LMFDB - Embedded newform 216.2.t.a.85.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			85.9
Character	$\chi$	$=$	216.85
Dual form			216.2.t.a.61.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959331 + 1.03908i) q^{2} +(0.643882 - 1.60792i) q^{3} +(-0.159370 - 1.99364i) q^{4} +(0.866185 + 0.152732i) q^{5} +(1.05306 + 2.21157i) q^{6} +(-1.10196 + 0.924651i) q^{7} +(2.22444 + 1.74696i) q^{8} +(-2.17083 - 2.07062i) q^{9} +O(q^{10})$	\(q+(-0.959331 + 1.03908i) q^{2} +(0.643882 - 1.60792i) q^{3} +(-0.159370 - 1.99364i) q^{4} +(0.866185 + 0.152732i) q^{5} +(1.05306 + 2.21157i) q^{6} +(-1.10196 + 0.924651i) q^{7} +(2.22444 + 1.74696i) q^{8} +(-2.17083 - 2.07062i) q^{9} +(-0.989658 + 0.753514i) q^{10} +(6.03310 - 1.06380i) q^{11} +(-3.30824 - 1.02741i) q^{12} +(-2.10092 - 5.77224i) q^{13} +(0.0963548 - 2.03206i) q^{14} +(0.803302 - 1.29442i) q^{15} +(-3.94920 + 0.635452i) q^{16} +(0.643173 - 1.11401i) q^{17} +(4.23409 - 0.269252i) q^{18} +(4.02158 - 2.32186i) q^{19} +(0.166448 - 1.75120i) q^{20} +(0.777238 + 2.36723i) q^{21} +(-4.68236 + 7.28940i) q^{22} +(1.35542 + 1.13733i) q^{23} +(4.24126 - 2.45189i) q^{24} +(-3.97151 - 1.44551i) q^{25} +(8.01330 + 3.35446i) q^{26} +(-4.72716 + 2.15729i) q^{27} +(2.01904 + 2.04954i) q^{28} +(-2.98881 + 8.21168i) q^{29} +(0.574370 + 2.07647i) q^{30} +(4.99440 + 4.19080i) q^{31} +(3.12831 - 4.71314i) q^{32} +(2.17410 - 10.3857i) q^{33} +(0.540527 + 1.73701i) q^{34} +(-1.09572 + 0.632615i) q^{35} +(-3.78212 + 4.65785i) q^{36} +(3.66503 + 2.11601i) q^{37} +(-1.44543 + 6.40618i) q^{38} +(-10.6341 - 0.338518i) q^{39} +(1.65996 + 1.85293i) q^{40} +(-1.25284 + 0.455997i) q^{41} +(-3.20536 - 1.46334i) q^{42} +(-3.73255 + 0.658149i) q^{43} +(-3.08232 - 11.8583i) q^{44} +(-1.56409 - 2.12510i) q^{45} +(-2.48208 + 0.317311i) q^{46} +(-3.37374 + 2.83091i) q^{47} +(-1.52106 + 6.75917i) q^{48} +(-0.856210 + 4.85581i) q^{49} +(5.31200 - 2.73999i) q^{50} +(-1.37711 - 1.75146i) q^{51} +(-11.1730 + 5.10841i) q^{52} -1.79372i q^{53} +(2.29332 - 6.98145i) q^{54} +5.38825 q^{55} +(-4.06656 + 0.131753i) q^{56} +(-1.14395 - 7.96140i) q^{57} +(-5.66533 - 10.9833i) q^{58} +(3.57530 + 0.630422i) q^{59} +(-2.70862 - 1.39520i) q^{60} +(-5.77574 - 6.88325i) q^{61} +(-9.14585 + 1.16921i) q^{62} +(4.30677 + 0.274475i) q^{63} +(1.89625 + 7.77202i) q^{64} +(-0.938184 - 5.32071i) q^{65} +(8.70590 + 12.2224i) q^{66} +(2.22419 + 6.11091i) q^{67} +(-2.32344 - 1.10472i) q^{68} +(2.70148 - 1.44710i) q^{69} +(0.393822 - 1.74543i) q^{70} +(-4.87414 + 8.44226i) q^{71} +(-1.21158 - 8.39834i) q^{72} +(0.531852 + 0.921195i) q^{73} +(-5.71467 + 1.77831i) q^{74} +(-4.88146 + 5.45515i) q^{75} +(-5.26988 - 7.64756i) q^{76} +(-5.66456 + 6.75076i) q^{77} +(10.5533 - 10.7249i) q^{78} +(4.22154 + 1.53651i) q^{79} +(-3.51779 - 0.0527496i) q^{80} +(0.425025 + 8.98996i) q^{81} +(0.728072 - 1.73925i) q^{82} +(-1.85556 + 5.09810i) q^{83} +(4.59553 - 1.92680i) q^{84} +(0.727252 - 0.866705i) q^{85} +(2.89688 - 4.50979i) q^{86} +(11.2793 + 10.0931i) q^{87} +(15.2787 + 8.17324i) q^{88} +(4.01233 + 6.94955i) q^{89} +(3.70863 + 0.413458i) q^{90} +(7.65243 + 4.41813i) q^{91} +(2.05142 - 2.88348i) q^{92} +(9.95429 - 5.33223i) q^{93} +(0.295000 - 6.22136i) q^{94} +(3.83806 - 1.39694i) q^{95} +(-5.56411 - 8.06478i) q^{96} +(-0.649675 - 3.68449i) q^{97} +(-4.22418 - 5.54799i) q^{98} +(-15.2996 - 10.1830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.959331	+	1.03908i	−0.678349	+	0.734740i
$2$	−0.959331	+	1.03908i	−0.678349	+	0.734740i
$3$	0.643882	−	1.60792i	0.371745	−	0.928335i
$3$	0.643882	−	1.60792i	0.371745	−	0.928335i
$4$	−0.159370	−	1.99364i	−0.0796849	−	0.996820i
$5$	0.866185	+	0.152732i	0.387370	+	0.0683037i	0.363942	−	0.931422i	$-0.381431\pi$
$5$	0.866185	+	0.152732i	0.387370	+	0.0683037i	0.0234282	+	0.999726i	$0.492542\pi$
$6$	1.05306	+	2.21157i	0.429911	+	0.902871i
$7$	−1.10196	+	0.924651i	−0.416500	+	0.349485i	−0.826830	−	0.562452i	$-0.809858\pi$
$7$	−1.10196	+	0.924651i	−0.416500	+	0.349485i	0.410330	+	0.911937i	$0.365414\pi$
$8$	2.22444	+	1.74696i	0.786458	+	0.617644i
$9$	−2.17083	−	2.07062i	−0.723611	−	0.690208i
$10$	−0.989658	+	0.753514i	−0.312957	+	0.238282i
$11$	6.03310	−	1.06380i	1.81905	−	0.320747i	0.842935	−	0.538015i	$-0.180826\pi$
$11$	6.03310	−	1.06380i	1.81905	−	0.320747i	0.976112	+	0.217268i	$0.0697146\pi$
$12$	−3.30824	−	1.02741i	−0.955005	−	0.296589i
$13$	−2.10092	−	5.77224i	−0.582692	−	1.60093i	−0.783561	−	0.621314i	$-0.786599\pi$
$13$	−2.10092	−	5.77224i	−0.582692	−	1.60093i	0.200870	−	0.979618i	$-0.435623\pi$
$14$	0.0963548	−	2.03206i	0.0257519	−	0.543092i
$15$	0.803302	−	1.29442i	0.207412	−	0.334217i
$16$	−3.94920	+	0.635452i	−0.987301	+	0.158863i
$17$	0.643173	−	1.11401i	0.155992	−	0.270187i	−0.777428	−	0.628973i	$-0.783476\pi$
$17$	0.643173	−	1.11401i	0.155992	−	0.270187i	0.933420	+	0.358786i	$0.116809\pi$
$18$	4.23409	−	0.269252i	0.997984	−	0.0634634i
$19$	4.02158	−	2.32186i	0.922615	−	0.532672i	0.0381464	−	0.999272i	$-0.487855\pi$
$19$	4.02158	−	2.32186i	0.922615	−	0.532672i	0.884468	+	0.466600i	$0.154521\pi$
$20$	0.166448	−	1.75120i	0.0372190	−	0.391581i
$21$	0.777238	+	2.36723i	0.169607	+	0.516571i
$22$	−4.68236	+	7.28940i	−0.998283	+	1.55410i
$23$	1.35542	+	1.13733i	0.282625	+	0.237150i	0.773069	−	0.634322i	$-0.218721\pi$
$23$	1.35542	+	1.13733i	0.282625	+	0.237150i	−0.490444	+	0.871473i	$0.663165\pi$
$24$	4.24126	−	2.45189i	0.865743	−	0.500489i
$25$	−3.97151	−	1.44551i	−0.794303	−	0.289103i
$26$	8.01330	+	3.35446i	1.57154	+	0.657864i
$27$	−4.72716	+	2.15729i	−0.909743	+	0.415171i
$28$	2.01904	+	2.04954i	0.381563	+	0.387327i
$29$	−2.98881	+	8.21168i	−0.555007	+	1.52487i	0.271782	+	0.962359i	$0.412387\pi$
$29$	−2.98881	+	8.21168i	−0.555007	+	1.52487i	−0.826790	+	0.562511i	$0.809835\pi$
$30$	0.574370	+	2.07647i	0.104865	+	0.379109i
$31$	4.99440	+	4.19080i	0.897021	+	0.752690i	0.969606	−	0.244672i	$-0.0786804\pi$
$31$	4.99440	+	4.19080i	0.897021	+	0.752690i	−0.0725851	+	0.997362i	$0.523125\pi$
$32$	3.12831	−	4.71314i	0.553012	−	0.833174i
$33$	2.17410	−	10.3857i	0.378462	−	1.80792i
$34$	0.540527	+	1.73701i	0.0926997	+	0.297895i
$35$	−1.09572	+	0.632615i	−0.185211	+	0.106931i
$36$	−3.78212	+	4.65785i	−0.630353	+	0.776309i
$37$	3.66503	+	2.11601i	0.602527	+	0.347869i	0.770035	−	0.638002i	$-0.220239\pi$
$37$	3.66503	+	2.11601i	0.602527	+	0.347869i	−0.167508	+	0.985871i	$0.553572\pi$
$38$	−1.44543	+	6.40618i	−0.234480	+	1.03922i
$39$	−10.6341	−	0.338518i	−1.70281	−	0.0542062i
$40$	1.65996	+	1.85293i	0.262462	+	0.292975i
$41$	−1.25284	+	0.455997i	−0.195661	+	0.0712147i	−0.437992	−	0.898979i	$-0.644310\pi$
$41$	−1.25284	+	0.455997i	−0.195661	+	0.0712147i	0.242331	+	0.970194i	$0.422088\pi$
$42$	−3.20536	−	1.46334i	−0.494598	−	0.225798i
$43$	−3.73255	+	0.658149i	−0.569208	+	0.100367i	−0.450843	−	0.892603i	$-0.648876\pi$
$43$	−3.73255	+	0.658149i	−0.569208	+	0.100367i	−0.118365	+	0.992970i	$0.537765\pi$
$44$	−3.08232	−	11.8583i	−0.464678	−	1.78770i
$45$	−1.56409	−	2.12510i	−0.233161	−	0.316791i
$46$	−2.48208	+	0.317311i	−0.365962	+	0.0467849i
$47$	−3.37374	+	2.83091i	−0.492111	+	0.412930i	−0.854782	−	0.518987i	$-0.826309\pi$
$47$	−3.37374	+	2.83091i	−0.492111	+	0.412930i	0.362671	+	0.931917i	$0.381865\pi$
$48$	−1.52106	+	6.75917i	−0.219546	+	0.975602i
$49$	−0.856210	+	4.85581i	−0.122316	+	0.693687i
$50$	5.31200	−	2.73999i	0.751230	−	0.387493i
$51$	−1.37711	−	1.75146i	−0.192834	−	0.245254i
$52$	−11.1730	+	5.10841i	−1.54941	+	0.708409i
$53$		−	1.79372i		−	0.246386i	−0.992383	−	0.123193i	$-0.960687\pi$
$53$		−	1.79372i		−	0.246386i	0.992383	−	0.123193i	$-0.0393135\pi$
$54$	2.29332	−	6.98145i	0.312081	−	0.950056i
$55$	5.38825			0.726552
$56$	−4.06656	+	0.131753i	−0.543417	+	0.0176062i
$57$	−1.14395	−	7.96140i	−0.151520	−	1.05451i
$58$	−5.66533	−	10.9833i	−0.743894	−	1.44218i
$59$	3.57530	+	0.630422i	0.465465	+	0.0820740i	0.401462	−	0.915876i	$-0.368502\pi$
$59$	3.57530	+	0.630422i	0.465465	+	0.0820740i	0.0640029	+	0.997950i	$0.479613\pi$
$60$	−2.70862	−	1.39520i	−0.349682	−	0.180120i
$61$	−5.77574	−	6.88325i	−0.739507	−	0.881310i	0.256862	−	0.966448i	$-0.417311\pi$
$61$	−5.77574	−	6.88325i	−0.739507	−	0.881310i	−0.996369	+	0.0851377i	$0.972867\pi$
$62$	−9.14585	+	1.16921i	−1.16152	+	0.148490i
$63$	4.30677	+	0.274475i	0.542601	+	0.0345807i
$64$	1.89625	+	7.77202i	0.237031	+	0.971502i
$65$	−0.938184	−	5.32071i	−0.116367	−	0.659953i
$66$	8.70590	+	12.2224i	1.07162	+	1.50447i
$67$	2.22419	+	6.11091i	0.271728	+	0.746566i	0.998234	+	0.0594060i	$0.0189206\pi$
$67$	2.22419	+	6.11091i	0.271728	+	0.746566i	−0.726506	+	0.687160i	$0.758857\pi$
$68$	−2.32344	−	1.10472i	−0.281758	−	0.133967i
$69$	2.70148	−	1.44710i	0.325219	−	0.174211i
$70$	0.393822	−	1.74543i	0.0470707	−	0.208618i
$71$	−4.87414	+	8.44226i	−0.578454	+	1.00191i	0.417203	+	0.908813i	$0.363010\pi$
$71$	−4.87414	+	8.44226i	−0.578454	+	1.00191i	−0.995657	+	0.0930983i	$0.970323\pi$
$72$	−1.21158	−	8.39834i	−0.142786	−	0.989754i
$73$	0.531852	+	0.921195i	0.0622486	+	0.107818i	0.895470	−	0.445121i	$-0.146840\pi$
$73$	0.531852	+	0.921195i	0.0622486	+	0.107818i	−0.833222	+	0.552939i	$0.813506\pi$
$74$	−5.71467	+	1.77831i	−0.664317	+	0.206724i
$75$	−4.88146	+	5.45515i	−0.563662	+	0.629906i
$76$	−5.26988	−	7.64756i	−0.604496	−	0.877235i
$77$	−5.66456	+	6.75076i	−0.645537	+	0.769321i
$78$	10.5533	−	10.7249i	1.19493	−	1.21435i
$79$	4.22154	+	1.53651i	0.474960	+	0.172871i	0.568398	−	0.822754i	$-0.307563\pi$
$79$	4.22154	+	1.53651i	0.474960	+	0.172871i	−0.0934380	+	0.995625i	$0.529786\pi$
$80$	−3.51779	−	0.0527496i	−0.393301	−	0.00589758i
$81$	0.425025	+	8.98996i	0.0472250	+	0.998884i
$82$	0.728072	−	1.73925i	0.0804021	−	0.192068i
$83$	−1.85556	+	5.09810i	−0.203674	+	0.559589i	−0.998908	−	0.0467126i	$-0.985125\pi$
$83$	−1.85556	+	5.09810i	−0.203674	+	0.559589i	0.795234	+	0.606302i	$0.207348\pi$
$84$	4.59553	−	1.92680i	0.501413	−	0.210231i
$85$	0.727252	−	0.866705i	0.0788815	−	0.0940073i
$86$	2.89688	−	4.50979i	0.312378	−	0.486303i
$87$	11.2793	+	10.0931i	1.20927	+	1.08210i
$88$	15.2787	+	8.17324i	1.62871	+	0.871270i
$89$	4.01233	+	6.94955i	0.425306	+	0.736651i	0.996449	−	0.0841993i	$-0.0268332\pi$
$89$	4.01233	+	6.94955i	0.425306	+	0.736651i	−0.571143	+	0.820850i	$0.693500\pi$
$90$	3.70863	+	0.413458i	0.390924	+	0.0435823i
$91$	7.65243	+	4.41813i	0.802193	+	0.463146i
$92$	2.05142	−	2.88348i	0.213875	−	0.300623i
$93$	9.95429	−	5.33223i	1.03221	−	0.552927i
$94$	0.295000	−	6.22136i	0.0304269	−	0.641685i
$95$	3.83806	−	1.39694i	0.393776	−	0.143323i
$96$	−5.56411	−	8.06478i	−0.567885	−	0.823108i
$97$	−0.649675	−	3.68449i	−0.0659645	−	0.374103i	−0.999863	−	0.0165645i	$-0.994727\pi$
$97$	−0.649675	−	3.68449i	−0.0659645	−	0.374103i	0.933898	−	0.357539i	$-0.116384\pi$
$98$	−4.22418	−	5.54799i	−0.426706	−	0.560432i
$99$	−15.2996	−	10.1830i	−1.53766	−	1.02343i
$100$	−2.24889	+	8.14814i	−0.224889	+	0.814814i
$101$	3.37222	+	4.01886i	0.335548	+	0.399891i	0.907265	−	0.420560i	$-0.138167\pi$
$101$	3.37222	+	4.01886i	0.335548	+	0.399891i	−0.571716	+	0.820452i	$0.693722\pi$
$102$	3.14101	+	0.249303i	0.311007	+	0.0246847i
$103$	−0.372833	+	2.11444i	−0.0367363	+	0.208342i	−0.997651	−	0.0685029i	$-0.978178\pi$
$103$	−0.372833	+	2.11444i	−0.0367363	+	0.208342i	0.960915	+	0.276845i	$0.0892889\pi$
$104$	5.41051	−	16.5102i	0.530545	−	1.61896i
$105$	0.311681	+	2.16916i	0.0304169	+	0.211689i
$106$	1.86382	+	1.72077i	0.181030	+	0.167136i
$107$		−	15.5945i		−	1.50758i	−0.657115	−	0.753791i	$-0.728223\pi$
$107$		−	15.5945i		−	1.50758i	0.657115	−	0.753791i	$-0.271777\pi$
$108$	5.05423	+	9.08046i	0.486344	+	0.873768i
$109$		−	13.6434i		−	1.30680i	−0.757014	−	0.653399i	$-0.773343\pi$
$109$		−	13.6434i		−	1.30680i	0.757014	−	0.653399i	$-0.226657\pi$
$110$	−5.16912	+	5.59882i	−0.492856	+	0.533827i
$111$	5.76222	−	4.53063i	0.546926	−	0.430028i
$112$	3.76427	−	4.35187i	0.355691	−	0.411213i
$113$	−3.09226	+	17.5371i	−0.290896	+	1.64975i	0.392535	+	0.919737i	$0.371598\pi$
$113$	−3.09226	+	17.5371i	−0.290896	+	1.64975i	−0.683431	+	0.730015i	$0.739513\pi$
$114$	9.36995	+	6.44896i	0.877576	+	0.604001i
$115$	1.00034	+	1.19216i	0.0932820	+	0.111169i
$116$	16.8475	+	4.64991i	1.56425	+	0.431733i
$117$	−7.39140	+	16.8808i	−0.683335	+	1.56063i
$118$	−4.08496	+	3.11024i	−0.376051	+	0.286321i
$119$	0.321320	+	1.82230i	0.0294554	+	0.167050i
$120$	4.04819	−	1.47601i	0.369548	−	0.134741i
$121$	24.9300	−	9.07377i	2.26636	−	0.824888i
$122$	12.6931	+	0.601871i	1.14918	+	0.0544908i
$123$	−0.0734739	+	2.30808i	−0.00662492	+	0.208113i
$124$	7.55899	−	10.6249i	0.678817	−	0.954146i
$125$	−7.02784	−	4.05753i	−0.628589	−	0.362916i
$126$	−4.41681	+	4.21176i	−0.393481	+	0.375213i
$127$	−7.85279	−	13.6014i	−0.696822	−	1.20693i	−0.969563	−	0.244844i	$-0.921263\pi$
$127$	−7.85279	−	13.6014i	−0.696822	−	1.20693i	0.272740	−	0.962088i	$-0.412070\pi$
$128$	−9.89487	−	5.48558i	−0.874591	−	0.484862i
$129$	−1.34507	+	6.42542i	−0.118427	+	0.565726i
$130$	6.42866	+	4.12947i	0.563831	+	0.362179i
$131$	6.73627	−	8.02798i	0.588551	−	0.701408i	−0.386776	−	0.922174i	$-0.626411\pi$
$131$	6.73627	−	8.02798i	0.588551	−	0.701408i	0.975327	+	0.220766i	$0.0708558\pi$
$132$	−21.0519	−	2.67920i	−1.83233	−	0.233194i
$133$	−2.28470	+	6.27715i	−0.198108	+	0.544298i
$134$	−8.48344	−	3.55127i	−0.732858	−	0.306783i
$135$	−4.42409	+	1.14663i	−0.380765	+	0.0986859i
$136$	3.37683	−	1.35444i	0.289561	−	0.116143i
$137$	−1.46453	−	0.533044i	−0.125123	−	0.0455410i	0.278700	−	0.960378i	$-0.410097\pi$
$137$	−1.46453	−	0.533044i	−0.125123	−	0.0455410i	−0.403823	+	0.914837i	$0.632319\pi$
$138$	−1.08795	+	4.19530i	−0.0926127	+	0.357127i
$139$	−1.56341	+	1.86320i	−0.132606	+	0.158034i	−0.828261	−	0.560342i	$-0.810670\pi$
$139$	−1.56341	+	1.86320i	−0.132606	+	0.158034i	0.695655	+	0.718376i	$0.255114\pi$
$140$	1.43583	+	2.08365i	0.121350	+	0.176101i
$141$	2.37959	+	7.24749i	0.200398	+	0.610349i
$142$	−4.09626	−	13.1635i	−0.343751	−	1.10466i
$143$	−18.8156	−	32.5895i	−1.57344	−	2.72527i
$144$	9.88884	+	6.79786i	0.824070	+	0.566488i
$145$	−3.84304	+	6.65635i	−0.319147	+	0.552779i
$146$	−1.46742	−	0.331094i	−0.121444	−	0.0274015i
$147$	7.25646	+	4.50328i	0.598503	+	0.371425i
$148$	3.63446	−	7.64398i	0.298751	−	0.628331i
$149$	2.52958	+	6.94997i	0.207231	+	0.569364i	0.999148	−	0.0412654i	$-0.0131389\pi$
$149$	2.52958	+	6.94997i	0.207231	+	0.569364i	−0.791917	+	0.610629i	$0.790917\pi$
$150$	−0.985397	−	10.3055i	−0.0804573	−	0.841441i
$151$	1.24115	+	7.03889i	0.101003	+	0.572817i	0.992742	+	0.120266i	$0.0383747\pi$
$151$	1.24115	+	7.03889i	0.101003	+	0.572817i	−0.891739	+	0.452551i	$0.850514\pi$
$152$	13.0020	+	1.86072i	1.05460	+	0.150924i
$153$	−3.70292	+	1.08656i	−0.299363	+	0.0878428i
$154$	−1.58039	−	12.3621i	−0.127351	−	0.996170i
$155$	3.68601	+	4.39281i	0.296067	+	0.352839i
$156$	1.01987	+	21.2545i	0.0816547	+	1.70172i
$157$	−13.0138	−	2.29469i	−1.03862	−	0.183136i	−0.371766	−	0.928327i	$-0.621247\pi$
$157$	−13.0138	−	2.29469i	−1.03862	−	0.183136i	−0.666852	+	0.745190i	$0.732359\pi$
$158$	−5.64641	+	2.91248i	−0.449204	+	0.231705i
$159$	−2.88416	−	1.15494i	−0.228729	−	0.0915930i
$160$	3.42954	−	3.60466i	0.271129	−	0.284973i
$161$	−2.54525			−0.200594
$162$	−9.74902	−	8.18271i	−0.765955	−	0.642894i
$163$			13.5197i			1.05894i	0.848328	+	0.529472i	$0.177610\pi$
$163$			13.5197i			1.05894i	−0.848328	+	0.529472i	$0.822390\pi$
$164$	1.10876	+	2.42504i	0.0865795	+	0.189364i
$165$	3.46940	−	8.66390i	0.270092	−	0.674483i
$166$	−3.51724	−	6.81884i	−0.272991	−	0.529244i
$167$	0.186326	−	1.05671i	0.0144183	−	0.0817703i	−0.976750	−	0.214384i	$-0.931226\pi$
$167$	0.186326	−	1.05671i	0.0144183	−	0.0817703i	0.991168	+	0.132613i	$0.0423368\pi$
$168$	−2.40654	+	6.62355i	−0.185668	+	0.511018i
$169$	−18.9463	+	15.8979i	−1.45741	+	1.22291i
$170$	0.202900	+	1.58713i	0.0155617	+	0.121727i
$171$	−13.5379	−	3.28682i	−1.03527	−	0.251349i
$172$	1.90697	+	7.33647i	0.145405	+	0.559400i
$173$	5.66245	−	0.998443i	0.430508	−	0.0759102i	0.0458046	−	0.998950i	$-0.485415\pi$
$173$	5.66245	−	0.998443i	0.430508	−	0.0759102i	0.384703	+	0.923040i	$0.374304\pi$
$174$	−21.3081	+	2.03745i	−1.61537	+	0.154459i
$175$	5.71303	−	2.07937i	0.431864	−	0.157186i
$176$	−23.1499	+	8.03490i	−1.74499	+	0.605653i
$177$	3.31574	−	5.34289i	0.249227	−	0.401597i
$178$	−11.0703	−	2.49780i	−0.829753	−	0.187218i
$179$	4.57599	+	2.64195i	0.342026	+	0.197469i	0.661167	−	0.750238i	$-0.270061\pi$
$179$	4.57599	+	2.64195i	0.342026	+	0.197469i	−0.319142	+	0.947707i	$0.603395\pi$
$180$	−3.98741	+	3.45691i	−0.297204	+	0.257663i
$181$	16.3392	−	9.43347i	1.21449	−	0.701184i	0.250753	−	0.968051i	$-0.419322\pi$
$181$	16.3392	−	9.43347i	1.21449	−	0.701184i	0.963733	+	0.266867i	$0.0859885\pi$
$182$	−11.9320	+	3.71303i	−0.884459	+	0.275228i
$183$	−14.7866	+	4.85494i	−1.09306	+	0.358887i
$184$	1.02817	+	4.89780i	0.0757978	+	0.361070i
$185$	2.85141	+	2.39262i	0.209640	+	0.175909i
$186$	−4.00884	+	15.4587i	−0.293943	+	1.13348i
$187$	2.69525	−	7.40513i	0.197096	−	0.541517i
$188$	6.18148	+	6.27487i	0.450831	+	0.457642i
$189$	3.21438	−	6.74822i	0.233812	−	0.490861i
$190$	−2.23044	+	5.32817i	−0.161813	+	0.386546i
$191$	−4.51564	−	1.64356i	−0.326740	−	0.118924i	0.173441	−	0.984844i	$-0.444511\pi$
$191$	−4.51564	−	1.64356i	−0.326740	−	0.118924i	−0.500182	+	0.865920i	$0.666733\pi$
$192$	13.7178	+	1.95524i	0.989994	+	0.141107i
$193$	−7.48231	−	6.27841i	−0.538589	−	0.451930i	0.332466	−	0.943115i	$-0.392119\pi$
$193$	−7.48231	−	6.27841i	−0.538589	−	0.451930i	−0.871055	+	0.491186i	$0.836564\pi$
$194$	4.45173	+	2.85958i	0.319615	+	0.205306i
$195$	−9.15937	−	1.91738i	−0.655916	−	0.137306i
$196$	9.81718	+	0.933105i	0.701227	+	0.0666504i
$197$	−3.72189	+	2.14883i	−0.265174	+	0.153098i	−0.626692	−	0.779267i	$-0.715592\pi$
$197$	−3.72189	+	2.14883i	−0.265174	+	0.153098i	0.361519	+	0.932365i	$0.382258\pi$
$198$	25.2582	−	6.12864i	1.79502	−	0.435543i
$199$	11.2215	−	19.4361i	0.795468	−	1.37779i	−0.127074	−	0.991893i	$-0.540559\pi$
$199$	11.2215	−	19.4361i	0.795468	−	1.37779i	0.922542	−	0.385897i	$-0.126108\pi$
$200$	−6.30913	−	10.1535i	−0.446123	−	0.717964i
$201$	11.2580	+	0.358379i	0.794077	+	0.0252781i
$202$	−7.41098	−	0.351408i	−0.521435	−	0.0247250i
$203$	−4.29940	−	11.8125i	−0.301759	−	0.829075i
$204$	−3.27232	+	3.02460i	−0.229108	+	0.211764i
$205$	−1.15484	+	0.203629i	−0.0806573	+	0.0142221i
$206$	−1.83940	−	2.41585i	−0.128157	−	0.168320i
$207$	−0.587401	−	5.27553i	−0.0408272	−	0.366675i
$208$	11.9650	+	21.4607i	0.829621	+	1.48803i
$209$	21.7926	−	18.2862i	1.50743	−	1.26488i
$210$	−2.55294	−	1.75708i	−0.176169	−	0.121250i
$211$	−4.88902	−	0.862066i	−0.336574	−	0.0593471i	0.00280699	−	0.999996i	$-0.499107\pi$
$211$	−4.88902	−	0.862066i	−0.336574	−	0.0593471i	−0.339381	+	0.940649i	$0.610218\pi$
$212$	−3.57603	+	0.285865i	−0.245603	+	0.0196333i
$213$	10.4361	+	13.2731i	0.715072	+	0.909455i
$214$	16.2040	+	14.9603i	1.10768	+	1.02267i
$215$	−3.33360			−0.227349
$216$	−14.2840	−	3.45941i	−0.971903	−	0.235383i
$217$	−9.37863			−0.636663
$218$	14.1765	+	13.0885i	0.960156	+	0.886465i
$219$	1.82366	−	0.262037i	0.123232	−	0.0177068i
$220$	−0.858725	−	10.7422i	−0.0578952	−	0.724242i
$221$	−7.78159	−	1.37210i	−0.523446	−	0.0922977i
$222$	−0.820195	+	10.3338i	−0.0550479	+	0.693557i
$223$	8.06763	−	6.76955i	0.540249	−	0.453322i	−0.331374	−	0.943499i	$-0.607512\pi$
$223$	8.06763	−	6.76955i	0.540249	−	0.453322i	0.871623	+	0.490177i	$0.163068\pi$
$224$	0.910755	+	8.08626i	0.0608524	+	0.540286i
$225$	5.62838	+	11.3615i	0.375225	+	0.757432i
$226$	−15.2559	−	20.0370i	−1.01481	−	1.33284i
$227$	14.8214	−	2.61342i	0.983733	−	0.173459i	0.341428	−	0.939908i	$-0.389089\pi$
$227$	14.8214	−	2.61342i	0.983733	−	0.173459i	0.642305	+	0.766449i	$0.277978\pi$
$228$	−15.6899	+	3.54943i	−1.03909	+	0.235067i
$229$	4.23471	+	11.6348i	0.279838	+	0.768848i	0.997381	+	0.0723333i	$0.0230445\pi$
$229$	4.23471	+	11.6348i	0.279838	+	0.768848i	−0.717543	+	0.696514i	$0.754733\pi$
$230$	−2.19840	−	0.104242i	−0.144958	−	0.00687351i
$231$	7.20740	+	13.4549i	0.474212	+	0.885266i
$232$	−20.9939	+	13.0450i	−1.37832	+	0.856448i
$233$	−7.79343	+	13.4986i	−0.510565	+	0.884324i	0.489360	+	0.872082i	$0.337230\pi$
$233$	−7.79343	+	13.4986i	−0.510565	+	0.884324i	−0.999925	+	0.0122424i	$0.996103\pi$
$234$	−10.4497	−	23.8745i	−0.683118	−	1.56073i
$235$	−3.35466	+	1.93681i	−0.218834	+	0.126344i
$236$	0.687040	−	7.22834i	0.0447225	−	0.470525i
$237$	5.18876	−	5.79857i	0.337046	−	0.376658i
$238$	−2.20176	−	1.41431i	−0.142719	−	0.0916761i
$239$	17.5419	+	14.7194i	1.13469	+	0.952122i	0.999252	−	0.0386637i	$-0.0123101\pi$
$239$	17.5419	+	14.7194i	1.13469	+	0.952122i	0.135442	+	0.990785i	$0.456755\pi$
$240$	−2.34986	+	5.62238i	−0.151683	+	0.362923i
$241$	−8.85425	−	3.22268i	−0.570352	−	0.207591i	0.0407139	−	0.999171i	$-0.487037\pi$
$241$	−8.85425	−	3.22268i	−0.570352	−	0.207591i	−0.611066	+	0.791580i	$0.709259\pi$
$242$	−14.4877	+	34.6090i	−0.931306	+	2.22475i
$243$	14.7288	+	5.10506i	0.944855	+	0.327490i
$244$	−12.8023	+	12.6117i	−0.819580	+	0.807383i
$245$	−1.48327	+	4.07526i	−0.0947628	+	0.260359i
$246$	−2.32779	−	2.29056i	−0.148415	−	0.146041i
$247$	−21.8514	−	18.3355i	−1.39037	−	1.16666i
$248$	3.78856	+	18.0472i	0.240574	+	1.14600i
$249$	7.00259	+	6.26617i	0.443771	+	0.397102i
$250$	10.9581	−	3.40997i	0.693052	−	0.215666i
$251$	−11.7523	+	6.78518i	−0.741797	+	0.428277i	−0.822722	−	0.568444i	$-0.807546\pi$
$251$	−11.7523	+	6.78518i	−0.741797	+	0.428277i	0.0809254	+	0.996720i	$0.474212\pi$
$252$	−0.139163	−	8.62988i	−0.00876645	−	0.543632i
$253$	9.38728	+	5.41975i	0.590173	+	0.340737i
$254$	21.6664	+	4.88860i	1.35947	+	0.306738i
$255$	−0.925330	−	1.72742i	−0.0579464	−	0.108175i
$256$	15.1924	−	5.01906i	0.949525	−	0.313691i
$257$	−5.52264	+	2.01008i	−0.344493	+	0.125385i	−0.508472	−	0.861079i	$-0.669789\pi$
$257$	−5.52264	+	2.01008i	−0.344493	+	0.125385i	0.163979	+	0.986464i	$0.447567\pi$
$258$	−5.38615	−	7.56173i	−0.335327	−	0.470773i
$259$	−5.99527	+	1.05713i	−0.372528	+	0.0656867i
$260$	−10.4581	+	2.71836i	−0.648581	+	0.168586i
$261$	23.4915	−	11.6375i	1.45409	−	0.720342i
$262$	1.87939	+	14.7010i	0.116109	+	0.908231i
$263$	10.3288	−	8.66691i	0.636902	−	0.534424i	−0.266163	−	0.963928i	$-0.585756\pi$
$263$	10.3288	−	8.66691i	0.636902	−	0.534424i	0.903065	+	0.429504i	$0.141311\pi$
$264$	22.9796	−	19.3043i	1.41430	−	1.18810i
$265$	0.273958	−	1.55369i	0.0168291	−	0.0954426i
$266$	−4.33068	−	8.39584i	−0.265531	−	0.514782i
$267$	13.7578	−	1.97682i	0.841964	−	0.120979i
$268$	11.8285	−	5.40812i	0.722539	−	0.330354i
$269$		−	29.1863i		−	1.77952i	−0.456431	−	0.889759i	$-0.650872\pi$
$269$		−	29.1863i		−	1.77952i	0.456431	−	0.889759i	$-0.349128\pi$
$270$	3.05273	−	5.69697i	0.185783	−	0.346706i
$271$	−22.0397			−1.33882			−0.669408	−	0.742895i	$-0.733452\pi$
$271$	−22.0397			−1.33882			−0.669408	+	0.742895i	$0.733452\pi$
$272$	−1.83212	+	4.80815i	−0.111089	+	0.291537i
$273$	12.0313	−	9.45977i	0.728166	−	0.572531i
$274$	1.95884	−	1.01039i	0.118338	−	0.0610400i
$275$	−25.4983	−	4.49603i	−1.53760	−	0.271121i
$276$	−3.31554	−	5.15515i	−0.199572	−	0.310303i
$277$	−10.8730	−	12.9579i	−0.653293	−	0.778565i	0.333113	−	0.942887i	$-0.391901\pi$
$277$	−10.8730	−	12.9579i	−0.653293	−	0.778565i	−0.986407	+	0.164322i	$0.947456\pi$
$278$	−0.436183	−	3.41192i	−0.0261605	−	0.204634i
$279$	−2.16443	−	19.4391i	−0.129581	−	1.16379i
$280$	−3.54252	−	0.506971i	−0.211706	−	0.0302973i
$281$	−3.11277	−	17.6534i	−0.185692	−	1.05311i	−0.925063	−	0.379815i	$-0.875988\pi$
$281$	−3.11277	−	17.6534i	−0.185692	−	1.05311i	0.739370	−	0.673299i	$-0.235123\pi$
$282$	−9.81353	−	4.48016i	−0.584387	−	0.266790i
$283$	10.0922	+	27.7281i	0.599919	+	1.64826i	0.751433	+	0.659809i	$0.229363\pi$
$283$	10.0922	+	27.7281i	0.599919	+	1.64826i	−0.151514	+	0.988455i	$0.548415\pi$
$284$	17.6076	+	8.37184i	1.04482	+	0.496777i
$285$	0.225086	−	7.07076i	0.0133329	−	0.418836i
$286$	51.9135	+	11.7133i	3.06971	+	0.692620i
$287$	0.958938	−	1.66093i	0.0566043	−	0.0980415i
$288$	−16.5502	+	3.75389i	−0.975228	+	0.221200i
$289$	7.67266	+	13.2894i	0.451333	+	0.781731i
$290$	−3.22972	−	10.3789i	−0.189656	−	0.609468i
$291$	−6.34269	−	1.32775i	−0.371815	−	0.0778340i
$292$	1.75177	−	1.20713i	0.102515	−	0.0706421i
$293$	−4.06429	+	4.84363i	−0.237438	+	0.282968i	−0.871585	−	0.490245i	$-0.836907\pi$
$293$	−4.06429	+	4.84363i	−0.237438	+	0.282968i	0.634146	+	0.773213i	$0.281352\pi$
$294$	−11.6406	+	3.21990i	−0.678895	+	0.187788i
$295$	3.00059	+	1.09212i	0.174701	+	0.0635860i
$296$	4.45605	+	11.1096i	0.259003	+	0.645732i
$297$	−26.2245	+	18.0439i	−1.52170	+	1.04701i
$298$	−9.64827	−	4.03888i	−0.558909	−	0.233966i
$299$	3.71733	−	10.2133i	0.214979	−	0.590649i
$300$	11.6536	+	8.86249i	0.672819	+	0.511676i
$301$	3.50454	−	4.17655i	0.201999	−	0.240732i
$302$	−8.50463	−	5.46297i	−0.489386	−	0.314359i
$303$	8.63332	−	2.83460i	0.495971	−	0.162844i
$304$	−14.4066	+	11.7250i	−0.826276	+	0.672477i
$305$	−3.95156	−	6.84431i	−0.226266	−	0.391904i
$306$	2.42330	−	4.88999i	0.138531	−	0.279542i
$307$	−18.0938	−	10.4464i	−1.03266	−	0.596209i	−0.114918	−	0.993375i	$-0.536661\pi$
$307$	−18.0938	−	10.4464i	−1.03266	−	0.596209i	−0.917747	+	0.397166i	$0.869994\pi$
$308$	14.3614	+	10.2172i	0.818314	+	0.582181i
$309$	3.15980	+	1.96094i	0.179755	+	0.111554i
$310$	−8.10057	−	0.384107i	−0.460082	−	0.0218158i
$311$	13.4309	−	4.88846i	0.761598	−	0.277199i	0.0681203	−	0.997677i	$-0.478300\pi$
$311$	13.4309	−	4.88846i	0.761598	−	0.277199i	0.693478	+	0.720478i	$0.256078\pi$
$312$	−23.0634	−	19.3303i	−1.30571	−	1.09436i
$313$	−1.92303	−	10.9060i	−0.108696	−	0.616445i	−0.989680	−	0.143298i	$-0.954229\pi$
$313$	−1.92303	−	10.9060i	−0.108696	−	0.616445i	0.880984	−	0.473147i	$-0.156882\pi$
$314$	14.8689	−	11.3210i	0.839103	−	0.638883i
$315$	3.68853	+	0.895526i	0.207825	+	0.0504572i
$316$	2.39047	−	8.66110i	0.134474	−	0.487225i
$317$	−15.3521	−	18.2959i	−0.862260	−	1.02760i	−0.999314	−	0.0370378i	$-0.988208\pi$
$317$	−15.3521	−	18.2959i	−0.862260	−	1.02760i	0.137054	−	0.990564i	$-0.456237\pi$
$318$	3.96694	−	1.88890i	0.222455	−	0.105924i
$319$	−9.29619	+	52.7213i	−0.520487	+	2.95183i
$320$	0.455466	+	7.02162i	0.0254613	+	0.392521i
$321$	−25.0748	−	10.0410i	−1.39954	−	0.560436i
$322$	2.44174	−	2.64472i	0.136073	−	0.147384i
$323$		−	5.97344i		−	0.332371i
$324$	17.8550	−	2.28008i	0.991945	−	0.126671i
$325$			25.9615i			1.44008i
$326$	−14.0480	−	12.9698i	−0.778048	−	0.718333i
$327$	−21.9375	−	8.78471i	−1.21315	−	0.485796i
$328$	−3.58348	−	1.17433i	−0.197864	−	0.0648415i
$329$	1.10012	−	6.23907i	0.0606514	−	0.343971i
$330$	5.67417	+	11.9165i	0.312353	+	0.655983i
$331$	4.52850	+	5.39685i	0.248909	+	0.296638i	0.876003	−	0.482305i	$-0.160200\pi$
$331$	4.52850	+	5.39685i	0.248909	+	0.296638i	−0.627094	+	0.778943i	$0.715756\pi$
$332$	10.4595	+	2.88683i	0.574040	+	0.158435i
$333$	−3.57471	−	12.1824i	−0.195893	−	0.667591i
$334$	0.919252	+	1.20734i	0.0502993	+	0.0660625i
$335$	0.993228	+	5.63288i	0.0542659	+	0.307757i
$336$	−4.57373	−	8.85476i	−0.249517	−	0.483067i
$337$	4.83933	−	1.76137i	0.263615	−	0.0959480i	−0.206831	−	0.978377i	$-0.566315\pi$
$337$	4.83933	−	1.76137i	0.263615	−	0.0959480i	0.470446	+	0.882429i	$0.344093\pi$
$338$	1.65666	−	34.9380i	0.0901107	−	1.90038i
$339$	26.2073	+	16.2639i	1.42338	+	0.883336i
$340$	−1.84380	−	1.31175i	−0.0999941	−	0.0711397i
$341$	34.5899	+	19.9705i	1.87315	+	1.08146i
$342$	16.4026	−	10.9138i	0.886950	−	0.590150i
$343$	−8.58117	−	14.8630i	−0.463340	−	0.802528i
$344$	−9.45258	−	5.05661i	−0.509649	−	0.272634i
$345$	2.56100	−	0.840859i	0.137879	−	0.0452703i
$346$	−4.39470	+	6.84157i	−0.236261	+	0.367805i
$347$	−17.7647	+	21.1711i	−0.953658	+	1.13653i	0.0368842	+	0.999320i	$0.488257\pi$
$347$	−17.7647	+	21.1711i	−0.953658	+	1.13653i	−0.990543	+	0.137206i	$0.956188\pi$
$348$	18.3245	−	24.0954i	0.982295	−	1.29165i
$349$	−6.04947	+	16.6208i	−0.323821	+	0.889691i	0.665818	+	0.746114i	$0.268083\pi$
$349$	−6.04947	+	16.6208i	−0.323821	+	0.889691i	−0.989639	+	0.143577i	$0.954140\pi$
$350$	−3.32005	+	7.93109i	−0.177464	+	0.423935i
$351$	22.3838	+	22.7540i	1.19476	+	1.21452i
$352$	13.8595	−	31.7627i	0.738716	−	1.69296i
$353$	13.8750	+	5.05009i	0.738492	+	0.268789i	0.683755	−	0.729712i	$-0.260346\pi$
$353$	13.8750	+	5.05009i	0.738492	+	0.268789i	0.0547372	+	0.998501i	$0.482568\pi$
$354$	2.37079	+	8.57092i	0.126006	+	0.455539i
$355$	−5.51131	+	6.56812i	−0.292510	+	0.348600i
$356$	13.2155	−	9.10668i	0.700418	−	0.482653i
$357$	3.13701	+	0.656687i	0.166028	+	0.0347555i
$358$	−7.13508	+	2.22031i	−0.377101	+	0.117347i
$359$	7.98331	+	13.8275i	0.421343	+	0.729788i	0.996071	−	0.0885568i	$-0.0282255\pi$
$359$	7.98331	+	13.8275i	0.421343	+	0.729788i	−0.574728	+	0.818345i	$0.694892\pi$
$360$	0.233242	−	7.45956i	0.0122930	−	0.393153i
$361$	1.28209	−	2.22065i	0.0674786	−	0.116876i
$362$	−5.87262	+	26.0276i	−0.308658	+	1.36798i
$363$	1.46204	−	45.9279i	0.0767371	−	2.41059i
$364$	7.58860	−	15.9603i	0.397751	−	0.836548i
$365$	0.319987	+	0.879156i	0.0167489	+	0.0460171i
$366$	9.14061	−	20.0220i	0.477787	−	1.04656i
$367$	5.34505	+	30.3133i	0.279009	+	1.58234i	0.725931	+	0.687768i	$0.241409\pi$
$367$	5.34505	+	30.3133i	0.279009	+	1.58234i	−0.446921	+	0.894573i	$0.647480\pi$
$368$	−6.07555	−	3.63025i	−0.316710	−	0.189240i
$369$	3.66391	+	1.60427i	0.190735	+	0.0835150i
$370$	−5.22157	+	0.667530i	−0.271456	+	0.0347032i
$371$	1.65856	+	1.97660i	0.0861084	+	0.102620i
$372$	−12.2170	−	18.9955i	−0.633420	−	0.984869i
$373$	−8.90834	−	1.57078i	−0.461256	−	0.0813319i	−0.0618088	−	0.998088i	$-0.519687\pi$
$373$	−8.90834	−	1.57078i	−0.461256	−	0.0813319i	−0.399447	+	0.916756i	$0.630798\pi$
$374$	5.10888	+	9.90454i	0.264174	+	0.512152i
$375$	−11.0493	+	8.68766i	−0.570583	+	0.448629i
$376$	−12.4502	+	0.403374i	−0.642069	+	0.0208024i
$377$	53.6791			2.76461
$378$	3.92827	+	9.81377i	0.202049	+	0.504766i
$379$		−	18.2242i		−	0.936115i	−0.883698	−	0.468058i	$-0.844954\pi$
$379$		−	18.2242i		−	0.936115i	0.883698	−	0.468058i	$-0.155046\pi$
$380$	−3.39666	−	7.42908i	−0.174245	−	0.381104i
$381$	−26.9263	+	3.86896i	−1.37948	+	0.198213i
$382$	6.03978	−	3.11539i	0.309022	−	0.159397i
$383$	3.14112	−	17.8142i	0.160504	−	0.910262i	−0.793076	−	0.609122i	$-0.791522\pi$
$383$	3.14112	−	17.8142i	0.160504	−	0.910262i	0.953580	−	0.301140i	$-0.0973670\pi$
$384$	−15.1915	+	12.3781i	−0.775239	+	0.631668i
$385$	−5.93762	+	4.98225i	−0.302609	+	0.253919i
$386$	13.7018	−	1.75165i	0.697402	−	0.0891565i
$387$	9.46551	+	6.29997i	0.481159	+	0.320246i
$388$	−7.24201	+	1.88241i	−0.367657	+	0.0955651i
$389$	−19.8551	+	3.50098i	−1.00669	+	0.177507i	−0.652599	−	0.757703i	$-0.726321\pi$
$389$	−19.8551	+	3.50098i	−1.00669	+	0.177507i	−0.354093	+	0.935210i	$0.615210\pi$
$390$	10.7792	−	7.67791i	0.545825	−	0.388786i
$391$	2.13877	−	0.778449i	0.108162	−	0.0393678i
$392$	−10.3875	+	9.30567i	−0.524648	+	0.470007i
$393$	−8.57100	−	16.0005i	−0.432350	−	0.807117i
$394$	1.33771	−	5.92878i	0.0673931	−	0.298688i
$395$	3.42196	+	1.97567i	0.172177	+	0.0994066i
$396$	−17.8629	+	32.1247i	−0.897642	+	1.61433i
$397$	−25.5093	+	14.7278i	−1.28028	+	0.739168i	−0.976899	−	0.213702i	$-0.931448\pi$
$397$	−25.5093	+	14.7278i	−1.28028	+	0.739168i	−0.303378	+	0.952870i	$0.598115\pi$
$398$	9.43058	+	30.3056i	0.472712	+	1.51908i
$399$	8.62210	+	7.71536i	0.431645	+	0.386251i
$400$	16.6029	+	3.18492i	0.830143	+	0.159246i
$401$	−18.4511	−	15.4823i	−0.921406	−	0.773152i	0.0528483	−	0.998603i	$-0.483170\pi$
$401$	−18.4511	−	15.4823i	−0.921406	−	0.773152i	−0.974255	+	0.225451i	$0.927614\pi$
$402$	−11.1725	+	11.3541i	−0.557234	+	0.566292i
$403$	13.6975	−	37.6334i	0.682319	−	1.87466i
$404$	7.47472	−	7.36348i	0.371881	−	0.366347i
$405$	−1.00490	+	7.85188i	−0.0499340	+	0.390163i
$406$	16.3987	+	6.86468i	0.813852	+	0.340688i
$407$	24.3625	+	8.86722i	1.20760	+	0.439532i
$408$	−0.00356165	−	6.30178i	−0.000176328	−	0.311985i
$409$	10.7412	+	9.01294i	0.531118	+	0.445661i	0.868487	−	0.495711i	$-0.165093\pi$
$409$	10.7412	+	9.01294i	0.531118	+	0.445661i	−0.337369	+	0.941372i	$0.609537\pi$
$410$	0.896284	−	1.39531i	0.0442643	−	0.0689097i
$411$	−1.80007	+	2.01163i	−0.0887911	+	0.0992262i
$412$	4.27485	+	0.406317i	0.210607	+	0.0200178i
$413$	−4.52275	+	2.61121i	−0.222550	+	0.128489i
$414$	6.04520	+	4.45062i	0.297105	+	0.218736i
$415$	−2.38590	+	4.13250i	−0.117119	+	0.202856i
$416$	−33.7777	−	8.15539i	−1.65609	−	0.399851i
$417$	1.98923	+	3.71352i	0.0974128	+	0.181852i
$418$	−1.90554	+	40.1867i	−0.0932031	+	1.96560i
$419$	5.92869	+	16.2889i	0.289635	+	0.795767i	0.996117	+	0.0880356i	$0.0280589\pi$
$419$	5.92869	+	16.2889i	0.289635	+	0.795767i	−0.706482	+	0.707731i	$0.749719\pi$
$420$	4.27486	−	0.967079i	0.208592	−	0.0471886i
$421$	22.5676	−	3.97928i	1.09988	−	0.193938i	0.405889	−	0.913922i	$-0.366962\pi$
$421$	22.5676	−	3.97928i	1.09988	−	0.193938i	0.693991	+	0.719984i	$0.255851\pi$
$422$	5.58594	−	4.25307i	0.271919	−	0.207036i
$423$	13.1856	+	0.840333i	0.641105	+	0.0408584i
$424$	3.13356	−	3.99002i	0.152179	−	0.193772i
$425$	−4.16469	+	3.49459i	−0.202017	+	0.169512i
$426$	−23.8035	−	1.88929i	−1.15328	−	0.0915363i
$427$	12.7292	+	2.24450i	0.616010	+	0.108619i
$428$	−31.0899	+	2.48530i	−1.50279	+	0.120131i
$429$	−64.5165	+	9.27019i	−3.11489	+	0.447569i
$430$	3.19802	−	3.46387i	0.154222	−	0.167043i
$431$	−20.5482			−0.989772			−0.494886	−	0.868958i	$-0.664790\pi$
$431$	−20.5482			−0.989772			−0.494886	+	0.868958i	$0.664790\pi$
$432$	17.2977	−	11.5235i	0.832235	−	0.554423i
$433$	8.82740			0.424218			0.212109	−	0.977246i	$-0.431967\pi$
$433$	8.82740			0.424218			0.212109	+	0.977246i	$0.431967\pi$
$434$	8.99721	−	9.74514i	0.431880	−	0.467782i
$435$	8.22842	+	10.4652i	0.394523	+	0.501769i
$436$	−27.2000	+	2.17434i	−1.30264	+	0.104132i
$437$	8.09167	+	1.42678i	0.387077	+	0.0682521i
$438$	−1.47722	+	2.14631i	−0.0705841	+	0.102555i
$439$	7.41763	−	6.22413i	0.354024	−	0.297061i	−0.448379	−	0.893843i	$-0.647999\pi$
$439$	7.41763	−	6.22413i	0.354024	−	0.297061i	0.802404	+	0.596782i	$0.203554\pi$
$440$	11.9858	+	9.41307i	0.571402	+	0.448751i
$441$	11.9132	−	8.76825i	0.567297	−	0.417536i
$442$	8.89084	−	6.76938i	0.422894	−	0.321987i
$443$	−6.34350	+	1.11853i	−0.301389	+	0.0531430i	−0.322298	−	0.946638i	$-0.604455\pi$
$443$	−6.34350	+	1.11853i	−0.301389	+	0.0531430i	0.0209088	+	0.999781i	$0.493344\pi$
$444$	−9.95077	−	10.7657i	−0.472242	−	0.510920i
$445$	2.41400	+	6.63241i	0.114435	+	0.314406i
$446$	−0.705432	+	14.8771i	−0.0334032	+	0.704453i
$447$	12.8038	+	0.407586i	0.605597	+	0.0192782i
$448$	−9.27598	−	6.81105i	−0.438249	−	0.321792i
$449$	−16.7458	+	29.0045i	−0.790282	+	1.36881i	0.135510	+	0.990776i	$0.456733\pi$
$449$	−16.7458	+	29.0045i	−0.790282	+	1.36881i	−0.925792	+	0.378033i	$0.876601\pi$
$450$	−17.2049	−	5.05109i	−0.811049	−	0.238111i
$451$	−7.07342	+	4.08384i	−0.333074	+	0.192301i
$452$	35.4555	+	3.36998i	1.66769	+	0.158510i
$453$	12.1171	+	2.53655i	0.569313	+	0.119177i
$454$	−11.5031	+	17.9078i	−0.539867	+	0.840453i
$455$	5.95363	+	4.99569i	0.279111	+	0.234202i
$456$	11.3636	−	19.7081i	0.532150	−	0.922916i
$457$	−13.0595	−	4.75327i	−0.610897	−	0.222348i	0.0179985	−	0.999838i	$-0.494271\pi$
$457$	−13.0595	−	4.75327i	−0.610897	−	0.222348i	−0.628896	+	0.777490i	$0.716493\pi$
$458$	−16.1519	−	6.76140i	−0.754731	−	0.315939i
$459$	−0.637143	+	6.65362i	−0.0297393	+	0.310564i
$460$	2.21731	−	2.18431i	0.103383	−	0.101844i
$461$	9.87206	−	27.1233i	0.459787	−	1.26326i	−0.465857	−	0.884860i	$-0.654254\pi$
$461$	9.87206	−	27.1233i	0.459787	−	1.26326i	0.925644	−	0.378395i	$-0.123524\pi$
$462$	−20.8950	−	5.41862i	−0.972121	−	0.252097i
$463$	−2.17687	−	1.82661i	−0.101168	−	0.0848900i	0.590801	−	0.806818i	$-0.298812\pi$
$463$	−2.17687	−	1.82661i	−0.101168	−	0.0848900i	−0.691969	+	0.721928i	$0.743256\pi$
$464$	6.58527	−	34.3288i	0.305714	−	1.59368i
$465$	9.43665	−	3.09836i	0.437614	−	0.143683i
$466$	−6.54965	−	21.0476i	−0.303407	−	0.975013i
$467$	−6.77051	+	3.90896i	−0.313302	+	0.180885i	−0.648403	−	0.761297i	$-0.724563\pi$
$467$	−6.77051	+	3.90896i	−0.313302	+	0.180885i	0.335101	+	0.942182i	$0.391230\pi$
$468$	34.8322	+	12.0455i	1.61012	+	0.556803i
$469$	−8.10141	−	4.67735i	−0.374088	−	0.215980i
$470$	1.20572	−	5.34379i	0.0556159	−	0.246491i
$471$	−12.0691	+	19.4477i	−0.556113	+	0.896105i
$472$	6.85172	+	7.64825i	0.315376	+	0.352039i
$473$	−21.8187	+	7.94135i	−1.00322	+	0.365144i
$474$	1.04743	+	10.9543i	0.0481101	+	0.503147i
$475$	−19.3281	+	3.40806i	−0.886832	+	0.156372i
$476$	3.58180	−	0.931017i	0.164172	−	0.0426731i
$477$	−3.71412	+	3.89387i	−0.170058	+	0.178288i
$478$	−32.1232	+	4.10666i	−1.46928	+	0.187834i
$479$	−32.9164	+	27.6201i	−1.50399	+	1.26199i	−0.629444	+	0.777045i	$0.716718\pi$
$479$	−32.9164	+	27.6201i	−1.50399	+	1.26199i	−0.874542	+	0.484949i	$0.838838\pi$
$480$	−3.58780	−	7.83541i	−0.163760	−	0.357636i
$481$	4.51415	−	25.6010i	0.205827	−	1.16731i
$482$	11.8428	−	6.10864i	0.539423	−	0.278241i
$483$	−1.63884	+	4.09257i	−0.0745698	+	0.186218i
$484$	−22.0629	−	48.2553i	−1.00286	−	2.19342i
$485$		−	3.29068i		−	0.149422i
$486$	−19.4344	+	10.4070i	−0.881561	+	0.472070i
$487$	15.0756			0.683141			0.341571	−	0.939856i	$-0.389041\pi$
$487$	15.0756			0.683141			0.341571	+	0.939856i	$0.389041\pi$
$488$	−0.822981	−	25.4014i	−0.0372546	−	1.14987i
$489$	21.7386	+	8.70508i	0.983054	+	0.393657i
$490$	−2.81156	−	5.45075i	−0.127014	−	0.246240i
$491$	7.89081	+	1.39136i	0.356107	+	0.0627913i	0.348840	−	0.937182i	$-0.386576\pi$
$491$	7.89081	+	1.39136i	0.356107	+	0.0627913i	0.00726714	+	0.999974i	$0.497687\pi$
$492$	4.61319	−	0.221358i	0.207979	−	0.00997958i
$493$	7.22556	+	8.61109i	0.325423	+	0.387824i
$494$	40.0148	−	5.11552i	1.80035	−	0.230158i
$495$	−11.6970	−	11.1571i	−0.525741	−	0.501472i
$496$	−22.3869	−	13.3766i	−1.00520	−	0.600628i
$497$	−2.43505	−	13.8099i	−0.109227	−	0.619457i
$498$	−13.2288	+	1.26492i	−0.592799	+	0.0566825i
$499$	−10.2208	−	28.0815i	−0.457547	−	1.25710i	−0.927305	−	0.374306i	$-0.877881\pi$
$499$	−10.2208	−	28.0815i	−0.457547	−	1.25710i	0.469758	−	0.882795i	$-0.344341\pi$
$500$	−6.96922	+	14.6576i	−0.311673	+	0.655509i
$501$	−1.57913	−	0.979991i	−0.0705503	−	0.0437828i
$502$	4.22398	−	18.7208i	0.188525	−	0.835549i
$503$	1.24155	−	2.15043i	0.0553581	−	0.0958830i	−0.837018	−	0.547175i	$-0.815703\pi$
$503$	1.24155	−	2.15043i	0.0553581	−	0.0958830i	0.892376	+	0.451292i	$0.149037\pi$
$504$	9.10063	+	8.13431i	0.405374	+	0.362331i
$505$	2.30716	+	3.99612i	0.102667	+	0.177825i
$506$	−14.6370	+	4.55479i	−0.650696	+	0.202485i
$507$	13.3633	+	40.7006i	0.593486	+	1.80758i
$508$	−25.8649	+	17.8233i	−1.14757	+	0.790781i
$509$	1.63562	−	1.94925i	0.0724974	−	0.0863991i	−0.728577	−	0.684964i	$-0.759818\pi$
$509$	1.63562	−	1.94925i	0.0724974	−	0.0863991i	0.801074	+	0.598565i	$0.204262\pi$
$510$	2.68262	+	0.695676i	0.118789	+	0.0308050i
$511$	−1.43786	−	0.523339i	−0.0636072	−	0.0231511i
$512$	−9.35934	+	20.6010i	−0.413628	+	0.910446i
$513$	−14.0018	+	19.6516i	−0.618192	+	0.867638i
$514$	3.20941	−	7.66679i	0.141561	−	0.338168i
$515$	−0.645885	+	1.77455i	−0.0284611	+	0.0781962i
$516$	13.0243	+	1.65756i	0.573364	+	0.0729701i
$517$	−17.3426	+	20.6681i	−0.762727	+	0.908983i
$518$	4.65300	−	7.24369i	0.204441	−	0.318269i
$519$	2.04053	−	9.74766i	0.0895693	−	0.427875i
$520$	7.20814	−	13.4746i	0.316098	−	0.590898i
$521$	−15.5710	−	26.9697i	−0.682176	−	1.18156i	−0.974315	−	0.225188i	$-0.927700\pi$
$521$	−15.5710	−	26.9697i	−0.682176	−	1.18156i	0.292139	−	0.956376i	$-0.405633\pi$
$522$	−10.4439	+	35.5737i	−0.457115	+	1.55702i
$523$	−11.8268	−	6.82820i	−0.517149	−	0.298576i	0.218618	−	0.975810i	$-0.429845\pi$
$523$	−11.8268	−	6.82820i	−0.517149	−	0.298576i	−0.735768	+	0.677234i	$0.763178\pi$
$524$	−17.0785	−	12.1503i	−0.746076	−	0.530788i
$525$	0.335045	−	10.5250i	0.0146226	−	0.459348i
$526$	−0.903150	+	19.0469i	−0.0393792	+	0.830484i
$527$	7.88085	−	2.86840i	0.343295	−	0.124949i
$528$	−1.98632	+	42.3968i	−0.0864437	+	1.84509i
$529$	−3.45027	−	19.5674i	−0.150012	−	0.850759i
$530$	1.35159	+	1.77517i	0.0587095	+	0.0771084i
$531$	−6.45602	−	8.77165i	−0.280167	−	0.380657i
$532$	12.8785	+	3.55447i	0.558353	+	0.154106i
$533$	5.26425	+	6.27369i	0.228020	+	0.271744i
$534$	−11.1442	+	16.1919i	−0.482257	+	0.700691i
$535$	2.38178	−	13.5078i	0.102973	−	0.583991i
$536$	−5.72795	+	17.4789i	−0.247410	+	0.754974i
$537$	7.19445	−	5.65674i	0.310463	−	0.244106i
$538$	30.3268	+	27.9993i	1.30748	+	1.20713i
$539$			30.2064i			1.30108i
$540$	2.99103	+	8.63730i	0.128713	+	0.371690i
$541$		−	30.2062i		−	1.29866i	−0.760505	−	0.649332i	$-0.775049\pi$
$541$		−	30.2062i		−	1.29866i	0.760505	−	0.649332i	$-0.224951\pi$
$542$	21.1433	−	22.9010i	0.908185	−	0.983681i
$543$	−4.64774	−	32.3463i	−0.199454	−	1.38811i
$544$	−3.23844	−	6.51633i	−0.138847	−	0.279385i
$545$	2.08378	−	11.8177i	0.0892591	−	0.506214i
$546$	−1.71253	+	21.5765i	−0.0732897	+	0.923389i
$547$	11.4189	+	13.6086i	0.488239	+	0.581860i	0.952769	−	0.303697i	$-0.0982211\pi$
$547$	11.4189	+	13.6086i	0.488239	+	0.581860i	−0.464530	+	0.885557i	$0.653777\pi$
$548$	−0.829296	+	3.00469i	−0.0354258	+	0.128354i
$549$	−1.71448	+	26.9018i	−0.0731724	+	1.14814i
$550$	29.1330	−	22.1815i	1.24223	−	0.945823i
$551$	7.04665	+	39.9635i	0.300197	+	1.70250i
$552$	8.53730	+	1.50038i	0.363372	+	0.0638605i
$553$	−6.07268	+	2.21028i	−0.258237	+	0.0939905i
$554$	23.8951	+	1.13304i	1.01520	+	0.0481381i
$555$	5.68312	−	3.04429i	0.241235	−	0.129223i
$556$	3.96370	+	2.81993i	0.168098	+	0.119592i
$557$	6.76671	+	3.90676i	0.286714	+	0.165535i	0.636459	−	0.771310i	$-0.280398\pi$
$557$	6.76671	+	3.90676i	0.286714	+	0.165535i	−0.349745	+	0.936845i	$0.613732\pi$
$558$	22.2751	+	16.3995i	0.942981	+	0.694244i
$559$	11.6408	+	20.1624i	0.492353	+	0.852781i
$560$	3.92523	−	3.19460i	0.165871	−	0.134997i
$561$	−10.1715	−	9.10178i	−0.429439	−	0.384277i
$562$	21.3295	+	13.7010i	0.899729	+	0.577943i
$563$	14.1088	−	16.8142i	0.594616	−	0.708636i	−0.381870	−	0.924216i	$-0.624720\pi$
$563$	14.1088	−	16.8142i	0.594616	−	0.708636i	0.976486	+	0.215580i	$0.0691643\pi$
$564$	14.0697	−	5.89907i	0.592439	−	0.248396i
$565$	−5.35695	+	14.7181i	−0.225368	+	0.619195i
$566$	−38.4934	−	16.1138i	−1.61800	−	0.677314i
$567$	−8.78093	−	9.51354i	−0.368764	−	0.399531i
$568$	−25.5905	+	10.2643i	−1.07375	+	0.430682i
$569$	−31.7319	−	11.5495i	−1.33027	−	0.484179i	−0.423536	−	0.905879i	$-0.639211\pi$
$569$	−31.7319	−	11.5495i	−1.33027	−	0.484179i	−0.906736	+	0.421700i	$0.861434\pi$
$570$	7.13115	+	7.01708i	0.298691	+	0.293913i
$571$	10.8727	−	12.9576i	0.455008	−	0.542257i	−0.488955	−	0.872309i	$-0.662622\pi$
$571$	10.8727	−	12.9576i	0.455008	−	0.542257i	0.943963	+	0.330052i	$0.107066\pi$
$572$	−61.9732	+	42.7053i	−2.59123	+	1.78560i
$573$	−5.55026	+	6.20255i	−0.231865	+	0.259115i
$574$	0.805898	+	2.58979i	0.0336375	+	0.108096i
$575$	−3.73904	−	6.47621i	−0.155929	−	0.270077i
$576$	11.9765	−	20.7982i	0.499021	−	0.866590i
$577$	2.26852	−	3.92920i	0.0944399	−	0.163575i	−0.814935	−	0.579553i	$-0.803227\pi$
$577$	2.26852	−	3.92920i	0.0944399	−	0.163575i	0.909375	+	0.415978i	$0.136561\pi$
$578$	−21.1694	−	4.77646i	−0.880530	−	0.198675i
$579$	−14.9129	+	7.98843i	−0.619760	+	0.331988i
$580$	13.8828	+	6.60082i	0.576453	+	0.274084i
$581$	−2.66922	−	7.33362i	−0.110738	−	0.304250i
$582$	7.46437	−	5.31680i	0.309408	−	0.220389i
$583$	−1.90816	−	10.8217i	−0.0790277	−	0.448189i
$584$	−0.426221	+	2.97827i	−0.0176371	+	0.123242i
$585$	−8.98055	+	13.4930i	−0.371300	+	0.557867i
$586$	−1.13392	−	8.86975i	−0.0468417	−	0.366406i
$587$	2.98040	+	3.55190i	0.123014	+	0.146603i	0.824036	−	0.566537i	$-0.191717\pi$
$587$	2.98040	+	3.55190i	0.123014	+	0.146603i	−0.701022	+	0.713139i	$0.747273\pi$
$588$	7.82147	−	15.1845i	0.322552	−	0.626197i
$589$	29.8159	+	5.25734i	1.22854	+	0.216625i
$590$	−4.01336	+	2.07014i	−0.165227	+	0.0852263i
$591$	1.05870	+	7.36811i	0.0435492	+	0.303083i
$592$	−15.8186	−	6.02758i	−0.650139	−	0.247732i
$593$	17.7662			0.729570			0.364785	−	0.931092i	$-0.381142\pi$
$593$	17.7662			0.729570			0.364785	+	0.931092i	$0.381142\pi$
$594$	6.40894	−	44.5594i	0.262962	−	1.82829i
$595$			1.62752i			0.0667220i
$596$	13.4526	−	6.15069i	0.551040	−	0.251942i
$597$	−24.0265	−	30.5578i	−0.983339	−	1.25065i
$598$	7.04625	+	13.6605i	0.288143	+	0.558619i
$599$	0.339252	−	1.92399i	0.0138614	−	0.0786122i	−0.977092	−	0.212816i	$-0.931737\pi$
$599$	0.339252	−	1.92399i	0.0138614	−	0.0786122i	0.990954	+	0.134204i	$0.0428477\pi$
$600$	−20.3884	+	3.60691i	−0.832355	+	0.147252i
$601$	25.1551	−	21.1077i	1.02610	−	0.861000i	0.0357176	−	0.999362i	$-0.488628\pi$
$601$	25.1551	−	21.1077i	1.02610	−	0.861000i	0.990382	+	0.138362i	$0.0441839\pi$
$602$	0.977752	+	7.64819i	0.0398502	+	0.311717i
$603$	7.82505	−	17.8712i	0.318661	−	0.727772i
$604$	13.8352	−	3.59618i	0.562947	−	0.146327i
$605$	22.9798	−	4.05196i	0.934263	−	0.164736i
$606$	−5.33683	+	11.6900i	−0.216794	+	0.474875i
$607$	−41.8794	+	15.2429i	−1.69983	+	0.618688i	−0.995806	−	0.0914862i	$-0.970838\pi$
$607$	−41.8794	+	15.2429i	−1.69983	+	0.618688i	−0.704026	+	0.710174i	$0.748616\pi$
$608$	1.63748	−	26.2178i	0.0664085	−	1.06327i
$609$	−21.7619	−	0.692754i	−0.881837	−	0.0280718i
$610$	10.9026	+	2.45997i	0.441435	+	0.0996012i
$611$	23.4287	+	13.5266i	0.947823	+	0.547226i
$612$	2.75633	+	7.20912i	0.111418	+	0.291411i
$613$	37.3794	−	21.5810i	1.50974	−	0.871649i	0.509806	−	0.860290i	$-0.329717\pi$
$613$	37.3794	−	21.5810i	1.50974	−	0.871649i	0.999935	−	0.0113598i	$-0.00361603\pi$
$614$	28.2126	−	8.77925i	1.13857	−	0.354302i
$615$	−0.416159	+	1.98800i	−0.0167812	+	0.0801640i
$616$	−24.3938	+	5.12088i	−0.982854	+	0.206326i
$617$	−7.67041	−	6.43624i	−0.308799	−	0.259113i	0.475196	−	0.879880i	$-0.342377\pi$
$617$	−7.67041	−	6.43624i	−0.308799	−	0.259113i	−0.783995	+	0.620767i	$0.786821\pi$
$618$	−5.06886	+	1.40209i	−0.203899	+	0.0564004i
$619$	12.1835	−	33.4738i	0.489695	−	1.34543i	−0.411262	−	0.911517i	$-0.634912\pi$
$619$	12.1835	−	33.4738i	0.489695	−	1.34543i	0.900957	−	0.433908i	$-0.142866\pi$
$620$	8.17025	−	8.04865i	0.328125	−	0.323242i
$621$	−8.86086	−	2.45232i	−0.355574	−	0.0984083i
$622$	−7.80520	+	18.6454i	−0.312960	+	0.747614i
$623$	−10.8473	−	3.94810i	−0.434588	−	0.158177i
$624$	42.2112	−	5.42057i	1.68980	−	0.216996i
$625$	10.7203	+	8.99543i	0.428814	+	0.359817i
$626$	13.1770	+	8.46431i	0.526660	+	0.338302i
$627$	−15.3709	−	46.8150i	−0.613854	−	1.86961i
$628$	−2.50077	+	26.3106i	−0.0997918	+	1.04991i
$629$	4.71450	−	2.72192i	0.187979	−	0.108530i
$630$	−4.46905	+	2.97357i	−0.178051	+	0.118470i
$631$	8.58886	−	14.8763i	0.341917	−	0.592218i	−0.642872	−	0.765974i	$-0.722257\pi$
$631$	8.58886	−	14.8763i	0.341917	−	0.592218i	0.984789	+	0.173756i	$0.0555904\pi$
$632$	6.70631	+	10.7927i	0.266763	+	0.429312i
$633$	−4.53409	+	7.30610i	−0.180214	+	0.290391i
$634$	33.7386	+	1.59979i	1.33993	+	0.0635359i
$635$	−4.72460	−	12.9807i	−0.187490	−	0.515124i
$636$	−1.84289	+	5.93405i	−0.0730755	+	0.235300i
$637$	29.8277	−	5.25943i	1.18182	−	0.208386i
$638$	−45.8635	−	60.2367i	−1.81575	−	2.38479i
$639$	28.0617	−	8.23421i	1.11010	−	0.325740i
$640$	−7.73296	−	6.26279i	−0.305672	−	0.247559i
$641$	−18.9061	+	15.8641i	−0.746746	+	0.626595i	−0.934640	−	0.355595i	$-0.884278\pi$
$641$	−18.9061	+	15.8641i	−0.746746	+	0.626595i	0.187894	+	0.982189i	$0.439834\pi$
$642$	34.4885	−	16.4220i	1.36115	−	0.648126i
$643$	15.5143	+	2.73559i	0.611825	+	0.107881i	0.470970	−	0.882149i	$-0.343904\pi$
$643$	15.5143	+	2.73559i	0.611825	+	0.107881i	0.140855	+	0.990030i	$0.455015\pi$
$644$	0.405636	+	5.07431i	0.0159843	+	0.199956i
$645$	−2.14644	+	5.36016i	−0.0845161	+	0.211056i
$646$	6.20688	+	5.73050i	0.244206	+	0.225464i
$647$	25.8669			1.01693			0.508466	−	0.861082i	$-0.330213\pi$
$647$	25.8669			1.01693			0.508466	+	0.861082i	$0.330213\pi$
$648$	−14.7597	+	20.7401i	−0.579815	+	0.814748i
$649$	22.2408			0.873027
$650$	−26.9760	−	24.9056i	−1.05809	−	0.976879i
$651$	−6.03873	+	15.0801i	−0.236677	+	0.591036i
$652$	26.9534	−	2.15463i	1.05558	−	0.0843818i
$653$	8.32982	+	1.46877i	0.325971	+	0.0574775i	0.334239	−	0.942488i	$-0.391521\pi$
$653$	8.32982	+	1.46877i	0.325971	+	0.0574775i	−0.00826793	+	0.999966i	$0.502632\pi$
$654$	30.1733	−	14.3673i	1.17987	−	0.561807i
$655$	7.06098	−	5.92487i	0.275895	−	0.231504i
$656$	4.65796	−	2.59694i	0.181863	−	0.101394i
$657$	0.752887	−	3.10103i	0.0293729	−	0.120983i
$658$	5.42751	+	7.12844i	0.211586	+	0.277895i
$659$	−41.5741	+	7.33064i	−1.61950	+	0.285561i	−0.908579	−	0.417713i	$-0.862832\pi$
$659$	−41.5741	+	7.33064i	−1.61950	+	0.285561i	−0.710919	+	0.703274i	$0.751721\pi$
$660$	−17.8256	−	5.53597i	−0.693861	−	0.215487i
$661$	1.35846	+	3.73233i	0.0528379	+	0.145171i	0.963304	−	0.268413i	$-0.0864991\pi$
$661$	1.35846	+	3.73233i	0.0528379	+	0.145171i	−0.910466	+	0.413584i	$0.864277\pi$
$662$	−9.95208	−	0.471900i	−0.386799	−	0.0183409i
$663$	−7.21666	+	11.6287i	−0.280272	+	0.451622i
$664$	−13.0338	+	8.09882i	−0.505808	+	0.314295i
$665$	−2.93769	+	5.08823i	−0.113919	+	0.197313i
$666$	16.0878	+	7.97254i	0.623390	+	0.308930i
$667$	−13.3905	+	7.73101i	−0.518482	+	0.299346i
$668$	−2.13639	−	0.203059i	−0.0826592	−	0.00785660i
$669$	−5.69031	−	17.3309i	−0.220000	−	0.670052i
$670$	−6.80584	−	4.37175i	−0.262933	−	0.168895i
$671$	−42.1680	−	35.3831i	−1.62788	−	1.36595i
$672$	13.5885	+	3.74217i	0.524188	+	0.144358i
$673$	33.2218	+	12.0918i	1.28061	+	0.466103i	0.890633	−	0.454723i	$-0.150262\pi$
$673$	33.2218	+	12.0918i	1.28061	+	0.466103i	0.389974	+	0.920826i	$0.372484\pi$
$674$	−2.81231	+	6.71818i	−0.108326	+	0.258775i
$675$	21.8924	−	1.73454i	0.842639	−	0.0667626i
$676$	34.7141	+	35.2385i	1.33516	+	1.35533i
$677$	7.56753	−	20.7916i	0.290844	−	0.799086i	−0.705100	−	0.709108i	$-0.749098\pi$
$677$	7.56753	−	20.7916i	0.290844	−	0.799086i	0.995944	−	0.0899785i	$-0.0286798\pi$
$678$	−42.0409	+	11.6289i	−1.61457	+	0.446605i
$679$	4.12278	+	3.45942i	0.158218	+	0.132760i
$680$	3.13183	−	0.657450i	0.120100	−	0.0252120i
$681$	5.34108	−	25.5145i	0.204671	−	0.977716i
$682$	−53.9340	+	16.7833i	−2.06524	+	0.642666i
$683$	−13.7796	+	7.95563i	−0.527260	+	0.304414i	−0.739900	−	0.672717i	$-0.765127\pi$
$683$	−13.7796	+	7.95563i	−0.527260	+	0.304414i	0.212640	+	0.977131i	$0.431794\pi$
$684$	−4.39520	+	27.5135i	−0.168055	+	1.05201i
$685$	−1.18714	−	0.685394i	−0.0453582	−	0.0261876i
$686$	23.6760	+	5.34204i	0.903955	+	0.203960i
$687$	21.4345	+	0.682331i	0.817776	+	0.0260325i
$688$	14.3224	−	4.97102i	0.546035	−	0.189518i
$689$	−10.3538	+	3.76847i	−0.394448	+	0.143567i
$690$	−1.58312	+	3.46774i	−0.0602685	+	0.132015i
$691$	−3.66819	+	0.646800i	−0.139544	+	0.0246054i	−0.242984	−	0.970030i	$-0.578126\pi$
$691$	−3.66819	+	0.646800i	−0.139544	+	0.0246054i	0.103440	+	0.994636i	$0.467015\pi$
$692$	−2.89296	−	11.1298i	−0.109974	−	0.423090i
$693$	26.2751	−	2.92559i	0.998109	−	0.111134i
$694$	−4.95627	−	38.7690i	−0.188137	−	1.47165i
$695$	−1.63877	+	1.37509i	−0.0621620	+	0.0521601i
$696$	7.45782	+	42.1560i	0.282688	+	1.59792i
$697$	−0.297809	+	1.68896i	−0.0112803	+	0.0639740i
$698$	−11.4669	−	22.2307i	−0.434027	−	0.841445i
$699$	16.6867	+	21.2228i	0.631149	+	0.802718i
$700$	−5.05600	−	11.0583i	−0.191099	−	0.417966i
$701$		−	15.8003i		−	0.596770i	−0.954446	−	0.298385i	$-0.903552\pi$
$701$		−	15.8003i		−	0.596770i	0.954446	−	0.298385i	$-0.0964479\pi$
$702$	−45.1167	+	1.42993i	−1.70282	+	0.0539693i
$703$	19.6523			0.741201
$704$	19.7081	+	44.8721i	0.742777	+	1.69118i
$705$	0.954242	+	6.64111i	0.0359388	+	0.250119i
$706$	−18.5582	+	9.57252i	−0.698446	+	0.360267i
$707$	−7.43207	−	1.31048i	−0.279512	−	0.0492855i
$708$	−11.1802	−	5.75890i	−0.420179	−	0.216433i
$709$	−10.6481	−	12.6899i	−0.399897	−	0.476579i	0.528091	−	0.849187i	$-0.322908\pi$
$709$	−10.6481	−	12.6899i	−0.399897	−	0.476579i	−0.927989	+	0.372609i	$0.878463\pi$
$710$	−1.53763	−	12.0277i	−0.0577062	−	0.451391i
$711$	−5.98270	−	12.0767i	−0.224369	−	0.452913i
$712$	−3.21544	+	22.4682i	−0.120504	+	0.842033i
$713$	2.00318	+	11.3606i	0.0750197	+	0.425458i
$714$	−3.69178	+	2.62962i	−0.138161	+	0.0984110i
$715$	−11.3203	−	31.1023i	−0.423356	−	1.16316i
$716$	4.53782	−	9.54393i	0.169586	−	0.356673i
$717$	34.9627	−	18.7285i	1.30570	−	0.699429i
$718$	−22.0265	−	4.96985i	−0.822022	−	0.185473i
$719$	−12.9134	+	22.3667i	−0.481590	+	0.834138i	−0.999777	−	0.0211293i	$-0.993274\pi$
$719$	−12.9134	+	22.3667i	−0.481590	+	0.834138i	0.518187	+	0.855267i	$0.326607\pi$
$720$	7.52731	+	7.39854i	0.280526	+	0.275727i
$721$	−1.54427	−	2.67476i	−0.0575118	−	0.0996133i
$722$	1.07748	+	3.46253i	0.0400997	+	0.128862i
$723$	−10.8829	+	12.1619i	−0.404740	+	0.452307i
$724$	−21.4109	−	31.0712i	−0.795731	−	1.15475i
$725$	23.7402	−	28.2924i	0.881688	−	1.05075i
$726$	46.3201	+	45.5792i	1.71910	+	1.69160i
$727$	6.13255	+	2.23206i	0.227444	+	0.0827827i	0.453228	−	0.891395i	$-0.350272\pi$
$727$	6.13255	+	2.23206i	0.227444	+	0.0827827i	−0.225785	+	0.974177i	$0.572495\pi$
$728$	9.30405	+	23.1964i	0.344831	+	0.859715i
$729$	17.6922	−	20.3958i	0.655266	−	0.755399i
$730$	−1.22049	−	0.510910i	−0.0451722	−	0.0189096i
$731$	−1.66749	+	4.58139i	−0.0616744	+	0.169449i
$732$	12.0355	+	28.7055i	0.444846	+	1.06099i
$733$	28.8936	−	34.4340i	1.06721	−	1.27185i	0.106494	−	0.994313i	$-0.466038\pi$
$733$	28.8936	−	34.4340i	1.06721	−	1.27185i	0.960715	−	0.277537i	$-0.0895180\pi$
$734$	−36.6256	−	23.5265i	−1.35187	−	0.868380i
$735$	5.59765	+	5.00897i	0.206472	+	0.184759i
$736$	9.60058	−	2.83037i	0.353882	−	0.104329i
$737$	19.9195	+	34.5016i	0.733744	+	1.27088i
$738$	−5.18186	+	2.26806i	−0.190747	+	0.0834885i
$739$	13.4296	+	7.75360i	0.494017	+	0.285221i	0.726239	−	0.687442i	$-0.241266\pi$
$739$	13.4296	+	7.75360i	0.494017	+	0.285221i	−0.232222	+	0.972663i	$0.574600\pi$
$740$	4.31559	−	6.06600i	0.158644	−	0.222991i
$741$	−43.5518	+	23.3295i	−1.59992	+	0.857030i
$742$	−3.64496	−	0.172834i	−0.133811	−	0.00634492i
$743$	−2.95018	+	1.07378i	−0.108232	+	0.0393931i	−0.395568	−	0.918437i	$-0.629452\pi$
$743$	−2.95018	+	1.07378i	−0.108232	+	0.0393931i	0.287337	+	0.957830i	$0.407230\pi$
$744$	31.4579	+	5.52854i	1.15330	+	0.202686i
$745$	1.12960	+	6.40631i	0.0413855	+	0.234709i
$746$	10.1782	−	7.74957i	0.372651	−	0.283732i
$747$	14.5844	−	7.22496i	0.533614	−	0.264347i
$748$	−15.1927	−	4.19320i	−0.555500	−	0.153319i
$749$	14.4195	+	17.1845i	0.526877	+	0.627908i
$750$	1.57276	−	19.8154i	0.0574290	−	0.723557i
$751$	3.85881	−	21.8844i	0.140810	−	0.798574i	−0.829826	−	0.558022i	$-0.811560\pi$
$751$	3.85881	−	21.8844i	0.140810	−	0.798574i	0.970636	−	0.240552i	$-0.0773284\pi$
$752$	11.5247	−	13.3237i	0.420262	−	0.485865i
$753$	3.34297	+	23.2656i	0.121824	+	0.847846i
$754$	−51.4960	+	55.7768i	−1.87537	+	2.03127i
$755$			6.28654i			0.228791i
$756$	−13.9658	−	5.33286i	−0.507931	−	0.193954i
$757$			45.2567i			1.64488i	0.568849	+	0.822442i	$0.307389\pi$
$757$			45.2567i			1.64488i	−0.568849	+	0.822442i	$0.692611\pi$
$758$	18.9364	+	17.4830i	0.687801	+	0.635013i
$759$	14.7588	−	11.6043i	0.535712	−	0.421211i
$760$	10.9779	+	3.59754i	0.398211	+	0.130496i
$761$	−5.12548	+	29.0680i	−0.185798	+	1.05372i	0.739127	+	0.673566i	$0.235238\pi$
$761$	−5.12548	+	29.0680i	−0.185798	+	1.05372i	−0.924925	+	0.380149i	$0.875873\pi$
$762$	21.8111	−	31.6902i	0.790132	−	1.14801i
$763$	12.6153	+	15.0344i	0.456706	+	0.544281i
$764$	−2.55701	+	9.26450i	−0.0925093	+	0.335178i
$765$	−3.37336	+	0.375605i	−0.121964	+	0.0135800i
$766$	15.4970	+	20.3536i	0.559928	+	0.735404i
$767$	−3.87249	−	21.9620i	−0.139828	−	0.793002i
$768$	1.71185	−	27.6599i	0.0617711	−	0.998090i
$769$	12.4343	−	4.52572i	0.448393	−	0.163202i	−0.107947	−	0.994157i	$-0.534428\pi$
$769$	12.4343	−	4.52572i	0.448393	−	0.163202i	0.556340	+	0.830955i	$0.312205\pi$
$770$	0.519184	−	10.9493i	0.0187101	−	0.394585i
$771$	−0.323880	+	10.1742i	−0.0116642	+	0.366416i
$772$	−11.3244	+	15.9176i	−0.407575	+	0.572888i
$773$	5.43624	+	3.13861i	0.195528	+	0.112888i	0.594568	−	0.804045i	$-0.297323\pi$
$773$	5.43624	+	3.13861i	0.195528	+	0.112888i	−0.399040	+	0.916934i	$0.630657\pi$
$774$	−15.6267	+	3.79166i	−0.561691	+	0.136288i
$775$	−13.7775	−	23.8633i	−0.494901	−	0.857194i
$776$	4.99150	−	9.33087i	0.179184	−	0.334959i
$777$	−2.16046	+	10.3206i	−0.0775062	+	0.370249i
$778$	15.4098	−	23.9896i	0.552467	−	0.860068i
$779$	−3.97964	+	4.74275i	−0.142586	+	0.169927i
$780$	−2.36284	+	18.5661i	−0.0846032	+	0.664772i
$781$	−20.4253	+	56.1181i	−0.730875	+	2.00806i
$782$	−1.24292	+	2.96914i	−0.0444467	+	0.106176i
$783$	−3.58642	−	45.2657i	−0.128168	−	1.61766i
$784$	0.295713	−	19.7206i	0.0105612	−	0.704309i
$785$	−10.9219	−	3.97525i	−0.389820	−	0.141883i
$786$	24.8482	+	6.44380i	0.886305	+	0.229843i
$787$	8.11260	−	9.66821i	0.289183	−	0.344635i	−0.601821	−	0.798631i	$-0.705558\pi$
$787$	8.11260	−	9.66821i	0.289183	−	0.344635i	0.891003	+	0.453997i	$0.150002\pi$
$788$	4.87716	+	7.07765i	0.173742	+	0.252131i
$789$	−7.28518	−	22.1884i	−0.259359	−	0.789928i
$790$	−5.33566	+	1.66036i	−0.189834	+	0.0590731i
$791$	−12.8082	−	22.1844i	−0.455406	−	0.788786i
$792$	−16.2437	−	49.3791i	−0.577195	−	1.75461i
$793$	−27.5974	+	47.8002i	−0.980013	+	1.69743i
$794$	9.16852	−	40.6351i	0.325379	−	1.44208i
$795$	−2.32182	−	1.44090i	−0.0823466	−	0.0511034i
$796$	−40.5370	−	19.2740i	−1.43680	−	0.683149i
$797$	10.7835	+	29.6275i	0.381973	+	1.04946i	0.970525	+	0.241002i	$0.0774760\pi$
$797$	10.7835	+	29.6275i	0.381973	+	1.04946i	−0.588552	+	0.808459i	$0.700302\pi$
$798$	−16.2883	+	1.55746i	−0.576600	+	0.0551336i
$799$	0.983754	+	5.57915i	0.0348027	+	0.197376i
$800$	−19.2370	+	14.1963i	−0.680131	+	0.501915i
$801$	5.67983	−	23.3943i	0.200687	−	0.826598i
$802$	33.7881	−	4.31950i	1.19310	−	0.152527i
$803$	4.18868	+	4.99188i	0.147815	+	0.176159i
$804$	−1.07970	−	22.5015i	−0.0380782	−	0.793566i
$805$	−2.20466	−	0.388741i	−0.0777039	−	0.0137013i
$806$	25.9637	+	50.3356i	0.914533	+	1.77300i
$807$	−46.9293	−	18.7925i	−1.65199	−	0.661528i
$808$	0.480506	+	14.8308i	0.0169041	+	0.521747i
$809$	−27.6700			−0.972824			−0.486412	−	0.873730i	$-0.661695\pi$
$809$	−27.6700			−0.972824			−0.486412	+	0.873730i	$0.661695\pi$
$810$	−7.19469	−	8.57672i	−0.252796	−	0.301355i
$811$		−	23.8915i		−	0.838946i	−0.907768	−	0.419473i	$-0.862215\pi$
$811$		−	23.8915i		−	0.838946i	0.907768	−	0.419473i	$-0.137785\pi$
$812$	−22.8647	+	10.4540i	−0.802393	+	0.366864i
$813$	−14.1910	+	35.4381i	−0.497699	+	1.24287i
$814$	−32.5854	+	16.8079i	−1.14212	+	0.589118i
$815$	−2.06489	+	11.7105i	−0.0723298	+	0.410203i
$816$	6.55147	+	6.04179i	0.229347	+	0.211505i
$817$	−13.4826	+	11.3133i	−0.471697	+	0.395801i
$818$	−19.6695	+	2.51457i	−0.687728	+	0.0879198i
$819$	−7.46385	−	25.4364i	−0.260808	−	0.888818i
$820$	0.590009	+	2.26988i	0.0206040	+	0.0792676i
$821$	−41.8153	+	7.37317i	−1.45937	+	0.257326i	−0.846300	−	0.532706i	$-0.821175\pi$
$821$	−41.8153	+	7.37317i	−1.45937	+	0.257326i	−0.613066	+	0.790032i	$0.710064\pi$
$822$	−0.363373	−	3.80023i	−0.0126741	−	0.132548i
$823$	7.73915	−	2.81682i	0.269770	−	0.0981882i	−0.203593	−	0.979056i	$-0.565262\pi$
$823$	7.73915	−	2.81682i	0.269770	−	0.0981882i	0.473363	+	0.880867i	$0.343040\pi$
$824$	−4.52319	+	4.05212i	−0.157573	+	0.141162i
$825$	−23.6471	+	38.1043i	−0.823288	+	1.32662i
$826$	1.62556	−	7.20450i	0.0565604	−	0.250677i
$827$	4.58334	+	2.64619i	0.159378	+	0.0920172i	0.577568	−	0.816343i	$-0.304002\pi$
$827$	4.58334	+	2.64619i	0.159378	+	0.0920172i	−0.418190	+	0.908360i	$0.637335\pi$
$828$	−10.4239	+	2.01183i	−0.362255	+	0.0699158i
$829$	−40.6483	+	23.4683i	−1.41177	+	0.815088i	−0.995556	−	0.0941762i	$-0.969978\pi$
$829$	−40.6483	+	23.4683i	−1.41177	+	0.815088i	−0.416219	+	0.909264i	$0.636645\pi$
$830$	−2.00512	−	6.44357i	−0.0695989	−	0.223659i
$831$	−27.8362	+	9.13954i	−0.965628	+	0.317047i
$832$	40.8781	−	27.2740i	1.41719	−	0.945557i
$833$	4.85872	+	4.07695i	0.168345	+	0.141258i
$834$	−5.76696	−	1.49553i	−0.199694	−	0.0517858i
$835$	0.322785	−	0.886845i	0.0111704	−	0.0306905i
$836$	−39.9291	−	40.5324i	−1.38098	−	1.40184i
$837$	−32.6501	−	9.03621i	−1.12855	−	0.312337i
$838$	−22.6131	−	9.46610i	−0.781155	−	0.327001i
$839$	−15.6236	−	5.68654i	−0.539388	−	0.196321i	0.0579373	−	0.998320i	$-0.481548\pi$
$839$	−15.6236	−	5.68654i	−0.539388	−	0.196321i	−0.597325	+	0.801999i	$0.703770\pi$
$840$	−3.09613	+	5.36966i	−0.106827	+	0.185271i
$841$	−36.2834	−	30.4454i	−1.25115	−	1.04984i
$842$	−17.5150	+	27.2670i	−0.603608	+	0.939683i
$843$	−30.3896	−	6.36161i	−1.04667	−	0.219105i
$844$	−0.939488	+	9.88434i	−0.0323385	+	0.340233i
$845$	−18.8391	+	10.8768i	−0.648086	+	0.374173i
$846$	−13.5225	+	12.8947i	−0.464913	+	0.443329i
$847$	−19.0817	+	33.0504i	−0.655654	+	1.13563i
$848$	1.13982	+	7.08377i	0.0391417	+	0.243257i
$849$	51.0828	+	1.62614i	1.75316	+	0.0558089i
$850$	0.364159	−	7.67990i	0.0124906	−	0.263418i
$851$	2.56105	+	7.03644i	0.0877918	+	0.241206i
$852$	24.7985	−	22.9212i	0.849582	−	0.785268i
$853$	15.3585	−	2.70812i	0.525865	−	0.0927241i	0.0955876	−	0.995421i	$-0.469527\pi$
$853$	15.3585	−	2.70812i	0.525865	−	0.0927241i	0.430277	+	0.902697i	$0.358416\pi$
$854$	−14.5437	+	11.0734i	−0.497676	+	0.378925i
$855$	−11.2243	−	4.91466i	−0.383864	−	0.168078i
$856$	27.2431	−	34.6891i	0.931149	−	1.18565i
$857$	22.2793	−	18.6945i	0.761046	−	0.638593i	−0.177353	−	0.984147i	$-0.556753\pi$
$857$	22.2793	−	18.6945i	0.761046	−	0.638593i	0.938399	+	0.345554i	$0.112309\pi$
$858$	52.2602	−	75.9309i	1.78413	−	2.59224i
$859$	−50.7631	−	8.95090i	−1.73201	−	0.305401i	−0.783325	−	0.621612i	$-0.786478\pi$
$859$	−50.7631	−	8.95090i	−1.73201	−	0.305401i	−0.948689	+	0.316212i	$0.897589\pi$
$860$	0.531275	+	6.64599i	0.0181163	+	0.226626i
$861$	−2.05320	−	2.61134i	−0.0699730	−	0.0889942i
$862$	19.7125	−	21.3512i	0.671411	−	0.727225i
$863$	38.4243			1.30798			0.653990	−	0.756503i	$-0.273094\pi$
$863$	38.4243			1.30798			0.653990	+	0.756503i	$0.273094\pi$
$864$	−4.62039	+	29.0285i	−0.157189	+	0.987569i
$865$	5.05722			0.171951
$866$	−8.46839	+	9.17236i	−0.287768	+	0.311690i
$867$	26.3087	−	3.78022i	0.893489	−	0.128383i
$868$	1.49467	+	18.6976i	0.0507324	+	0.634638i
$869$	27.1035	+	4.77907i	0.919422	+	0.162119i
$870$	−18.7680	−	1.48962i	−0.636294	−	0.0505028i
$871$	30.6008	−	25.6771i	1.03687	−	0.870036i
$872$	23.8344	−	30.3488i	0.807136	−	1.02774i
$873$	−6.21886	+	9.34364i	−0.210477	+	0.316234i
$874$	−9.24512	+	7.03913i	−0.312721	+	0.238102i
$875$	11.4962	−	2.02708i	0.388641	−	0.0685279i
$876$	−0.813043	−	3.59396i	−0.0274702	−	0.121429i
$877$	−16.7126	−	45.9175i	−0.564344	−	1.55052i	−0.813201	−	0.581983i	$-0.802277\pi$
$877$	−16.7126	−	45.9175i	−0.564344	−	1.55052i	0.248856	−	0.968540i	$-0.419945\pi$
$878$	−0.648596	+	13.6785i	−0.0218891	+	0.461627i
$879$	5.17126	+	9.65378i	0.174422	+	0.325614i
$880$	−21.2793	+	3.42398i	−0.717325	+	0.115422i
$881$	16.9656	−	29.3853i	0.571586	−	0.990015i	−0.424818	−	0.905279i	$-0.639662\pi$
$881$	16.9656	−	29.3853i	0.571586	−	0.990015i	0.996403	−	0.0847364i	$-0.0270048\pi$
$882$	−2.31783	+	20.7904i	−0.0780454	+	0.700051i
$883$	−10.7143	+	6.18593i	−0.360566	+	0.208173i	−0.669329	−	0.742966i	$-0.733418\pi$
$883$	−10.7143	+	6.18593i	−0.360566	+	0.208173i	0.308763	+	0.951139i	$0.400085\pi$
$884$	−1.49533	+	15.7324i	−0.0502934	+	0.529137i
$885$	3.68808	−	4.12152i	0.123973	−	0.138543i
$886$	4.92327	−	7.66443i	0.165401	−	0.257492i
$887$	36.6437	+	30.7478i	1.23038	+	1.03241i	0.998214	+	0.0597313i	$0.0190244\pi$
$887$	36.6437	+	30.7478i	1.23038	+	1.03241i	0.232162	+	0.972677i	$0.425420\pi$
$888$	20.7325	−	0.0117176i	0.695738	−	0.000393218i
$889$	21.2300	+	7.72708i	0.712031	+	0.259158i
$890$	−9.20742	−	3.85434i	−0.308633	−	0.129198i
$891$	12.1277	+	53.7851i	0.406294	+	1.80187i
$892$	−14.7818	−	15.0051i	−0.494930	−	0.502408i
$893$	−6.99482	+	19.2181i	−0.234073	+	0.643109i
$894$	−12.7066	+	12.9131i	−0.424971	+	0.431879i
$895$	3.56015	+	2.98732i	0.119003	+	0.0998550i
$896$	15.9760	−	3.10442i	0.533719	−	0.103712i
$897$	−14.0286	−	12.5533i	−0.468402	−	0.419143i
$898$	−14.0733	−	45.2251i	−0.469631	−	1.50918i
$899$	−49.3408	+	28.4869i	−1.64561	+	0.950092i
$900$	21.7537	−	13.0316i	0.725124	−	0.434388i
$901$	−1.99822	−	1.15367i	−0.0665704	−	0.0384344i
$902$	2.54232	−	11.2676i	0.0846499	−	0.375170i
$903$	−4.45906	−	8.32424i	−0.148388	−	0.277013i
$904$	−37.5152	+	33.6081i	−1.24774	+	1.11779i
$905$	15.5936	−	5.67560i	0.518349	−	0.188663i
$906$	−14.2600	+	10.1573i	−0.473757	+	0.337453i
$907$	−29.7648	+	5.24833i	−0.988323	+	0.174268i	−0.644366	−	0.764717i	$-0.722879\pi$
$907$	−29.7648	+	5.24833i	−0.988323	+	0.174268i	−0.343957	+	0.938985i	$0.611767\pi$
$908$	−7.57231	−	29.1321i	−0.251296	−	0.966783i
$909$	1.00102	−	15.7069i	0.0332017	−	0.520964i
$910$	−10.9024	+	1.39378i	−0.361412	+	0.0462032i
$911$	17.1660	−	14.4040i	0.568734	−	0.477225i	−0.312491	−	0.949921i	$-0.601163\pi$
$911$	17.1660	−	14.4040i	0.568734	−	0.477225i	0.881226	+	0.472696i	$0.156719\pi$
$912$	9.57679	+	30.7143i	0.317119	+	1.01705i
$913$	−5.77141	+	32.7313i	−0.191006	+	1.08325i
$914$	17.4674	−	9.00989i	0.577770	−	0.298021i
$915$	−13.5495	+	1.94688i	−0.447931	+	0.0643620i
$916$	22.5207	−	10.2967i	0.744104	−	0.340213i
$917$			15.0752i			0.497826i
$918$	−6.30240	−	7.04506i	−0.208010	−	0.232522i
$919$	−45.7620			−1.50955			−0.754774	−	0.655985i	$-0.772253\pi$
$919$	−45.7620			−1.50955			−0.754774	+	0.655985i	$0.772253\pi$
$920$	0.142538	+	4.39943i	0.00469933	+	0.145045i
$921$	−28.4473	+	22.3671i	−0.937370	+	0.737021i
$922$	18.7126	+	36.2780i	0.616268	+	1.19475i
$923$	58.9710	+	10.3982i	1.94105	+	0.342260i
$924$	25.6755	−	16.5133i	0.844663	−	0.543246i
$925$	−11.4970	−	13.7016i	−0.378019	−	0.450506i
$926$	3.98634	−	0.509617i	0.130999	−	0.0167471i
$927$	5.18757	−	3.81810i	0.170382	−	0.125403i
$928$	29.3529	+	39.7753i	0.963556	+	1.30569i
$929$	6.75967	+	38.3360i	0.221778	+	1.25776i	0.868750	+	0.495251i	$0.164924\pi$
$929$	6.75967	+	38.3360i	0.221778	+	1.25776i	−0.646972	+	0.762513i	$0.723965\pi$
$930$	−5.83343	+	12.7778i	−0.191286	+	0.419000i
$931$	7.83120	+	21.5160i	0.256657	+	0.705160i
$932$	28.1534	+	13.3860i	0.922196	+	0.438474i
$933$	0.787667	−	24.7435i	0.0257871	−	0.810065i
$934$	2.43345	−	10.7851i	0.0796248	−	0.352899i
$935$	3.46558	−	6.00256i	0.113337	−	0.196305i
$936$	−45.9318	+	24.6378i	−1.50133	+	0.805312i
$937$	19.1659	+	33.1962i	0.626121	+	1.08447i	0.988323	+	0.152374i	$0.0486919\pi$
$937$	19.1659	+	33.1962i	0.626121	+	1.08447i	−0.362202	+	0.932100i	$0.617975\pi$
$938$	12.6321	−	3.93088i	0.412452	−	0.128348i
$939$	−18.7742	−	3.93011i	−0.612674	−	0.128254i
$940$	4.39594	+	6.37931i	0.143380	+	0.208070i
$941$	−11.4086	+	13.5962i	−0.371909	+	0.443224i	−0.919243	−	0.393691i	$-0.871198\pi$
$941$	−11.4086	+	13.5962i	−0.371909	+	0.443224i	0.547334	+	0.836914i	$0.315643\pi$
$942$	−8.62952	−	31.1975i	−0.281165	−	1.01647i
$943$	−2.21675	−	0.806830i	−0.0721872	−	0.0262740i
$944$	−14.5202	−	0.217732i	−0.472592	−	0.00708656i
$945$	3.81492	−	5.35427i	0.124099	−	0.174174i
$946$	12.6796	−	30.2897i	0.412250	−	0.984803i
$947$	5.18830	−	14.2547i	0.168597	−	0.463217i	−0.826404	−	0.563077i	$-0.809617\pi$
$947$	5.18830	−	14.2547i	0.168597	−	0.463217i	0.995001	+	0.0998603i	$0.0318396\pi$
$948$	−12.3872	−	9.42041i	−0.402317	−	0.305961i
$949$	4.19998	−	5.00534i	0.136337	−	0.162480i
$950$	15.0008	−	23.3528i	0.486689	−	0.757666i
$951$	−39.3034	+	12.9046i	−1.27450	+	0.418460i
$952$	−2.46873	+	4.61493i	−0.0800120	+	0.149571i
$953$	−8.98693	−	15.5658i	−0.291115	−	0.504227i	0.682958	−	0.730457i	$-0.260693\pi$
$953$	−8.98693	−	15.5658i	−0.291115	−	0.504227i	−0.974074	+	0.226231i	$0.927360\pi$
$954$	−0.482963	−	7.59477i	−0.0156365	−	0.245890i
$955$	−3.66036	−	2.11331i	−0.118446	−	0.0683851i
$956$	26.5496	−	37.3182i	0.858676	−	1.20696i
$957$	78.7862	+	48.8939i	2.54680	+	1.58051i
$958$	2.87820	−	60.6995i	0.0929905	−	1.96111i
$959$	2.10672	−	0.766784i	0.0680296	−	0.0247607i
$960$	11.5835	+	3.78874i	0.373856	+	0.122281i
$961$	1.99814	+	11.3320i	0.0644561	+	0.365549i
$962$	22.2709	+	29.2504i	0.718043	+	0.943070i
$963$	−32.2904	+	33.8531i	−1.04054	+	1.09090i
$964$	−5.01377	+	18.1658i	−0.161483	+	0.585080i
$965$	−5.52216	−	6.58105i	−0.177764	−	0.211851i
$966$	−2.68031	−	5.62901i	−0.0862375	−	0.181110i
$967$	5.30231	−	30.0709i	0.170511	−	0.967016i	−0.772688	−	0.634786i	$-0.781088\pi$
$967$	5.30231	−	30.0709i	0.170511	−	0.967016i	0.943199	−	0.332229i	$-0.107801\pi$
$968$	71.3067	+	23.3677i	2.29188	+	0.751066i
$969$	−9.60483	−	3.84619i	−0.308552	−	0.123557i
$970$	3.41927	+	3.15685i	0.109786	+	0.101360i
$971$		−	35.7987i		−	1.14884i	−0.818562	−	0.574418i	$-0.805229\pi$
$971$		−	35.7987i		−	1.14884i	0.818562	−	0.574418i	$-0.194771\pi$
$972$	7.83033	−	30.1776i	0.251158	−	0.967946i
$973$		−	3.49876i		−	0.112165i
$974$	−14.4625	+	15.6648i	−0.463408	+	0.501931i
$975$	41.7440	+	16.7161i	1.33688	+	0.535344i
$976$	27.1835	+	23.5132i	0.870124	+	0.752638i
$977$	5.37402	−	30.4776i	0.171930	−	0.975064i	−0.769698	−	0.638409i	$-0.779593\pi$
$977$	5.37402	−	30.4776i	0.171930	−	0.975064i	0.941628	−	0.336656i	$-0.109296\pi$
$978$	−29.8998	+	14.2371i	−0.956089	+	0.455252i
$979$	31.5997	+	37.6590i	1.00993	+	1.20359i
$980$	8.36098	+	2.30764i	0.267082	+	0.0737148i
$981$	−28.2503	+	29.6175i	−0.901962	+	0.945613i
$982$	−9.01563	+	6.86439i	−0.287700	+	0.219052i
$983$	4.76022	+	26.9965i	0.151827	+	0.861056i	0.961629	+	0.274352i	$0.0884635\pi$
$983$	4.76022	+	26.9965i	0.151827	+	0.861056i	−0.809802	+	0.586703i	$0.800425\pi$
$984$	−4.19557	+	5.00582i	−0.133750	+	0.159580i
$985$	−3.55204	+	1.29284i	−0.113177	+	0.0411932i
$986$	−15.8793	−	0.752952i	−0.505700	−	0.0239789i
$987$	−9.32360	−	5.78613i	−0.296773	−	0.184174i
$988$	−33.0719	+	46.4860i	−1.05216	+	1.47892i
$989$	−5.80771	−	3.35308i	−0.184674	−	0.106622i
$990$	22.8143	−	1.45080i	0.725087	−	0.0461094i
$991$	24.6260	+	42.6535i	0.782271	+	1.35493i	0.930616	+	0.365998i	$0.119272\pi$
$991$	24.6260	+	42.6535i	0.782271	+	1.35493i	−0.148345	+	0.988936i	$0.547395\pi$
$992$	35.3758	−	10.4292i	1.12318	−	0.331128i
$993$	11.5935	−	3.80654i	0.367910	−	0.120797i
$994$	16.6856	+	10.7180i	0.529234	+	0.339955i
$995$	12.6884	−	15.1214i	0.402248	−	0.479381i
$996$	11.3765	−	14.9593i	0.360478	−	0.474003i
$997$	0.295302	−	0.811337i	0.00935232	−	0.0256953i	−0.934929	−	0.354836i	$-0.884537\pi$
$997$	0.295302	−	0.811337i	0.00935232	−	0.0256953i	0.944281	+	0.329141i	$0.106759\pi$
$998$	38.9841	+	16.3192i	1.23402	+	0.516575i
$999$	−21.8900	−	2.09617i	−0.692570	−	0.0663197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.85.9	yes	204
3.2	odd	2		648.2.t.a.469.26		204
4.3	odd	2		864.2.bf.a.625.13		204
8.3	odd	2		864.2.bf.a.625.22		204
8.5	even	2	inner	216.2.t.a.85.18	yes	204
24.5	odd	2		648.2.t.a.469.17		204
27.7	even	9	inner	216.2.t.a.61.18	yes	204
27.20	odd	18		648.2.t.a.181.17		204
108.7	odd	18		864.2.bf.a.817.22		204
216.61	even	18	inner	216.2.t.a.61.9	✓	204
216.101	odd	18		648.2.t.a.181.26		204
216.115	odd	18		864.2.bf.a.817.13		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.61.9	✓	204	216.61	even	18	inner
216.2.t.a.61.18	yes	204	27.7	even	9	inner
216.2.t.a.85.9	yes	204	1.1	even	1	trivial
216.2.t.a.85.18	yes	204	8.5	even	2	inner
648.2.t.a.181.17		204	27.20	odd	18
648.2.t.a.181.26		204	216.101	odd	18
648.2.t.a.469.17		204	24.5	odd	2
648.2.t.a.469.26		204	3.2	odd	2
864.2.bf.a.625.13		204	4.3	odd	2
864.2.bf.a.625.22		204	8.3	odd	2
864.2.bf.a.817.13		204	216.115	odd	18
864.2.bf.a.817.22		204	108.7	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959331 + 1.03908i) q^{2} +(0.643882 - 1.60792i) q^{3} +(-0.159370 - 1.99364i) q^{4} +(0.866185 + 0.152732i) q^{5} +(1.05306 + 2.21157i) q^{6} +(-1.10196 + 0.924651i) q^{7} +(2.22444 + 1.74696i) q^{8} +(-2.17083 - 2.07062i) q^{9} +O(q^{10})\)	\(q+(-0.959331 + 1.03908i) q^{2} +(0.643882 - 1.60792i) q^{3} +(-0.159370 - 1.99364i) q^{4} +(0.866185 + 0.152732i) q^{5} +(1.05306 + 2.21157i) q^{6} +(-1.10196 + 0.924651i) q^{7} +(2.22444 + 1.74696i) q^{8} +(-2.17083 - 2.07062i) q^{9} +(-0.989658 + 0.753514i) q^{10} +(6.03310 - 1.06380i) q^{11} +(-3.30824 - 1.02741i) q^{12} +(-2.10092 - 5.77224i) q^{13} +(0.0963548 - 2.03206i) q^{14} +(0.803302 - 1.29442i) q^{15} +(-3.94920 + 0.635452i) q^{16} +(0.643173 - 1.11401i) q^{17} +(4.23409 - 0.269252i) q^{18} +(4.02158 - 2.32186i) q^{19} +(0.166448 - 1.75120i) q^{20} +(0.777238 + 2.36723i) q^{21} +(-4.68236 + 7.28940i) q^{22} +(1.35542 + 1.13733i) q^{23} +(4.24126 - 2.45189i) q^{24} +(-3.97151 - 1.44551i) q^{25} +(8.01330 + 3.35446i) q^{26} +(-4.72716 + 2.15729i) q^{27} +(2.01904 + 2.04954i) q^{28} +(-2.98881 + 8.21168i) q^{29} +(0.574370 + 2.07647i) q^{30} +(4.99440 + 4.19080i) q^{31} +(3.12831 - 4.71314i) q^{32} +(2.17410 - 10.3857i) q^{33} +(0.540527 + 1.73701i) q^{34} +(-1.09572 + 0.632615i) q^{35} +(-3.78212 + 4.65785i) q^{36} +(3.66503 + 2.11601i) q^{37} +(-1.44543 + 6.40618i) q^{38} +(-10.6341 - 0.338518i) q^{39} +(1.65996 + 1.85293i) q^{40} +(-1.25284 + 0.455997i) q^{41} +(-3.20536 - 1.46334i) q^{42} +(-3.73255 + 0.658149i) q^{43} +(-3.08232 - 11.8583i) q^{44} +(-1.56409 - 2.12510i) q^{45} +(-2.48208 + 0.317311i) q^{46} +(-3.37374 + 2.83091i) q^{47} +(-1.52106 + 6.75917i) q^{48} +(-0.856210 + 4.85581i) q^{49} +(5.31200 - 2.73999i) q^{50} +(-1.37711 - 1.75146i) q^{51} +(-11.1730 + 5.10841i) q^{52} -1.79372i q^{53} +(2.29332 - 6.98145i) q^{54} +5.38825 q^{55} +(-4.06656 + 0.131753i) q^{56} +(-1.14395 - 7.96140i) q^{57} +(-5.66533 - 10.9833i) q^{58} +(3.57530 + 0.630422i) q^{59} +(-2.70862 - 1.39520i) q^{60} +(-5.77574 - 6.88325i) q^{61} +(-9.14585 + 1.16921i) q^{62} +(4.30677 + 0.274475i) q^{63} +(1.89625 + 7.77202i) q^{64} +(-0.938184 - 5.32071i) q^{65} +(8.70590 + 12.2224i) q^{66} +(2.22419 + 6.11091i) q^{67} +(-2.32344 - 1.10472i) q^{68} +(2.70148 - 1.44710i) q^{69} +(0.393822 - 1.74543i) q^{70} +(-4.87414 + 8.44226i) q^{71} +(-1.21158 - 8.39834i) q^{72} +(0.531852 + 0.921195i) q^{73} +(-5.71467 + 1.77831i) q^{74} +(-4.88146 + 5.45515i) q^{75} +(-5.26988 - 7.64756i) q^{76} +(-5.66456 + 6.75076i) q^{77} +(10.5533 - 10.7249i) q^{78} +(4.22154 + 1.53651i) q^{79} +(-3.51779 - 0.0527496i) q^{80} +(0.425025 + 8.98996i) q^{81} +(0.728072 - 1.73925i) q^{82} +(-1.85556 + 5.09810i) q^{83} +(4.59553 - 1.92680i) q^{84} +(0.727252 - 0.866705i) q^{85} +(2.89688 - 4.50979i) q^{86} +(11.2793 + 10.0931i) q^{87} +(15.2787 + 8.17324i) q^{88} +(4.01233 + 6.94955i) q^{89} +(3.70863 + 0.413458i) q^{90} +(7.65243 + 4.41813i) q^{91} +(2.05142 - 2.88348i) q^{92} +(9.95429 - 5.33223i) q^{93} +(0.295000 - 6.22136i) q^{94} +(3.83806 - 1.39694i) q^{95} +(-5.56411 - 8.06478i) q^{96} +(-0.649675 - 3.68449i) q^{97} +(-4.22418 - 5.54799i) q^{98} +(-15.2996 - 10.1830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

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