pi$
$503$	9.36478	+	16.2203i	0.417555	+	0.723226i	−0.578138	+	0.815939i	$0.696221\pi$
$504$	−8.73431	+	1.40566i	−0.389057	+	0.0626132i
$505$	−22.2541	+	38.5453i	−0.990295	+	1.71524i
$506$	−1.19142	+	6.75688i	−0.0529651	+	0.300380i
$507$	−5.54467	−	21.3302i	−0.246247	−	0.947305i
$508$	2.65084	+	0.964826i	0.117612	+	0.0428072i
$509$	−3.29245	−	18.6724i	−0.145935	−	0.827639i	−0.966612	−	0.256246i	$-0.917514\pi$
$509$	−3.29245	−	18.6724i	−0.145935	−	0.827639i	0.820677	−	0.571393i	$-0.193597\pi$
$510$	1.88404	−	19.8249i	0.0834266	−	0.877862i
$511$	1.55918	+	1.30830i	0.0689739	+	0.0578760i
$512$	−7.15417			−0.316172
$513$	−10.4038	−	10.8817i	−0.459337	−	0.480437i
$514$	5.87185			0.258996
$515$	42.6550	+	35.7918i	1.87961	+	1.57718i
$516$	9.67881	+	6.88568i	0.426086	+	0.303125i
$517$	−6.14879	−	34.8715i	−0.270423	−	1.53365i
$518$	−4.50477	−	1.63960i	−0.197928	−	0.0720401i
$519$	−15.8714	+	15.6356i	−0.696675	+	0.686326i
$520$	−1.08359	+	6.14536i	−0.0475187	+	0.269492i
$521$	8.88223	−	15.3845i	0.389138	−	0.674006i	−0.603196	−	0.797593i	$-0.706106\pi$
$521$	8.88223	−	15.3845i	0.389138	−	0.674006i	0.992334	+	0.123587i	$0.0394397\pi$
$522$	3.14270	+	1.87770i	0.137552	+	0.0821848i
$523$	−8.14752	−	14.1119i	−0.356266	−	0.617071i	0.631068	−	0.775728i	$-0.282617\pi$
$523$	−8.14752	−	14.1119i	−0.356266	−	0.617071i	−0.987334	+	0.158657i	$0.949284\pi$
$524$	−1.06126	+	0.386268i	−0.0463615	+	0.0168742i
$525$	−8.35814	+	17.5795i	−0.364779	+	0.767230i
$526$	13.9164	−	11.6772i	0.606784	−	0.509152i
$527$	−15.0750	+	12.6494i	−0.656678	+	0.551018i
$528$	1.97931	−	4.16302i	0.0861383	−	0.181172i
$529$	18.8107	−	6.84653i	0.817856	−	0.297675i
$530$	20.4183	+	35.3656i	0.886915	+	1.53618i
$531$	34.6678	−	19.3295i	1.50445	−	0.838831i
$532$	1.57635	−	2.73032i	0.0683435	−	0.118374i
$533$	0.922096	−	5.22947i	0.0399404	−	0.226513i
$534$	−12.0752	+	11.8958i	−0.522544	+	0.514782i
$535$	−32.6670	−	11.8898i	−1.41232	−	0.514041i
$536$	−1.39764	−	7.92644i	−0.0603691	−	0.342370i
$537$	−23.2862	−	16.5662i	−1.00487	−	0.714886i
$538$	14.5531	+	12.2115i	0.627430	+	0.526476i
$539$	4.16076			0.179216
$540$	−20.4285	−	10.0903i	−0.879101	−	0.434215i
$541$	16.6054			0.713923			0.356961	−	0.934119i	$-0.383813\pi$
$541$	16.6054			0.713923			0.356961	+	0.934119i	$0.383813\pi$
$542$	−4.02075	−	3.37381i	−0.172706	−	0.144918i
$543$	0.357156	−	3.75820i	0.0153270	−	0.161280i
$544$	2.74316	+	15.5573i	0.117612	+	0.667012i
$545$	59.8810	+	21.7949i	2.56502	+	0.933591i
$546$	0.218510	+	0.840601i	0.00935137	+	0.0359744i
$547$	−5.55686	+	31.5145i	−0.237594	+	1.34746i	0.599487	+	0.800384i	$0.295371\pi$
$547$	−5.55686	+	31.5145i	−0.237594	+	1.34746i	−0.837081	+	0.547078i	$0.815740\pi$
$548$	−1.90381	+	3.29750i	−0.0813269	+	0.140862i
$549$	−19.5625	−	24.0351i	−0.834905	−	1.02579i
$550$	−22.3256	−	38.6691i	−0.951967	−	1.64886i
$551$	−3.47927	+	1.26635i	−0.148222	+	0.0539483i
$552$	8.79220	−	0.702966i	0.374221	−	0.0299202i
$553$	3.06523	−	2.57203i	0.130347	−	0.109374i
$554$	6.02040	−	5.05172i	0.255782	−	0.214627i
$555$	−19.8824	−	28.8521i	−0.843961	−	1.22470i
$556$	12.5998	−	4.58596i	0.534352	−	0.194488i
$557$	−11.4867	−	19.8955i	−0.486706	−	0.843000i	0.513177	−	0.858283i	$-0.328468\pi$
$557$	−11.4867	−	19.8955i	−0.486706	−	0.843000i	−0.999883	+	0.0152830i	$0.995135\pi$
$558$	−6.18703	−	17.8243i	−0.261918	−	0.754562i
$559$	1.65477	−	2.86615i	0.0699893	−	0.121225i
$560$	−0.447580	+	2.53835i	−0.0189137	+	0.107265i
$561$	−20.7570	−	5.72862i	−0.876360	−	0.241863i
$562$	−18.3448	−	6.67697i	−0.773830	−	0.281651i
$563$	−0.736048	−	4.17434i	−0.0310207	−	0.175927i	0.965361	−	0.260918i	$-0.0840251\pi$
$563$	−0.736048	−	4.17434i	−0.0310207	−	0.175927i	−0.996382	+	0.0849904i	$0.972914\pi$
$564$	−14.5872	+	6.66970i	−0.614233	+	0.280845i
$565$	24.9500	+	20.9355i	1.04965	+	0.880765i
$566$	12.7865			0.537455
$567$	−8.99597	−	0.269340i	−0.377795	−	0.0113112i
$568$	−4.38336			−0.183922
$569$	28.1874	+	23.6520i	1.18168	+	0.991544i	0.999966	+	0.00819179i	$0.00260756\pi$
$569$	28.1874	+	23.6520i	1.18168	+	0.991544i	0.181710	+	0.983352i	$0.441837\pi$
$570$	−17.5616	+	8.02966i	−0.735573	+	0.336325i
$571$	−3.50151	−	19.8580i	−0.146533	−	0.831033i	−0.966123	−	0.258082i	$-0.916910\pi$
$571$	−3.50151	−	19.8580i	−0.146533	−	0.831033i	0.819590	−	0.572951i	$-0.194201\pi$
$572$	2.23415	+	0.813164i	0.0934145	+	0.0340001i
$573$	−26.3335	−	7.26766i	−1.10010	−	0.303611i
$574$	1.67676	−	9.50941i	0.0699868	−	0.396915i
$575$	9.70353	−	16.8070i	0.404665	−	0.700901i
$576$	−18.6438	−	3.57588i	−0.776825	−	0.148995i
$577$	10.6679	+	18.4773i	0.444109	+	0.769220i	0.997990	−	0.0633766i	$-0.0201869\pi$
$577$	10.6679	+	18.4773i	0.444109	+	0.769220i	−0.553881	+	0.832596i	$0.686854\pi$
$578$	7.24339	−	2.63638i	0.301285	−	0.109659i
$579$	−8.62422	−	12.5149i	−0.358410	−	0.520103i
$580$	−4.29259	+	3.60191i	−0.178240	+	0.149561i
$581$	−3.89731	+	3.27024i	−0.161688	+	0.135672i
$582$	19.8814	−	1.58958i	0.824110	−	0.0658904i
$583$	41.4931	−	15.1023i	1.71847	−	0.625472i
$584$	3.00104	+	5.19795i	0.124184	+	0.215093i
$585$	−2.26027	+	5.93228i	−0.0934508	+	0.245270i
$586$	−2.13212	+	3.69294i	−0.0880771	+	0.152554i
$587$	−2.14277	+	12.1522i	−0.0884414	+	0.501576i	0.908119	+	0.418711i	$0.137518\pi$
$587$	−2.14277	+	12.1522i	−0.0884414	+	0.501576i	−0.996561	+	0.0828648i	$0.973593\pi$
$588$	−0.474168	−	1.82411i	−0.0195544	−	0.0752250i
$589$	17.9313	+	6.52647i	0.738848	+	0.268919i
$590$	−8.84072	−	50.1382i	−0.363967	−	2.06416i
$591$	−1.61233	+	16.9659i	−0.0663225	+	0.697884i
$592$	−2.45986	−	2.06406i	−0.101099	−	0.0848325i
$593$	−27.5842			−1.13275			−0.566373	−	0.824149i	$-0.691654\pi$
$593$	−27.5842			−1.13275			−0.566373	+	0.824149i	$0.691654\pi$
$594$	12.2181	−	16.6414i	0.501316	−	0.682804i
$595$	12.0404			0.493608
$596$	−9.83700	−	8.25422i	−0.402939	−	0.338106i
$597$	−27.5009	−	19.5646i	−1.12554	−	0.800726i
$598$	−0.150369	−	0.852786i	−0.00614905	−	0.0348730i
$599$	−12.9966	−	4.73037i	−0.531026	−	0.193278i	0.0625703	−	0.998041i	$-0.480070\pi$
$599$	−12.9966	−	4.73037i	−0.531026	−	0.193278i	−0.593597	+	0.804763i	$0.702292\pi$
$600$	−40.8913	+	40.2838i	−1.66938	+	1.64458i
$601$	3.75872	−	21.3168i	0.153321	−	0.869529i	−0.806983	−	0.590575i	$-0.798901\pi$
$601$	3.75872	−	21.3168i	0.153321	−	0.869529i	0.960304	−	0.278954i	$-0.0899879\pi$
$602$	3.00908	−	5.21188i	0.122641	−	0.212420i
$603$	0.122536	−	8.18727i	0.00499007	−	0.333411i
$604$	−10.7550	−	18.6283i	−0.437617	−	0.757974i
$605$	−23.9009	+	8.69923i	−0.971712	+	0.353674i
$606$	−7.84410	+	16.4983i	−0.318645	+	0.670197i
$607$	−5.59833	+	4.69756i	−0.227229	+	0.190668i	−0.749293	−	0.662238i	$-0.769607\pi$
$607$	−5.59833	+	4.69756i	−0.227229	+	0.190668i	0.522064	+	0.852906i	$0.325162\pi$
$608$	11.7343	−	9.84628i	0.475890	−	0.399319i
$609$	−0.950425	+	1.99900i	−0.0385132	+	0.0810037i
$610$	−37.3523	+	13.5951i	−1.51235	+	0.550450i
$611$	2.23451	+	3.87029i	0.0903987	+	0.156575i
$612$	−0.145968	+	9.75287i	−0.00590042	+	0.394236i
$613$	11.2255	−	19.4432i	0.453395	−	0.785303i	−0.545200	−	0.838306i	$-0.683546\pi$
$613$	11.2255	−	19.4432i	0.453395	−	0.785303i	0.998594	+	0.0530037i	$0.0168795\pi$
$614$	−0.668820	+	3.79307i	−0.0269914	+	0.153076i
$615$	50.2783	−	49.5315i	2.02742	−	1.99730i
$616$	11.5297	+	4.19647i	0.464545	+	0.169081i
$617$	4.60952	+	26.1419i	0.185572	+	1.05243i	0.925218	+	0.379437i	$0.123882\pi$
$617$	4.60952	+	26.1419i	0.185572	+	1.05243i	−0.739645	+	0.672997i	$0.765007\pi$
$618$	18.6226	+	13.2484i	0.749110	+	0.532931i
$619$	−16.5534	−	13.8899i	−0.665337	−	0.558284i	0.246344	−	0.969182i	$-0.420771\pi$
$619$	−16.5534	−	13.8899i	−0.665337	−	0.558284i	−0.911681	+	0.410899i	$0.865215\pi$
$620$	28.8796			1.15983
$621$	8.91915	+	0.982508i	0.357913	+	0.0394267i
$622$	15.7241			0.630480
$623$	−7.85082	−	6.58762i	−0.314536	−	0.263927i
$624$	−0.0550405	+	0.579168i	−0.00220339	+	0.0231853i
$625$	7.83280	+	44.4220i	0.313312	+	1.77688i
$626$	−3.79504	−	1.38128i	−0.151680	−	0.0552071i
$627$	5.25304	+	20.2083i	0.209786	+	0.807040i
$628$	2.58831	−	14.6791i	0.103285	−	0.585758i
$629$	−7.50009	+	12.9905i	−0.299048	+	0.517967i
$630$	−4.11014	+	10.7874i	−0.163752	+	0.429781i
$631$	−3.79456	−	6.57237i	−0.151059	−	0.261642i	0.780558	−	0.625083i	$-0.214935\pi$
$631$	−3.79456	−	6.57237i	−0.151059	−	0.261642i	−0.931617	+	0.363441i	$0.881602\pi$
$632$	11.0880	−	4.03571i	0.441058	−	0.160532i
$633$	21.1263	−	1.68912i	0.839696	−	0.0671365i
$634$	−7.82858	+	6.56896i	−0.310913	+	0.260887i
$635$	8.00263	−	6.71500i	0.317575	−	0.266477i
$636$	−11.3496	−	16.4698i	−0.450041	−	0.653071i
$637$	−0.493460	+	0.179605i	−0.0195516	+	0.00711620i
$638$	−2.53870	−	4.39716i	−0.100508	−	0.174085i
$639$	−4.37949	−	0.839985i	−0.173250	−	0.0332293i
$640$	9.13018	−	15.8139i	0.360902	−	0.625101i
$641$	−0.283856	+	1.60983i	−0.0112117	+	0.0635844i	−0.989900	−	0.141765i	$-0.954722\pi$
$641$	−0.283856	+	1.60983i	−0.0112117	+	0.0635844i	0.978689	+	0.205350i	$0.0658332\pi$
$642$	−13.7542	−	3.79596i	−0.542836	−	0.149815i
$643$	25.9497	+	9.44493i	1.02336	+	0.372472i	0.798548	−	0.601931i	$-0.205602\pi$
$643$	25.9497	+	9.44493i	1.02336	+	0.372472i	0.224810	+	0.974403i	$0.427824\pi$
$644$	0.326302	+	1.85055i	0.0128581	+	0.0729218i
$645$	40.0045	−	18.2912i	1.57517	−	0.720216i
$646$	6.33259	+	5.31368i	0.249153	+	0.209064i
$647$	−44.8015			−1.76133			−0.880663	−	0.473743i	$-0.842903\pi$
$647$	−44.8015			−1.76133			−0.880663	+	0.473743i	$0.842903\pi$
$648$	−24.6567	−	9.81954i	−0.968607	−	0.385748i
$649$	−55.0501			−2.16091
$650$	4.31699	+	3.62238i	0.169326	+	0.142082i
$651$	10.3746	−	4.74355i	0.406611	−	0.185914i
$652$	3.87156	+	21.9567i	0.151622	+	0.859891i
$653$	−3.19930	−	1.16445i	−0.125198	−	0.0455685i	0.278661	−	0.960389i	$-0.410109\pi$
$653$	−3.19930	−	1.16445i	−0.125198	−	0.0455685i	−0.403860	+	0.914821i	$0.632332\pi$
$654$	25.2125	+	6.95829i	0.985887	+	0.272091i
$655$	−0.726255	+	4.11880i	−0.0283771	+	0.160935i
$656$	3.23400	−	5.60146i	0.126267	−	0.218700i
$657$	2.00230	+	5.76845i	0.0781172	+	0.225049i
$658$	4.06330	+	7.03784i	0.158404	+	0.274364i
$659$	−0.0175194	+	0.00637655i	−0.000682460	+	0.000248395i	−0.342361	−	0.939568i	$-0.611227\pi$
$659$	−0.0175194	+	0.00637655i	−0.000682460	+	0.000248395i	0.341679	+	0.939817i	$0.389004\pi$
$660$	17.9310	+	26.0204i	0.697963	+	1.01284i
$661$	−28.5778	+	23.9796i	−1.11155	+	0.932698i	−0.998147	−	0.0608514i	$-0.980618\pi$
$661$	−28.5778	+	23.9796i	−1.11155	+	0.932698i	−0.113399	+	0.993549i	$0.536174\pi$
$662$	11.1670	−	9.37022i	0.434017	−	0.364184i
$663$	2.70903	−	0.216596i	0.105210	−	0.00841190i
$664$	−14.0980	+	5.13125i	−0.547108	+	0.199131i
$665$	−5.83760	−	10.1110i	−0.226372	−	0.392088i
$666$	−9.07844	−	11.1541i	−0.351782	−	0.432212i
$667$	1.10341	−	1.91117i	0.0427243	−	0.0740007i
$668$	−2.39071	+	13.5584i	−0.0924992	+	0.524589i
$669$	7.69613	+	29.6068i	0.297550	+	1.14466i
$670$	−9.86924	−	3.59211i	−0.381282	−	0.138775i
$671$	7.46349	+	42.3276i	0.288125	+	1.63404i
$672$	0.866356	−	9.11630i	0.0334204	−	0.351669i
$673$	24.1602	+	20.2728i	0.931307	+	0.781460i	0.976052	−	0.217539i	$-0.0698029\pi$
$673$	24.1602	+	20.2728i	0.931307	+	0.781460i	−0.0447443	+	0.998998i	$0.514247\pi$
$674$	30.0202			1.15634
$675$	−48.5748	+	32.4123i	−1.86964	+	1.24755i
$676$	13.8459			0.532534
$677$	2.41097	+	2.02304i	0.0926610	+	0.0777518i	0.687941	−	0.725766i	$-0.258515\pi$
$677$	2.41097	+	2.02304i	0.0926610	+	0.0777518i	−0.595280	+	0.803518i	$0.702959\pi$
$678$	10.8928	+	7.74934i	0.418336	+	0.297612i
$679$	2.09401	+	11.8757i	0.0803606	+	0.455748i
$680$	33.3647	+	12.1438i	1.27948	+	0.465692i
$681$	16.0368	−	15.7986i	0.614533	−	0.605405i
$682$	−4.54398	+	25.7702i	−0.173998	+	0.986792i
$683$	−17.6653	+	30.5971i	−0.675943	+	1.17077i	0.300250	+	0.953861i	$0.402930\pi$
$683$	−17.6653	+	30.5971i	−0.675943	+	1.17077i	−0.976192	+	0.216907i	$0.930403\pi$
$684$	8.26081	−	4.60595i	0.315860	−	0.176113i
$685$	7.05027	+	12.2114i	0.269377	+	0.466575i
$686$	−0.897321	+	0.326598i	−0.0342599	+	0.0124696i
$687$	−6.12023	+	12.8725i	−0.233501	+	0.491117i
$688$	3.08806	−	2.59119i	0.117731	−	0.0987883i
$689$	−4.26912	+	3.58221i	−0.162640	+	0.136472i
$690$	4.94200	−	10.3944i	0.188139	−	0.395707i
$691$	13.1245	−	4.77694i	0.499281	−	0.181723i	−0.0800898	−	0.996788i	$-0.525521\pi$
$691$	13.1245	−	4.77694i	0.499281	−	0.181723i	0.579370	+	0.815064i	$0.303298\pi$
$692$	−6.99844	−	12.1217i	−0.266041	−	0.460796i
$693$	10.7154	+	6.40221i	0.407043	+	0.243200i
$694$	13.7086	−	23.7439i	0.520370	−	0.901308i
$695$	8.62245	−	48.9003i	0.327068	−	1.85489i
$696$	−4.64985	+	4.58077i	−0.176252	+	0.173634i
$697$	−28.3921	−	10.3339i	−1.07543	−	0.391423i
$698$	−5.69476	−	32.2966i	−0.215550	−	1.22244i
$699$	−6.53551	−	4.64948i	−0.247196	−	0.175860i
$700$	−9.36789	−	7.86059i	−0.354073	−	0.297102i
$701$	−43.9837			−1.66124			−0.830621	−	0.556839i	$-0.812014\pi$
$701$	−43.9837			−1.66124			−0.830621	+	0.556839i	$0.812014\pi$
$702$	−0.730706	+	2.50106i	−0.0275787	+	0.0943963i
$703$	14.5452			0.548583
$704$	20.1690	+	16.9238i	0.760148	+	0.637840i
$705$	−5.61957	+	59.1323i	−0.211645	+	2.22705i
$706$	3.69225	+	20.9398i	0.138960	+	0.788079i
$707$	−10.3790	−	3.77765i	−0.390343	−	0.142073i
$708$	6.27362	+	24.1344i	0.235777	+	0.907026i
$709$	2.98700	−	16.9401i	0.112179	−	0.636199i	−0.875929	−	0.482439i	$-0.839751\pi$
$709$	2.98700	−	16.9401i	0.112179	−	0.636199i	0.988108	−	0.153759i	$-0.0491380\pi$
$710$	−2.85988	+	4.95346i	−0.107330	+	0.185900i
$711$	11.8516	−	1.90735i	0.444470	−	0.0715310i
$712$	−15.1109	−	26.1729i	−0.566306	−	0.980870i
$713$	−10.6876	+	3.88996i	−0.400252	+	0.145680i
$714$	4.92618	−	0.393865i	0.184358	−	0.0147400i
$715$	6.74469	−	5.65947i	0.252237	−	0.211652i
$716$	13.7534	−	11.5405i	0.513988	−	0.431287i
$717$	−4.31869	−	6.26702i	−0.161284	−	0.234046i
$718$	0.857129	−	0.311970i	0.0319878	−	0.0116426i
$719$	1.85884	+	3.21960i	0.0693229	+	0.120071i	0.898603	−	0.438762i	$-0.144583\pi$
$719$	1.85884	+	3.21960i	0.0693229	+	0.120071i	−0.829281	+	0.558833i	$0.811249\pi$
$720$	−5.05846	+	5.84841i	−0.188518	+	0.217958i
$721$	−6.90902	+	11.9668i	−0.257305	+	0.445666i
$722$	−1.75860	+	9.97354i	−0.0654484	+	0.371177i
$723$	7.14627	+	1.97227i	0.265773	+	0.0733494i
$724$	2.22867	+	0.811169i	0.0828278	+	0.0301469i
$725$	2.49389	+	14.1435i	0.0926206	+	0.525278i
$726$	−9.49420	+	4.34102i	−0.352363	+	0.161111i
$727$	−26.6008	−	22.3208i	−0.986571	−	0.827831i	−0.00150311	−	0.999999i	$-0.500478\pi$
$727$	−26.6008	−	22.3208i	−0.986571	−	0.827831i	−0.985068	+	0.172168i	$0.944923\pi$
$728$	−1.54855			−0.0573932
$729$	−22.7532	−	14.5359i	−0.842712	−	0.538365i
$730$	7.83200			0.289875
$731$	−14.4254	−	12.1043i	−0.533542	−	0.447695i
$732$	17.7062	−	8.09579i	0.654439	−	0.299229i
$733$	2.65215	+	15.0411i	0.0979595	+	0.555556i	0.993800	+	0.111181i	$0.0354632\pi$
$733$	2.65215	+	15.0411i	0.0979595	+	0.555556i	−0.895841	+	0.444375i	$0.853426\pi$
$734$	7.20844	+	2.62366i	0.266068	+	0.0968409i
$735$	−6.72807	−	1.85685i	−0.248169	−	0.0684909i
$736$	−1.58541	+	8.99130i	−0.0584389	+	0.331424i
$737$	−5.67817	+	9.83488i	−0.209158	+	0.362273i
$738$	18.9505	−	21.9099i	0.697577	−	0.806514i
$739$	−13.3250	−	23.0795i	−0.490167	−	0.848995i	0.509769	−	0.860312i	$-0.329731\pi$
$739$	−13.3250	−	23.0795i	−0.490167	−	0.848995i	−0.999936	+	0.0113168i	$0.996398\pi$
$740$	20.6857	−	7.52897i	0.760420	−	0.276770i
$741$	−1.49532	−	2.16992i	−0.0549319	−	0.0797139i
$742$	−7.76308	+	6.51400i	−0.284992	+	0.239136i
$743$	11.4662	−	9.62125i	0.420653	−	0.352970i	−0.407759	−	0.913090i	$-0.633690\pi$
$743$	11.4662	−	9.62125i	0.420653	−	0.352970i	0.828411	+	0.560120i	$0.189245\pi$
$744$	33.5328	−	2.68106i	1.22937	−	0.0982924i
$745$	−44.6864	+	16.2645i	−1.63718	+	0.595886i
$746$	4.58944	+	7.94915i	0.168031	+	0.291039i
$747$	−15.0689	+	2.42511i	−0.551340	+	0.0887303i
$748$	6.76398	−	11.7155i	0.247315	−	0.428363i
$749$	1.49804	−	8.49581i	0.0547372	−	0.310430i
$750$	10.4602	+	40.2400i	0.381952	+	1.46936i
$751$	−5.51346	−	2.00674i	−0.201189	−	0.0732268i	0.239460	−	0.970906i	$-0.423030\pi$
$751$	−5.51346	−	2.00674i	−0.201189	−	0.0732268i	−0.440649	+	0.897679i	$0.645252\pi$
$752$	0.945252	+	5.36079i	0.0344698	+	0.195488i
$753$	−0.399493	+	4.20370i	−0.0145583	+	0.153191i
$754$	0.490895	+	0.411910i	0.0178774	+	0.0150009i
$755$	−79.6569			−2.89901
$756$	1.58564	−	5.42730i	0.0576690	−	0.197389i
$757$	35.2022			1.27944			0.639722	−	0.768606i	$-0.279049\pi$
$757$	35.2022			1.27944			0.639722	+	0.768606i	$0.279049\pi$
$758$	−17.0602	−	14.3152i	−0.619656	−	0.519953i
$759$	−10.1406	−	7.21422i	−0.368081	−	0.261859i
$760$	−5.97853	−	33.9059i	−0.216864	−	1.22990i
$761$	21.4866	+	7.82050i	0.778890	+	0.283493i	0.700710	−	0.713446i	$-0.252867\pi$
$761$	21.4866	+	7.82050i	0.778890	+	0.283493i	0.0781805	+	0.996939i	$0.475089\pi$
$762$	3.05451	−	3.00914i	0.110653	−	0.109010i
$763$	−2.74602	+	15.5735i	−0.0994126	+	0.563797i
$764$	8.58117	−	14.8630i	0.310456	−	0.537725i
$765$	31.0081	+	18.5267i	1.12110	+	0.669835i
$766$	1.83702	+	3.18182i	0.0663744	+	0.114964i
$767$	6.52886	−	2.37631i	0.235744	−	0.0858036i
$768$	12.6306	−	26.5655i	0.455766	−	0.958600i
$769$	−20.4868	+	17.1905i	−0.738773	+	0.619904i	−0.932508	−	0.361150i	$-0.882384\pi$
$769$	−20.4868	+	17.1905i	−0.738773	+	0.619904i	0.193735	+	0.981054i	$0.437940\pi$
$770$	12.2647	−	10.2913i	0.441990	−	0.370874i
$771$	−4.57324	+	9.61877i	−0.164701	+	0.346411i
$772$	8.97264	−	3.26578i	0.322933	−	0.117538i
$773$	−12.1028	−	20.9627i	−0.435309	−	0.753977i	0.562012	−	0.827129i	$-0.310027\pi$
$773$	−12.1028	−	20.9627i	−0.435309	−	0.753977i	−0.997321	+	0.0731522i	$0.976694\pi$
$774$	15.7690	−	8.79224i	0.566804	−	0.316031i
$775$	37.0085	−	64.1006i	1.32938	−	2.30256i
$776$	−6.17502	+	35.0203i	−0.221670	+	1.25715i
$777$	6.19436	−	6.10235i	0.222222	−	0.218920i
$778$	19.5080	+	7.10034i	0.699397	+	0.254560i
$779$	5.08750	+	28.8527i	0.182279	+	1.03375i
$780$	−3.24979	−	2.31196i	−0.116361	−	0.0827815i
$781$	4.73776	+	3.97545i	0.169530	+	0.142253i
$782$	−4.92713			−0.176194
$783$	−5.52356	+	3.68568i	−0.197396	+	0.131715i
$784$	−0.639632			−0.0228440
$785$	−42.2846	−	35.4810i	−1.50920	−	1.26637i
$786$	−0.162404	+	1.70891i	−0.00579277	+	0.0609548i
$787$	1.26486	+	7.17338i	0.0450874	+	0.255703i	0.999017	−	0.0443270i	$-0.0141143\pi$
$787$	1.26486	+	7.17338i	0.0450874	+	0.255703i	−0.953930	+	0.300030i	$0.903003\pi$
$788$	−10.0610	−	3.66192i	−0.358410	−	0.130450i
$789$	8.29001	+	31.8914i	0.295132	+	1.13536i
$790$	2.67369	−	15.1632i	0.0951255	−	0.539484i
$791$	−4.04126	+	6.99967i	−0.143691	+	0.248880i
$792$	23.2357	+	28.5482i	0.825646	+	1.01442i
$793$	−2.71229	−	4.69782i	−0.0963161	−	0.166824i
$794$	−15.5332	+	5.65362i	−0.551252	+	0.200639i
$795$	−73.8355	+	5.90339i	−2.61867	+	0.209372i
$796$	16.2427	−	13.6292i	0.575706	−	0.483075i
$797$	−15.7226	+	13.1929i	−0.556925	+	0.467315i	−0.877278	−	0.479983i	$-0.840643\pi$
$797$	−15.7226	+	13.1929i	−0.556925	+	0.467315i	0.320353	+	0.947298i	$0.396198\pi$
$798$	−2.71913	−	3.94583i	−0.0962561	−	0.139681i
$799$	23.8948	−	8.69701i	0.845338	−	0.307678i
$800$	−29.7084	−	51.4565i	−1.05035	−	1.81926i
$801$	−10.0821	−	29.0455i	−0.356232	−	1.02627i
$802$	0.633324	−	1.09695i	0.0223634	−	0.0387346i
$803$	1.47056	−	8.33998i	0.0518950	−	0.294311i
$804$	4.95879	+	1.36855i	0.174883	+	0.0482652i
$805$	6.53907	+	2.38003i	0.230472	+	0.0838850i
$806$	−0.573496	−	3.25246i	−0.0202005	−	0.114563i
$807$	−31.3384	+	14.3289i	−1.10317	+	0.504400i
$808$	−24.9508	−	20.9362i	−0.877766	−	0.736533i
$809$	38.2426			1.34454			0.672269	−	0.740307i	$-0.265320\pi$
$809$	38.2426			1.34454			0.672269	+	0.740307i	$0.265320\pi$
$810$	−27.1838	+	21.4569i	−0.955140	+	0.753920i
$811$	−1.70505			−0.0598725			−0.0299362	−	0.999552i	$-0.509530\pi$
$811$	−1.70505			−0.0598725			−0.0299362	+	0.999552i	$0.509530\pi$
$812$	−1.06525	−	0.893847i	−0.0373828	−	0.0313679i
$813$	8.65821	−	3.95879i	0.303657	−	0.138841i
$814$	3.46362	+	19.6431i	0.121400	+	0.688492i
$815$	77.5859	+	28.2390i	2.71772	+	0.989168i
$816$	3.19097	+	0.880660i	0.111706	+	0.0308293i
$817$	−3.17078	+	17.9824i	−0.110932	+	0.629125i
$818$	−6.19714	+	10.7338i	−0.216678	+	0.375297i
$819$	−1.54719	−	0.296750i	−0.0540630	−	0.0103693i
$820$	22.1701	+	38.3998i	0.774215	+	1.34098i
$821$	19.7561	−	7.19062i	0.689491	−	0.250954i	0.0265739	−	0.999647i	$-0.491540\pi$
$821$	19.7561	−	7.19062i	0.689491	−	0.250954i	0.662917	+	0.748693i	$0.269318\pi$
$822$	3.28399	+	4.76552i	0.114542	+	0.166217i
$823$	−35.2842	+	29.6070i	−1.22993	+	1.03204i	−0.231688	+	0.972790i	$0.574425\pi$
$823$	−35.2842	+	29.6070i	−1.22993	+	1.03204i	−0.998243	+	0.0592449i	$0.981131\pi$
$824$	−31.2148	+	26.1923i	−1.08742	+	0.912453i
$825$	80.7325	−	6.45484i	2.81075	−	0.224729i
$826$	11.8723	−	4.32115i	0.413089	−	0.150352i
$827$	5.75106	+	9.96113i	0.199984	+	0.346382i	0.948523	−	0.316708i	$-0.102578\pi$
$827$	5.75106	+	9.96113i	0.199984	+	0.346382i	−0.748539	+	0.663091i	$0.769244\pi$
$828$	−2.00713	+	5.26787i	−0.0697524	+	0.183071i
$829$	−0.313043	+	0.542206i	−0.0108724	+	0.0188316i	−0.871410	−	0.490555i	$-0.836794\pi$
$829$	−0.313043	+	0.542206i	−0.0108724	+	0.0188316i	0.860538	+	0.509386i	$0.170128\pi$
$830$	−3.39949	+	19.2794i	−0.117998	+	0.669199i
$831$	3.58636	+	13.7966i	0.124409	+	0.478598i
$832$	−3.12255	−	1.13652i	−0.108255	−	0.0394016i
$833$	0.518850	+	2.94254i	0.0179771	+	0.101953i
$834$	1.92814	−	20.2890i	0.0667660	−	0.702550i
$835$	39.0563	+	32.7722i	1.35160	+	1.13413i
$836$	−13.1176			−0.453683
$837$	34.0169	+	3.74721i	1.17580	+	0.129522i
$838$	7.65666			0.264495
$839$	4.69808	+	3.94215i	0.162196	+	0.136098i	0.720273	−	0.693690i	$-0.244016\pi$
$839$	4.69808	+	3.94215i	0.162196	+	0.136098i	−0.558078	+	0.829789i	$0.688461\pi$
$840$	−16.7711	−	11.9313i	−0.578658	−	0.411668i
$841$	−4.75221	−	26.9511i	−0.163869	−	0.929349i
$842$	28.0397	+	10.2056i	0.966311	+	0.351709i
$843$	25.2254	−	24.8506i	0.868807	−	0.855901i
$844$	−2.31209	+	13.1125i	−0.0795856	+	0.451352i
$845$	25.6373	−	44.4050i	0.881949	−	1.52758i
$846$	−0.364844	+	24.3771i	−0.0125436	+	0.838101i
$847$	−3.15594	−	5.46626i	−0.108440	−	0.187823i
$848$	−6.37873	+	2.32167i	−0.219047	+	0.0797264i
$849$	−9.95862	+	20.9457i	−0.341779	+	0.718854i
$850$	24.5633	−	20.6110i	0.842514	−	0.706953i
$851$	−6.64110	+	5.57254i	−0.227654	+	0.191024i
$852$	1.20295	−	2.53012i	0.0412122	−	0.0866805i
$853$	7.98491	−	2.90627i	0.273398	−	0.0995088i	−0.201683	−	0.979451i	$-0.564641\pi$
$853$	7.98491	−	2.90627i	0.273398	−	0.0995088i	0.475081	+	0.879942i	$0.342419\pi$
$854$	−4.93209	−	8.54264i	−0.168773	−	0.292323i
$855$	0.524159	−	35.0217i	0.0179259	−	1.19772i
$856$	12.7199	−	22.0315i	0.434757	−	0.753021i
$857$	−3.77946	+	21.4344i	−0.129104	+	0.732184i	0.849682	+	0.527296i	$0.176794\pi$
$857$	−3.77946	+	21.4344i	−0.129104	+	0.732184i	−0.978785	+	0.204888i	$0.934317\pi$
$858$	2.57437	−	2.53613i	0.0878876	−	0.0865820i
$859$	−7.59180	−	2.76319i	−0.259029	−	0.0942788i	0.209242	−	0.977864i	$-0.432900\pi$
$859$	−7.59180	−	2.76319i	−0.259029	−	0.0942788i	−0.468270	+	0.883585i	$0.655123\pi$
$860$	4.79878	+	27.2152i	0.163637	+	0.928031i
$861$	14.2716	+	10.1530i	0.486374	+	0.346015i
$862$	0.640236	+	0.537222i	0.0218065	+	0.0182978i
$863$	−27.0043			−0.919238			−0.459619	−	0.888116i	$-0.652014\pi$
$863$	−27.0043			−0.919238			−0.459619	+	0.888116i	$0.652014\pi$
$864$	16.2585	−	22.1445i	0.553126	−	0.753370i
$865$	−51.8338			−1.76240
$866$	−2.74477	−	2.30313i	−0.0932710	−	0.0782637i
$867$	−1.32276	+	13.9188i	−0.0449232	+	0.472708i
$868$	1.24449	+	7.05785i	0.0422407	+	0.239559i
$869$	−15.6447	−	5.69420i	−0.530709	−	0.193162i
$870$	2.14280	+	8.24330i	0.0726479	+	0.279474i
$871$	0.248887	−	1.41151i	0.00843322	−	0.0478272i
$872$	−23.3165	+	40.3854i	−0.789597	+	1.36762i
$873$	−12.8805	+	33.8060i	−0.435939	+	1.14416i
$874$	2.38884	+	4.13759i	0.0808037	+	0.139956i
$875$	−23.6222	+	8.59776i	−0.798574	+	0.290657i
$876$	−3.82390	+	0.305734i	−0.129198	+	0.0103298i
$877$	36.9626	−	31.0153i	1.24814	−	1.04731i	0.251296	−	0.967910i	$-0.419143\pi$
$877$	36.9626	−	31.0153i	1.24814	−	1.04731i	0.996843	−	0.0794019i	$-0.0253010\pi$
$878$	−27.7908	+	23.3192i	−0.937892	+	0.786985i
$879$	−4.38888	−	6.36887i	−0.148033	−	0.214817i
$880$	10.0776	−	3.66796i	0.339717	−	0.123647i
$881$	17.3922	+	30.1241i	0.585957	+	1.01491i	0.994755	+	0.102282i	$0.0326145\pi$
$881$	17.3922	+	30.1241i	0.585957	+	1.01491i	−0.408799	+	0.912625i	$0.634052\pi$
$882$	−2.81344	−	0.539618i	−0.0947336	−	0.0181699i
$883$	12.6838	−	21.9690i	0.426843	−	0.739315i	−0.569747	−	0.821820i	$-0.692959\pi$
$883$	12.6838	−	21.9690i	0.426843	−	0.739315i	0.996591	+	0.0825055i	$0.0262922\pi$
$884$	−0.296480	+	1.68142i	−0.00997171	+	0.0565524i
$885$	89.0177	+	24.5676i	2.99230	+	0.825830i
$886$	−6.70687	−	2.44110i	−0.225322	−	0.0820104i
$887$	1.54005	+	8.73407i	0.0517099	+	0.293261i	0.999685	−	0.0250819i	$-0.00798466\pi$
$887$	1.54005	+	8.73407i	0.0517099	+	0.293261i	−0.947976	+	0.318343i	$0.896874\pi$
$888$	23.3197	−	10.6624i	0.782557	−	0.357808i
$889$	1.98592	+	1.66639i	0.0666058	+	0.0558889i
$890$	−39.4360			−1.32190
$891$	17.7445	+	32.9757i	0.594463	+	1.10473i
$892$	−19.2184			−0.643479
$893$	−18.8884	−	15.8493i	−0.632076	−	0.530375i
$894$	−17.7508	+	8.11620i	−0.593677	+	0.271446i
$895$	−11.5454	−	65.4770i	−0.385919	−	2.18865i
$896$	4.25820	+	1.54986i	0.142256	+	0.0517771i
$897$	1.51407	+	0.417862i	0.0505535	+	0.0139520i
$898$	−2.11837	+	12.0139i	−0.0706908	+	0.400907i
$899$	4.20833	−	7.28904i	0.140356	−	0.243103i
$900$	−12.0303	−	34.6582i	−0.401010	−	1.15527i
$901$	15.8548	+	27.4612i	0.528198	+	0.914866i
$902$	−37.7537	+	13.7412i	−1.25706	+	0.457533i
$903$	6.19406	+	8.98844i	0.206125	+	0.299117i
$904$	−18.2583	+	15.3206i	−0.607263	+	0.509554i
$905$	6.72814	−	5.64558i	0.223651	−	0.187665i
$906$	−32.5906	+	2.60573i	−1.08275	+	0.0865696i
$907$	−1.41772	+	0.516006i	−0.0470745	+	0.0171337i	−0.365450	−	0.930831i	$-0.619085\pi$
$907$	−1.41772	+	0.516006i	−0.0470745	+	0.0171337i	0.318376	+	0.947965i	$0.396863\pi$
$908$	7.07142	+	12.2481i	0.234673	+	0.406466i
$909$	−20.9168	−	25.6991i	−0.693765	−	0.852384i
$910$	−1.01034	+	1.74996i	−0.0334924	+	0.0580106i
$911$	0.690573	−	3.91643i	0.0228797	−	0.129757i	−0.971229	−	0.238150i	$-0.923459\pi$
$911$	0.690573	−	3.91643i	0.0228797	−	0.129757i	0.994108	+	0.108392i	$0.0345703\pi$
$912$	−0.807548	−	3.10661i	−0.0267406	−	0.102870i
$913$	19.8916	+	7.23995i	0.658316	+	0.239607i
$914$	−1.81413	−	10.2884i	−0.0600060	−	0.340311i
$915$	6.82112	−	71.7757i	0.225499	−	2.37283i
$916$	−6.85962	−	5.75590i	−0.226648	−	0.190180i
$917$	−1.03788			−0.0342740
$918$	13.2926	+	6.56564i	0.438722	+	0.216698i
$919$	−2.10751			−0.0695202			−0.0347601	−	0.999396i	$-0.511067\pi$
$919$	−2.10751			−0.0695202			−0.0347601	+	0.999396i	$0.511067\pi$
$920$	15.7197	+	13.1904i	0.518263	+	0.434875i
$921$	−5.69257	−	4.04980i	−0.187577	−	0.133445i
$922$	−3.50881	−	19.8995i	−0.115557	−	0.655354i
$923$	−0.733497	−	0.266971i	−0.0241434	−	0.00878746i
$924$	−5.58640	+	5.50341i	−0.183779	+	0.181049i
$925$	9.79704	−	55.5618i	0.322125	−	1.82686i
$926$	11.3930	−	19.7332i	0.374396	−	0.648473i
$927$	−36.2065	+	20.1875i	−1.18918	+	0.663044i
$928$	−3.37822	−	5.85124i	−0.110895	−	0.192076i
$929$	−20.6143	+	7.50298i	−0.676332	+	0.246165i	−0.657272	−	0.753654i	$-0.728290\pi$
$929$	−20.6143	+	7.50298i	−0.676332	+	0.246165i	−0.0190602	+	0.999818i	$0.506067\pi$
$930$	18.8484	−	39.6433i	0.618064	−	1.29996i
$931$	2.21947	−	1.86235i	0.0727400	−	0.0610361i
$932$	3.86003	−	3.23895i	0.126439	−	0.106095i
$933$	−12.2466	+	25.7579i	−0.400936	+	0.843277i
$934$	−8.60625	+	3.13242i	−0.281605	+	0.102496i
$935$	−25.0486	−	43.3854i	−0.819177	−	1.41886i
$936$	−3.98805	−	2.38278i	−0.130353	−	0.0778835i
$937$	−1.68308	+	2.91517i	−0.0549837	+	0.0952346i	−0.892207	−	0.451626i	$-0.850844\pi$
$937$	−1.68308	+	2.91517i	−0.0549837	+	0.0952346i	0.837223	+	0.546861i	$0.184177\pi$
$938$	0.452583	−	2.56673i	0.0147774	−	0.0838066i
$939$	5.21843	−	5.14091i	0.170297	−	0.167767i
$940$	−35.0664	−	12.7631i	−1.14374	−	0.416287i
$941$	−10.5413	−	59.7827i	−0.343637	−	1.94886i	−0.314405	−	0.949289i	$-0.601805\pi$
$941$	−10.5413	−	59.7827i	−0.343637	−	1.94886i	−0.0292315	−	0.999573i	$-0.509306\pi$
$942$	−18.4609	−	13.1334i	−0.601487	−	0.427909i
$943$	−13.3769	−	11.2245i	−0.435611	−	0.365521i
$944$	8.46284			0.275442
$945$	−14.4699	−	15.1346i	−0.470706	−	0.492328i
$946$	−25.0401			−0.814124
$947$	7.27513	+	6.10455i	0.236410	+	0.198371i	0.753294	−	0.657684i	$-0.228464\pi$
$947$	7.27513	+	6.10455i	0.236410	+	0.198371i	−0.516884	+	0.856055i	$0.672908\pi$
$948$	−0.713483	+	7.50767i	−0.0231728	+	0.243838i
$949$	0.185600	+	1.05259i	0.00602482	+	0.0341685i
$950$	−29.2174	−	10.6343i	−0.947937	−	0.345021i
$951$	−4.66349	−	17.9403i	−0.151224	−	0.581754i
$952$	−1.53004	+	8.67727i	−0.0495888	+	0.281232i
$953$	20.2653	−	35.1006i	0.656458	−	1.13702i	−0.325068	−	0.945691i	$-0.605387\pi$
$953$	20.2653	−	35.1006i	0.656458	−	1.13702i	0.981526	−	0.191328i	$-0.0612795\pi$
$954$	−30.0157	+	4.83060i	−0.971795	+	0.156396i
$955$	−31.7781	−	55.0412i	−1.02831	−	1.78109i
$956$	4.49317	−	1.63538i	0.145320	−	0.0528920i
$957$	9.18029	−	0.733995i	0.296757	−	0.0237267i
$958$	−1.62644	+	1.36474i	−0.0525477	+	0.0440928i
$959$	−2.68053	+	2.24923i	−0.0865587	+	0.0726314i
$960$	−25.0612	−	36.3672i	−0.808846	−	1.17375i
$961$	−11.6311	+	4.23336i	−0.375196	+	0.136560i
$962$	−1.25870	−	2.18014i	−0.0405822	−	0.0702904i
$963$	16.9306	−	19.5745i	0.545580	−	0.630780i
$964$	−2.32872	+	4.03346i	−0.0750031	+	0.129909i
$965$	6.14025	−	34.8231i	0.197662	−	1.12100i
$966$	2.75323	+	0.759852i	0.0885838	+	0.0244479i
$967$	−17.8146	−	6.48397i	−0.572877	−	0.208510i	0.0393045	−	0.999227i	$-0.487486\pi$
$967$	−17.8146	−	6.48397i	−0.572877	−	0.208510i	−0.612182	+	0.790717i	$0.709708\pi$
$968$	−3.23214	−	18.3304i	−0.103885	−	0.589160i
$969$	−13.6365	+	6.23500i	−0.438067	+	0.200297i
$970$	35.5462	+	29.8268i	1.14132	+	0.957681i
$971$	−10.9285			−0.350712			−0.175356	−	0.984505i	$-0.556108\pi$
$971$	−10.9285			−0.350712			−0.175356	+	0.984505i	$0.556108\pi$
$972$	12.4346	−	11.5373i	0.398840	−	0.370059i
$973$	12.3223			0.395034
$974$	9.25263	+	7.76388i	0.296474	+	0.248771i
$975$	−9.29613	+	4.25046i	−0.297714	+	0.136124i
$976$	−1.14736	−	6.50701i	−0.0367261	−	0.208284i
$977$	6.15227	+	2.23924i	0.196829	+	0.0716398i	0.438554	−	0.898705i	$-0.355491\pi$
$977$	6.15227	+	2.23924i	0.196829	+	0.0716398i	−0.241725	+	0.970345i	$0.577713\pi$
$978$	32.6670	+	9.01563i	1.04458	+	0.288288i
$979$	−7.40463	+	41.9937i	−0.236653	+	1.34213i
$980$	2.19244	−	3.79742i	0.0700350	−	0.121304i
$981$	−31.0350	+	35.8816i	−0.990871	+	1.14561i
$982$	−9.28736	−	16.0862i	−0.296371	−	0.513330i
$983$	22.8534	−	8.31794i	0.728909	−	0.265301i	0.0492059	−	0.998789i	$-0.484331\pi$
$983$	22.8534	−	8.31794i	0.728909	−	0.265301i	0.679703	+	0.733488i	$0.262109\pi$
$984$	29.3072	+	42.5288i	0.934278	+	1.35577i
$985$	−30.3733	+	25.4862i	−0.967774	+	0.812059i
$986$	2.79315	−	2.34373i	0.0889520	−	0.0746396i
$987$	−14.6935	+	1.17479i	−0.467698	+	0.0373940i
$988$	1.55573	−	0.566240i	0.0494944	−	0.0180145i
$989$	−5.44167	−	9.42526i	−0.173035	−	0.299706i
$990$	47.4212	−	7.63176i	1.50714	−	0.242553i
$991$	27.1742	−	47.0671i	0.863218	−	1.49514i	−0.00558795	−	0.999984i	$-0.501779\pi$
$991$	27.1742	−	47.0671i	0.863218	−	1.49514i	0.868806	−	0.495153i	$-0.164888\pi$
$992$	−6.04662	+	34.2921i	−0.191980	+	1.08878i
$993$	6.65218	+	25.5907i	0.211101	+	0.812097i
$994$	−1.33381	−	0.485468i	−0.0423059	−	0.0153981i
$995$	−13.6350	−	77.3279i	−0.432258	−	2.45146i
$996$	0.907165	−	9.54571i	0.0287446	−	0.302467i
$997$	35.1207	+	29.4698i	1.11228	+	0.933317i	0.998189	−	0.0601524i	$-0.0191587\pi$
$997$	35.1207	+	29.4698i	1.11228	+	0.933317i	0.114095	+	0.993470i	$0.463603\pi$
$998$	10.5166			0.332897
$999$	25.3423	−	6.18426i	0.801796	−	0.195661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.v.a.43.5	yes	54
3.2	odd	2		567.2.v.b.127.5		54
27.5	odd	18		567.2.v.b.442.5		54
27.7	even	9		5103.2.a.i.1.15		27
27.20	odd	18		5103.2.a.f.1.13		27
27.22	even	9	inner	189.2.v.a.22.5	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.a.22.5	✓	54	27.22	even	9	inner
189.2.v.a.43.5	yes	54	1.1	even	1	trivial
567.2.v.b.127.5		54	3.2	odd	2
567.2.v.b.442.5		54	27.5	odd	18
5103.2.a.f.1.13		27	27.20	odd	18
5103.2.a.i.1.15		27	27.7	even	9

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.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.731503 + 0.613803i) q^{2} +(-1.57520 + 0.720230i) q^{3} +(-0.188955 - 1.07162i) q^{4} +(-3.78665 - 1.37823i) q^{5} +(-1.59435 - 0.440016i) q^{6} +(0.173648 - 0.984808i) q^{7} +(1.47445 - 2.55382i) q^{8} +(1.96254 - 2.26902i) q^{9} +O(q^{10})\)	\(q+(0.731503 + 0.613803i) q^{2} +(-1.57520 + 0.720230i) q^{3} +(-0.188955 - 1.07162i) q^{4} +(-3.78665 - 1.37823i) q^{5} +(-1.59435 - 0.440016i) q^{6} +(0.173648 - 0.984808i) q^{7} +(1.47445 - 2.55382i) q^{8} +(1.96254 - 2.26902i) q^{9} +(-1.92398 - 3.33244i) q^{10} +(-3.90983 + 1.42306i) q^{11} +(1.06945 + 1.55193i) q^{12} +(0.402272 - 0.337546i) q^{13} +(0.731503 - 0.613803i) q^{14} +(6.95740 - 0.556267i) q^{15} +(0.601058 - 0.218767i) q^{16} +(-1.49397 - 2.58763i) q^{17} +(2.82833 - 0.455179i) q^{18} +(-1.44865 + 2.50914i) q^{19} +(-0.761427 + 4.31827i) q^{20} +(0.435756 + 1.67634i) q^{21} +(-3.73353 - 1.35889i) q^{22} +(-0.299868 - 1.70064i) q^{23} +(-0.483222 + 5.08474i) q^{24} +(8.60901 + 7.22382i) q^{25} +0.501450 q^{26} +(-1.45719 + 4.98765i) q^{27} -1.08815 q^{28} +(0.978952 + 0.821438i) q^{29} +(5.43079 + 3.86356i) q^{30} +(-1.14367 - 6.48610i) q^{31} +(-4.96817 - 1.80826i) q^{32} +(5.13385 - 5.05759i) q^{33} +(0.495454 - 2.80986i) q^{34} +(-2.01484 + 3.48980i) q^{35} +(-2.80235 - 1.67435i) q^{36} +(-2.51013 - 4.34766i) q^{37} +(-2.59981 + 0.946255i) q^{38} +(-0.390550 + 0.821433i) q^{39} +(-9.10299 + 7.63831i) q^{40} +(7.74629 - 6.49991i) q^{41} +(-0.710187 + 1.49372i) q^{42} +(5.92226 - 2.15553i) q^{43} +(2.26376 + 3.92095i) q^{44} +(-10.5587 + 5.88716i) q^{45} +(0.824503 - 1.42808i) q^{46} +(-1.47781 + 8.38105i) q^{47} +(-0.789226 + 0.777503i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(1.86351 + 10.5685i) q^{50} +(4.21699 + 3.00004i) q^{51} +(-0.437732 - 0.367301i) q^{52} -10.6125 q^{53} +(-4.12737 + 2.75405i) q^{54} +16.7665 q^{55} +(-2.25899 - 1.89552i) q^{56} +(0.474767 - 4.99577i) q^{57} +(0.211904 + 1.20177i) q^{58} +(12.4329 + 4.52520i) q^{59} +(-1.91074 - 7.35056i) q^{60} +(1.79378 - 10.1730i) q^{61} +(3.14459 - 5.44659i) q^{62} +(-1.89376 - 2.32673i) q^{63} +(-3.16394 - 5.48010i) q^{64} +(-1.98848 + 0.723748i) q^{65} +(6.85979 - 0.548464i) q^{66} +(2.09084 - 1.75442i) q^{67} +(-2.49066 + 2.08991i) q^{68} +(1.69720 + 2.46288i) q^{69} +(-3.61591 + 1.31608i) q^{70} +(-0.743219 - 1.28729i) q^{71} +(-2.90100 - 8.35753i) q^{72} +(-1.01768 + 1.76267i) q^{73} +(0.832449 - 4.72105i) q^{74} +(-18.7638 - 5.17853i) q^{75} +(2.96257 + 1.07829i) q^{76} +(0.722508 + 4.09754i) q^{77} +(-0.789887 + 0.361159i) q^{78} +(3.06523 + 2.57203i) q^{79} -2.57751 q^{80} +(-1.29689 - 8.90607i) q^{81} +9.65610 q^{82} +(-3.89731 - 3.27024i) q^{83} +(1.71406 - 0.783717i) q^{84} +(2.09079 + 11.8575i) q^{85} +(5.65522 + 2.05833i) q^{86} +(-2.13367 - 0.588863i) q^{87} +(-2.13060 + 12.0833i) q^{88} +(5.12426 - 8.87547i) q^{89} +(-11.3373 - 2.17448i) q^{90} +(-0.262564 - 0.454775i) q^{91} +(-1.76577 + 0.642689i) q^{92} +(6.47301 + 9.39323i) q^{93} +(-6.22534 + 5.22368i) q^{94} +(8.94372 - 7.50467i) q^{95} +(9.12824 - 0.729834i) q^{96} +(-11.3317 + 4.12439i) q^{97} +(-0.477454 - 0.826975i) q^{98} +(-4.44424 + 11.6643i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9}+O(q^{10}) \) 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9	\( 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9} - 6 q^{11} + 24 q^{12} - 9 q^{13} - 9 q^{15} - 30 q^{17} - 27 q^{18} - 12 q^{20} - 3 q^{21} - 9 q^{22} - 12 q^{23} + 36 q^{24} + 27 q^{25} + 18 q^{26} + 63 q^{27} + 54 q^{28} + 6 q^{29} - 72 q^{30} - 9 q^{31} - 9 q^{32} - 36 q^{33} - 9 q^{34} - 12 q^{35} + 54 q^{38} + 12 q^{39} - 45 q^{40} - 15 q^{41} - 18 q^{42} - 9 q^{43} - 42 q^{44} - 9 q^{45} - 45 q^{47} - 93 q^{48} + 18 q^{50} + 72 q^{51} - 63 q^{52} + 132 q^{53} + 54 q^{54} - 9 q^{56} + 3 q^{57} - 27 q^{58} - 9 q^{60} - 36 q^{62} - 9 q^{63} - 27 q^{64} + 66 q^{65} + 153 q^{66} + 45 q^{67} + 87 q^{68} - 72 q^{71} - 45 q^{72} - 72 q^{74} - 39 q^{75} + 54 q^{76} + 3 q^{77} - 54 q^{78} - 36 q^{79} + 42 q^{80} + 27 q^{81} + 24 q^{83} - 12 q^{84} + 18 q^{85} - 90 q^{86} - 99 q^{87} + 54 q^{88} - 42 q^{89} - 9 q^{90} + 87 q^{92} + 93 q^{93} - 90 q^{94} + 12 q^{95} + 108 q^{96} - 18 q^{97} - 9 q^{98} - 117 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9 - 6 * q^11 + 24 * q^12 - 9 * q^13 - 9 * q^15 - 30 * q^17 - 27 * q^18 - 12 * q^20 - 3 * q^21 - 9 * q^22 - 12 * q^23 + 36 * q^24 + 27 * q^25 + 18 * q^26 + 63 * q^27 + 54 * q^28 + 6 * q^29 - 72 * q^30 - 9 * q^31 - 9 * q^32 - 36 * q^33 - 9 * q^34 - 12 * q^35 + 54 * q^38 + 12 * q^39 - 45 * q^40 - 15 * q^41 - 18 * q^42 - 9 * q^43 - 42 * q^44 - 9 * q^45 - 45 * q^47 - 93 * q^48 + 18 * q^50 + 72 * q^51 - 63 * q^52 + 132 * q^53 + 54 * q^54 - 9 * q^56 + 3 * q^57 - 27 * q^58 - 9 * q^60 - 36 * q^62 - 9 * q^63 - 27 * q^64 + 66 * q^65 + 153 * q^66 + 45 * q^67 + 87 * q^68 - 72 * q^71 - 45 * q^72 - 72 * q^74 - 39 * q^75 + 54 * q^76 + 3 * q^77 - 54 * q^78 - 36 * q^79 + 42 * q^80 + 27 * q^81 + 24 * q^83 - 12 * q^84 + 18 * q^85 - 90 * q^86 - 99 * q^87 + 54 * q^88 - 42 * q^89 - 9 * q^90 + 87 * q^92 + 93 * q^93 - 90 * q^94 + 12 * q^95 + 108 * q^96 - 18 * q^97 - 9 * q^98 - 117 * q^99

Introduction

L-functions

Modular forms

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