LMFDB - Embedded newform 81.2.g.a.34.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,2,Mod(4,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			34.2
Character	$\chi$	$=$	81.34
Dual form			81.2.g.a.31.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.685792 + 1.58984i) q^{2} +(0.844542 - 1.51220i) q^{3} +(-0.684812 - 0.725858i) q^{4} +(0.0800683 + 1.37472i) q^{5} +(1.82498 + 2.37974i) q^{6} +(3.19962 + 0.758323i) q^{7} +(-1.63042 + 0.593424i) q^{8} +(-1.57350 - 2.55423i) q^{9} +(-2.24050 - 0.815476i) q^{10} +(0.171563 + 0.112839i) q^{11} +(-1.67599 + 0.422555i) q^{12} +(-5.21927 - 0.610045i) q^{13} +(-3.39989 + 4.56684i) q^{14} +(2.14647 + 1.03993i) q^{15} +(0.290724 - 4.99154i) q^{16} +(3.88762 - 3.26210i) q^{17} +(5.13993 - 0.749946i) q^{18} +(-2.25026 - 1.88819i) q^{19} +(0.943020 - 0.999543i) q^{20} +(3.84895 - 4.19803i) q^{21} +(-0.297052 + 0.195374i) q^{22} +(-3.66075 + 0.867613i) q^{23} +(-0.479581 + 2.96669i) q^{24} +(3.08275 - 0.360321i) q^{25} +(4.54921 - 7.87946i) q^{26} +(-5.19140 + 0.222289i) q^{27} +(-1.64070 - 2.84178i) q^{28} +(-3.76701 - 5.05998i) q^{29} +(-3.12536 + 2.69938i) q^{30} +(-1.45734 + 4.86786i) q^{31} +(4.63538 + 2.32798i) q^{32} +(0.315526 - 0.164140i) q^{33} +(2.52014 + 8.41784i) q^{34} +(-0.786294 + 4.45930i) q^{35} +(-0.776460 + 2.89131i) q^{36} +(1.44468 + 8.19321i) q^{37} +(4.54514 - 2.28266i) q^{38} +(-5.33040 + 7.37737i) q^{39} +(-0.946337 - 2.19386i) q^{40} +(-1.09418 - 2.53659i) q^{41} +(4.03463 + 8.99820i) q^{42} +(-1.41783 + 0.712061i) q^{43} +(-0.0355834 - 0.201803i) q^{44} +(3.38537 - 2.36763i) q^{45} +(1.13114 - 6.41502i) q^{46} +(0.596924 + 1.99387i) q^{47} +(-7.30267 - 4.65519i) q^{48} +(3.40707 + 1.71109i) q^{49} +(-1.54127 + 5.14819i) q^{50} +(-1.64969 - 8.63385i) q^{51} +(3.13141 + 4.20621i) q^{52} +(4.51663 + 7.82303i) q^{53} +(3.20681 - 8.40596i) q^{54} +(-0.141385 + 0.244885i) q^{55} +(-5.66673 + 0.662345i) q^{56} +(-4.75576 + 1.80819i) q^{57} +(10.6280 - 2.51887i) q^{58} +(12.4036 - 8.15798i) q^{59} +(-0.715089 - 2.27019i) q^{60} +(1.03396 - 1.09593i) q^{61} +(-6.73971 - 5.65528i) q^{62} +(-3.09766 - 9.36579i) q^{63} +(0.780406 - 0.654838i) q^{64} +(0.420743 - 7.22388i) q^{65} +(0.0445720 + 0.614204i) q^{66} +(-8.00722 + 10.7556i) q^{67} +(-5.03012 - 0.587936i) q^{68} +(-1.77965 + 6.26851i) q^{69} +(-6.55035 - 4.30824i) q^{70} +(4.39214 + 1.59861i) q^{71} +(4.08121 + 3.23072i) q^{72} +(15.3008 - 5.56905i) q^{73} +(-14.0167 - 3.32202i) q^{74} +(2.05863 - 4.96604i) q^{75} +(0.170445 + 2.92643i) q^{76} +(0.463367 + 0.491140i) q^{77} +(-8.07332 - 13.5338i) q^{78} +(-0.588953 + 1.36535i) q^{79} +6.88524 q^{80} +(-4.04821 + 8.03816i) q^{81} +4.78316 q^{82} +(-5.64471 + 13.0859i) q^{83} +(-5.68298 + 0.0810685i) q^{84} +(4.79576 + 5.08320i) q^{85} +(-0.159730 - 2.74246i) q^{86} +(-10.8331 + 1.42312i) q^{87} +(-0.346680 - 0.0821648i) q^{88} +(-4.83016 + 1.75803i) q^{89} +(1.44251 + 7.00591i) q^{90} +(-16.2370 - 5.90980i) q^{91} +(3.13669 + 2.06303i) q^{92} +(6.13039 + 6.31490i) q^{93} +(-3.57930 - 0.418360i) q^{94} +(2.41556 - 3.24466i) q^{95} +(7.43514 - 5.04355i) q^{96} +(0.104394 - 1.79238i) q^{97} +(-5.05691 + 4.24325i) q^{98} +(0.0182623 - 0.615762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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 $

$2$	−0.685792	+	1.58984i	−0.484928	+	1.12419i	0.483601	+	0.875289i	$0.339329\pi$
$2$	−0.685792	+	1.58984i	−0.484928	+	1.12419i	−0.968529	+	0.248901i	$0.919931\pi$
$3$	0.844542	−	1.51220i	0.487596	−	0.873069i
$3$	0.844542	−	1.51220i	0.487596	−	0.873069i
$4$	−0.684812	−	0.725858i	−0.342406	−	0.362929i
$5$	0.0800683	+	1.37472i	0.0358076	+	0.614794i	0.967707	+	0.252077i	$0.0811136\pi$
$5$	0.0800683	+	1.37472i	0.0358076	+	0.614794i	−0.931900	+	0.362717i	$0.881849\pi$
$6$	1.82498	+	2.37974i	0.745046	+	0.971527i
$7$	3.19962	+	0.758323i	1.20934	+	0.286619i	0.785353	−	0.619048i	$-0.212481\pi$
$7$	3.19962	+	0.758323i	1.20934	+	0.286619i	0.423989	+	0.905667i	$0.360630\pi$
$8$	−1.63042	+	0.593424i	−0.576441	+	0.209807i
$9$	−1.57350	−	2.55423i	−0.524499	−	0.851411i
$10$	−2.24050	−	0.815476i	−0.708509	−	0.257876i
$11$	0.171563	+	0.112839i	0.0517281	+	0.0340221i	0.575110	−	0.818076i	$-0.304959\pi$
$11$	0.171563	+	0.112839i	0.0517281	+	0.0340221i	−0.523382	+	0.852098i	$0.675330\pi$
$12$	−1.67599	+	0.422555i	−0.483818	+	0.121981i
$13$	−5.21927	−	0.610045i	−1.44756	−	0.169196i	−0.644279	−	0.764791i	$-0.722842\pi$
$13$	−5.21927	−	0.610045i	−1.44756	−	0.169196i	−0.803285	+	0.595595i	$0.796916\pi$
$14$	−3.39989	+	4.56684i	−0.908658	+	1.22054i
$15$	2.14647	+	1.03993i	0.554217	+	0.268509i
$16$	0.290724	−	4.99154i	0.0726810	−	1.24788i
$17$	3.88762	−	3.26210i	0.942887	−	0.791176i	−0.0351981	−	0.999380i	$-0.511206\pi$
$17$	3.88762	−	3.26210i	0.942887	−	0.791176i	0.978085	+	0.208204i	$0.0667618\pi$
$18$	5.13993	−	0.749946i	1.21149	−	0.176764i
$19$	−2.25026	−	1.88819i	−0.516245	−	0.433181i	0.347075	−	0.937837i	$-0.387175\pi$
$19$	−2.25026	−	1.88819i	−0.516245	−	0.433181i	−0.863320	+	0.504656i	$0.831619\pi$
$20$	0.943020	−	0.999543i	0.210866	−	0.223505i
$21$	3.84895	−	4.19803i	0.839909	−	0.916084i
$22$	−0.297052	+	0.195374i	−0.0633317	+	0.0416539i
$23$	−3.66075	+	0.867613i	−0.763318	+	0.180910i	−0.593795	−	0.804616i	$-0.702371\pi$
$23$	−3.66075	+	0.867613i	−0.763318	+	0.180910i	−0.169523	+	0.985526i	$0.554223\pi$
$24$	−0.479581	+	2.96669i	−0.0978941	+	0.605574i
$25$	3.08275	−	0.360321i	0.616549	−	0.0720643i
$26$	4.54921	−	7.87946i	0.892173	−	1.54529i
$27$	−5.19140	+	0.222289i	−0.999085	+	0.0427795i
$28$	−1.64070	−	2.84178i	−0.310063	−	0.537045i
$29$	−3.76701	−	5.05998i	−0.699517	−	0.939614i	0.300382	−	0.953819i	$-0.402886\pi$
$29$	−3.76701	−	5.05998i	−0.699517	−	0.939614i	−0.999899	+	0.0142046i	$0.995478\pi$
$30$	−3.12536	+	2.69938i	−0.570610	+	0.492838i
$31$	−1.45734	+	4.86786i	−0.261746	+	0.874293i	0.721563	+	0.692349i	$0.243424\pi$
$31$	−1.45734	+	4.86786i	−0.261746	+	0.874293i	−0.983309	+	0.181944i	$0.941761\pi$
$32$	4.63538	+	2.32798i	0.819428	+	0.411532i
$33$	0.315526	−	0.164140i	0.0549261	−	0.0285731i
$34$	2.52014	+	8.41784i	0.432200	+	1.44365i
$35$	−0.786294	+	4.45930i	−0.132908	+	0.753759i
$36$	−0.776460	+	2.89131i	−0.129410	+	0.481884i
$37$	1.44468	+	8.19321i	0.237505	+	1.34696i	0.837274	+	0.546783i	$0.184148\pi$
$37$	1.44468	+	8.19321i	0.237505	+	1.34696i	−0.599770	+	0.800173i	$0.704741\pi$
$38$	4.54514	−	2.28266i	0.737319	−	0.370296i
$39$	−5.33040	+	7.37737i	−0.853547	+	1.18132i
$40$	−0.946337	−	2.19386i	−0.149629	−	0.346879i
$41$	−1.09418	−	2.53659i	−0.170882	−	0.396148i	0.811157	−	0.584829i	$-0.198838\pi$
$41$	−1.09418	−	2.53659i	−0.170882	−	0.396148i	−0.982039	+	0.188680i	$0.939579\pi$
$42$	4.03463	+	8.99820i	0.622557	+	1.38845i
$43$	−1.41783	+	0.712061i	−0.216217	+	0.108588i	−0.553611	−	0.832775i	$-0.686751\pi$
$43$	−1.41783	+	0.712061i	−0.216217	+	0.108588i	0.337394	+	0.941363i	$0.390454\pi$
$44$	−0.0355834	−	0.201803i	−0.00536439	−	0.0304230i
$45$	3.38537	−	2.36763i	0.504661	−	0.352946i
$46$	1.13114	−	6.41502i	0.166778	−	0.945843i
$47$	0.596924	+	1.99387i	0.0870703	+	0.290835i	0.990424	−	0.138062i	$-0.0440874\pi$
$47$	0.596924	+	1.99387i	0.0870703	+	0.290835i	−0.903353	+	0.428897i	$0.858902\pi$
$48$	−7.30267	−	4.65519i	−1.05405	−	0.671919i
$49$	3.40707	+	1.71109i	0.486724	+	0.244442i
$50$	−1.54127	+	5.14819i	−0.217968	+	0.728065i
$51$	−1.64969	−	8.63385i	−0.231003	−	1.20898i
$52$	3.13141	+	4.20621i	0.434248	+	0.583297i
$53$	4.51663	+	7.82303i	0.620407	+	1.07458i	0.989410	+	0.145148i	$0.0463659\pi$
$53$	4.51663	+	7.82303i	0.620407	+	1.07458i	−0.369003	+	0.929428i	$0.620301\pi$
$54$	3.20681	−	8.40596i	0.436392	−	1.14391i
$55$	−0.141385	+	0.244885i	−0.0190643	+	0.0330203i
$56$	−5.66673	+	0.662345i	−0.757248	+	0.0885096i
$57$	−4.75576	+	1.80819i	−0.629916	+	0.239500i
$58$	10.6280	−	2.51887i	1.39552	−	0.330744i
$59$	12.4036	−	8.15798i	1.61481	−	1.06208i	0.666136	−	0.745830i	$-0.267947\pi$
$59$	12.4036	−	8.15798i	1.61481	−	1.06208i	0.948676	−	0.316249i	$-0.102423\pi$
$60$	−0.715089	−	2.27019i	−0.0923176	−	0.293080i
$61$	1.03396	−	1.09593i	0.132385	−	0.140320i	−0.657790	−	0.753202i	$-0.728508\pi$
$61$	1.03396	−	1.09593i	0.132385	−	0.140320i	0.790175	+	0.612882i	$0.209990\pi$
$62$	−6.73971	−	5.65528i	−0.855943	−	0.718222i
$63$	−3.09766	−	9.36579i	−0.390268	−	1.17998i
$64$	0.780406	−	0.654838i	0.0975508	−	0.0818548i
$65$	0.420743	−	7.22388i	0.0521867	−	0.896012i
$66$	0.0445720	+	0.614204i	0.00548644	+	0.0756033i
$67$	−8.00722	+	10.7556i	−0.978238	+	1.31400i	−0.0289544	+	0.999581i	$0.509218\pi$
$67$	−8.00722	+	10.7556i	−0.978238	+	1.31400i	−0.949284	+	0.314421i	$0.898190\pi$
$68$	−5.03012	−	0.587936i	−0.609991	−	0.0712977i
$69$	−1.77965	+	6.26851i	−0.214245	+	0.754641i
$70$	−6.55035	−	4.30824i	−0.782917	−	0.514933i
$71$	4.39214	+	1.59861i	0.521252	+	0.189720i	0.589228	−	0.807967i	$-0.299432\pi$
$71$	4.39214	+	1.59861i	0.521252	+	0.189720i	−0.0679763	+	0.997687i	$0.521654\pi$
$72$	4.08121	+	3.23072i	0.480975	+	0.380744i
$73$	15.3008	−	5.56905i	1.79083	−	0.651808i	0.791662	−	0.610960i	$-0.209216\pi$
$73$	15.3008	−	5.56905i	1.79083	−	0.651808i	0.999165	−	0.0408483i	$-0.0130060\pi$
$74$	−14.0167	−	3.32202i	−1.62941	−	0.386176i
$75$	2.05863	−	4.96604i	0.237710	−	0.573429i
$76$	0.170445	+	2.92643i	0.0195514	+	0.335684i
$77$	0.463367	+	0.491140i	0.0528055	+	0.0559706i
$78$	−8.07332	−	13.5338i	−0.914124	−	1.53241i
$79$	−0.588953	+	1.36535i	−0.0662624	+	0.153613i	−0.948129	−	0.317885i	$-0.897027\pi$
$79$	−0.588953	+	1.36535i	−0.0662624	+	0.153613i	0.881867	+	0.471498i	$0.156287\pi$
$80$	6.88524			0.769794
$81$	−4.04821	+	8.03816i	−0.449801	+	0.893129i
$82$	4.78316			0.528211
$83$	−5.64471	+	13.0859i	−0.619587	+	1.43636i	0.262339	+	0.964976i	$0.415506\pi$
$83$	−5.64471	+	13.0859i	−0.619587	+	1.43636i	−0.881926	+	0.471388i	$0.843753\pi$
$84$	−5.68298	+	0.0810685i	−0.620063	+	0.00884530i
$85$	4.79576	+	5.08320i	0.520173	+	0.551351i
$86$	−0.159730	−	2.74246i	−0.0172241	−	0.295727i
$87$	−10.8331	+	1.42312i	−1.16143	+	0.152574i
$88$	−0.346680	−	0.0821648i	−0.0369562	−	0.00875879i
$89$	−4.83016	+	1.75803i	−0.511996	+	0.186351i	−0.585082	−	0.810974i	$-0.698938\pi$
$89$	−4.83016	+	1.75803i	−0.511996	+	0.186351i	0.0730859	+	0.997326i	$0.476715\pi$
$90$	1.44251	+	7.00591i	0.152054	+	0.738488i
$91$	−16.2370	−	5.90980i	−1.70210	−	0.619515i
$92$	3.13669	+	2.06303i	0.327022	+	0.215086i
$93$	6.13039	+	6.31490i	0.635692	+	0.654825i
$94$	−3.57930	−	0.418360i	−0.369177	−	0.0431506i
$95$	2.41556	−	3.24466i	0.247831	−	0.332895i
$96$	7.43514	−	5.04355i	0.758846	−	0.514756i
$97$	0.104394	−	1.79238i	0.0105996	−	0.181989i	−0.988853	−	0.148897i	$-0.952428\pi$
$97$	0.104394	−	1.79238i	0.0105996	−	0.181989i	0.999452	−	0.0330916i	$-0.0105353\pi$
$98$	−5.05691	+	4.24325i	−0.510825	+	0.428633i
$99$	0.0182623	−	0.615762i	0.00183543	−	0.0618864i
$100$	−2.37264	−	1.99088i	−0.237264	−	0.199088i
$101$	7.87467	−	8.34666i	0.783559	−	0.830524i	−0.205406	−	0.978677i	$-0.565851\pi$
$101$	7.87467	−	8.34666i	0.783559	−	0.830524i	0.988964	+	0.148153i	$0.0473329\pi$
$102$	14.8578	+	3.29827i	1.47114	+	0.326577i
$103$	−0.417908	+	0.274862i	−0.0411777	+	0.0270830i	−0.569931	−	0.821693i	$-0.693030\pi$
$103$	−0.417908	+	0.274862i	−0.0411777	+	0.0270830i	0.528753	+	0.848776i	$0.322660\pi$
$104$	8.87161	−	2.10261i	0.869933	−	0.206178i
$105$	6.07929	+	4.95510i	0.593278	+	0.483568i
$106$	−15.5349	+	1.81577i	−1.50888	+	0.176363i
$107$	−2.72183	+	4.71434i	−0.263129	+	0.455752i	−0.967072	−	0.254504i	$-0.918088\pi$
$107$	−2.72183	+	4.71434i	−0.263129	+	0.455752i	0.703943	+	0.710257i	$0.251421\pi$
$108$	3.71648	+	3.61599i	0.357618	+	0.347949i
$109$	−8.38980	−	14.5316i	−0.803597	−	1.39187i	−0.917234	−	0.398348i	$-0.869584\pi$
$109$	−8.38980	−	14.5316i	−0.803597	−	1.39187i	0.113637	−	0.993522i	$-0.463750\pi$
$110$	−0.292369	−	0.392720i	−0.0278763	−	0.0374444i
$111$	13.6099	+	4.73486i	1.29179	+	0.449413i
$112$	4.71540	−	15.7505i	0.445564	−	1.48829i
$113$	−7.89295	−	3.96399i	−0.742506	−	0.372901i	0.0369833	−	0.999316i	$-0.488225\pi$
$113$	−7.89295	−	3.96399i	−0.742506	−	0.372901i	−0.779490	+	0.626415i	$0.784521\pi$
$114$	0.386729	−	8.80096i	0.0362205	−	0.824286i
$115$	−1.48583	−	4.96303i	−0.138555	−	0.462805i
$116$	−1.09313	+	6.19945i	−0.101495	+	0.575604i
$117$	6.65431	+	14.2911i	0.615191	+	1.32121i
$118$	4.46363	+	25.3145i	0.410910	+	2.33039i
$119$	14.9126	−	7.48941i	1.36704	−	0.686553i
$120$	−4.11677	−	0.421752i	−0.375808	−	0.0385005i
$121$	−4.34018	−	10.0617i	−0.394561	−	0.914696i
$122$	1.03328	+	2.39542i	0.0935490	+	0.216871i
$123$	−4.75990	−	0.487639i	−0.429186	−	0.0439689i
$124$	4.53138	−	2.27574i	0.406930	−	0.204368i
$125$	1.93778	+	10.9897i	0.173321	+	0.982950i
$126$	17.0145	+	1.49818i	1.51577	+	0.133469i
$127$	−1.21170	+	6.87190i	−0.107521	+	0.609783i	0.882662	+	0.470008i	$0.155749\pi$
$127$	−1.21170	+	6.87190i	−0.107521	+	0.609783i	−0.990183	+	0.139775i	$0.955362\pi$
$128$	3.48126	+	11.6282i	0.307703	+	1.02780i
$129$	−0.120638	+	2.74541i	−0.0106216	+	0.241720i
$130$	11.1963	+	5.62299i	0.981980	+	0.493169i
$131$	−1.61749	+	5.40278i	−0.141320	+	0.472043i	−0.999120	−	0.0419413i	$-0.986646\pi$
$131$	−1.61749	+	5.40278i	−0.141320	+	0.472043i	0.857800	+	0.513984i	$0.171831\pi$
$132$	−0.335219	−	0.116622i	−0.0291770	−	0.0101507i
$133$	−5.76811	−	7.74792i	−0.500159	−	0.671829i
$134$	−11.6084	−	20.1063i	−1.00281	−	1.73692i
$135$	−0.721251	−	7.11892i	−0.0620754	−	0.612699i
$136$	−4.40265	+	7.62561i	−0.377524	+	0.653891i
$137$	1.10693	−	0.129381i	0.0945712	−	0.0110538i	−0.0686757	−	0.997639i	$-0.521877\pi$
$137$	1.10693	−	0.129381i	0.0945712	−	0.0110538i	0.163247	+	0.986585i	$0.447803\pi$
$138$	−8.74550	−	7.12826i	−0.744466	−	0.606798i
$139$	−4.62972	+	1.09726i	−0.392688	+	0.0930687i	−0.422216	−	0.906495i	$-0.638748\pi$
$139$	−4.62972	+	1.09726i	−0.392688	+	0.0930687i	0.0295282	+	0.999564i	$0.490600\pi$
$140$	3.77528	−	2.48304i	0.319069	−	0.209855i
$141$	3.51925	+	0.781234i	0.296374	+	0.0657918i
$142$	−5.55364	+	5.88651i	−0.466051	+	0.493985i
$143$	−0.826595	−	0.693595i	−0.0691233	−	0.0580014i
$144$	−13.2070	+	7.11160i	−1.10058	+	0.592633i
$145$	6.65443	−	5.58373i	0.552621	−	0.463704i
$146$	−1.63927	+	28.1452i	−0.135667	+	2.32931i
$147$	5.46493	−	3.70708i	0.450740	−	0.305755i
$148$	4.95777	−	6.65944i	0.407526	−	0.547403i
$149$	−7.62562	−	0.891307i	−0.624715	−	0.0730187i	−0.202155	−	0.979354i	$-0.564794\pi$
$149$	−7.62562	−	0.891307i	−0.624715	−	0.0730187i	−0.422560	+	0.906335i	$0.638868\pi$
$150$	6.48344	+	6.67857i	0.529370	+	0.545303i
$151$	−2.58058	−	1.69727i	−0.210005	−	0.138122i	0.440150	−	0.897924i	$-0.354925\pi$
$151$	−2.58058	−	1.69727i	−0.210005	−	0.138122i	−0.650154	+	0.759802i	$0.725296\pi$
$152$	4.78937	+	1.74319i	0.388469	+	0.141391i
$153$	−14.4493	−	4.79698i	−1.16816	−	0.387813i
$154$	−1.09861	+	0.399861i	−0.0885285	+	0.0322217i
$155$	−6.80863	−	1.61367i	−0.546882	−	0.129613i
$156$	9.00524	−	1.18300i	0.720996	−	0.0947154i
$157$	−0.356474	−	6.12042i	−0.0284497	−	0.488463i	−0.982197	−	0.187853i	$-0.939847\pi$
$157$	−0.356474	−	6.12042i	−0.0284497	−	0.488463i	0.953747	−	0.300609i	$-0.0971900\pi$
$158$	−1.76679	−	1.87269i	−0.140558	−	0.148983i
$159$	15.6445	−	0.223171i	1.24069	−	0.0176986i
$160$	−2.82917	+	6.55875i	−0.223666	+	0.518515i
$161$	−12.3709			−0.974965
$162$	−10.0032	−	11.9485i	−0.785926	−	0.938765i
$163$	−0.171894			−0.0134638			−0.00673188	−	0.999977i	$-0.502143\pi$
$163$	−0.171894			−0.0134638			−0.00673188	+	0.999977i	$0.502143\pi$
$164$	−1.09190	+	2.53130i	−0.0852628	+	0.197661i
$165$	0.250911	+	0.420618i	0.0195334	+	0.0327451i
$166$	−16.9335	−	17.9484i	−1.31429	−	1.39307i
$167$	0.0171142	+	0.293839i	0.00132434	+	0.0227380i	0.998906	−	0.0467721i	$-0.0148934\pi$
$167$	0.0171142	+	0.293839i	0.00132434	+	0.0227380i	−0.997581	+	0.0695100i	$0.977856\pi$
$168$	−3.78419	+	9.12861i	−0.291957	+	0.704287i
$169$	14.2190	+	3.36997i	1.09377	+	0.259228i
$170$	−11.3704	+	4.13849i	−0.872069	+	0.317407i
$171$	−1.28210	+	8.71875i	−0.0980447	+	0.666740i
$172$	1.48780	+	0.541516i	0.113444	+	0.0412902i
$173$	2.24492	+	1.47651i	0.170678	+	0.112257i	0.631974	−	0.774990i	$-0.282245\pi$
$173$	2.24492	+	1.47651i	0.170678	+	0.112257i	−0.461296	+	0.887246i	$0.652615\pi$
$174$	5.16672	−	18.1989i	0.391688	−	1.37966i
$175$	10.1369	+	1.18483i	0.766274	+	0.0895646i
$176$	0.613115	−	0.823556i	0.0462153	−	0.0620779i
$177$	−1.86114	−	25.6465i	−0.139892	−	1.92771i
$178$	0.517483	−	8.88485i	0.0387870	−	0.665947i
$179$	−1.83356	+	1.53854i	−0.137047	+	0.114996i	−0.708734	−	0.705476i	$-0.750733\pi$
$179$	−1.83356	+	1.53854i	−0.137047	+	0.114996i	0.571687	+	0.820471i	$0.306289\pi$
$180$	−4.03691	−	0.835913i	−0.300893	−	0.0623053i
$181$	12.8278	+	10.7638i	0.953481	+	0.800065i	0.979880	−	0.199586i	$-0.0639598\pi$
$181$	12.8278	+	10.7638i	0.953481	+	0.800065i	−0.0263995	+	0.999651i	$0.508404\pi$
$182$	20.5309	−	21.7615i	1.52185	−	1.61307i
$183$	−0.784049	−	2.48912i	−0.0579585	−	0.184001i
$184$	5.45369	−	3.58695i	0.402051	−	0.264433i
$185$	−11.1477	+	2.64205i	−0.819595	+	0.194248i
$186$	−14.2439	+	5.41566i	−1.04441	+	0.397095i
$187$	1.03506	−	0.120981i	0.0756912	−	0.00884704i
$188$	1.03848	−	1.79870i	0.0757391	−	0.131184i
$189$	−16.7790	−	3.22552i	−1.22050	−	0.234622i
$190$	3.50193	+	6.06553i	0.254057	+	0.440040i
$191$	8.47415	+	11.3828i	0.613168	+	0.823627i	0.994923	−	0.100636i	$-0.0320877\pi$
$191$	8.47415	+	11.3828i	0.613168	+	0.823627i	−0.381755	+	0.924263i	$0.624680\pi$
$192$	−0.331161	−	1.73317i	−0.0238995	−	0.125081i
$193$	1.19766	−	4.00046i	0.0862094	−	0.287959i	−0.904003	−	0.427525i	$-0.859386\pi$
$193$	1.19766	−	4.00046i	0.0862094	−	0.287959i	0.990213	+	0.139566i	$0.0445707\pi$
$194$	2.77802	+	1.39517i	0.199450	+	0.100168i
$195$	−10.5686	−	6.73711i	−0.756834	−	0.482455i
$196$	−1.09119	−	3.64483i	−0.0779421	−	0.260345i
$197$	3.59768	−	20.4035i	0.256324	−	1.45369i	−0.536326	−	0.844011i	$-0.680188\pi$
$197$	3.59768	−	20.4035i	0.256324	−	1.45369i	0.792650	−	0.609677i	$-0.208701\pi$
$198$	0.966442	+	0.451319i	0.0686820	+	0.0320738i
$199$	0.499478	+	2.83268i	0.0354071	+	0.200803i	0.997380	−	0.0723417i	$-0.0230472\pi$
$199$	0.499478	+	2.83268i	0.0354071	+	0.200803i	−0.961973	+	0.273145i	$0.911936\pi$
$200$	−4.81235	+	2.41685i	−0.340285	+	0.170897i
$201$	9.50214	+	21.1921i	0.670229	+	1.49477i
$202$	7.86951	+	18.2436i	0.553697	+	1.28361i
$203$	−8.21590	−	19.0466i	−0.576643	−	1.33681i
$204$	−5.13722	+	7.11000i	−0.359677	+	0.497800i
$205$	3.39949	−	1.70729i	0.237431	−	0.119242i
$206$	−0.150390	−	0.852907i	−0.0104782	−	0.0594248i
$207$	7.97626	+	7.98521i	0.554389	+	0.555010i
$208$	−4.56243	+	25.8748i	−0.316347	+	1.79409i
$209$	−0.173000	−	0.577859i	−0.0119666	−	0.0399714i
$210$	−12.0470	+	6.26696i	−0.831319	+	0.432461i
$211$	−9.48492	−	4.76351i	−0.652969	−	0.327933i	0.0912903	−	0.995824i	$-0.470901\pi$
$211$	−9.48492	−	4.76351i	−0.652969	−	0.327933i	−0.744259	+	0.667891i	$0.767197\pi$
$212$	2.58537	−	8.63574i	0.177564	−	0.593105i
$213$	6.12677	−	5.29171i	0.419799	−	0.362582i
$214$	−5.62846	−	7.56034i	−0.384754	−	0.516814i
$215$	−1.09241	−	1.89211i	−0.0745016	−	0.129041i
$216$	8.33224	−	3.44312i	0.566937	−	0.234275i
$217$	−8.35434	+	14.4701i	−0.567130	+	0.982298i
$218$	28.8566	−	3.37285i	1.95441	−	0.228438i
$219$	4.50068	−	27.8412i	0.304128	−	1.88134i
$220$	0.274574	−	0.0650752i	0.0185118	−	0.00438737i
$221$	−22.2806	+	14.6542i	−1.49875	+	0.985746i
$222$	−16.8612	+	18.3905i	−1.13165	+	1.23429i
$223$	16.2468	−	17.2206i	1.08797	−	1.15318i	0.100568	−	0.994930i	$-0.467934\pi$
$223$	16.2468	−	17.2206i	1.08797	−	1.15318i	0.987399	−	0.158248i	$-0.0505844\pi$
$224$	13.0661	+	10.9638i	0.873015	+	0.732547i
$225$	−5.77104	−	7.30709i	−0.384736	−	0.487139i
$226$	11.7150	−	9.83009i	0.779273	−	0.653888i
$227$	−0.0266893	+	0.458237i	−0.00177143	+	0.0304143i	−0.999078	−	0.0429309i	$-0.986330\pi$
$227$	−0.0266893	+	0.458237i	−0.00177143	+	0.0304143i	0.997307	+	0.0733452i	$0.0233675\pi$
$228$	4.56929	+	2.21374i	0.302609	+	0.146609i
$229$	9.55048	−	12.8285i	0.631113	−	0.847732i	−0.365427	−	0.930840i	$-0.619077\pi$
$229$	9.55048	−	12.8285i	0.631113	−	0.847732i	0.996541	+	0.0831075i	$0.0264845\pi$
$230$	8.90942	+	1.04136i	0.587470	+	0.0686654i
$231$	1.13403	−	0.285915i	0.0746140	−	0.0188118i
$232$	9.14453	+	6.01445i	0.600368	+	0.394868i
$233$	−7.46875	−	2.71840i	−0.489294	−	0.178089i	0.0855784	−	0.996331i	$-0.472726\pi$
$233$	−7.46875	−	2.71840i	−0.489294	−	0.178089i	−0.574873	+	0.818243i	$0.694948\pi$
$234$	−27.2841	+	0.778583i	−1.78362	+	0.0508976i
$235$	−2.69321	+	0.980249i	−0.175686	+	0.0639444i
$236$	−14.4157	−	3.41658i	−0.938381	−	0.222400i
$237$	1.56728	+	2.04371i	0.101806	+	0.132753i
$238$	1.68003	+	28.8450i	0.108900	+	1.86974i
$239$	14.5603	+	15.4330i	0.941828	+	0.998280i	1.00000		2.70339e-5i	$-8.60516e-6\pi$
$239$	14.5603	+	15.4330i	0.941828	+	0.998280i	−0.0581718	+	0.998307i	$0.518527\pi$
$240$	5.81488	−	10.4119i	0.375349	−	0.672083i
$241$	−7.15707	+	16.5920i	−0.461028	+	1.06878i	0.516177	+	0.856482i	$0.327355\pi$
$241$	−7.15707	+	16.5920i	−0.461028	+	1.06878i	−0.977205	+	0.212300i	$0.931905\pi$
$242$	18.9729			1.21963
$243$	8.73643	+	12.9103i	0.560442	+	0.828194i
$244$	−1.50356			−0.0962556
$245$	−2.07948	+	4.82077i	−0.132853	+	0.307988i
$246$	4.03957	−	7.23309i	0.257554	−	0.461165i
$247$	10.5928	+	11.2277i	0.674005	+	0.714404i
$248$	−0.512628	−	8.80148i	−0.0325519	−	0.558894i
$249$	15.0213	+	19.5875i	0.951937	+	1.24131i
$250$	−18.8008	−	4.45588i	−1.18907	−	0.281815i
$251$	7.58786	−	2.76176i	0.478942	−	0.174321i	−0.0912569	−	0.995827i	$-0.529088\pi$
$251$	7.58786	−	2.76176i	0.478942	−	0.174321i	0.570199	+	0.821507i	$0.306866\pi$
$252$	−4.67692	+	8.66226i	−0.294618	+	0.545671i
$253$	−0.725947	−	0.264223i	−0.0456399	−	0.0166116i
$254$	−10.0943	−	6.63911i	−0.633371	−	0.416575i
$255$	11.7370	−	2.95916i	0.735002	−	0.185310i
$256$	−18.8508	−	2.20334i	−1.17817	−	0.137709i
$257$	9.87311	−	13.2619i	0.615868	−	0.827254i	−0.379317	−	0.925267i	$-0.623841\pi$
$257$	9.87311	−	13.2619i	0.615868	−	0.827254i	0.995185	+	0.0980126i	$0.0312485\pi$
$258$	−4.28204	−	2.07458i	−0.266588	−	0.129157i
$259$	−1.59067	+	27.3107i	−0.0988392	+	1.69700i
$260$	−5.53164	+	4.64160i	−0.343058	+	0.287860i
$261$	−6.99697	+	17.5837i	−0.433101	+	1.08840i
$262$	−7.48032	−	6.27673i	−0.462135	−	0.387778i
$263$	0.0115217	−	0.0122123i	0.000710459	−	0.000753043i	−0.727018	−	0.686618i	$-0.759094\pi$
$263$	0.0115217	−	0.0122123i	0.000710459	−	0.000753043i	0.727729	+	0.685865i	$0.240576\pi$
$264$	−0.417036	+	0.454859i	−0.0256668	+	0.0279946i
$265$	−10.3928	+	6.83548i	−0.638427	+	0.419900i
$266$	16.2737	−	3.85694i	0.997805	−	0.236484i
$267$	−1.42077	+	8.78890i	−0.0869498	+	0.537872i
$268$	13.2905	−	1.55343i	0.811844	−	0.0948909i
$269$	−3.16338	+	5.47913i	−0.192874	+	0.334068i	−0.946202	−	0.323578i	$-0.895114\pi$
$269$	−3.16338	+	5.47913i	−0.192874	+	0.334068i	0.753327	+	0.657646i	$0.228448\pi$
$270$	11.8126	+	3.73542i	0.718892	+	0.227330i
$271$	−9.98751	−	17.2989i	−0.606698	−	1.05083i	−0.991781	−	0.127950i	$-0.959160\pi$
$271$	−9.98751	−	17.2989i	−0.606698	−	1.05083i	0.385082	−	0.922882i	$-0.374173\pi$
$272$	−15.1527	−	20.3536i	−0.918766	−	1.23412i
$273$	−22.6497	+	19.5626i	−1.37082	+	1.18398i
$274$	−0.553426	+	1.84857i	−0.0334337	+	0.111676i
$275$	0.569542	+	0.286035i	0.0343447	+	0.0172486i
$276$	5.76878	−	3.00098i	0.347240	−	0.180638i
$277$	−1.79418	−	5.99296i	−0.107802	−	0.360082i	0.887019	−	0.461734i	$-0.152772\pi$
$277$	−1.79418	−	5.99296i	−0.107802	−	0.360082i	−0.994820	+	0.101652i	$0.967587\pi$
$278$	1.43055	−	8.11303i	0.0857985	−	0.486587i
$279$	14.7268	−	3.93718i	0.881668	−	0.235713i
$280$	−1.36427	−	7.73713i	−0.0815304	−	0.462382i
$281$	−5.20235	+	2.61272i	−0.310346	+	0.155862i	−0.597154	−	0.802126i	$-0.703702\pi$
$281$	−5.20235	+	2.61272i	−0.310346	+	0.155862i	0.286808	+	0.957988i	$0.407406\pi$
$282$	−3.65551	+	5.05930i	−0.217683	+	0.301277i
$283$	−3.40508	−	7.89386i	−0.202411	−	0.469241i	0.786530	−	0.617552i	$-0.211876\pi$
$283$	−3.40508	−	7.89386i	−0.202411	−	0.469241i	−0.988941	+	0.148311i	$0.952616\pi$
$284$	−1.84743	−	4.28282i	−0.109625	−	0.254139i
$285$	−2.86654	−	6.39306i	−0.169799	−	0.378692i
$286$	1.66958	−	0.838495i	0.0987244	−	0.0495812i
$287$	−1.57739	−	8.94585i	−0.0931106	−	0.528057i
$288$	−1.34757	−	15.5029i	−0.0794066	−	0.913518i
$289$	1.52028	−	8.62194i	0.0894282	−	0.507173i
$290$	4.31371	+	14.4088i	0.253310	+	0.846114i
$291$	−2.62228	−	1.67161i	−0.153721	−	0.0979913i
$292$	−14.5205	−	7.29248i	−0.849750	−	0.426760i
$293$	−1.84582	+	6.16547i	−0.107834	+	0.360190i	−0.994826	−	0.101594i	$-0.967606\pi$
$293$	−1.84582	+	6.16547i	−0.107834	+	0.360190i	0.886992	+	0.461785i	$0.152791\pi$
$294$	2.14588	+	11.2307i	0.125150	+	0.654986i
$295$	12.2081	+	16.3983i	0.710782	+	0.954746i
$296$	−7.21749	−	12.5011i	−0.419508	−	0.726610i
$297$	−0.915732	−	0.547653i	−0.0531362	−	0.0317781i
$298$	6.64663	−	11.5123i	0.385029	−	0.666889i
$299$	19.6357	−	2.29508i	1.13556	−	0.132728i
$300$	−5.01441	+	1.90653i	−0.289507	+	0.110073i
$301$	−5.07649	+	1.20315i	−0.292604	+	0.0693484i
$302$	4.46814	−	2.93874i	0.257113	−	0.169106i
$303$	−5.97133	−	18.9572i	−0.343044	−	1.08906i
$304$	−10.0792	+	10.6833i	−0.578081	+	0.612730i
$305$	1.58939	+	1.33366i	0.0910082	+	0.0763649i
$306$	17.5357	−	19.6825i	1.00245	−	1.12517i
$307$	18.8060	−	15.7801i	1.07332	−	0.900619i	0.0779670	−	0.996956i	$-0.475157\pi$
$307$	18.8060	−	15.7801i	1.07332	−	0.900619i	0.995349	+	0.0963370i	$0.0307127\pi$
$308$	0.0391790	−	0.672677i	0.00223243	−	0.0383293i
$309$	0.0627062	+	0.864093i	0.00356723	+	0.0491565i
$310$	7.23480	−	9.71802i	0.410909	−	0.551946i
$311$	12.8990	+	1.50767i	0.731433	+	0.0854923i	0.473653	−	0.880711i	$-0.342935\pi$
$311$	12.8990	+	1.50767i	0.731433	+	0.0854923i	0.257780	+	0.966204i	$0.417009\pi$
$312$	4.31288	−	15.1914i	0.244169	−	0.860043i
$313$	−4.36800	−	2.87288i	−0.246894	−	0.162385i	0.420031	−	0.907510i	$-0.362019\pi$
$313$	−4.36800	−	2.87288i	−0.246894	−	0.162385i	−0.666925	+	0.745125i	$0.732390\pi$
$314$	9.97498	+	3.63060i	0.562921	+	0.204886i
$315$	12.6273	−	5.00832i	0.711468	−	0.282187i
$316$	1.39437	−	0.507509i	0.0784394	−	0.0285496i
$317$	−29.7332	−	7.04690i	−1.66998	−	0.395793i	−0.716582	−	0.697502i	$-0.754295\pi$
$317$	−29.7332	−	7.04690i	−1.66998	−	0.395793i	−0.953400	+	0.301709i	$0.902443\pi$
$318$	−10.3741	+	25.0253i	−0.581748	+	1.40335i
$319$	−0.0753184	−	1.29317i	−0.00421702	−	0.0724035i
$320$	0.962705	+	1.02041i	0.0538169	+	0.0570425i
$321$	4.83033	+	8.09740i	0.269603	+	0.451953i
$322$	8.48388	−	19.6678i	0.472788	−	1.09605i
$323$	−14.9076			−0.829483
$324$	8.60682	−	2.56621i	0.478157	−	0.142567i
$325$	−16.3095			−0.904688
$326$	0.117883	−	0.273284i	0.00652896	−	0.0151358i
$327$	−29.0602	+	0.414548i	−1.60703	+	0.0229245i
$328$	3.28924	+	3.48639i	0.181618	+	0.192504i
$329$	0.397934	+	6.83227i	0.0219388	+	0.376675i
$330$	−0.840789	+	0.110452i	−0.0462839	+	0.00608020i
$331$	3.09786	+	0.734205i	0.170274	+	0.0403556i	0.314868	−	0.949135i	$-0.398040\pi$
$331$	3.09786	+	0.734205i	0.170274	+	0.0403556i	−0.144595	+	0.989491i	$0.546188\pi$
$332$	13.3641	−	4.86412i	0.733449	−	0.266953i
$333$	18.6542	−	16.5821i	1.02224	−	0.908691i
$334$	−0.478896	−	0.174304i	−0.0262040	−	0.00953748i
$335$	−15.4270	−	10.1465i	−0.842868	−	0.554363i
$336$	−19.8356	−	20.4326i	−1.08212	−	1.11469i
$337$	32.5501	+	3.80456i	1.77312	+	0.207247i	0.938900	−	0.344191i	$-0.111847\pi$
$337$	32.5501	+	3.80456i	1.77312	+	0.207247i	0.834216	+	0.551438i	$0.185921\pi$
$338$	−15.1090	+	20.2949i	−0.821821	+	1.10390i
$339$	−12.6603	+	8.58797i	−0.687611	+	0.466434i
$340$	0.405495	−	6.96208i	0.0219910	−	0.377572i
$341$	−0.799307	+	0.670699i	−0.0432849	+	0.0363204i
$342$	−12.9822	−	8.01759i	−0.701997	−	0.433542i
$343$	−8.02888	−	6.73703i	−0.433519	−	0.363765i
$344$	1.88910	−	2.00233i	0.101854	−	0.107959i
$345$	−8.75995	−	1.94461i	−0.471620	−	0.104694i
$346$	−3.88696	+	2.55649i	−0.208964	+	0.137438i
$347$	−21.8032	+	5.16746i	−1.17046	+	0.277404i	−0.769472	−	0.638681i	$-0.779481\pi$
$347$	−21.8032	+	5.16746i	−1.17046	+	0.277404i	−0.400986	+	0.916084i	$0.631332\pi$
$348$	8.45162	+	6.88873i	0.453054	+	0.369274i
$349$	−21.9185	+	2.56190i	−1.17327	+	0.137136i	−0.680315	−	0.732919i	$-0.738157\pi$
$349$	−21.9185	+	2.56190i	−1.17327	+	0.137136i	−0.492955	+	0.870055i	$0.664083\pi$
$350$	−8.83546	+	15.3035i	−0.472275	+	0.818005i
$351$	27.2309	+	2.00680i	1.45348	+	0.107115i
$352$	0.532573	+	0.922444i	0.0283863	+	0.0491664i
$353$	−6.51907	−	8.75663i	−0.346975	−	0.466068i	0.594039	−	0.804436i	$-0.297533\pi$
$353$	−6.51907	−	8.75663i	−0.346975	−	0.466068i	−0.941014	+	0.338368i	$0.890125\pi$
$354$	42.0503	+	14.6292i	2.23495	+	0.777536i
$355$	−1.84597	+	6.16597i	−0.0979739	+	0.327256i
$356$	4.58383	+	2.30209i	0.242943	+	0.122010i
$357$	1.26886	−	28.8760i	0.0671553	−	1.52828i
$358$	−1.18860	−	3.97019i	−0.0628194	−	0.209831i
$359$	−4.30460	+	24.4126i	−0.227188	+	1.28845i	0.631269	+	0.775564i	$0.282534\pi$
$359$	−4.30460	+	24.4126i	−0.227188	+	1.28845i	−0.858457	+	0.512885i	$0.828577\pi$
$360$	−4.11456	+	5.86920i	−0.216856	+	0.309334i
$361$	−1.80092	−	10.2135i	−0.0947851	−	0.537553i
$362$	−25.9099	+	13.0125i	−1.36180	+	0.683919i
$363$	−18.8807	−	1.93428i	−0.990980	−	0.101523i
$364$	6.82964	+	15.8329i	0.357971	+	0.829869i
$365$	8.88099	+	20.5885i	0.464853	+	1.07765i
$366$	4.49500	+	0.460501i	0.234958	+	0.0240708i
$367$	−11.4819	+	5.76642i	−0.599350	+	0.301005i	−0.722487	−	0.691385i	$-0.757001\pi$
$367$	−11.4819	+	5.76642i	−0.599350	+	0.301005i	0.123137	+	0.992390i	$0.460705\pi$
$368$	3.26645	+	18.5250i	0.170276	+	0.965681i
$369$	−4.75735	+	6.78610i	−0.247658	+	0.353270i
$370$	3.44455	−	19.5350i	0.179074	−	1.01558i
$371$	8.51910	+	28.4558i	0.442290	+	1.47735i
$372$	0.385558	−	8.77431i	0.0199903	−	0.454927i
$373$	1.99340	+	1.00112i	0.103214	+	0.0518362i	0.499657	−	0.866223i	$-0.333459\pi$
$373$	1.99340	+	1.00112i	0.103214	+	0.0518362i	−0.396443	+	0.918059i	$0.629756\pi$
$374$	−0.517496	+	1.72856i	−0.0267591	+	0.0893815i
$375$	18.2552	+	6.35095i	0.942694	+	0.327962i
$376$	−2.15645	−	2.89661i	−0.111210	−	0.149381i
$377$	16.5742	+	28.7074i	0.853617	+	1.47851i
$378$	16.6350	−	24.4640i	0.855612	−	1.25829i
$379$	3.67947	−	6.37302i	0.189001	−	0.327360i	−0.755916	−	0.654668i	$-0.772808\pi$
$379$	3.67947	−	6.37302i	0.189001	−	0.327360i	0.944918	+	0.327308i	$0.106142\pi$
$380$	−4.00937	+	0.468628i	−0.205676	+	0.0240401i
$381$	9.36836	+	7.63594i	0.479955	+	0.391201i
$382$	−23.9083	+	5.66638i	−1.22326	+	0.289917i
$383$	−12.0779	+	7.94378i	−0.617154	+	0.405908i	−0.819233	−	0.573461i	$-0.805600\pi$
$383$	−12.0779	+	7.94378i	−0.617154	+	0.405908i	0.202079	+	0.979369i	$0.435230\pi$
$384$	20.5243	+	4.55616i	1.04738	+	0.232505i
$385$	−0.638079	+	0.676324i	−0.0325195	+	0.0344687i
$386$	5.53876	+	4.64757i	0.281916	+	0.236555i
$387$	4.04972	+	2.50104i	0.205859	+	0.127135i
$388$	−1.37251	+	1.15167i	−0.0696784	+	0.0584671i
$389$	0.494471	−	8.48974i	0.0250707	−	0.430447i	−0.962297	−	0.272001i	$-0.912315\pi$
$389$	0.494471	−	8.48974i	0.0250707	−	0.430447i	0.987368	−	0.158446i	$-0.0506484\pi$
$390$	17.9588	−	12.1822i	0.909381	−	0.616869i
$391$	−11.4014	+	15.3147i	−0.576592	+	0.774497i
$392$	−6.57036	−	0.767965i	−0.331853	−	0.0387881i
$393$	6.80405	+	7.00883i	0.343219	+	0.353549i
$394$	29.9711	+	19.7123i	1.50992	+	0.993091i
$395$	−1.92413	−	0.700325i	−0.0968133	−	0.0352372i
$396$	−0.459462	+	0.408425i	−0.0230888	+	0.0205241i
$397$	−5.16106	+	1.87847i	−0.259026	+	0.0942779i	−0.468269	−	0.883586i	$-0.655122\pi$
$397$	−5.16106	+	1.87847i	−0.259026	+	0.0942779i	0.209243	+	0.977864i	$0.432900\pi$
$398$	−4.84606	−	1.14854i	−0.242911	−	0.0575710i
$399$	−16.5878	+	2.17910i	−0.830429	+	0.109091i
$400$	−0.902330	−	15.4924i	−0.0451165	−	0.774620i
$401$	−6.45676	−	6.84377i	−0.322435	−	0.341762i	0.545799	−	0.837916i	$-0.316226\pi$
$401$	−6.45676	−	6.84377i	−0.322435	−	0.341762i	−0.868234	+	0.496155i	$0.834745\pi$
$402$	−40.2086	+	0.573581i	−2.00542	+	0.0286076i
$403$	10.5759	−	24.5176i	0.526821	−	1.22131i
$404$	−11.4512			−0.569716
$405$	−11.3744	−	4.92155i	−0.565196	−	0.244554i
$406$	35.9155			1.78246
$407$	−0.676656	+	1.56867i	−0.0335406	+	0.0777558i
$408$	7.81323	+	13.0978i	0.386812	+	0.648439i
$409$	10.5830	+	11.2174i	0.523297	+	0.554663i	0.934077	−	0.357072i	$-0.116225\pi$
$409$	10.5830	+	11.2174i	0.523297	+	0.554663i	−0.410780	+	0.911735i	$0.634743\pi$
$410$	0.382979	+	6.57550i	0.0189140	+	0.324741i
$411$	0.739196	−	1.78316i	0.0364619	−	0.0879570i
$412$	0.485699	+	0.115113i	0.0239287	+	0.00567120i
$413$	45.8732	−	16.6965i	2.25727	−	0.821580i
$414$	−18.1653	+	7.20482i	−0.892776	+	0.354098i
$415$	−18.4414	−	6.71212i	−0.905253	−	0.329485i
$416$	−22.7731	−	14.9781i	−1.11654	−	0.734363i
$417$	−2.25071	+	7.92775i	−0.110218	+	0.388224i
$418$	1.03735	+	0.121249i	0.0507384	+	0.00593046i
$419$	14.7527	−	19.8163i	0.720715	−	0.968088i	−0.279254	−	0.960217i	$-0.590087\pi$
$419$	14.7527	−	19.8163i	0.720715	−	0.968088i	0.999969	−	0.00787086i	$-0.00250540\pi$
$420$	−0.566473	−	7.80601i	−0.0276410	−	0.380894i
$421$	0.0108029	−	0.185479i	0.000526502	−	0.00903969i	−0.998035	−	0.0626641i	$-0.980040\pi$
$421$	0.0108029	−	0.185479i	0.000526502	−	0.00903969i	0.998561	+	0.0536244i	$0.0170774\pi$
$422$	14.0779	−	11.8128i	0.685302	−	0.575037i
$423$	4.15354	−	4.66203i	0.201952	−	0.226675i
$424$	−12.0064	−	10.0746i	−0.583082	−	0.489264i
$425$	10.8092	−	11.4570i	0.524321	−	0.555748i
$426$	4.21131	+	13.3696i	0.204038	+	0.647760i
$427$	4.13935	−	2.72249i	0.200317	−	0.131751i
$428$	5.28588	−	1.25278i	0.255503	−	0.0605552i
$429$	−1.74695	+	0.664206i	−0.0843435	+	0.0320682i
$430$	3.75732	−	0.439168i	0.181194	−	0.0211785i
$431$	7.27612	−	12.6026i	0.350478	−	0.607046i	−0.635855	−	0.771808i	$-0.719352\pi$
$431$	7.27612	−	12.6026i	0.350478	−	0.607046i	0.986333	+	0.164762i	$0.0526857\pi$
$432$	−0.399700	+	25.9777i	−0.0192306	+	1.24985i
$433$	17.3096	+	29.9811i	0.831846	+	1.44080i	0.896573	+	0.442897i	$0.146049\pi$
$433$	17.3096	+	29.9811i	0.831846	+	1.44080i	−0.0647264	+	0.997903i	$0.520617\pi$
$434$	−17.2759	−	23.2056i	−0.829272	−	1.11391i
$435$	−2.82377	−	14.7785i	−0.135390	−	0.708576i
$436$	−4.80242	+	16.0412i	−0.229994	+	0.768233i
$437$	9.87585	+	4.95984i	0.472426	+	0.237261i
$438$	41.1767	+	26.2487i	1.96750	+	1.25421i
$439$	0.563799	+	1.88322i	0.0269087	+	0.0898812i	0.970389	−	0.241547i	$-0.0776548\pi$
$439$	0.563799	+	1.88322i	0.0269087	+	0.0898812i	−0.943480	+	0.331428i	$0.892470\pi$
$440$	0.0851954	−	0.483167i	0.00406153	−	0.0230341i
$441$	−0.990485	−	11.3948i	−0.0471660	−	0.542612i
$442$	−8.01800	−	45.4724i	−0.381378	−	2.16290i
$443$	28.4252	−	14.2757i	1.35052	−	0.678257i	0.381300	−	0.924451i	$-0.375477\pi$
$443$	28.4252	−	14.2757i	1.35052	−	0.678257i	0.969220	+	0.246195i	$0.0791803\pi$
$444$	−5.88337	−	13.1213i	−0.279212	−	0.622710i
$445$	−2.80355	−	6.49935i	−0.132901	−	0.308099i
$446$	16.2362	+	37.6397i	0.768805	+	1.78229i
$447$	−7.78799	+	10.7787i	−0.368359	+	0.509816i
$448$	2.99358	−	1.50343i	0.141433	−	0.0710305i
$449$	−5.17251	−	29.3348i	−0.244106	−	1.38439i	−0.822560	−	0.568679i	$-0.807455\pi$
$449$	−5.17251	−	29.3348i	−0.244106	−	1.38439i	0.578454	−	0.815715i	$-0.303656\pi$
$450$	15.5749	−	4.16392i	0.734206	−	0.196289i
$451$	0.0985049	−	0.558649i	0.00463841	−	0.0263057i
$452$	2.52789	+	8.44375i	0.118902	+	0.397160i
$453$	−4.74603	+	2.46893i	−0.222988	+	0.116001i
$454$	−0.710223	−	0.356687i	−0.0333324	−	0.0167402i
$455$	6.82425	−	22.7946i	0.319926	−	1.06863i
$456$	6.68087	−	5.77029i	0.312860	−	0.270218i
$457$	7.61163	+	10.2242i	0.356057	+	0.478267i	0.943676	−	0.330870i	$-0.107342\pi$
$457$	7.61163	+	10.2242i	0.356057	+	0.478267i	−0.587619	+	0.809137i	$0.699935\pi$
$458$	13.8457	+	23.9815i	0.646968	+	1.12058i
$459$	−19.4571	+	17.7990i	−0.908178	+	0.830788i
$460$	−2.58494	+	4.47725i	−0.120523	+	0.208753i
$461$	−20.5283	+	2.39941i	−0.956097	+	0.111752i	−0.579810	−	0.814752i	$-0.696873\pi$
$461$	−20.5283	+	2.39941i	−0.956097	+	0.111752i	−0.376287	+	0.926503i	$0.622799\pi$
$462$	−0.323152	+	1.99902i	−0.0150344	+	0.0930027i
$463$	−16.2014	+	3.83980i	−0.752943	+	0.178451i	−0.589127	−	0.808040i	$-0.700528\pi$
$463$	−16.2014	+	3.83980i	−0.752943	+	0.178451i	−0.163816	+	0.986491i	$0.552380\pi$
$464$	−26.3522	+	17.3321i	−1.22337	+	0.804624i
$465$	−8.19037	+	8.93320i	−0.379819	+	0.414267i
$466$	9.44385	−	10.0099i	0.437478	−	0.463700i
$467$	−22.4416	−	18.8308i	−1.03848	−	0.871384i	−0.0466403	−	0.998912i	$-0.514851\pi$
$467$	−22.4416	−	18.8308i	−1.03848	−	0.871384i	−0.991835	+	0.127527i	$0.959296\pi$
$468$	5.81638	−	14.6168i	0.268862	−	0.675663i
$469$	−33.7762	+	28.3416i	−1.55964	+	1.30870i
$470$	0.288540	−	4.95403i	0.0133093	−	0.228513i
$471$	−9.55636	−	4.62989i	−0.440334	−	0.213334i
$472$	−15.3819	+	20.6615i	−0.708012	+	0.951025i
$473$	−0.323595	−	0.0378228i	−0.0148789	−	0.00173909i
$474$	−4.32401	+	1.09018i	−0.198608	+	0.0500735i
$475$	−7.61734	−	5.01000i	−0.349507	−	0.229875i
$476$	−15.6486	−	5.69562i	−0.717252	−	0.261059i
$477$	12.8749	−	23.8461i	0.589503	−	1.09184i
$478$	−34.5215	+	12.5648i	−1.57897	+	0.574700i
$479$	21.7592	+	5.15702i	0.994201	+	0.235630i	0.695351	−	0.718670i	$-0.255249\pi$
$479$	21.7592	+	5.15702i	0.994201	+	0.235630i	0.298850	+	0.954300i	$0.403397\pi$
$480$	7.52880	+	9.81741i	0.343641	+	0.448102i
$481$	−2.54197	−	43.6439i	−0.115904	−	1.98999i
$482$	−21.4704	−	22.7573i	−0.977949	−	1.03657i
$483$	−10.4478	+	18.7073i	−0.475389	+	0.851212i
$484$	−4.33113	+	10.0407i	−0.196870	+	0.456395i
$485$	2.47238			0.112265
$486$	−26.5167	+	5.03581i	−1.20282	+	0.228429i
$487$	3.73936			0.169447			0.0847233	−	0.996405i	$-0.472999\pi$
$487$	3.73936			0.169447			0.0847233	+	0.996405i	$0.472999\pi$
$488$	−1.03544	+	2.40041i	−0.0468720	+	0.108661i
$489$	−0.145171	+	0.259938i	−0.00656488	+	0.0117548i
$490$	−6.23819	−	6.61209i	−0.281813	−	0.298704i
$491$	0.0701629	+	1.20465i	0.00316641	+	0.0543651i	0.999521	−	0.0309407i	$-0.00985030\pi$
$491$	0.0701629	+	1.20465i	0.00316641	+	0.0543651i	−0.996355	+	0.0853058i	$0.972813\pi$
$492$	2.90568	+	3.78896i	0.130998	+	0.170819i
$493$	−31.1509	−	7.38290i	−1.40297	−	0.332509i
$494$	−25.1148	+	9.14105i	−1.12997	+	0.411275i
$495$	0.847963	−	0.0241976i	0.0381131	−	0.00108760i
$496$	23.8744	+	8.68957i	1.07199	+	0.390173i
$497$	12.8409	+	8.44560i	0.575994	+	0.378837i
$498$	−41.4426	+	10.4486i	−1.85709	+	0.468212i
$499$	−3.31533	−	0.387506i	−0.148415	−	0.0173472i	0.0415612	−	0.999136i	$-0.486767\pi$
$499$	−3.31533	−	0.387506i	−0.148415	−	0.0173472i	−0.189976	+	0.981789i	$0.560841\pi$
$500$	6.64995	−	8.93244i	0.297395	−	0.399471i
$501$	0.458798	+	0.222280i	0.0204976	+	0.00993072i
$502$	−0.812933	+	13.9575i	−0.0362830	+	0.622954i
$503$	18.7108	−	15.7002i	0.834274	−	0.700039i	−0.121994	−	0.992531i	$-0.538929\pi$
$503$	18.7108	−	15.7002i	0.834274	−	0.700039i	0.956268	+	0.292492i	$0.0944844\pi$
$504$	10.6084	+	13.4319i	0.472534	+	0.598306i
$505$	12.1048	+	10.1572i	0.538658	+	0.451988i
$506$	0.917923	−	0.972941i	0.0408066	−	0.0432525i
$507$	17.1046	−	18.6559i	0.759642	−	0.828538i
$508$	5.81781	−	3.82643i	0.258124	−	0.169771i
$509$	30.1051	−	7.13503i	1.33438	−	0.316255i	0.499325	−	0.866415i	$-0.333582\pi$
$509$	30.1051	−	7.13503i	1.33438	−	0.316255i	0.835059	+	0.550160i	$0.185433\pi$
$510$	−3.34456	+	20.6894i	−0.148099	+	0.916144i
$511$	53.1800	−	6.21585i	2.35254	−	0.274973i
$512$	4.29252	−	7.43487i	0.189705	−	0.328578i
$513$	12.1017	+	9.30214i	0.534304	+	0.410700i
$514$	14.3134	+	24.7916i	0.631339	+	1.09351i
$515$	−0.411320	−	0.552499i	−0.0181249	−	0.0243460i
$516$	2.07539	−	1.79252i	0.0913640	−	0.0789114i
$517$	−0.122575	+	0.409429i	−0.00539084	+	0.0180067i
$518$	−42.3289	−	21.2584i	−1.85982	−	0.934039i
$519$	4.12870	−	2.14779i	0.181230	−	0.0942777i
$520$	3.60084	+	12.0276i	0.157907	+	0.527447i
$521$	2.47495	−	14.0361i	0.108430	−	0.614934i	−0.881365	−	0.472435i	$-0.843375\pi$
$521$	2.47495	−	14.0361i	0.108430	−	0.614934i	0.989795	−	0.142499i	$-0.0455138\pi$
$522$	−23.1569	−	23.1828i	−1.01355	−	1.01469i
$523$	0.234960	+	1.33253i	0.0102741	+	0.0582673i	0.989514	−	0.144439i	$-0.0461376\pi$
$523$	0.234960	+	1.33253i	0.0102741	+	0.0582673i	−0.979240	+	0.202706i	$0.935026\pi$
$524$	5.02932	−	2.52582i	0.219707	−	0.110341i
$525$	10.3527	−	14.3283i	0.451829	−	0.625339i
$526$	0.0115142	+	0.0266928i	0.000502042	+	0.00116386i
$527$	10.2139	+	23.6784i	0.444923	+	1.03145i
$528$	−0.727581	−	1.62268i	−0.0316639	−	0.0706181i
$529$	−7.90524	+	3.97016i	−0.343706	+	0.172616i
$530$	−3.74002	−	21.2107i	−0.162456	−	0.921335i
$531$	−40.3544	−	18.8451i	−1.75123	−	0.817809i
$532$	−1.67382	+	9.49269i	−0.0725692	+	0.411560i
$533$	4.16337	+	13.9066i	0.180335	+	0.602362i
$534$	−12.9986	−	8.28616i	−0.562506	−	0.358577i
$535$	−6.69883	−	3.36428i	−0.289616	−	0.145450i
$536$	6.67252	−	22.2878i	0.288209	−	0.962685i
$537$	0.778062	+	4.07207i	0.0335759	+	0.175723i
$538$	−6.54154	−	8.78682i	−0.282026	−	0.378827i
$539$	0.391448	+	0.678008i	0.0168609	+	0.0292039i
$540$	−4.67340	+	5.39864i	−0.201111	+	0.232321i
$541$	12.5060	−	21.6611i	0.537676	−	0.931283i	−0.461352	−	0.887217i	$-0.652636\pi$
$541$	12.5060	−	21.6611i	0.537676	−	0.931283i	0.999029	−	0.0440659i	$-0.0140312\pi$
$542$	34.3519	−	4.01516i	1.47554	−	0.172466i
$543$	27.1106	−	10.3077i	1.16343	−	0.442346i
$544$	25.6147	−	6.07080i	1.09822	−	0.260284i
$545$	19.3051	−	12.6971i	0.826938	−	0.543886i
$546$	−15.5685	−	49.4253i	−0.666271	−	2.11521i
$547$	−19.4886	+	20.6567i	−0.833273	+	0.883218i	−0.994611	−	0.103681i	$-0.966938\pi$
$547$	−19.4886	+	20.6567i	−0.833273	+	0.883218i	0.161337	+	0.986899i	$0.448419\pi$
$548$	−0.851950	−	0.714871i	−0.0363935	−	0.0305378i
$549$	−4.42620	−	0.916524i	−0.188906	−	0.0391163i
$550$	−0.845339	+	0.709324i	−0.0360454	+	0.0302457i
$551$	−1.07745	+	18.4991i	−0.0459009	+	0.788089i
$552$	−0.818315	−	11.2764i	−0.0348298	−	0.479955i
$553$	−2.91980	+	3.92197i	−0.124162	+	0.166779i
$554$	10.7583	+	1.25747i	0.457077	+	0.0534246i
$555$	−5.41938	+	19.0889i	−0.230040	+	0.810278i
$556$	3.96695	+	2.60910i	0.168236	+	0.110651i
$557$	−34.6621	−	12.6160i	−1.46868	−	0.534556i	−0.520938	−	0.853594i	$-0.674418\pi$
$557$	−34.6621	−	12.6160i	−1.46868	−	0.534556i	−0.947742	+	0.319039i	$0.896640\pi$
$558$	−3.83999	+	26.1134i	−0.162560	+	1.10547i
$559$	7.83442	−	2.85150i	0.331361	−	0.120605i
$560$	22.0301	+	5.22124i	0.930943	+	0.220638i
$561$	0.691205	−	1.66739i	0.0291827	−	0.0703975i
$562$	−0.586086	−	10.0627i	−0.0247226	−	0.424470i
$563$	−15.2051	−	16.1164i	−0.640817	−	0.679226i	0.322814	−	0.946462i	$-0.395371\pi$
$563$	−15.2051	−	16.1164i	−0.640817	−	0.679226i	−0.963631	+	0.267236i	$0.913890\pi$
$564$	−1.84296	−	3.08947i	−0.0776026	−	0.130090i
$565$	4.81740	−	11.1680i	0.202670	−	0.469841i
$566$	14.8852			0.625671
$567$	−19.0482	+	22.6492i	−0.799951	+	0.951177i
$568$	−8.10969			−0.340275
$569$	2.53616	−	5.87948i	0.106321	−	0.246480i	−0.856747	−	0.515736i	$-0.827518\pi$
$569$	2.53616	−	5.87948i	0.106321	−	0.246480i	0.963069	+	0.269256i	$0.0867777\pi$
$570$	12.1298	−	0.173034i	0.508062	−	0.00724759i
$571$	3.79067	+	4.01787i	0.158634	+	0.168143i	0.801816	−	0.597571i	$-0.203867\pi$
$571$	3.79067	+	4.01787i	0.158634	+	0.168143i	−0.643182	+	0.765714i	$0.722386\pi$
$572$	0.0626100	+	1.07497i	0.00261786	+	0.0449469i
$573$	24.3698	−	3.20140i	1.01806	−	0.133740i
$574$	15.3043	+	3.62718i	0.638788	+	0.151395i
$575$	−10.9725	+	3.99368i	−0.457586	+	0.166548i
$576$	−2.90058	−	0.962951i	−0.120857	−	0.0401230i
$577$	36.7599	+	13.3795i	1.53033	+	0.556996i	0.963703	−	0.266977i	$-0.0860246\pi$
$577$	36.7599	+	13.3795i	1.53033	+	0.556996i	0.566630	+	0.823972i	$0.308247\pi$
$578$	12.6649	+	8.32986i	0.526792	+	0.346477i
$579$	−5.03802	−	5.18965i	−0.209373	−	0.215675i
$580$	−8.61003	−	1.00637i	−0.357512	−	0.0417872i
$581$	−27.9842	+	37.5894i	−1.16098	+	1.55947i
$582$	4.45593	−	3.02264i	0.184704	−	0.125292i
$583$	−0.107855	+	1.85179i	−0.00446688	+	0.0766933i
$584$	−21.6420	+	18.1598i	−0.895551	+	0.751457i
$585$	−19.1135	+	10.2921i	−0.790246	+	0.425525i
$586$	−8.53628	−	7.16279i	−0.352631	−	0.295892i
$587$	−9.54436	+	10.1164i	−0.393938	+	0.417550i	−0.893737	−	0.448592i	$-0.851926\pi$
$587$	−9.54436	+	10.1164i	−0.393938	+	0.417550i	0.499799	+	0.866141i	$0.333407\pi$
$588$	−6.43326	−	1.42811i	−0.265303	−	0.0588943i
$589$	12.4708	−	8.20221i	0.513852	−	0.337966i
$590$	−34.4429	+	8.16313i	−1.41799	+	0.336071i
$591$	−27.8157	−	22.6720i	−1.14419	−	0.932602i
$592$	41.3167	−	4.82923i	1.69811	−	0.198480i
$593$	8.67989	−	15.0340i	0.356441	−	0.617373i	−0.630923	−	0.775846i	$-0.717324\pi$
$593$	8.67989	−	15.0340i	0.356441	−	0.617373i	0.987363	+	0.158472i	$0.0506569\pi$
$594$	1.49869	−	1.08030i	0.0614918	−	0.0443251i
$595$	11.4899	+	19.9010i	0.471039	+	0.815863i
$596$	4.57515	+	6.14549i	0.187405	+	0.251729i
$597$	4.70541	+	1.63701i	0.192580	+	0.0669982i
$598$	−9.81717	+	32.7916i	−0.401454	+	1.34095i
$599$	37.1512	+	18.6580i	1.51796	+	0.762346i	0.995891	−	0.0905596i	$-0.0288656\pi$
$599$	37.1512	+	18.6580i	1.51796	+	0.762346i	0.522065	+	0.852906i	$0.325162\pi$
$600$	−0.409465	+	9.31837i	−0.0167163	+	0.380421i
$601$	2.64850	+	8.84660i	0.108035	+	0.360860i	0.994862	−	0.101240i	$-0.0322811\pi$
$601$	2.64850	+	8.84660i	0.108035	+	0.360860i	−0.886827	+	0.462101i	$0.847096\pi$
$602$	1.56859	−	8.89594i	0.0639311	−	0.362571i
$603$	40.0716	+	3.52844i	1.63184	+	0.143689i
$604$	0.535232	+	3.03545i	0.0217783	+	0.123511i
$605$	13.4845	−	6.77215i	0.548221	−	0.275327i
$606$	34.2341	+	3.50719i	1.39066	+	0.142470i
$607$	−5.34301	−	12.3865i	−0.216866	−	0.502752i	0.774704	−	0.632324i	$-0.217899\pi$
$607$	−5.34301	−	12.3865i	−0.216866	−	0.502752i	−0.991570	+	0.129572i	$0.958640\pi$
$608$	−6.03515	−	13.9910i	−0.244758	−	0.567412i
$609$	−35.7410	−	3.66156i	−1.44830	−	0.148374i
$610$	−3.21030	+	1.61227i	−0.129981	+	0.0652790i
$611$	−1.89916	−	10.7707i	−0.0768317	−	0.435734i
$612$	6.41315	+	13.7732i	0.259236	+	0.556749i
$613$	−0.675007	+	3.82815i	−0.0272633	+	0.154618i	−0.995400	−	0.0958034i	$-0.969458\pi$
$613$	−0.675007	+	3.82815i	−0.0272633	+	0.154618i	0.968137	+	0.250421i	$0.0805691\pi$
$614$	12.1909	+	40.7205i	0.491986	+	1.64335i
$615$	0.289250	−	6.58258i	0.0116637	−	0.265435i
$616$	−1.04694	−	0.525792i	−0.0421823	−	0.0211847i
$617$	−6.88741	+	23.0055i	−0.277276	+	0.926168i	0.699990	+	0.714153i	$0.253188\pi$
$617$	−6.88741	+	23.0055i	−0.277276	+	0.926168i	−0.977266	+	0.212015i	$0.931997\pi$
$618$	−1.41678	−	0.492895i	−0.0569911	−	0.0198271i
$619$	−6.07827	−	8.16453i	−0.244306	−	0.328160i	0.663009	−	0.748612i	$-0.269279\pi$
$619$	−6.07827	−	8.16453i	−0.244306	−	0.328160i	−0.907315	+	0.420451i	$0.861872\pi$
$620$	3.49133	+	6.04716i	0.140215	+	0.242860i
$621$	18.8115	−	5.31786i	0.754880	−	0.213398i
$622$	−11.2430	+	19.4734i	−0.450802	+	0.780812i
$623$	−16.7878	+	1.96221i	−0.672590	+	0.0786144i
$624$	35.2747	+	28.7517i	1.41212	+	1.15099i
$625$	0.147739	−	0.0350147i	0.00590955	−	0.00140059i
$626$	7.56297	−	4.97425i	0.302277	−	0.198811i
$627$	−1.01994	−	0.226416i	−0.0407326	−	0.00904219i
$628$	−4.19844	+	4.45009i	−0.167536	+	0.177578i
$629$	32.3435	+	27.1394i	1.28962	+	1.08212i
$630$	−0.697262	+	23.5101i	−0.0277796	+	0.936666i
$631$	−37.7162	+	31.6476i	−1.50146	+	1.25987i	−0.622836	+	0.782352i	$0.714020\pi$
$631$	−37.7162	+	31.6476i	−1.50146	+	1.25987i	−0.878621	+	0.477520i	$0.841536\pi$
$632$	0.150011	−	2.57559i	0.00596711	−	0.102451i
$633$	−15.2138	+	10.3201i	−0.604694	+	0.410188i
$634$	31.5943	−	42.4384i	1.25477	−	1.68545i
$635$	−9.54396	−	1.11553i	−0.378740	−	0.0442684i
$636$	−10.8755	−	11.2028i	−0.431242	−	0.444222i
$637$	−16.7386	−	11.0091i	−0.663206	−	0.436197i
$638$	2.10759	+	0.767099i	0.0834402	+	0.0303698i
$639$	−2.82781	−	13.7340i	−0.111866	−	0.543307i
$640$	−15.7068	+	5.71682i	−0.620867	+	0.225977i
$641$	−33.1606	−	7.85921i	−1.30976	−	0.310420i	−0.484314	−	0.874894i	$-0.660931\pi$
$641$	−33.1606	−	7.85921i	−1.30976	−	0.310420i	−0.825451	+	0.564474i	$0.809079\pi$
$642$	−16.1862	+	2.12634i	−0.638819	+	0.0839200i
$643$	1.15570	+	19.8426i	0.0455764	+	0.782516i	0.941230	+	0.337765i	$0.109671\pi$
$643$	1.15570	+	19.8426i	0.0455764	+	0.782516i	−0.895654	+	0.444751i	$0.853292\pi$
$644$	8.47175	+	8.97953i	0.333834	+	0.353843i
$645$	−3.78383	+	0.0539769i	−0.148988	+	0.00212534i
$646$	10.2235	−	23.7008i	0.402240	−	0.932497i
$647$	−37.1636			−1.46105			−0.730525	−	0.682886i	$-0.760725\pi$
$647$	−37.1636			−1.46105			−0.730525	+	0.682886i	$0.760725\pi$
$648$	1.83023	−	15.5079i	0.0718984	−	0.609207i
$649$	3.04853			0.119665
$650$	11.1849	−	25.9296i	0.438709	−	1.01704i
$651$	14.8262	+	24.8541i	0.581083	+	0.974108i
$652$	0.117715	+	0.124771i	0.00461007	+	0.00488639i
$653$	0.320235	+	5.49823i	0.0125318	+	0.215162i	0.998760	+	0.0497749i	$0.0158504\pi$
$653$	0.320235	+	5.49823i	0.0125318	+	0.215162i	−0.986229	+	0.165387i	$0.947113\pi$
$654$	19.2702	−	46.4854i	0.753523	−	1.81772i
$655$	−7.55681	−	1.79100i	−0.295269	−	0.0699801i
$656$	−12.9796	+	4.72418i	−0.506767	+	0.184448i
$657$	−38.3005	−	30.3190i	−1.49424	−	1.18286i
$658$	−11.1351	−	4.05286i	−0.434093	−	0.157997i
$659$	−31.8182	−	20.9272i	−1.23946	−	0.815207i	−0.251194	−	0.967937i	$-0.580823\pi$
$659$	−31.8182	−	20.9272i	−1.23946	−	0.815207i	−0.988268	+	0.152730i	$0.951194\pi$
$660$	0.133482	−	0.470170i	0.00519580	−	0.0183013i
$661$	27.9872	+	3.27123i	1.08857	+	0.127236i	0.641397	−	0.767209i	$-0.278355\pi$
$661$	27.9872	+	3.27123i	1.08857	+	0.127236i	0.447177	+	0.894445i	$0.352429\pi$
$662$	−3.29176	+	4.42160i	−0.127938	+	0.171850i
$663$	3.34315	+	46.0687i	0.129837	+	1.78916i
$664$	1.43775	−	24.6852i	0.0557955	−	0.957972i
$665$	10.1894	−	8.54990i	0.395127	−	0.331551i
$666$	13.5700	+	41.0291i	0.525828	+	1.58984i
$667$	18.1802	+	15.2550i	0.703939	+	0.590675i
$668$	0.201566	−	0.213647i	0.00779881	−	0.00826626i
$669$	−12.3199	−	39.1120i	−0.476315	−	1.51216i
$670$	26.7111	−	17.5682i	1.03194	−	0.678718i
$671$	0.301053	−	0.0713508i	0.0116220	−	0.00275447i
$672$	27.6143	−	10.4992i	1.06524	−	0.405016i
$673$	−24.6772	+	2.88436i	−0.951238	+	0.111184i	−0.577536	−	0.816365i	$-0.695986\pi$
$673$	−24.6772	+	2.88436i	−0.951238	+	0.111184i	−0.373702	+	0.927549i	$0.621912\pi$
$674$	−28.3712	+	49.1404i	−1.09282	+	1.89282i
$675$	−15.9237	+	2.55583i	−0.612902	+	0.0983740i
$676$	−7.29123	−	12.6288i	−0.280432	−	0.485722i
$677$	21.0707	+	28.3029i	0.809813	+	1.08777i	0.994476	+	0.104965i	$0.0334731\pi$
$677$	21.0707	+	28.3029i	0.809813	+	1.08777i	−0.184663	+	0.982802i	$0.559119\pi$
$678$	−4.97122	−	26.0174i	−0.190919	−	0.999193i
$679$	1.69323	−	5.65577i	0.0649801	−	0.217049i
$680$	−10.8356	−	5.44184i	−0.415526	−	0.208685i
$681$	0.670406	+	0.427360i	0.0256900	+	0.0163765i
$682$	−0.518148	−	1.73073i	−0.0198409	−	0.0662732i
$683$	−6.86569	+	38.9372i	−0.262708	+	1.48989i	0.512774	+	0.858523i	$0.328618\pi$
$683$	−6.86569	+	38.9372i	−0.262708	+	1.48989i	−0.775483	+	0.631369i	$0.782493\pi$
$684$	7.20658	−	5.04008i	0.275550	−	0.192712i
$685$	0.266493	+	1.51136i	0.0101822	+	0.0577460i
$686$	16.2170	−	8.14447i	0.619167	−	0.310957i
$687$	−11.3335	−	25.2765i	−0.432400	−	0.964357i
$688$	3.14208	+	7.28417i	0.119791	+	0.277706i
$689$	−18.8011	−	43.5859i	−0.716265	−	1.66049i
$690$	9.09913	−	12.5934i	0.346398	−	0.479421i
$691$	−15.1837	+	7.62552i	−0.577613	+	0.290088i	−0.713522	−	0.700633i	$-0.752901\pi$
$691$	−15.1837	+	7.62552i	−0.577613	+	0.290088i	0.135908	+	0.990721i	$0.456605\pi$
$692$	−0.465612	−	2.64062i	−0.0176999	−	0.100381i
$693$	0.525379	−	1.95635i	0.0199575	−	0.0743158i
$694$	6.73702	−	38.2075i	0.255734	−	1.45034i
$695$	−1.87913	−	6.27672i	−0.0712793	−	0.238089i
$696$	16.8180	−	8.74890i	0.637484	−	0.331626i
$697$	−12.5284	−	6.29198i	−0.474545	−	0.238326i
$698$	10.9585	−	36.6039i	0.414785	−	1.38548i
$699$	−10.4184	+	8.99844i	−0.394062	+	0.340352i
$700$	−6.08182	−	8.16930i	−0.229871	−	0.308771i
$701$	16.3741	+	28.3608i	0.618442	+	1.07117i	0.989770	+	0.142672i	$0.0455693\pi$
$701$	16.3741	+	28.3608i	0.618442	+	1.07117i	−0.371328	+	0.928502i	$0.621097\pi$
$702$	−21.8652	+	41.9166i	−0.825250	+	1.58204i
$703$	12.2194	−	21.1647i	0.460865	−	0.798241i
$704$	0.207780	−	0.0242859i	0.00783099	−	0.000915311i
$705$	−0.792197	+	4.90054i	−0.0298359	+	0.184565i
$706$	18.3924	−	4.35908i	0.692207	−	0.164056i
$707$	31.5254	−	20.7346i	1.18563	−	0.779804i
$708$	−17.3412	+	18.9139i	−0.651722	+	0.710830i
$709$	−22.5220	+	23.8719i	−0.845830	+	0.896527i	−0.995743	−	0.0921719i	$-0.970619\pi$
$709$	−22.5220	+	23.8719i	−0.845830	+	0.896527i	0.149913	+	0.988699i	$0.452101\pi$
$710$	−8.53698	−	7.16337i	−0.320387	−	0.268837i
$711$	4.41413	−	0.644048i	0.165543	−	0.0241537i
$712$	6.83193	−	5.73267i	0.256037	−	0.214841i
$713$	1.11154	−	19.0844i	0.0416275	−	0.714716i
$714$	45.0382	+	21.8202i	1.68551	+	0.816602i
$715$	0.887315	−	1.19187i	0.0331837	−	0.0445735i
$716$	2.37241	+	0.277294i	0.0886610	+	0.0103630i
$717$	35.6346	−	8.98427i	1.33080	−	0.335524i
$718$	−35.8602	−	23.5856i	−1.33829	−	0.880208i
$719$	−15.8250	−	5.75983i	−0.590173	−	0.214806i	0.0296323	−	0.999561i	$-0.490566\pi$
$719$	−15.8250	−	5.75983i	−0.590173	−	0.214806i	−0.619806	+	0.784755i	$0.712789\pi$
$720$	−10.8339	−	17.5865i	−0.403756	−	0.655411i
$721$	−1.54558	+	0.562545i	−0.0575604	+	0.0209503i
$722$	17.4729	+	4.14116i	0.650275	+	0.154118i
$723$	19.0459	+	24.8355i	0.708325	+	0.923643i
$724$	−0.971634	−	16.6823i	−0.0361105	−	0.619993i
$725$	−13.4360	−	14.2413i	−0.498999	−	0.528908i
$726$	16.0234	−	28.6909i	0.594685	−	1.06482i
$727$	−3.32819	+	7.71562i	−0.123436	+	0.286157i	−0.968718	−	0.248163i	$-0.920173\pi$
$727$	−3.32819	+	7.71562i	−0.123436	+	0.286157i	0.845282	+	0.534320i	$0.179432\pi$
$728$	29.9802			1.11114
$729$	26.9012	−	2.30798i	0.996340	−	0.0854807i
$730$	−38.8230			−1.43690
$731$	−3.18917	+	7.39334i	−0.117956	+	0.273452i
$732$	−1.26982	+	2.27368i	−0.0469339	+	0.0840378i
$733$	−8.47275	−	8.98059i	−0.312948	−	0.331705i	0.551739	−	0.834017i	$-0.313965\pi$
$733$	−8.47275	−	8.98059i	−0.312948	−	0.331705i	−0.864687	+	0.502312i	$0.832483\pi$
$734$	−1.29353	−	22.2090i	−0.0477449	−	0.819749i
$735$	5.53376	+	7.21593i	0.204116	+	0.266163i
$736$	−18.9887	−	4.50042i	−0.699934	−	0.165888i
$737$	−2.58738	+	0.941730i	−0.0953075	+	0.0346891i
$738$	−7.52629	−	12.2173i	−0.277047	−	0.449725i
$739$	37.3973	+	13.6115i	1.37568	+	0.500707i	0.920866	−	0.389879i	$-0.127483\pi$
$739$	37.3973	+	13.6115i	1.37568	+	0.500707i	0.454815	+	0.890586i	$0.349705\pi$
$740$	9.55183	+	6.28234i	0.351132	+	0.230943i
$741$	25.9247	−	6.53618i	0.952366	−	0.240112i
$742$	−51.0826	−	5.97070i	−1.87530	−	0.219191i
$743$	11.8466	−	15.9127i	0.434608	−	0.583780i	−0.529825	−	0.848107i	$-0.677742\pi$
$743$	11.8466	−	15.9127i	0.434608	−	0.583780i	0.964433	+	0.264327i	$0.0851497\pi$
$744$	−13.7425	−	6.65802i	−0.503826	−	0.244095i
$745$	0.614727	−	10.5545i	0.0225219	−	0.386685i
$746$	−2.95869	+	2.48263i	−0.108325	+	0.0908957i
$747$	42.3064	−	6.17275i	1.54791	−	0.225849i
$748$	−0.796638	−	0.668459i	−0.0291280	−	0.0244413i
$749$	−12.2838	+	13.0201i	−0.448840	+	0.475743i
$750$	−22.6163	+	24.6675i	−0.825830	+	0.900729i
$751$	−32.0641	+	21.0889i	−1.17004	+	0.769545i	−0.977332	−	0.211712i	$-0.932096\pi$
$751$	−32.0641	+	21.0889i	−1.17004	+	0.769545i	−0.192704	+	0.981257i	$0.561726\pi$
$752$	10.1260	−	2.39990i	0.369257	−	0.0875155i
$753$	2.23194	−	13.8068i	0.0813364	−	0.503147i
$754$	−57.0068	+	6.66314i	−2.07607	+	0.242657i
$755$	2.12665	−	3.68347i	0.0773969	−	0.134055i
$756$	9.14922	+	14.3881i	0.332754	+	0.523289i
$757$	7.07444	+	12.2533i	0.257125	+	0.445353i	0.965470	−	0.260513i	$-0.0838915\pi$
$757$	7.07444	+	12.2533i	0.257125	+	0.445353i	−0.708346	+	0.705866i	$0.750558\pi$
$758$	7.60877	+	10.2203i	0.276363	+	0.371220i
$759$	−1.01265	+	0.874630i	−0.0367569	+	0.0317471i
$760$	−2.01292	+	6.72361i	−0.0730162	+	0.243891i
$761$	8.47080	+	4.25420i	0.307066	+	0.154215i	0.595659	−	0.803237i	$-0.296891\pi$
$761$	8.47080	+	4.25420i	0.307066	+	0.154215i	−0.288593	+	0.957452i	$0.593187\pi$
$762$	−18.5647	+	9.65756i	−0.672528	+	0.349857i
$763$	−15.8245	−	52.8576i	−0.572886	−	1.91357i
$764$	2.45907	−	13.9461i	0.0889660	−	0.504551i
$765$	5.43757	−	20.2479i	0.196596	−	0.732064i
$766$	−4.34643	−	24.6498i	−0.157043	−	0.890634i
$767$	−69.7145	+	35.0119i	−2.51724	+	1.26421i
$768$	−19.2522	+	26.6453i	−0.694703	+	0.961481i
$769$	−4.95943	−	11.4972i	−0.178841	−	0.414601i	0.805089	−	0.593154i	$-0.202118\pi$
$769$	−4.95943	−	11.4972i	−0.178841	−	0.414601i	−0.983930	+	0.178553i	$0.942858\pi$
$770$	−0.637661	−	1.47826i	−0.0229797	−	0.0532730i
$771$	−11.7164	−	26.1303i	−0.421955	−	0.941061i
$772$	−3.72394	+	1.87023i	−0.134027	+	0.0673111i
$773$	6.23462	+	35.3583i	0.224244	+	1.27175i	0.864125	+	0.503277i	$0.167872\pi$
$773$	6.23462	+	35.3583i	0.224244	+	1.27175i	−0.639882	+	0.768474i	$0.721017\pi$
$774$	−6.75353	+	4.72324i	−0.242751	+	0.169773i
$775$	−2.73862	+	15.5315i	−0.0983742	+	0.557908i
$776$	0.893437	+	2.98429i	0.0320725	+	0.107130i
$777$	39.9558	+	25.4704i	1.43341	+	0.913746i
$778$	13.1583	+	6.60833i	0.471747	+	0.236920i
$779$	−2.32738	+	7.77399i	−0.0833871	+	0.278532i
$780$	2.34732	+	12.2850i	0.0840476	+	0.439872i
$781$	0.573143	+	0.769865i	0.0205087	+	0.0275479i
$782$	−16.5290	−	28.6291i	−0.591076	−	1.02377i
$783$	20.6808	+	25.4310i	0.739073	+	0.908829i
$784$	9.53150	−	16.5091i	0.340411	−	0.589609i
$785$	8.38532	−	0.980104i	0.299285	−	0.0349814i
$786$	−15.8091	+	6.01077i	−0.563892	+	0.214397i
$787$	38.8743	−	9.21338i	1.38572	−	0.328421i	0.530938	−	0.847411i	$-0.321840\pi$
$787$	38.8743	−	9.21338i	1.38572	−	0.328421i	0.854781	+	0.518989i	$0.173691\pi$
$788$	−17.2738	+	11.3611i	−0.615352	+	0.404724i
$789$	−0.00873688	−	0.0277369i	−0.000311041	−	0.000987461i
$790$	2.43296	−	2.57878i	0.0865607	−	0.0917490i
$791$	−22.2484	−	18.6687i	−0.791063	−	0.663781i
$792$	0.335633	+	1.01479i	0.0119262	+	0.0360589i
$793$	−6.06508	+	5.08921i	−0.215377	+	0.180723i
$794$	0.552935	−	9.49353i	0.0196229	−	0.336913i
$795$	1.55942	+	21.4889i	0.0553071	+	0.762133i
$796$	1.71408	−	2.30240i	0.0607538	−	0.0816065i
$797$	33.8557	+	3.95716i	1.19923	+	0.140170i	0.692165	−	0.721739i	$-0.256657\pi$
$797$	33.8557	+	3.95716i	1.19923	+	0.140170i	0.507063	+	0.861909i	$0.330731\pi$
$798$	7.91136	−	27.8664i	0.280059	−	0.986461i
$799$	8.82481	+	5.80417i	0.312199	+	0.205337i
$800$	15.1285	+	5.50634i	0.534875	+	0.194678i
$801$	12.0907	+	9.57108i	0.427203	+	0.338178i
$802$	15.3085	−	5.57185i	0.540563	−	0.196749i
$803$	3.25346	+	0.771083i	0.114812	+	0.0272109i
$804$	8.87525	−	21.4098i	0.313006	−	0.755064i
$805$	−0.990519	−	17.0065i	−0.0349112	−	0.599402i
$806$	31.7263	+	33.6280i	1.11751	+	1.18449i
$807$	5.61393	+	9.41101i	0.197620	+	0.331283i
$808$	−7.88590	+	18.2816i	−0.277425	+	0.643144i
$809$	7.57622			0.266366			0.133183	−	0.991091i	$-0.457480\pi$
$809$	7.57622			0.266366			0.133183	+	0.991091i	$0.457480\pi$
$810$	15.6249	−	14.7083i	0.549004	−	0.516797i
$811$	20.5558			0.721810			0.360905	−	0.932602i	$-0.382468\pi$
$811$	20.5558			0.721810			0.360905	+	0.932602i	$0.382468\pi$
$812$	−8.19879	+	19.0069i	−0.287721	+	0.667012i
$813$	−34.5942	+	0.493492i	−1.21327	+	0.0173075i
$814$	−2.02989	−	2.15156i	−0.0711475	−	0.0754120i
$815$	−0.0137632	−	0.236306i	−0.000482106	−	0.00827743i
$816$	−43.5758	+	5.72444i	−1.52546	+	0.200395i
$817$	4.53499	+	1.07481i	0.158659	+	0.0376030i
$818$	−25.0916	+	9.13260i	−0.877308	+	0.319314i
$819$	10.4540	+	50.7722i	0.365291	+	1.77413i
$820$	−3.56726	−	1.29838i	−0.124574	−	0.0453412i
$821$	25.4615	+	16.7463i	0.888613	+	0.584450i	0.909672	−	0.415328i	$-0.136333\pi$
$821$	25.4615	+	16.7463i	0.888613	+	0.584450i	−0.0210583	+	0.999778i	$0.506704\pi$
$822$	2.32802	+	2.39809i	0.0811990	+	0.0836429i
$823$	22.1674	+	2.59100i	0.772707	+	0.0903165i	0.493304	−	0.869857i	$-0.335789\pi$
$823$	22.1674	+	2.59100i	0.772707	+	0.0903165i	0.279404	+	0.960174i	$0.409863\pi$
$824$	0.518255	−	0.696138i	0.0180543	−	0.0242511i
$825$	0.913545	−	0.619694i	0.0318055	−	0.0215750i
$826$	−4.91467	+	84.3816i	−0.171003	+	2.93601i
$827$	−27.2509	+	22.8662i	−0.947606	+	0.795136i	−0.978893	−	0.204374i	$-0.934484\pi$
$827$	−27.2509	+	22.8662i	−0.947606	+	0.795136i	0.0312864	+	0.999510i	$0.490040\pi$
$828$	0.333889	−	11.2580i	0.0116035	−	0.391242i
$829$	−13.4520	−	11.2875i	−0.467206	−	0.392032i	0.378568	−	0.925573i	$-0.376416\pi$
$829$	−13.4520	−	11.2875i	−0.467206	−	0.392032i	−0.845774	+	0.533541i	$0.820861\pi$
$830$	23.3182	−	24.7159i	0.809387	−	0.857900i
$831$	−10.5778	−	2.34816i	−0.366940	−	0.0814566i
$832$	−4.47263	+	2.94169i	−0.155060	+	0.101985i
$833$	18.8272	−	4.46212i	0.652323	−	0.154603i
$834$	−11.0604	−	9.01507i	−0.382989	−	0.312166i
$835$	−0.402577	+	0.0470545i	−0.0139317	+	0.00162839i
$836$	−0.300972	+	0.521298i	−0.0104093	+	0.0180295i
$837$	6.48356	−	25.5949i	0.224105	−	0.884690i
$838$	21.3875	+	37.0443i	0.738820	+	1.27967i
$839$	−22.8900	−	30.7466i	−0.790251	−	1.06149i	−0.996549	−	0.0830022i	$-0.973549\pi$
$839$	−22.8900	−	30.7466i	−0.790251	−	1.06149i	0.206298	−	0.978489i	$-0.433858\pi$
$840$	−12.8523	−	4.47129i	−0.443445	−	0.154274i
$841$	−3.09569	+	10.3403i	−0.106748	+	0.356563i
$842$	0.287474	+	0.144375i	0.00990701	+	0.00497549i
$843$	−0.442649	+	10.0735i	−0.0152456	+	0.346951i
$844$	3.03776	+	10.1468i	0.104564	+	0.349268i
$845$	−3.49427	+	19.8170i	−0.120206	+	0.681725i
$846$	4.56344	+	9.80066i	0.156894	+	0.336954i
$847$	−6.25691	−	35.4847i	−0.214990	−	1.21927i
$848$	40.3621	−	20.2706i	1.38604	−	0.696095i
$849$	−14.8128	−	1.51753i	−0.508375	−	0.0520816i
$850$	10.8021	+	25.0420i	0.370508	+	0.858934i
$851$	−12.3972	−	28.7398i	−0.424969	−	0.985189i
$852$	−8.03671	−	0.823339i	−0.275333	−	0.0282071i
$853$	7.50175	−	3.76752i	0.256855	−	0.128997i	−0.315713	−	0.948855i	$-0.602244\pi$
$853$	7.50175	−	3.76752i	0.256855	−	0.128997i	0.572568	+	0.819857i	$0.305947\pi$
$854$	1.48961	+	8.44799i	0.0509733	+	0.289084i
$855$	−12.0885	−	1.06443i	−0.413418	−	0.0364029i
$856$	1.64011	−	9.30155i	0.0560580	−	0.317920i
$857$	−13.8014	−	46.0999i	−0.471447	−	1.57474i	−0.781424	−	0.624000i	$-0.785507\pi$
$857$	−13.8014	−	46.0999i	−0.471447	−	1.57474i	0.309977	−	0.950744i	$-0.399679\pi$
$858$	0.142058	−	3.23288i	0.00484980	−	0.110369i
$859$	45.6471	+	22.9248i	1.55746	+	0.782185i	0.998882	−	0.0472690i	$-0.0150518\pi$
$859$	45.6471	+	22.9248i	1.55746	+	0.782185i	0.558575	+	0.829454i	$0.311348\pi$
$860$	−0.625307	+	2.08867i	−0.0213228	+	0.0712231i
$861$	−14.8601	−	5.16980i	−0.506430	−	0.176186i
$862$	15.0463	+	20.2107i	0.512478	+	0.688378i
$863$	−18.3885	−	31.8499i	−0.625953	−	1.08418i	−0.988356	−	0.152161i	$-0.951377\pi$
$863$	−18.3885	−	31.8499i	−0.625953	−	1.08418i	0.362403	−	0.932022i	$-0.381957\pi$
$864$	−24.5816	−	11.0551i	−0.836283	−	0.376101i
$865$	−1.85003	+	3.20435i	−0.0629031	+	0.108951i
$866$	−59.5361	+	6.95877i	−2.02312	+	0.236469i
$867$	−11.7542	−	9.58055i	−0.399192	−	0.325373i
$868$	16.2244	−	3.84526i	0.550693	−	0.130517i
$869$	−0.255106	+	0.167786i	−0.00865388	+	0.00569175i
$870$	25.4321	+	5.64564i	0.862229	+	0.191405i
$871$	48.3532	−	51.2514i	1.63839	−	1.73659i
$872$	22.3023	+	18.7138i	0.755250	+	0.633730i
$873$	−4.74243	+	2.55366i	−0.160507	+	0.0864284i
$874$	−14.6581	+	12.2996i	−0.495819	+	0.416042i
$875$	−2.13359	+	36.6323i	−0.0721285	+	1.23840i
$876$	−23.2909	+	15.7991i	−0.786926	+	0.533804i
$877$	−2.42437	+	3.25649i	−0.0818651	+	0.109964i	−0.841169	−	0.540772i	$-0.818132\pi$
$877$	−2.42437	+	3.25649i	−0.0818651	+	0.109964i	0.759304	+	0.650736i	$0.225540\pi$
$878$	−3.38068	−	0.395144i	−0.114092	−	0.0133355i
$879$	7.76455	+	7.99824i	0.261892	+	0.269774i
$880$	1.18125	+	0.776921i	0.0398200	+	0.0261900i
$881$	38.2223	+	13.9118i	1.28774	+	0.468700i	0.892986	−	0.450085i	$-0.148606\pi$
$881$	38.2223	+	13.9118i	1.28774	+	0.468700i	0.394758	+	0.918785i	$0.370829\pi$
$882$	18.7953	+	6.23978i	0.632871	+	0.210104i
$883$	−24.6043	+	8.95523i	−0.828000	+	0.301367i	−0.721038	−	0.692896i	$-0.756335\pi$
$883$	−24.6043	+	8.95523i	−0.828000	+	0.301367i	−0.106962	+	0.994263i	$0.534112\pi$
$884$	25.8948	+	6.13719i	0.870938	+	0.206416i
$885$	35.1077	−	4.61201i	1.18013	−	0.155031i
$886$	3.20232	+	54.9817i	0.107584	+	1.84715i
$887$	−14.9184	−	15.8126i	−0.500910	−	0.530933i	0.426745	−	0.904372i	$-0.359660\pi$
$887$	−14.9184	−	15.8126i	−0.500910	−	0.530933i	−0.927655	+	0.373438i	$0.878179\pi$
$888$	−24.9996	+	0.356623i	−0.838931	+	0.0119675i
$889$	−9.08810	+	21.0686i	−0.304805	+	0.706618i
$890$	12.2556			0.410809
$891$	−1.60154	+	0.922255i	−0.0536534	+	0.0308967i
$892$	−23.6257			−0.791048
$893$	2.42157	−	5.61382i	0.0810346	−	0.187859i
$894$	−11.7955	−	19.7736i	−0.394502	−	0.661330i
$895$	−2.26187	−	2.39744i	−0.0756060	−	0.0801377i
$896$	2.32075	+	39.8458i	0.0775310	+	1.33116i
$897$	13.1125	−	31.6314i	0.437815	−	1.05614i
$898$	50.1850	+	11.8941i	1.67470	+	0.396910i
$899$	30.1211	−	10.9632i	1.00459	−	0.365642i
$900$	−1.35183	+	9.19294i	−0.0450610	+	0.306431i
$901$	43.0785	+	15.6793i	1.43515	+	0.522353i
$902$	0.820611	+	0.539724i	0.0273234	+	0.0179709i
$903$	−2.46790	+	8.69278i	−0.0821267	+	0.289277i
$904$	15.2212	+	1.77910i	0.506248	+	0.0591719i
$905$	−13.7701	+	18.4964i	−0.457733	+	0.614842i
$906$	−0.670436	−	9.23862i	−0.0222737	−	0.306933i
$907$	3.06495	−	52.6232i	0.101770	−	1.74733i	−0.432160	−	0.901797i	$-0.642248\pi$
$907$	3.06495	−	52.6232i	0.101770	−	1.74733i	0.533930	−	0.845529i	$-0.320714\pi$
$908$	0.350892	−	0.294434i	0.0116448	−	0.00977113i
$909$	−33.7101	−	6.98027i	−1.11809	−	0.231521i
$910$	31.5598	+	26.4818i	1.04620	+	0.877864i
$911$	−29.5444	+	31.3152i	−0.978850	+	1.03752i	0.0204380	+	0.999791i	$0.493494\pi$
$911$	−29.5444	+	31.3152i	−0.978850	+	1.03752i	−0.999288	+	0.0377293i	$0.987988\pi$
$912$	7.64301	+	24.2642i	0.253085	+	0.803469i
$913$	−2.44501	+	1.60811i	−0.0809182	+	0.0532207i
$914$	−21.4749	+	5.08964i	−0.710325	+	0.168350i
$915$	3.35906	−	1.27715i	0.111047	−	0.0422212i
$916$	−15.8520	+	1.85283i	−0.523764	+	0.0612192i
$917$	−9.27238	+	16.0602i	−0.306201	+	0.530356i
$918$	−14.9542	−	43.1402i	−0.493563	−	1.42384i
$919$	−25.2136	−	43.6712i	−0.831719	−	1.44058i	−0.896674	−	0.442691i	$-0.854024\pi$
$919$	−25.2136	−	43.6712i	−0.831719	−	1.44058i	0.0649552	−	0.997888i	$-0.479310\pi$
$920$	5.36772	+	7.21010i	0.176968	+	0.237710i
$921$	−7.98023	−	41.7654i	−0.262958	−	1.37622i
$922$	10.2634	−	34.2823i	0.338008	−	1.12903i
$923$	−21.9485	−	11.0230i	−0.722445	−	0.362826i
$924$	−0.984134	−	0.627350i	−0.0323756	−	0.0206383i
$925$	7.40579	+	24.7370i	0.243501	+	0.813349i
$926$	5.00610	−	28.3910i	0.164511	−	0.932987i
$927$	1.35964	+	0.634938i	0.0446564	+	0.0208541i
$928$	−5.68204	−	32.2245i	−0.186522	−	1.05782i
$929$	−14.2000	+	7.13149i	−0.465886	+	0.233977i	−0.666226	−	0.745750i	$-0.732091\pi$
$929$	−14.2000	+	7.13149i	−0.465886	+	0.233977i	0.200340	+	0.979726i	$0.435795\pi$
$930$	−8.58550	−	19.1477i	−0.281530	−	0.627879i
$931$	−4.43591	−	10.2836i	−0.145381	−	0.337032i
$932$	3.14152	+	7.28285i	0.102904	+	0.238558i
$933$	13.1736	−	18.2325i	0.431285	−	0.596906i
$934$	45.3283	−	22.7647i	1.48319	−	0.744885i
$935$	0.249191	+	1.41323i	0.00814943	+	0.0462177i
$936$	−19.3300	−	19.3517i	−0.631822	−	0.632530i
$937$	3.98093	−	22.5770i	0.130051	−	0.737557i	−0.848128	−	0.529792i	$-0.822270\pi$
$937$	3.98093	−	22.5770i	0.130051	−	0.737557i	0.978179	−	0.207765i	$-0.0666189\pi$
$938$	−21.8953	−	73.1355i	−0.714907	−	2.38796i
$939$	−8.03333	+	4.17903i	−0.262158	+	0.136377i
$940$	2.55586	+	1.28360i	0.0833631	+	0.0418665i
$941$	−4.05531	+	13.5457i	−0.132199	+	0.441576i	−0.998299	−	0.0582943i	$-0.981434\pi$
$941$	−4.05531	+	13.5457i	−0.132199	+	0.441576i	0.866100	+	0.499870i	$0.166619\pi$
$942$	13.9145	−	12.0180i	0.453358	−	0.391567i
$943$	6.20628	+	8.33648i	0.202104	+	0.271473i
$944$	−37.1148	−	64.2848i	−1.20799	−	2.09229i
$945$	3.09071	−	23.3248i	0.100541	−	0.758754i
$946$	0.282051	−	0.488527i	0.00917027	−	0.0158834i
$947$	56.7038	−	6.62773i	1.84263	−	0.215372i	0.877940	−	0.478771i	$-0.158918\pi$
$947$	56.7038	−	6.62773i	1.84263	−	0.215372i	0.964687	+	0.263399i	$0.0848436\pi$
$948$	0.410148	−	2.53718i	0.0133210	−	0.0824037i
$949$	−83.2565	+	19.7322i	−2.70262	+	0.640533i
$950$	13.1890	−	8.67456i	0.427909	−	0.281440i
$951$	−35.7672	+	39.0111i	−1.15983	+	1.26502i
$952$	−19.8695	+	21.0604i	−0.643973	+	0.682572i
$953$	−13.5816	−	11.3963i	−0.439951	−	0.369163i	0.395740	−	0.918363i	$-0.370488\pi$
$953$	−13.5816	−	11.3963i	−0.439951	−	0.369163i	−0.835691	+	0.549200i	$0.814933\pi$
$954$	29.0820	+	36.8226i	0.941564	+	1.19218i
$955$	−14.9696	+	12.5610i	−0.484405	+	0.406464i
$956$	1.23112	−	21.1374i	0.0398171	−	0.683634i
$957$	−2.01914	−	0.978237i	−0.0652695	−	0.0316219i
$958$	−23.1211	+	31.0570i	−0.747009	+	1.00341i
$959$	3.63986	+	0.425438i	0.117537	+	0.0137381i
$960$	2.35611	−	0.594026i	0.0760430	−	0.0191721i
$961$	4.32792	+	2.84652i	0.139610	+	0.0918231i
$962$	71.1302	+	25.8893i	2.29333	+	0.834704i
$963$	16.3243	−	0.465832i	0.526043	−	0.0150112i
$964$	16.9447	−	6.16735i	0.545751	−	0.198637i
$965$	5.59541	+	1.32614i	0.180122	+	0.0426898i
$966$	−22.5767	−	29.4396i	−0.726394	−	0.947204i
$967$	1.28606	+	22.0808i	0.0413568	+	0.710070i	0.953722	+	0.300691i	$0.0972174\pi$
$967$	1.28606	+	22.0808i	0.0413568	+	0.710070i	−0.912365	+	0.409378i	$0.865746\pi$
$968$	13.0471	+	13.8292i	0.419351	+	0.444486i
$969$	−12.5901	+	22.5433i	−0.404453	+	0.724196i
$970$	−1.69554	+	3.93070i	−0.0544405	+	0.126207i
$971$	−5.09901			−0.163635			−0.0818176	−	0.996647i	$-0.526072\pi$
$971$	−5.09901			−0.163635			−0.0818176	+	0.996647i	$0.526072\pi$
$972$	3.38821	−	15.1825i	0.108677	−	0.486979i
$973$	−15.6454			−0.501569
$974$	−2.56442	+	5.94500i	−0.0821694	+	0.190490i
$975$	−13.7740	+	24.6632i	−0.441123	+	0.789855i
$976$	−5.16980	−	5.47966i	−0.165481	−	0.175400i
$977$	−1.35086	−	23.1934i	−0.0432178	−	0.742022i	−0.948415	−	0.317030i	$-0.897314\pi$
$977$	−1.35086	−	23.1934i	−0.0432178	−	0.742022i	0.905198	−	0.424991i	$-0.139723\pi$
$978$	−0.313703	−	0.409063i	−0.0100311	−	0.0130804i
$979$	−1.02705	−	0.243415i	−0.0328246	−	0.00777958i
$980$	4.92325	−	1.79191i	0.157267	−	0.0572406i
$981$	−23.9156	+	44.2949i	−0.763568	+	1.41423i
$982$	−1.96332	−	0.714592i	−0.0626522	−	0.0228035i
$983$	14.0814	+	9.26149i	0.449127	+	0.295396i	0.753851	−	0.657045i	$-0.228194\pi$
$983$	14.0814	+	9.26149i	0.449127	+	0.295396i	−0.304724	+	0.952441i	$0.598564\pi$
$984$	8.05002	−	2.02959i	0.256625	−	0.0647009i
$985$	28.3371	+	3.31214i	0.902896	+	0.105533i
$986$	33.1007	−	44.4620i	1.05414	−	1.41596i
$987$	10.6678	+	5.16838i	0.339561	+	0.164511i
$988$	0.895653	−	15.3778i	0.0284945	−	0.489232i
$989$	4.57252	−	3.83680i	0.145398	−	0.122003i
$990$	−0.543056	+	1.36472i	−0.0172594	+	0.0433738i
$991$	−0.316451	−	0.265534i	−0.0100524	−	0.00843496i	0.637748	−	0.770245i	$-0.279866\pi$
$991$	−0.316451	−	0.265534i	−0.0100524	−	0.00843496i	−0.647800	+	0.761810i	$0.724311\pi$
$992$	−18.0876	+	19.1717i	−0.574282	+	0.608703i
$993$	3.72653	−	4.06451i	0.118258	−	0.128983i
$994$	−22.2334	+	14.6231i	−0.705200	+	0.463818i
$995$	−3.85415	+	0.913450i	−0.122185	+	0.0289583i
$996$	3.93099	−	24.3171i	0.124558	−	0.770517i
$997$	−5.80233	+	0.678195i	−0.183762	+	0.0214787i	−0.207476	−	0.978240i	$-0.566525\pi$
$997$	−5.80233	+	0.678195i	−0.183762	+	0.0214787i	0.0237143	+	0.999719i	$0.492451\pi$
$998$	2.88970	−	5.00511i	0.0914719	−	0.158434i
$999$	−9.32119	−	42.2131i	−0.294909	−	1.33556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.34.2	yes	144
3.2	odd	2		243.2.g.a.181.7		144
9.2	odd	6		729.2.g.b.298.2		144
9.4	even	3		729.2.g.d.541.2		144
9.5	odd	6		729.2.g.a.541.7		144
9.7	even	3		729.2.g.c.298.7		144
81.4	even	27		729.2.g.d.190.2		144
81.23	odd	54		729.2.g.b.433.2		144
81.29	odd	54		6561.2.a.d.1.56		72
81.31	even	27	inner	81.2.g.a.31.2	✓	144
81.50	odd	54		243.2.g.a.145.7		144
81.52	even	27		6561.2.a.c.1.17		72
81.58	even	27		729.2.g.c.433.7		144
81.77	odd	54		729.2.g.a.190.7		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.31.2	✓	144	81.31	even	27	inner
81.2.g.a.34.2	yes	144	1.1	even	1	trivial
243.2.g.a.145.7		144	81.50	odd	54
243.2.g.a.181.7		144	3.2	odd	2
729.2.g.a.190.7		144	81.77	odd	54
729.2.g.a.541.7		144	9.5	odd	6
729.2.g.b.298.2		144	9.2	odd	6
729.2.g.b.433.2		144	81.23	odd	54
729.2.g.c.298.7		144	9.7	even	3
729.2.g.c.433.7		144	81.58	even	27
729.2.g.d.190.2		144	81.4	even	27
729.2.g.d.541.2		144	9.4	even	3
6561.2.a.c.1.17		72	81.52	even	27
6561.2.a.d.1.56		72	81.29	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.685792 + 1.58984i) q^{2} +(0.844542 - 1.51220i) q^{3} +(-0.684812 - 0.725858i) q^{4} +(0.0800683 + 1.37472i) q^{5} +(1.82498 + 2.37974i) q^{6} +(3.19962 + 0.758323i) q^{7} +(-1.63042 + 0.593424i) q^{8} +(-1.57350 - 2.55423i) q^{9} +(-2.24050 - 0.815476i) q^{10} +(0.171563 + 0.112839i) q^{11} +(-1.67599 + 0.422555i) q^{12} +(-5.21927 - 0.610045i) q^{13} +(-3.39989 + 4.56684i) q^{14} +(2.14647 + 1.03993i) q^{15} +(0.290724 - 4.99154i) q^{16} +(3.88762 - 3.26210i) q^{17} +(5.13993 - 0.749946i) q^{18} +(-2.25026 - 1.88819i) q^{19} +(0.943020 - 0.999543i) q^{20} +(3.84895 - 4.19803i) q^{21} +(-0.297052 + 0.195374i) q^{22} +(-3.66075 + 0.867613i) q^{23} +(-0.479581 + 2.96669i) q^{24} +(3.08275 - 0.360321i) q^{25} +(4.54921 - 7.87946i) q^{26} +(-5.19140 + 0.222289i) q^{27} +(-1.64070 - 2.84178i) q^{28} +(-3.76701 - 5.05998i) q^{29} +(-3.12536 + 2.69938i) q^{30} +(-1.45734 + 4.86786i) q^{31} +(4.63538 + 2.32798i) q^{32} +(0.315526 - 0.164140i) q^{33} +(2.52014 + 8.41784i) q^{34} +(-0.786294 + 4.45930i) q^{35} +(-0.776460 + 2.89131i) q^{36} +(1.44468 + 8.19321i) q^{37} +(4.54514 - 2.28266i) q^{38} +(-5.33040 + 7.37737i) q^{39} +(-0.946337 - 2.19386i) q^{40} +(-1.09418 - 2.53659i) q^{41} +(4.03463 + 8.99820i) q^{42} +(-1.41783 + 0.712061i) q^{43} +(-0.0355834 - 0.201803i) q^{44} +(3.38537 - 2.36763i) q^{45} +(1.13114 - 6.41502i) q^{46} +(0.596924 + 1.99387i) q^{47} +(-7.30267 - 4.65519i) q^{48} +(3.40707 + 1.71109i) q^{49} +(-1.54127 + 5.14819i) q^{50} +(-1.64969 - 8.63385i) q^{51} +(3.13141 + 4.20621i) q^{52} +(4.51663 + 7.82303i) q^{53} +(3.20681 - 8.40596i) q^{54} +(-0.141385 + 0.244885i) q^{55} +(-5.66673 + 0.662345i) q^{56} +(-4.75576 + 1.80819i) q^{57} +(10.6280 - 2.51887i) q^{58} +(12.4036 - 8.15798i) q^{59} +(-0.715089 - 2.27019i) q^{60} +(1.03396 - 1.09593i) q^{61} +(-6.73971 - 5.65528i) q^{62} +(-3.09766 - 9.36579i) q^{63} +(0.780406 - 0.654838i) q^{64} +(0.420743 - 7.22388i) q^{65} +(0.0445720 + 0.614204i) q^{66} +(-8.00722 + 10.7556i) q^{67} +(-5.03012 - 0.587936i) q^{68} +(-1.77965 + 6.26851i) q^{69} +(-6.55035 - 4.30824i) q^{70} +(4.39214 + 1.59861i) q^{71} +(4.08121 + 3.23072i) q^{72} +(15.3008 - 5.56905i) q^{73} +(-14.0167 - 3.32202i) q^{74} +(2.05863 - 4.96604i) q^{75} +(0.170445 + 2.92643i) q^{76} +(0.463367 + 0.491140i) q^{77} +(-8.07332 - 13.5338i) q^{78} +(-0.588953 + 1.36535i) q^{79} +6.88524 q^{80} +(-4.04821 + 8.03816i) q^{81} +4.78316 q^{82} +(-5.64471 + 13.0859i) q^{83} +(-5.68298 + 0.0810685i) q^{84} +(4.79576 + 5.08320i) q^{85} +(-0.159730 - 2.74246i) q^{86} +(-10.8331 + 1.42312i) q^{87} +(-0.346680 - 0.0821648i) q^{88} +(-4.83016 + 1.75803i) q^{89} +(1.44251 + 7.00591i) q^{90} +(-16.2370 - 5.90980i) q^{91} +(3.13669 + 2.06303i) q^{92} +(6.13039 + 6.31490i) q^{93} +(-3.57930 - 0.418360i) q^{94} +(2.41556 - 3.24466i) q^{95} +(7.43514 - 5.04355i) q^{96} +(0.104394 - 1.79238i) q^{97} +(-5.05691 + 4.24325i) q^{98} +(0.0182623 - 0.615762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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