LMFDB - Embedded newform 342.2.u.e.199.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [342,2,Mod(55,342)] 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("342.55"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(342, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.u (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,9,0,9,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			199.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	342.199
Dual form			342.2.u.e.55.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(3.20574 + 1.16679i) q^{5} +(2.43969 - 4.22567i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.592396 + 3.35965i) q^{10} +(-1.70574 - 2.95442i) q^{11} +(2.08125 + 1.74638i) q^{13} +(4.58512 + 1.66885i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.205737 - 1.16679i) q^{17} +(-2.52094 + 3.55596i) q^{19} -3.41147 q^{20} +(2.61334 - 2.19285i) q^{22} +(-3.20574 + 1.16679i) q^{23} +(5.08512 + 4.26692i) q^{25} +(-1.35844 + 2.35289i) q^{26} +(-0.847296 + 4.80526i) q^{28} +(-0.655230 + 3.71599i) q^{29} +(-3.30793 + 5.72951i) q^{31} +(0.766044 + 0.642788i) q^{32} +(1.11334 - 0.405223i) q^{34} +(12.7515 - 10.6998i) q^{35} +6.75877 q^{37} +(-3.93969 - 1.86516i) q^{38} +(-0.592396 - 3.35965i) q^{40} +(-5.02094 + 4.21307i) q^{41} +(-3.91875 - 1.42631i) q^{43} +(2.61334 + 2.19285i) q^{44} +(-1.70574 - 2.95442i) q^{46} +(-0.496130 + 2.81369i) q^{47} +(-8.40420 - 14.5565i) q^{49} +(-3.31908 + 5.74881i) q^{50} +(-2.55303 - 0.929228i) q^{52} +(0.592396 - 0.215615i) q^{53} +(-2.02094 - 11.4613i) q^{55} -4.87939 q^{56} -3.77332 q^{58} +(-2.02094 - 11.4613i) q^{59} +(-6.48545 + 2.36051i) q^{61} +(-6.21688 - 2.26276i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(4.63429 + 8.02682i) q^{65} +(0.123141 - 0.698367i) q^{67} +(0.592396 + 1.02606i) q^{68} +(12.7515 + 10.6998i) q^{70} +(7.47818 + 2.72183i) q^{71} +(-9.76264 + 8.19183i) q^{73} +(1.17365 + 6.65609i) q^{74} +(1.15270 - 4.20372i) q^{76} -16.6459 q^{77} +(0.228026 - 0.191336i) q^{79} +(3.20574 - 1.16679i) q^{80} +(-5.02094 - 4.21307i) q^{82} +(7.80200 - 13.5135i) q^{83} +(0.701867 - 3.98048i) q^{85} +(0.724155 - 4.10689i) q^{86} +(-1.70574 + 2.95442i) q^{88} +(-5.18866 - 4.35381i) q^{89} +(12.4572 - 4.53406i) q^{91} +(2.61334 - 2.19285i) q^{92} -2.85710 q^{94} +(-12.2306 + 8.45805i) q^{95} +(-1.23736 - 7.01741i) q^{97} +(12.8760 - 10.8042i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{5} + 9 q^{7} - 3 q^{8} + 15 q^{13} + 6 q^{14} + 9 q^{17} - 12 q^{19} + 9 q^{22} - 9 q^{23} + 9 q^{25} - 3 q^{28} + 9 q^{29} - 9 q^{31} + 36 q^{35} + 18 q^{37} - 18 q^{38} - 27 q^{41} - 21 q^{43}+ \cdots + 24 q^{98}+O(q^{100}) $ 6 * q + 9 * q^5 + 9 * q^7 - 3 * q^8 + 15 * q^13 + 6 * q^14 + 9 * q^17 - 12 * q^19 + 9 * q^22 - 9 * q^23 + 9 * q^25 - 3 * q^28 + 9 * q^29 - 9 * q^31 + 36 * q^35 + 18 * q^37 - 18 * q^38 - 27 * q^41 - 21 * q^43 + 9 * q^44 - 27 * q^47 - 12 * q^49 - 3 * q^50 - 3 * q^52 - 9 * q^55 - 18 * q^56 - 36 * q^58 - 9 * q^59 - 3 * q^61 - 21 * q^62 - 3 * q^64 + 18 * q^65 - 3 * q^67 + 36 * q^70 - 9 * q^71 - 12 * q^73 + 6 * q^74 + 9 * q^76 - 18 * q^77 - 21 * q^79 + 9 * q^80 - 27 * q^82 + 9 * q^83 + 18 * q^85 + 6 * q^86 + 24 * q^91 + 9 * q^92 - 18 * q^94 - 36 * q^95 - 54 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	3.20574	+	1.16679i	1.43365	+	0.521806i	0.937975	−	0.346703i	$-0.112699\pi$
$5$	3.20574	+	1.16679i	1.43365	+	0.521806i	0.495674	+	0.868509i	$0.334921\pi$
$6$		0			0
$7$	2.43969	−	4.22567i	0.922117	−	1.59715i	0.125984	−	0.992032i	$-0.459791\pi$
$7$	2.43969	−	4.22567i	0.922117	−	1.59715i	0.796133	−	0.605121i	$-0.206875\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$		0			0
$10$	−0.592396	+	3.35965i	−0.187332	+	1.06241i
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	−0.999862	−	0.0165906i	$-0.994719\pi$
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	0.485563	−	0.874202i	$-0.338615\pi$
$12$		0			0
$13$	2.08125	+	1.74638i	0.577235	+	0.484358i	0.884038	−	0.467415i	$-0.154815\pi$
$13$	2.08125	+	1.74638i	0.577235	+	0.484358i	−0.306803	+	0.951773i	$0.599259\pi$
$14$	4.58512	+	1.66885i	1.22543	+	0.446018i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.205737	−	1.16679i	−0.0498986	−	0.282989i	0.949641	−	0.313341i	$-0.101448\pi$
$17$	−0.205737	−	1.16679i	−0.0498986	−	0.282989i	−0.999539	+	0.0303521i	$0.990337\pi$
$18$		0			0
$19$	−2.52094	+	3.55596i	−0.578344	+	0.815793i
$19$	−2.52094	+	3.55596i	−0.578344	+	0.815793i
$20$	−3.41147			−0.762829
$21$		0			0
$22$	2.61334	−	2.19285i	0.557166	−	0.467518i
$23$	−3.20574	+	1.16679i	−0.668442	+	0.243293i	−0.653877	−	0.756601i	$-0.726859\pi$
$23$	−3.20574	+	1.16679i	−0.668442	+	0.243293i	−0.0145653	+	0.999894i	$0.504636\pi$
$24$		0			0
$25$	5.08512	+	4.26692i	1.01702	+	0.853385i
$26$	−1.35844	+	2.35289i	−0.266412	+	0.461439i
$27$		0			0
$28$	−0.847296	+	4.80526i	−0.160124	+	0.908108i
$29$	−0.655230	+	3.71599i	−0.121673	+	0.690043i	0.861555	+	0.507664i	$0.169491\pi$
$29$	−0.655230	+	3.71599i	−0.121673	+	0.690043i	−0.983228	+	0.182379i	$0.941620\pi$
$30$		0			0
$31$	−3.30793	+	5.72951i	−0.594122	+	1.02905i	0.399548	+	0.916712i	$0.369167\pi$
$31$	−3.30793	+	5.72951i	−0.594122	+	1.02905i	−0.993670	+	0.112338i	$0.964166\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$		0			0
$34$	1.11334	−	0.405223i	0.190936	−	0.0694952i
$35$	12.7515	−	10.6998i	2.15540	−	1.80859i
$36$		0			0
$37$	6.75877			1.11114			0.555568	−	0.831471i	$-0.312501\pi$
$37$	6.75877			1.11114			0.555568	+	0.831471i	$0.312501\pi$
$38$	−3.93969	−	1.86516i	−0.639103	−	0.302569i
$39$		0			0
$40$	−0.592396	−	3.35965i	−0.0936661	−	0.531207i
$41$	−5.02094	+	4.21307i	−0.784140	+	0.657971i	−0.944288	−	0.329122i	$-0.893247\pi$
$41$	−5.02094	+	4.21307i	−0.784140	+	0.657971i	0.160148	+	0.987093i	$0.448803\pi$
$42$		0			0
$43$	−3.91875	−	1.42631i	−0.597603	−	0.217510i	0.0254669	−	0.999676i	$-0.491893\pi$
$43$	−3.91875	−	1.42631i	−0.597603	−	0.217510i	−0.623070	+	0.782166i	$0.714115\pi$
$44$	2.61334	+	2.19285i	0.393976	+	0.330585i
$45$		0			0
$46$	−1.70574	−	2.95442i	−0.251497	−	0.435606i
$47$	−0.496130	+	2.81369i	−0.0723679	+	0.410419i	0.927006	+	0.375046i	$0.122373\pi$
$47$	−0.496130	+	2.81369i	−0.0723679	+	0.410419i	−0.999374	+	0.0353731i	$0.988738\pi$
$48$		0			0
$49$	−8.40420	−	14.5565i	−1.20060	−	2.07950i
$50$	−3.31908	+	5.74881i	−0.469388	+	0.813005i
$51$		0			0
$52$	−2.55303	−	0.929228i	−0.354042	−	0.128861i
$53$	0.592396	−	0.215615i	0.0813719	−	0.0296169i	−0.301013	−	0.953620i	$-0.597325\pi$
$53$	0.592396	−	0.215615i	0.0813719	−	0.0296169i	0.382385	+	0.924003i	$0.375103\pi$
$54$		0			0
$55$	−2.02094	−	11.4613i	−0.272504	−	1.54545i
$56$	−4.87939			−0.652035
$57$		0			0
$58$	−3.77332			−0.495461
$59$	−2.02094	−	11.4613i	−0.263105	−	1.49214i	−0.774379	−	0.632722i	$-0.781937\pi$
$59$	−2.02094	−	11.4613i	−0.263105	−	1.49214i	0.511274	−	0.859418i	$-0.329174\pi$
$60$		0			0
$61$	−6.48545	+	2.36051i	−0.830377	+	0.302233i	−0.722014	−	0.691879i	$-0.756783\pi$
$61$	−6.48545	+	2.36051i	−0.830377	+	0.302233i	−0.108363	+	0.994111i	$0.534561\pi$
$62$	−6.21688	−	2.26276i	−0.789545	−	0.287371i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	4.63429	+	8.02682i	0.574812	+	0.995604i
$66$		0			0
$67$	0.123141	−	0.698367i	0.0150441	−	0.0853191i	−0.976361	−	0.216145i	$-0.930652\pi$
$67$	0.123141	−	0.698367i	0.0150441	−	0.0853191i	0.991405	+	0.130826i	$0.0417628\pi$
$68$	0.592396	+	1.02606i	0.0718386	+	0.124428i
$69$		0			0
$70$	12.7515	+	10.6998i	1.52410	+	1.27887i
$71$	7.47818	+	2.72183i	0.887496	+	0.323022i	0.745231	−	0.666806i	$-0.232339\pi$
$71$	7.47818	+	2.72183i	0.887496	+	0.323022i	0.142265	+	0.989829i	$0.454561\pi$
$72$		0			0
$73$	−9.76264	+	8.19183i	−1.14263	+	0.958781i	−0.999522	−	0.0309259i	$-0.990154\pi$
$73$	−9.76264	+	8.19183i	−1.14263	+	0.958781i	−0.143109	+	0.989707i	$0.545710\pi$
$74$	1.17365	+	6.65609i	0.136434	+	0.773755i
$75$		0			0
$76$	1.15270	−	4.20372i	0.132224	−	0.482200i
$77$	−16.6459			−1.89698
$78$		0			0
$79$	0.228026	−	0.191336i	0.0256549	−	0.0215270i	−0.629870	−	0.776701i	$-0.716892\pi$
$79$	0.228026	−	0.191336i	0.0256549	−	0.0215270i	0.655525	+	0.755174i	$0.272447\pi$
$80$	3.20574	−	1.16679i	0.358412	−	0.130451i
$81$		0			0
$82$	−5.02094	−	4.21307i	−0.554471	−	0.465256i
$83$	7.80200	−	13.5135i	0.856381	−	1.48330i	−0.0189766	−	0.999820i	$-0.506041\pi$
$83$	7.80200	−	13.5135i	0.856381	−	1.48330i	0.875358	−	0.483476i	$-0.160626\pi$
$84$		0			0
$85$	0.701867	−	3.98048i	0.0761281	−	0.431744i
$86$	0.724155	−	4.10689i	0.0780877	−	0.442857i
$87$		0			0
$88$	−1.70574	+	2.95442i	−0.181832	+	0.314943i
$89$	−5.18866	−	4.35381i	−0.549997	−	0.461502i	0.324943	−	0.945734i	$-0.394655\pi$
$89$	−5.18866	−	4.35381i	−0.549997	−	0.461502i	−0.874940	+	0.484231i	$0.839099\pi$
$90$		0			0
$91$	12.4572	−	4.53406i	1.30587	−	0.475299i
$92$	2.61334	−	2.19285i	0.272460	−	0.228621i
$93$		0			0
$94$	−2.85710			−0.294687
$95$	−12.2306	+	8.45805i	−1.25483	+	0.867777i
$96$		0			0
$97$	−1.23736	−	7.01741i	−0.125635	−	0.712510i	−0.980929	−	0.194367i	$-0.937735\pi$
$97$	−1.23736	−	7.01741i	−0.125635	−	0.712510i	0.855294	−	0.518143i	$-0.173376\pi$
$98$	12.8760	−	10.8042i	1.30067	−	1.09139i
$99$		0			0
$100$	−6.23783	−	2.27038i	−0.623783	−	0.227038i
$101$	3.55896	+	2.98632i	0.354130	+	0.297150i	0.802446	−	0.596725i	$-0.203532\pi$
$101$	3.55896	+	2.98632i	0.354130	+	0.297150i	−0.448316	+	0.893875i	$0.647976\pi$
$102$		0			0
$103$	6.19119	+	10.7235i	0.610036	+	1.05661i	0.991234	+	0.132120i	$0.0421784\pi$
$103$	6.19119	+	10.7235i	0.610036	+	1.05661i	−0.381198	+	0.924494i	$0.624488\pi$
$104$	0.471782	−	2.67561i	0.0462620	−	0.262365i
$105$		0			0
$106$	0.315207	+	0.545955i	0.0306157	+	0.0530279i
$107$	1.94949	−	3.37662i	0.188465	−	0.326430i	−0.756274	−	0.654255i	$-0.772982\pi$
$107$	1.94949	−	3.37662i	0.188465	−	0.326430i	0.944739	+	0.327825i	$0.106316\pi$
$108$		0			0
$109$	10.8969	+	3.96616i	1.04374	+	0.379889i	0.806295	−	0.591513i	$-0.201469\pi$
$109$	10.8969	+	3.96616i	1.04374	+	0.379889i	0.237441	+	0.971402i	$0.423691\pi$
$110$	10.9363	−	3.98048i	1.04273	−	0.379524i
$111$		0			0
$112$	−0.847296	−	4.80526i	−0.0800620	−	0.454054i
$113$	−1.94087			−0.182582			−0.0912911	−	0.995824i	$-0.529099\pi$
$113$	−1.94087			−0.182582			−0.0912911	+	0.995824i	$0.529099\pi$
$114$		0			0
$115$	−11.6382			−1.08526
$116$	−0.655230	−	3.71599i	−0.0608366	−	0.345021i
$117$		0			0
$118$	10.9363	−	3.98048i	1.00677	−	0.366433i
$119$	−5.43242	−	1.97724i	−0.497989	−	0.181253i
$120$		0			0
$121$	−0.319078	+	0.552659i	−0.0290071	+	0.0502417i
$122$	−3.45084	−	5.97702i	−0.312424	−	0.541134i
$123$		0			0
$124$	1.14883	−	6.51536i	0.103168	−	0.585096i
$125$	2.79426	+	4.83981i	0.249926	+	0.432885i
$126$		0			0
$127$	−4.66044	−	3.91058i	−0.413548	−	0.347008i	0.412155	−	0.911114i	$-0.364776\pi$
$127$	−4.66044	−	3.91058i	−0.413548	−	0.347008i	−0.825702	+	0.564106i	$0.809221\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$		0			0
$130$	−7.10014	+	5.95772i	−0.622723	+	0.522527i
$131$	3.23055	+	18.3214i	0.282255	+	1.60075i	0.714930	+	0.699196i	$0.246458\pi$
$131$	3.23055	+	18.3214i	0.282255	+	1.60075i	−0.432676	+	0.901550i	$0.642430\pi$
$132$		0			0
$133$	8.87598	+	19.3281i	0.769645	+	1.67596i
$134$	0.709141			0.0612604
$135$		0			0
$136$	−0.907604	+	0.761570i	−0.0778264	+	0.0653041i
$137$	4.27244	−	1.55504i	0.365019	−	0.132856i	−0.152998	−	0.988227i	$-0.548893\pi$
$137$	4.27244	−	1.55504i	0.365019	−	0.132856i	0.518017	+	0.855370i	$0.326670\pi$
$138$		0			0
$139$	−2.30928	−	1.93771i	−0.195870	−	0.164355i	0.539578	−	0.841936i	$-0.318584\pi$
$139$	−2.30928	−	1.93771i	−0.195870	−	0.164355i	−0.735448	+	0.677581i	$0.763028\pi$
$140$	−8.32295	+	14.4158i	−0.703418	+	1.21835i
$141$		0			0
$142$	−1.38191	+	7.83721i	−0.115967	+	0.657684i
$143$	1.60947	−	9.12776i	0.134591	−	0.763302i
$144$		0			0
$145$	−6.43629	+	11.1480i	−0.534505	+	0.925789i
$146$	−9.76264	−	8.19183i	−0.807962	−	0.677961i
$147$		0			0
$148$	−6.35117	+	2.31164i	−0.522063	+	0.190015i
$149$	−0.907604	+	0.761570i	−0.0743538	+	0.0623902i	−0.679207	−	0.733947i	$-0.737676\pi$
$149$	−0.907604	+	0.761570i	−0.0743538	+	0.0623902i	0.604853	+	0.796337i	$0.293232\pi$
$150$		0			0
$151$	−3.63816			−0.296069			−0.148034	−	0.988982i	$-0.547295\pi$
$151$	−3.63816			−0.296069			−0.148034	+	0.988982i	$0.547295\pi$
$152$	4.34002	+	0.405223i	0.352022	+	0.0328679i
$153$		0			0
$154$	−2.89053	−	16.3930i	−0.232926	−	1.32099i
$155$	−17.2895	+	14.5076i	−1.38873	+	1.16528i
$156$		0			0
$157$	−5.89306	−	2.14490i	−0.470317	−	0.171181i	0.0959789	−	0.995383i	$-0.469402\pi$
$157$	−5.89306	−	2.14490i	−0.470317	−	0.171181i	−0.566296	+	0.824202i	$0.691624\pi$
$158$	0.228026	+	0.191336i	0.0181408	+	0.0152219i
$159$		0			0
$160$	1.70574	+	2.95442i	0.134850	+	0.233568i
$161$	−2.89053	+	16.3930i	−0.227806	+	1.29195i
$162$		0			0
$163$	9.64930	+	16.7131i	0.755792	+	1.30907i	0.944980	+	0.327128i	$0.106081\pi$
$163$	9.64930	+	16.7131i	0.755792	+	1.30907i	−0.189188	+	0.981941i	$0.560586\pi$
$164$	3.27719	−	5.67626i	0.255905	−	0.443241i
$165$		0			0
$166$	14.6630	+	5.33688i	1.13807	+	0.414223i
$167$	−7.25624	+	2.64106i	−0.561505	+	0.204371i	−0.607151	−	0.794587i	$-0.707688\pi$
$167$	−7.25624	+	2.64106i	−0.561505	+	0.204371i	0.0456458	+	0.998958i	$0.485465\pi$
$168$		0			0
$169$	−0.975652	−	5.53320i	−0.0750501	−	0.425631i
$170$	4.04189			0.309999
$171$		0			0
$172$	4.17024			0.317978
$173$	2.51707	+	14.2750i	0.191370	+	1.08531i	0.917495	+	0.397748i	$0.130208\pi$
$173$	2.51707	+	14.2750i	0.191370	+	1.08531i	−0.726125	+	0.687563i	$0.758681\pi$
$174$		0			0
$175$	30.4368	−	11.0781i	2.30080	−	0.837424i
$176$	−3.20574	−	1.16679i	−0.241642	−	0.0879503i
$177$		0			0
$178$	3.38666	−	5.86587i	0.253841	−	0.439665i
$179$	−4.91147	−	8.50692i	−0.367101	−	0.635837i	0.622010	−	0.783009i	$-0.286316\pi$
$179$	−4.91147	−	8.50692i	−0.367101	−	0.635837i	−0.989111	+	0.147172i	$0.952983\pi$
$180$		0			0
$181$	3.28446	−	18.6271i	0.244132	−	1.38454i	−0.578367	−	0.815777i	$-0.696310\pi$
$181$	3.28446	−	18.6271i	0.244132	−	1.38454i	0.822499	−	0.568766i	$-0.192579\pi$
$182$	6.62836	+	11.4806i	0.491326	+	0.851002i
$183$		0			0
$184$	2.61334	+	2.19285i	0.192658	+	0.161659i
$185$	21.6668	+	7.88609i	1.59298	+	0.579797i
$186$		0			0
$187$	−3.09627	+	2.59808i	−0.226421	+	0.189990i
$188$	−0.496130	−	2.81369i	−0.0361840	−	0.205209i
$189$		0			0
$190$	−10.4534	−	10.5760i	−0.758367	−	0.767265i
$191$	10.0915			0.730197			0.365098	−	0.930969i	$-0.381035\pi$
$191$	10.0915			0.730197			0.365098	+	0.930969i	$0.381035\pi$
$192$		0			0
$193$	1.93376	−	1.62262i	0.139195	−	0.116799i	−0.570532	−	0.821276i	$-0.693263\pi$
$193$	1.93376	−	1.62262i	0.139195	−	0.116799i	0.709727	+	0.704477i	$0.248818\pi$
$194$	6.69594	−	2.43712i	0.480740	−	0.174975i
$195$		0			0
$196$	12.8760	+	10.8042i	0.919713	+	0.771731i
$197$	7.42855	−	12.8666i	0.529262	−	0.916709i	−0.470155	−	0.882584i	$-0.655802\pi$
$197$	7.42855	−	12.8666i	0.529262	−	0.916709i	0.999418	−	0.0341253i	$-0.0108645\pi$
$198$		0			0
$199$	1.40121	−	7.94664i	0.0993289	−	0.563322i	−0.894006	−	0.448056i	$-0.852117\pi$
$199$	1.40121	−	7.94664i	0.0993289	−	0.563322i	0.993335	−	0.115267i	$-0.0367723\pi$
$200$	1.15270	−	6.53731i	0.0815085	−	0.462257i
$201$		0			0
$202$	−2.32295	+	4.02346i	−0.163442	+	0.283090i
$203$	14.1040	+	11.8347i	0.989907	+	0.830631i
$204$		0			0
$205$	−21.0116	+	7.64760i	−1.46751	+	0.534132i
$206$	−9.48545	+	7.95924i	−0.660883	+	0.554546i
$207$		0			0
$208$	2.71688			0.188382
$209$	14.8059	+	1.38241i	1.02414	+	0.0956231i
$210$		0			0
$211$	1.37939	+	7.82288i	0.0949608	+	0.538549i	0.994759	+	0.102244i	$0.0326022\pi$
$211$	1.37939	+	7.82288i	0.0949608	+	0.538549i	−0.899799	+	0.436306i	$0.856287\pi$
$212$	−0.482926	+	0.405223i	−0.0331675	+	0.0278308i
$213$		0			0
$214$	3.66385	+	1.33353i	0.250455	+	0.0911583i
$215$	−10.8983	−	9.14473i	−0.743256	−	0.623666i
$216$		0			0
$217$	16.1407	+	27.9565i	1.09570	+	1.89781i
$218$	−2.01367	+	11.4201i	−0.136383	+	0.773466i
$219$		0			0
$220$	5.81908	+	10.0789i	0.392322	+	0.679522i
$221$	1.60947	−	2.78768i	0.108265	−	0.187520i
$222$		0			0
$223$	−11.2464	−	4.09337i	−0.753118	−	0.274112i	−0.0632006	−	0.998001i	$-0.520131\pi$
$223$	−11.2464	−	4.09337i	−0.753118	−	0.274112i	−0.689917	+	0.723888i	$0.742353\pi$
$224$	4.58512	−	1.66885i	0.306356	−	0.111505i
$225$		0			0
$226$	−0.337029	−	1.91139i	−0.0224189	−	0.127144i
$227$	−26.5945			−1.76514			−0.882570	−	0.470181i	$-0.844189\pi$
$227$	−26.5945			−1.76514			−0.882570	+	0.470181i	$0.844189\pi$
$228$		0			0
$229$	−19.9026			−1.31520			−0.657601	−	0.753367i	$-0.728429\pi$
$229$	−19.9026			−1.31520			−0.657601	+	0.753367i	$0.728429\pi$
$230$	−2.02094	−	11.4613i	−0.133257	−	0.755739i
$231$		0			0
$232$	3.54576	−	1.29055i	0.232791	−	0.0847288i
$233$	−4.05051	−	1.47426i	−0.265358	−	0.0965822i	0.205915	−	0.978570i	$-0.433983\pi$
$233$	−4.05051	−	1.47426i	−0.265358	−	0.0965822i	−0.471273	+	0.881988i	$0.656205\pi$
$234$		0			0
$235$	−4.87346	+	8.44107i	−0.317909	+	0.550635i
$236$	5.81908	+	10.0789i	0.378790	+	0.656083i
$237$		0			0
$238$	1.00387	−	5.69323i	0.0650713	−	0.369037i
$239$	0.142903	+	0.247516i	0.00924366	+	0.0160105i	0.870610	−	0.491973i	$-0.163724\pi$
$239$	0.142903	+	0.247516i	0.00924366	+	0.0160105i	−0.861367	+	0.507984i	$0.830391\pi$
$240$		0			0
$241$	7.32816	+	6.14906i	0.472048	+	0.396096i	0.847541	−	0.530730i	$-0.178082\pi$
$241$	7.32816	+	6.14906i	0.472048	+	0.396096i	−0.375493	+	0.926825i	$0.622526\pi$
$242$	−0.599670	−	0.218262i	−0.0385483	−	0.0140304i
$243$		0			0
$244$	5.28699	−	4.43631i	0.338465	−	0.284006i
$245$	−9.95723	−	56.4703i	−0.636144	−	3.60775i
$246$		0			0
$247$	−11.4568	+	2.99832i	−0.728977	+	0.190779i
$248$	6.61587			0.420108
$249$		0			0
$250$	−4.28106	+	3.59224i	−0.270758	+	0.227193i
$251$	27.8974	−	10.1538i	1.76087	−	0.640903i	0.760900	−	0.648870i	$-0.224758\pi$
$251$	27.8974	−	10.1538i	1.76087	−	0.640903i	0.999968	+	0.00796619i	$0.00253575\pi$
$252$		0			0
$253$	8.91534	+	7.48086i	0.560503	+	0.470318i
$254$	3.04189	−	5.26871i	0.190865	−	0.330588i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−2.74304	+	15.5566i	−0.171106	+	0.970391i	0.771437	+	0.636306i	$0.219538\pi$
$257$	−2.74304	+	15.5566i	−0.171106	+	0.970391i	−0.942543	+	0.334085i	$0.891573\pi$
$258$		0			0
$259$	16.4893	−	28.5603i	1.02460	−	1.77465i
$260$	−7.10014	−	5.95772i	−0.440332	−	0.369482i
$261$		0			0
$262$	−17.4820	+	6.36295i	−1.08004	+	0.393104i
$263$	−8.32295	+	6.98378i	−0.513215	+	0.430638i	−0.862259	−	0.506468i	$-0.830951\pi$
$263$	−8.32295	+	6.98378i	−0.513215	+	0.430638i	0.349044	+	0.937106i	$0.386506\pi$
$264$		0			0
$265$	2.15064			0.132113
$266$	−17.4932	+	12.0974i	−1.07258	+	0.741741i
$267$		0			0
$268$	0.123141	+	0.698367i	0.00752203	+	0.0426596i
$269$	13.2476	−	11.1161i	0.807722	−	0.677759i	−0.142341	−	0.989818i	$-0.545463\pi$
$269$	13.2476	−	11.1161i	0.807722	−	0.677759i	0.950063	+	0.312058i	$0.101018\pi$
$270$		0			0
$271$	−1.35844	−	0.494432i	−0.0825194	−	0.0300346i	0.300431	−	0.953804i	$-0.402870\pi$
$271$	−1.35844	−	0.494432i	−0.0825194	−	0.0300346i	−0.382950	+	0.923769i	$0.625092\pi$
$272$	−0.907604	−	0.761570i	−0.0550316	−	0.0461770i
$273$		0			0
$274$	2.27332	+	3.93750i	0.137336	+	0.237873i
$275$	3.93242	−	22.3019i	0.237134	−	1.34485i
$276$		0			0
$277$	−10.5954	−	18.3518i	−0.636615	−	1.10265i	−0.986170	−	0.165734i	$-0.947001\pi$
$277$	−10.5954	−	18.3518i	−0.636615	−	1.10265i	0.349555	−	0.936916i	$-0.386333\pi$
$278$	1.50727	−	2.61068i	0.0904003	−	0.156578i
$279$		0			0
$280$	−15.6420	−	5.69323i	−0.934790	−	0.340236i
$281$	−22.8983	+	8.33429i	−1.36600	+	0.497182i	−0.917903	−	0.396805i	$-0.870119\pi$
$281$	−22.8983	+	8.33429i	−1.36600	+	0.497182i	−0.448093	+	0.893987i	$0.647897\pi$
$282$		0			0
$283$	−0.716415	−	4.06299i	−0.0425864	−	0.241520i	0.956083	−	0.293098i	$-0.0946861\pi$
$283$	−0.716415	−	4.06299i	−0.0425864	−	0.241520i	−0.998669	+	0.0515779i	$0.983575\pi$
$284$	−7.95811			−0.472227
$285$		0			0
$286$	9.26857			0.548062
$287$	5.55350	+	31.4955i	0.327813	+	1.85912i
$288$		0			0
$289$	14.6557	−	5.33424i	0.862100	−	0.313779i
$290$	−12.0963	−	4.40268i	−0.710317	−	0.258534i
$291$		0			0
$292$	6.37211	−	11.0368i	0.372900	−	0.645881i
$293$	1.39053	+	2.40847i	0.0812356	+	0.140704i	0.903781	−	0.427995i	$-0.140780\pi$
$293$	1.39053	+	2.40847i	0.0812356	+	0.140704i	−0.822545	+	0.568700i	$0.807447\pi$
$294$		0			0
$295$	6.89440	−	39.1001i	0.401407	−	2.27649i
$296$	−3.37939	−	5.85327i	−0.196423	−	0.340214i
$297$		0			0
$298$	−0.907604	−	0.761570i	−0.0525761	−	0.0441166i
$299$	−8.70961	−	3.17004i	−0.503690	−	0.183328i
$300$		0			0
$301$	−15.5876	+	13.0796i	−0.898457	+	0.753895i
$302$	−0.631759	−	3.58288i	−0.0363537	−	0.206172i
$303$		0			0
$304$	0.354570	+	4.34445i	0.0203360	+	0.249172i
$305$	−23.5449			−1.34818
$306$		0			0
$307$	−19.1689	+	16.0846i	−1.09403	+	0.917998i	−0.997009	−	0.0772850i	$-0.975375\pi$
$307$	−19.1689	+	16.0846i	−1.09403	+	0.917998i	−0.0970179	+	0.995283i	$0.530930\pi$
$308$	15.6420	−	5.69323i	0.891287	−	0.324402i
$309$		0			0
$310$	−17.2895	−	14.5076i	−0.981978	−	0.823978i
$311$	11.9868	−	20.7617i	0.679709	−	1.17729i	−0.295360	−	0.955386i	$-0.595439\pi$
$311$	11.9868	−	20.7617i	0.679709	−	1.17729i	0.975068	−	0.221904i	$-0.0712272\pi$
$312$		0			0
$313$	−2.19459	+	12.4462i	−0.124046	+	0.703498i	0.857824	+	0.513943i	$0.171816\pi$
$313$	−2.19459	+	12.4462i	−0.124046	+	0.703498i	−0.981870	+	0.189555i	$0.939295\pi$
$314$	1.08899	−	6.17598i	0.0614554	−	0.348531i
$315$		0			0
$316$	−0.148833	+	0.257787i	−0.00837252	+	0.0145016i
$317$	10.8268	+	9.08478i	0.608095	+	0.510252i	0.894036	−	0.447995i	$-0.147862\pi$
$317$	10.8268	+	9.08478i	0.608095	+	0.510252i	−0.285941	+	0.958247i	$0.592306\pi$
$318$		0			0
$319$	12.0963	−	4.40268i	0.677261	−	0.246503i
$320$	−2.61334	+	2.19285i	−0.146090	+	0.122584i
$321$		0			0
$322$	−16.6459			−0.927640
$323$	4.66772	+	2.20983i	0.259719	+	0.122958i
$324$		0			0
$325$	3.13176	+	17.7611i	0.173719	+	0.985208i
$326$	−14.7836	+	12.4049i	−0.818787	+	0.687044i
$327$		0			0
$328$	6.15910	+	2.24173i	0.340079	+	0.123779i
$329$	10.6793	+	8.96102i	0.588770	+	0.494037i
$330$		0			0
$331$	−14.7490	−	25.5460i	−0.810677	−	1.40413i	−0.912391	−	0.409320i	$-0.865766\pi$
$331$	−14.7490	−	25.5460i	−0.810677	−	1.40413i	0.101714	−	0.994814i	$-0.467567\pi$
$332$	−2.70961	+	15.3669i	−0.148709	+	0.843371i
$333$		0			0
$334$	−3.86097	−	6.68739i	−0.211263	−	0.365918i
$335$	1.20961	−	2.09510i	0.0660879	−	0.114468i
$336$		0			0
$337$	20.9072	+	7.60960i	1.13889	+	0.414521i	0.841511	−	0.540239i	$-0.181666\pi$
$337$	20.9072	+	7.60960i	1.13889	+	0.414521i	0.297376	+	0.954760i	$0.403889\pi$
$338$	5.27972	−	1.92166i	0.287179	−	0.104524i
$339$		0			0
$340$	0.701867	+	3.98048i	0.0380641	+	0.215872i
$341$	22.5699			1.22223
$342$		0			0
$343$	−47.8590			−2.58414
$344$	0.724155	+	4.10689i	0.0390438	+	0.221429i
$345$		0			0
$346$	−13.6211	+	4.95767i	−0.732274	+	0.266526i
$347$	−13.1792	−	4.79682i	−0.707495	−	0.257507i	−0.0368873	−	0.999319i	$-0.511744\pi$
$347$	−13.1792	−	4.79682i	−0.707495	−	0.257507i	−0.670607	+	0.741812i	$0.733966\pi$
$348$		0			0
$349$	17.0560	−	29.5419i	0.912988	−	1.58134i	0.103168	−	0.994664i	$-0.467102\pi$
$349$	17.0560	−	29.5419i	0.912988	−	1.58134i	0.809820	−	0.586678i	$-0.199565\pi$
$350$	16.1951	+	28.0507i	0.865662	+	1.49937i
$351$		0			0
$352$	0.592396	−	3.35965i	0.0315748	−	0.179070i
$353$	15.2219	+	26.3652i	0.810182	+	1.40328i	0.912737	+	0.408549i	$0.133965\pi$
$353$	15.2219	+	26.3652i	0.810182	+	1.40328i	−0.102555	+	0.994727i	$0.532702\pi$
$354$		0			0
$355$	20.7973	+	17.4510i	1.10380	+	0.926201i
$356$	6.36484	+	2.31661i	0.337336	+	0.122780i
$357$		0			0
$358$	7.52481	−	6.31407i	0.397699	−	0.333709i
$359$	−2.36959	−	13.4386i	−0.125062	−	0.709261i	−0.981271	−	0.192632i	$-0.938298\pi$
$359$	−2.36959	−	13.4386i	−0.125062	−	0.709261i	0.856209	−	0.516629i	$-0.172813\pi$
$360$		0			0
$361$	−6.28968	−	17.9287i	−0.331036	−	0.943618i
$362$	18.9145			0.994122
$363$		0			0
$364$	−10.1552	+	8.52125i	−0.532279	+	0.446635i
$365$	−40.8546	+	14.8699i	−2.13843	+	0.778324i
$366$		0			0
$367$	18.2062	+	15.2768i	0.950356	+	0.797443i	0.979357	−	0.202136i	$-0.0647883\pi$
$367$	18.2062	+	15.2768i	0.950356	+	0.797443i	−0.0290014	+	0.999579i	$0.509233\pi$
$368$	−1.70574	+	2.95442i	−0.0889177	+	0.154010i
$369$		0			0
$370$	−4.00387	+	22.7071i	−0.208151	+	1.18048i
$371$	0.534148	−	3.02931i	0.0277316	−	0.157274i
$372$		0			0
$373$	11.6172	−	20.1216i	0.601516	−	1.04186i	−0.391075	−	0.920359i	$-0.627897\pi$
$373$	11.6172	−	20.1216i	0.601516	−	1.04186i	0.992592	−	0.121498i	$-0.0387699\pi$
$374$	−3.09627	−	2.59808i	−0.160104	−	0.134343i
$375$		0			0
$376$	2.68479	−	0.977185i	0.138458	−	0.0503944i
$377$	−7.85323	+	6.58964i	−0.404462	+	0.339384i
$378$		0			0
$379$	−4.50030			−0.231165			−0.115583	−	0.993298i	$-0.536873\pi$
$379$	−4.50030			−0.231165			−0.115583	+	0.993298i	$0.536873\pi$
$380$	8.60014	−	12.1311i	0.441178	−	0.622310i
$381$		0			0
$382$	1.75237	+	9.93821i	0.0896592	+	0.508483i
$383$	−3.34002	+	2.80261i	−0.170667	+	0.143207i	−0.724121	−	0.689673i	$-0.757754\pi$
$383$	−3.34002	+	2.80261i	−0.170667	+	0.143207i	0.553453	+	0.832880i	$0.313310\pi$
$384$		0			0
$385$	−53.3624	−	19.4223i	−2.71960	−	0.989853i
$386$	1.93376	+	1.62262i	0.0984259	+	0.0825892i
$387$		0			0
$388$	3.56283	+	6.17101i	0.180875	+	0.313286i
$389$	0.227559	−	1.29055i	0.0115377	−	0.0654335i	−0.978495	−	0.206269i	$-0.933868\pi$
$389$	0.227559	−	1.29055i	0.0115377	−	0.0654335i	0.990033	+	0.140836i	$0.0449789\pi$
$390$		0			0
$391$	2.02094	+	3.50038i	0.102204	+	0.177022i
$392$	−8.40420	+	14.5565i	−0.424476	+	0.735214i
$393$		0			0
$394$	13.9611	+	5.08143i	0.703350	+	0.255999i
$395$	0.954241	−	0.347315i	0.0480131	−	0.0174753i
$396$		0			0
$397$	−3.30154	−	18.7239i	−0.165699	−	0.939728i	−0.948340	−	0.317255i	$-0.897239\pi$
$397$	−3.30154	−	18.7239i	−0.165699	−	0.939728i	0.782641	−	0.622473i	$-0.213872\pi$
$398$	8.06923			0.404474
$399$		0			0
$400$	6.63816			0.331908
$401$	−6.22756	−	35.3182i	−0.310989	−	1.76371i	−0.593877	−	0.804556i	$-0.702403\pi$
$401$	−6.22756	−	35.3182i	−0.310989	−	1.76371i	0.282888	−	0.959153i	$-0.408708\pi$
$402$		0			0
$403$	−16.8905	+	6.14765i	−0.841377	+	0.306236i
$404$	−4.36571	−	1.58899i	−0.217202	−	0.0790552i
$405$		0			0
$406$	−9.20574	+	15.9448i	−0.456873	+	0.791327i
$407$	−11.5287	−	19.9683i	−0.571456	−	0.989790i
$408$		0			0
$409$	−5.05468	+	28.6665i	−0.249938	+	1.41747i	0.558801	+	0.829301i	$0.311261\pi$
$409$	−5.05468	+	28.6665i	−0.249938	+	1.41747i	−0.808739	+	0.588167i	$0.799850\pi$
$410$	−11.1800	−	19.3644i	−0.552143	−	0.956340i
$411$		0			0
$412$	−9.48545	−	7.95924i	−0.467315	−	0.392124i
$413$	−53.3624	−	19.4223i	−2.62579	−	0.955710i
$414$		0			0
$415$	40.7786	−	34.2173i	2.00174	−	1.67966i
$416$	0.471782	+	2.67561i	0.0231310	+	0.131182i
$417$		0			0
$418$	1.20961	+	14.8210i	0.0591638	+	0.724918i
$419$	−13.1584			−0.642829			−0.321415	−	0.946939i	$-0.604158\pi$
$419$	−13.1584			−0.642829			−0.321415	+	0.946939i	$0.604158\pi$
$420$		0			0
$421$	−0.115400	+	0.0968323i	−0.00562426	+	0.00471932i	−0.645595	−	0.763680i	$-0.723391\pi$
$421$	−0.115400	+	0.0968323i	−0.00562426	+	0.00471932i	0.639971	+	0.768399i	$0.278946\pi$
$422$	−7.46451	+	2.71686i	−0.363367	+	0.132255i
$423$		0			0
$424$	−0.482926	−	0.405223i	−0.0234530	−	0.0196794i
$425$	3.93242	−	6.81115i	0.190750	−	0.330389i
$426$		0			0
$427$	−5.84776	+	33.1643i	−0.282993	+	1.60493i
$428$	−0.677052	+	3.83975i	−0.0327265	+	0.185601i
$429$		0			0
$430$	7.11334	−	12.3207i	0.343036	−	0.594155i
$431$	23.5915	+	19.7956i	1.13636	+	0.953522i	0.999314	−	0.0370420i	$-0.0117935\pi$
$431$	23.5915	+	19.7956i	1.13636	+	0.953522i	0.137050	+	0.990564i	$0.456238\pi$
$432$		0			0
$433$	27.6587	−	10.0669i	1.32919	−	0.483786i	0.422800	−	0.906223i	$-0.361047\pi$
$433$	27.6587	−	10.0669i	1.32919	−	0.483786i	0.906392	+	0.422437i	$0.138825\pi$
$434$	−24.7290	+	20.7501i	−1.18703	+	0.996035i
$435$		0			0
$436$	−11.5963			−0.555360
$437$	3.93242	−	14.3409i	0.188113	−	0.686018i
$438$		0			0
$439$	3.43835	+	19.4998i	0.164103	+	0.930677i	0.949984	+	0.312298i	$0.101099\pi$
$439$	3.43835	+	19.4998i	0.164103	+	0.930677i	−0.785881	+	0.618378i	$0.787790\pi$
$440$	−8.91534	+	7.48086i	−0.425022	+	0.356636i
$441$		0			0
$442$	3.02481	+	1.10094i	0.143876	+	0.0523665i
$443$	14.2383	+	11.9473i	0.676482	+	0.567636i	0.914976	−	0.403508i	$-0.132209\pi$
$443$	14.2383	+	11.9473i	0.676482	+	0.567636i	−0.238494	+	0.971144i	$0.576654\pi$
$444$		0			0
$445$	−11.5535	−	20.0112i	−0.547688	−	0.948624i
$446$	2.07826	−	11.7864i	0.0984084	−	0.558102i
$447$		0			0
$448$	2.43969	+	4.22567i	0.115265	+	0.199644i
$449$	1.68954	−	2.92637i	0.0797343	−	0.138104i	−0.823401	−	0.567460i	$-0.807926\pi$
$449$	1.68954	−	2.92637i	0.0797343	−	0.138104i	0.903135	+	0.429356i	$0.141259\pi$
$450$		0			0
$451$	21.0116	+	7.64760i	0.989398	+	0.360111i
$452$	1.82383	−	0.663818i	0.0857855	−	0.0312234i
$453$		0			0
$454$	−4.61809	−	26.1905i	−0.216738	−	1.22918i
$455$	45.2249			2.12018
$456$		0			0
$457$	21.7912			1.01935			0.509674	−	0.860368i	$-0.329766\pi$
$457$	21.7912			1.01935			0.509674	+	0.860368i	$0.329766\pi$
$458$	−3.45605	−	19.6002i	−0.161491	−	0.915859i
$459$		0			0
$460$	10.9363	−	3.98048i	0.509907	−	0.185591i
$461$	11.0544	+	4.02346i	0.514854	+	0.187391i	0.586363	−	0.810049i	$-0.300559\pi$
$461$	11.0544	+	4.02346i	0.514854	+	0.187391i	−0.0715092	+	0.997440i	$0.522782\pi$
$462$		0			0
$463$	−8.49660	+	14.7165i	−0.394870	+	0.683935i	−0.993085	−	0.117401i	$-0.962544\pi$
$463$	−8.49660	+	14.7165i	−0.394870	+	0.683935i	0.598214	+	0.801336i	$0.295877\pi$
$464$	1.88666	+	3.26779i	0.0875860	+	0.151703i
$465$		0			0
$466$	0.748503	−	4.24497i	0.0346738	−	0.196645i
$467$	−5.85251	−	10.1368i	−0.270822	−	0.469077i	0.698251	−	0.715853i	$-0.253962\pi$
$467$	−5.85251	−	10.1368i	−0.270822	−	0.469077i	−0.969073	+	0.246776i	$0.920629\pi$
$468$		0			0
$469$	−2.65064	−	2.22415i	−0.122395	−	0.102702i
$470$	−9.15910	−	3.33364i	−0.422478	−	0.153769i
$471$		0			0
$472$	−8.91534	+	7.48086i	−0.410362	+	0.344335i
$473$	2.47044	+	14.0105i	0.113591	+	0.644206i
$474$		0			0
$475$	−27.9923	+	7.32580i	−1.28438	+	0.336131i
$476$	5.78106			0.264974
$477$		0			0
$478$	−0.218941	+	0.183713i	−0.0100141	+	0.00840284i
$479$	28.1716	−	10.2536i	1.28719	−	0.468500i	0.394388	−	0.918944i	$-0.370957\pi$
$479$	28.1716	−	10.2536i	1.28719	−	0.468500i	0.892805	+	0.450444i	$0.148734\pi$
$480$		0			0
$481$	14.0667	+	11.8034i	0.641386	+	0.538187i
$482$	−4.78312	+	8.28460i	−0.217865	+	0.377353i
$483$		0			0
$484$	0.110815	−	0.628461i	0.00503703	−	0.0285664i
$485$	4.22122	−	23.9397i	0.191676	−	1.08705i
$486$		0			0
$487$	−7.25537	+	12.5667i	−0.328772	+	0.569450i	−0.982268	−	0.187480i	$-0.939968\pi$
$487$	−7.25537	+	12.5667i	−0.328772	+	0.569450i	0.653496	+	0.756930i	$0.273301\pi$
$488$	5.28699	+	4.43631i	0.239331	+	0.200822i
$489$		0			0
$490$	53.8833	−	19.6119i	2.43420	−	0.885976i
$491$	8.92855	−	7.49194i	0.402940	−	0.338107i	−0.418689	−	0.908130i	$-0.637510\pi$
$491$	8.92855	−	7.49194i	0.402940	−	0.338107i	0.821629	+	0.570023i	$0.193066\pi$
$492$		0			0
$493$	4.47060			0.201346
$494$	−4.94222	−	10.7621i	−0.222361	−	0.484208i
$495$		0			0
$496$	1.14883	+	6.51536i	0.0515841	+	0.292548i
$497$	29.7460	−	24.9599i	1.33429	−	1.11960i
$498$		0			0
$499$	1.58512	+	0.576937i	0.0709598	+	0.0258273i	0.377256	−	0.926109i	$-0.376868\pi$
$499$	1.58512	+	0.576937i	0.0709598	+	0.0258273i	−0.306296	+	0.951936i	$0.599090\pi$
$500$	−4.28106	−	3.59224i	−0.191455	−	0.160650i
$501$		0			0
$502$	14.8439	+	25.7104i	0.662515	+	1.14751i
$503$	−3.00299	+	17.0308i	−0.133897	+	0.759367i	0.841725	+	0.539907i	$0.181541\pi$
$503$	−3.00299	+	17.0308i	−0.133897	+	0.759367i	−0.975622	+	0.219460i	$0.929571\pi$
$504$		0			0
$505$	7.92468	+	13.7259i	0.352644	+	0.610797i
$506$	−5.81908	+	10.0789i	−0.258690	+	0.448063i
$507$		0			0
$508$	5.71688	+	2.08077i	0.253646	+	0.0923194i
$509$	30.4859	−	11.0960i	1.35126	−	0.491820i	0.437922	−	0.899013i	$-0.355714\pi$
$509$	30.4859	−	11.0960i	1.35126	−	0.491820i	0.913342	+	0.407193i	$0.133492\pi$
$510$		0			0
$511$	10.7981	+	61.2393i	0.477681	+	2.70907i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−15.7965			−0.696756
$515$	7.33527	+	41.6004i	0.323231	+	1.83313i
$516$		0			0
$517$	9.15910	−	3.33364i	0.402817	−	0.146613i
$518$	30.9898	+	11.2794i	1.36161	+	0.495587i
$519$		0			0
$520$	4.63429	−	8.02682i	0.203227	−	0.351999i
$521$	15.5822	+	26.9891i	0.682668	+	1.18242i	0.974164	+	0.225843i	$0.0725138\pi$
$521$	15.5822	+	26.9891i	0.682668	+	1.18242i	−0.291496	+	0.956572i	$0.594153\pi$
$522$		0			0
$523$	−2.89306	+	16.4073i	−0.126504	+	0.717443i	0.853898	+	0.520440i	$0.174232\pi$
$523$	−2.89306	+	16.4073i	−0.126504	+	0.717443i	−0.980403	+	0.197003i	$0.936879\pi$
$524$	−9.30200	−	16.1115i	−0.406360	−	0.703836i
$525$		0			0
$526$	−8.32295	−	6.98378i	−0.362898	−	0.304507i
$527$	7.36571	+	2.68090i	0.320856	+	0.116782i
$528$		0			0
$529$	−8.70368	+	7.30325i	−0.378421	+	0.317533i
$530$	0.373455	+	2.11797i	0.0162219	+	0.0919988i
$531$		0			0
$532$	−14.9513	−	15.1267i	−0.648221	−	0.655827i
$533$	−17.8075			−0.771327
$534$		0			0
$535$	10.1894	−	8.54990i	0.440525	−	0.369645i
$536$	−0.666374	+	0.242540i	−0.0287830	+	0.0104761i
$537$		0			0
$538$	13.2476	+	11.1161i	0.571146	+	0.479248i
$539$	−28.6707	+	49.6591i	−1.23493	+	2.13897i
$540$		0			0
$541$	6.29385	−	35.6942i	0.270594	−	1.53461i	−0.482025	−	0.876157i	$-0.660099\pi$
$541$	6.29385	−	35.6942i	0.270594	−	1.53461i	0.752619	−	0.658456i	$-0.228790\pi$
$542$	0.251030	−	1.42366i	0.0107826	−	0.0611514i
$543$		0			0
$544$	0.592396	−	1.02606i	0.0253988	−	0.0439920i
$545$	30.3050	+	25.4289i	1.29812	+	1.08925i
$546$		0			0
$547$	16.1604	−	5.88192i	0.690971	−	0.251493i	0.0274199	−	0.999624i	$-0.491271\pi$
$547$	16.1604	−	5.88192i	0.690971	−	0.251493i	0.663551	+	0.748131i	$0.269049\pi$
$548$	−3.48293	+	2.92252i	−0.148783	+	0.124844i
$549$		0			0
$550$	22.6459			0.965624
$551$	−11.5621	−	11.6978i	−0.492563	−	0.498342i
$552$		0			0
$553$	−0.252212	−	1.43036i	−0.0107251	−	0.0608253i
$554$	16.2331	−	13.6212i	0.689677	−	0.578708i
$555$		0			0
$556$	2.83275	+	1.03104i	0.120135	+	0.0437257i
$557$	12.6932	+	10.6509i	0.537830	+	0.451293i	0.870795	−	0.491646i	$-0.163605\pi$
$557$	12.6932	+	10.6509i	0.537830	+	0.451293i	−0.332965	+	0.942939i	$0.608049\pi$
$558$		0			0
$559$	−5.66503	−	9.81212i	−0.239605	−	0.415008i
$560$	2.89053	−	16.3930i	0.122147	−	0.692731i
$561$		0			0
$562$	−12.1839	−	21.1032i	−0.513947	−	0.890183i
$563$	−15.3486	+	26.5846i	−0.646868	+	1.12041i	0.336999	+	0.941505i	$0.390588\pi$
$563$	−15.3486	+	26.5846i	−0.646868	+	1.12041i	−0.983867	+	0.178903i	$0.942745\pi$
$564$		0			0
$565$	−6.22193	−	2.26460i	−0.261759	−	0.0952724i
$566$	3.87686	−	1.41106i	0.162957	−	0.0593113i
$567$		0			0
$568$	−1.38191	−	7.83721i	−0.0579837	−	0.328842i
$569$	−13.4534			−0.563994			−0.281997	−	0.959415i	$-0.590997\pi$
$569$	−13.4534			−0.563994			−0.281997	+	0.959415i	$0.590997\pi$
$570$		0			0
$571$	−9.47565			−0.396544			−0.198272	−	0.980147i	$-0.563533\pi$
$571$	−9.47565			−0.396544			−0.198272	+	0.980147i	$0.563533\pi$
$572$	1.60947	+	9.12776i	0.0672953	+	0.381651i
$573$		0			0
$574$	−30.0526	+	10.9383i	−1.25437	+	0.456554i
$575$	−21.2802	−	7.74535i	−0.887445	−	0.323004i
$576$		0			0
$577$	9.38191	−	16.2499i	0.390574	−	0.676494i	−0.601951	−	0.798533i	$-0.705610\pi$
$577$	9.38191	−	16.2499i	0.390574	−	0.676494i	0.992525	+	0.122039i	$0.0389432\pi$
$578$	7.79813	+	13.5068i	0.324360	+	0.561807i
$579$		0			0
$580$	2.23530	−	12.6770i	0.0928158	−	0.526384i
$581$	−38.0690	−	65.9374i	−1.57937	−	2.73554i
$582$		0			0
$583$	−1.64749	−	1.38241i	−0.0682320	−	0.0572535i
$584$	11.9757	+	4.35878i	0.495556	+	0.180368i
$585$		0			0
$586$	−2.13041	+	1.78763i	−0.0880066	+	0.0738463i
$587$	3.15611	+	17.8992i	0.130266	+	0.738778i	0.978040	+	0.208419i	$0.0668317\pi$
$587$	3.15611	+	17.8992i	0.130266	+	0.738778i	−0.847773	+	0.530359i	$0.822057\pi$
$588$		0			0
$589$	−12.0348	−	26.2066i	−0.495884	−	1.07983i
$590$	39.7033			1.63456
$591$		0			0
$592$	5.17752	−	4.34445i	0.212795	−	0.178556i
$593$	−30.7221	+	11.1819i	−1.26161	+	0.459187i	−0.884307	−	0.466905i	$-0.845369\pi$
$593$	−30.7221	+	11.1819i	−1.26161	+	0.459187i	−0.377298	+	0.926092i	$0.623147\pi$
$594$		0			0
$595$	−15.1079	−	12.6770i	−0.619363	−	0.519707i
$596$	0.592396	−	1.02606i	0.0242655	−	0.0420291i
$597$		0			0
$598$	1.60947	−	9.12776i	0.0658161	−	0.373262i
$599$	−1.53343	+	8.69653i	−0.0626544	+	0.355331i	0.937322	+	0.348464i	$0.113297\pi$
$599$	−1.53343	+	8.69653i	−0.0626544	+	0.355331i	−0.999976	+	0.00686632i	$0.997814\pi$
$600$		0			0
$601$	−16.5262	+	28.6241i	−0.674116	+	1.16760i	0.302610	+	0.953114i	$0.402142\pi$
$601$	−16.5262	+	28.6241i	−0.674116	+	1.16760i	−0.976726	+	0.214489i	$0.931191\pi$
$602$	−15.5876	−	13.0796i	−0.635305	−	0.533084i
$603$		0			0
$604$	3.41875	−	1.24432i	0.139107	−	0.0506308i
$605$	−1.66772	+	1.39938i	−0.0678024	+	0.0568930i
$606$		0			0
$607$	5.16250			0.209540			0.104770	−	0.994497i	$-0.466589\pi$
$607$	5.16250			0.209540			0.104770	+	0.994497i	$0.466589\pi$
$608$	−4.21688	+	1.10359i	−0.171017	+	0.0447565i
$609$		0			0
$610$	−4.08853	−	23.1872i	−0.165540	−	0.938822i
$611$	−5.94634	+	4.98957i	−0.240563	+	0.201856i
$612$		0			0
$613$	44.2486	+	16.1052i	1.78718	+	0.650481i	0.999404	+	0.0345227i	$0.0109911\pi$
$613$	44.2486	+	16.1052i	1.78718	+	0.650481i	0.787779	+	0.615959i	$0.211231\pi$
$614$	−19.1689	−	16.0846i	−0.773594	−	0.649122i
$615$		0			0
$616$	8.32295	+	14.4158i	0.335341	+	0.580828i
$617$	7.36009	−	41.7411i	0.296306	−	1.68044i	−0.365540	−	0.930796i	$-0.619116\pi$
$617$	7.36009	−	41.7411i	0.296306	−	1.68044i	0.661846	−	0.749640i	$-0.269773\pi$
$618$		0			0
$619$	0.928081	+	1.60748i	0.0373027	+	0.0646102i	0.884074	−	0.467347i	$-0.154790\pi$
$619$	0.928081	+	1.60748i	0.0373027	+	0.0646102i	−0.846771	+	0.531957i	$0.821457\pi$
$620$	11.2849	−	19.5461i	0.453214	−	0.784989i
$621$		0			0
$622$	22.5278	+	8.19945i	0.903283	+	0.328768i
$623$	−31.0565	+	11.3036i	−1.24425	+	0.452871i
$624$		0			0
$625$	−2.45290	−	13.9111i	−0.0981159	−	0.556443i
$626$	−12.6382			−0.505122
$627$		0			0
$628$	6.27126			0.250250
$629$	−1.39053	−	7.88609i	−0.0554440	−	0.314439i
$630$		0			0
$631$	−23.1618	+	8.43020i	−0.922056	+	0.335601i	−0.759056	−	0.651025i	$-0.774339\pi$
$631$	−23.1618	+	8.43020i	−0.922056	+	0.335601i	−0.163000	+	0.986626i	$0.552117\pi$
$632$	−0.279715	−	0.101808i	−0.0111265	−	0.00404970i
$633$		0			0
$634$	−7.06670	+	12.2399i	−0.280655	+	0.486108i
$635$	−10.3773	−	17.9741i	−0.411812	−	0.713279i
$636$		0			0
$637$	7.92989	−	44.9727i	0.314194	−	1.78188i
$638$	6.43629	+	11.1480i	0.254815	+	0.441353i
$639$		0			0
$640$	−2.61334	−	2.19285i	−0.103301	−	0.0866801i
$641$	16.5744	+	6.03260i	0.654651	+	0.238274i	0.647925	−	0.761704i	$-0.275637\pi$
$641$	16.5744	+	6.03260i	0.654651	+	0.238274i	0.00672584	+	0.999977i	$0.497859\pi$
$642$		0			0
$643$	22.8653	−	19.1863i	0.901720	−	0.756633i	−0.0688062	−	0.997630i	$-0.521919\pi$
$643$	22.8653	−	19.1863i	0.901720	−	0.756633i	0.970526	+	0.240997i	$0.0774746\pi$
$644$	−2.89053	−	16.3930i	−0.113903	−	0.645975i
$645$		0			0
$646$	−1.36571	+	4.98054i	−0.0537333	+	0.195957i
$647$	−23.9391			−0.941144			−0.470572	−	0.882362i	$-0.655952\pi$
$647$	−23.9391			−0.941144			−0.470572	+	0.882362i	$0.655952\pi$
$648$		0			0
$649$	−30.4145	+	25.5208i	−1.19387	+	1.00178i
$650$	−16.9474	+	6.16836i	−0.664733	+	0.241943i
$651$		0			0
$652$	−14.7836	−	12.4049i	−0.578970	−	0.485813i
$653$	−13.2430	+	22.9376i	−0.518240	+	0.897618i	0.481535	+	0.876427i	$0.340079\pi$
$653$	−13.2430	+	22.9376i	−0.518240	+	0.897618i	−0.999775	+	0.0211916i	$0.993254\pi$
$654$		0			0
$655$	−11.0209	+	62.5029i	−0.430624	+	2.44219i
$656$	−1.13816	+	6.45480i	−0.0444375	+	0.252018i
$657$		0			0
$658$	−6.97044	+	12.0732i	−0.271736	+	0.470660i
$659$	4.05509	+	3.40263i	0.157964	+	0.132548i	0.718344	−	0.695688i	$-0.244900\pi$
$659$	4.05509	+	3.40263i	0.157964	+	0.132548i	−0.560380	+	0.828236i	$0.689345\pi$
$660$		0			0
$661$	−43.3264	+	15.7695i	−1.68520	+	0.613363i	−0.994008	−	0.109306i	$-0.965137\pi$
$661$	−43.3264	+	15.7695i	−1.68520	+	0.613363i	−0.691194	+	0.722669i	$0.742915\pi$
$662$	22.5967	−	18.9609i	0.878247	−	0.736937i
$663$		0			0
$664$	−15.6040			−0.605553
$665$	5.90214	+	72.3173i	0.228875	+	2.80435i
$666$		0			0
$667$	−2.23530	−	12.6770i	−0.0865512	−	0.490856i
$668$	5.91534	−	4.96356i	0.228872	−	0.192046i
$669$		0			0
$670$	2.27332	+	0.827420i	0.0878260	+	0.0319660i
$671$	18.0364	+	15.1344i	0.696289	+	0.584255i
$672$		0			0
$673$	−1.19072	−	2.06239i	−0.0458990	−	0.0794994i	0.842163	−	0.539223i	$-0.181282\pi$
$673$	−1.19072	−	2.06239i	−0.0458990	−	0.0794994i	−0.888062	+	0.459723i	$0.847949\pi$
$674$	−3.86349	+	21.9110i	−0.148816	+	0.843979i
$675$		0			0
$676$	2.80928	+	4.86581i	0.108049	+	0.187147i
$677$	7.97431	−	13.8119i	0.306478	−	0.530835i	−0.671112	−	0.741356i	$-0.734183\pi$
$677$	7.97431	−	13.8119i	0.306478	−	0.530835i	0.977589	+	0.210522i	$0.0675162\pi$
$678$		0			0
$679$	−32.6721	−	11.8917i	−1.25384	−	0.456360i
$680$	−3.79813	+	1.38241i	−0.145652	+	0.0530129i
$681$		0			0
$682$	3.91921	+	22.2270i	0.150074	+	0.851115i
$683$	1.26083			0.0482443			0.0241222	−	0.999709i	$-0.492321\pi$
$683$	1.26083			0.0482443			0.0241222	+	0.999709i	$0.492321\pi$
$684$		0			0
$685$	15.5107			0.592635
$686$	−8.31062	−	47.1319i	−0.317301	−	1.79950i
$687$		0			0
$688$	−3.91875	+	1.42631i	−0.149401	+	0.0543775i
$689$	1.60947	+	0.585799i	0.0613159	+	0.0223172i
$690$		0			0
$691$	4.05438	−	7.02239i	0.154236	−	0.267144i	−0.778545	−	0.627589i	$-0.784042\pi$
$691$	4.05438	−	7.02239i	0.154236	−	0.267144i	0.932780	+	0.360445i	$0.117375\pi$
$692$	−7.24763	−	12.5533i	−0.275513	−	0.477203i
$693$		0			0
$694$	2.43541	−	13.8119i	0.0924470	−	0.524293i
$695$	−5.14203	−	8.90625i	−0.195048	−	0.337833i
$696$		0			0
$697$	5.94878	+	4.99162i	0.225326	+	0.189071i
$698$	32.0548	+	11.6670i	1.21329	+	0.441603i
$699$		0			0
$700$	−24.8123	+	20.8200i	−0.937816	+	0.786921i
$701$	−1.77615	−	10.0730i	−0.0670842	−	0.380454i	−0.999803	−	0.0198489i	$-0.993681\pi$
$701$	−1.77615	−	10.0730i	−0.0670842	−	0.380454i	0.932719	−	0.360605i	$-0.117430\pi$
$702$		0			0
$703$	−17.0385	+	24.0339i	−0.642619	+	0.906456i
$704$	3.41147			0.128575
$705$		0			0
$706$	−23.3214	+	19.5689i	−0.877711	+	0.736487i
$707$	21.3020	−	7.75330i	0.801144	−	0.291593i
$708$		0			0
$709$	0.156574	+	0.131381i	0.00588026	+	0.00493413i	0.645723	−	0.763572i	$-0.276556\pi$
$709$	0.156574	+	0.131381i	0.00588026	+	0.00493413i	−0.639843	+	0.768506i	$0.721001\pi$
$710$	−13.5744	+	23.5116i	−0.509440	+	0.882376i
$711$		0			0
$712$	−1.17617	+	6.67042i	−0.0440790	+	0.249984i
$713$	3.91921	−	22.2270i	0.146776	−	0.832407i
$714$		0			0
$715$	15.8097	−	27.3833i	0.591251	−	1.02408i
$716$	7.52481	+	6.31407i	0.281216	+	0.235968i
$717$		0			0
$718$	12.8229	−	4.66717i	0.478548	−	0.174177i
$719$	−12.2103	+	10.2457i	−0.455368	+	0.382099i	−0.841423	−	0.540376i	$-0.818282\pi$
$719$	−12.2103	+	10.2457i	−0.455368	+	0.382099i	0.386055	+	0.922476i	$0.373837\pi$
$720$		0			0
$721$	60.4184			2.25010
$722$	16.5642	−	9.30742i	0.616455	−	0.346386i
$723$		0			0
$724$	3.28446	+	18.6271i	0.122066	+	0.692271i
$725$	−19.1878	+	16.1005i	−0.712616	+	0.597956i
$726$		0			0
$727$	29.0959	+	10.5900i	1.07911	+	0.392762i	0.819575	−	0.572972i	$-0.194210\pi$
$727$	29.0959	+	10.5900i	1.07911	+	0.392762i	0.259531	+	0.965735i	$0.416432\pi$
$728$	−10.1552	−	8.52125i	−0.376378	−	0.315819i
$729$		0			0
$730$	−21.7383	−	37.6518i	−0.804570	−	1.39356i
$731$	−0.857974	+	4.86581i	−0.0317333	+	0.179969i
$732$		0			0
$733$	−1.97906	−	3.42782i	−0.0730981	−	0.126610i	0.827160	−	0.561967i	$-0.189955\pi$
$733$	−1.97906	−	3.42782i	−0.0730981	−	0.126610i	−0.900258	+	0.435358i	$0.856622\pi$
$734$	−11.8833	+	20.5824i	−0.438619	+	0.759710i
$735$		0			0
$736$	−3.20574	−	1.16679i	−0.118165	−	0.0430086i
$737$	−2.27332	+	0.827420i	−0.0837388	+	0.0304784i
$738$		0			0
$739$	−4.48070	−	25.4113i	−0.164825	−	0.934771i	−0.949244	−	0.314540i	$-0.898150\pi$
$739$	−4.48070	−	25.4113i	−0.164825	−	0.934771i	0.784419	−	0.620231i	$-0.212961\pi$
$740$	−23.0574			−0.847606
$741$		0			0
$742$	3.07604			0.112925
$743$	−5.54189	−	31.4296i	−0.203312	−	1.15304i	−0.900074	−	0.435738i	$-0.856487\pi$
$743$	−5.54189	−	31.4296i	−0.203312	−	1.15304i	0.696761	−	0.717303i	$-0.254624\pi$
$744$		0			0
$745$	−3.79813	+	1.38241i	−0.139153	+	0.0506475i
$746$	21.8332	+	7.94664i	0.799371	+	0.290947i
$747$		0			0
$748$	2.02094	−	3.50038i	0.0738931	−	0.127987i
$749$	−9.51233	−	16.4758i	−0.347573	−	0.602014i
$750$		0			0
$751$	−0.0882212	+	0.500327i	−0.00321924	+	0.0182572i	−0.986375	−	0.164512i	$-0.947395\pi$
$751$	−0.0882212	+	0.500327i	−0.00321924	+	0.0182572i	0.983156	+	0.182769i	$0.0585061\pi$
$752$	1.42855	+	2.47432i	0.0520938	+	0.0902291i
$753$		0			0
$754$	−7.85323	−	6.58964i	−0.285998	−	0.239981i
$755$	−11.6630	−	4.24497i	−0.424459	−	0.154490i
$756$		0			0
$757$	−36.8999	+	30.9627i	−1.34115	+	1.12536i	−0.359822	+	0.933021i	$0.617162\pi$
$757$	−36.8999	+	30.9627i	−1.34115	+	1.12536i	−0.981329	+	0.192338i	$0.938393\pi$
$758$	−0.781470	−	4.43193i	−0.0283843	−	0.160975i
$759$		0			0
$760$	13.4402	+	6.36295i	0.487526	+	0.230808i
$761$	−5.15064			−0.186711			−0.0933554	−	0.995633i	$-0.529759\pi$
$761$	−5.15064			−0.186711			−0.0933554	+	0.995633i	$0.529759\pi$
$762$		0			0
$763$	43.3448	−	36.3706i	1.56919	−	1.31671i
$764$	−9.48293	+	3.45150i	−0.343080	+	0.124871i
$765$		0			0
$766$	−3.34002	−	2.80261i	−0.120680	−	0.101262i
$767$	15.8097	−	27.3833i	0.570857	−	0.988753i
$768$		0			0
$769$	3.39874	−	19.2752i	0.122562	−	0.695081i	−0.860165	−	0.510016i	$-0.829639\pi$
$769$	3.39874	−	19.2752i	0.122562	−	0.695081i	0.982726	−	0.185065i	$-0.0592496\pi$
$770$	9.86097	−	55.9243i	0.355365	−	2.01537i
$771$		0			0
$772$	−1.26217	+	2.18615i	−0.0454266	+	0.0786812i
$773$	−17.1552	−	14.3949i	−0.617031	−	0.517750i	0.279838	−	0.960047i	$-0.409719\pi$
$773$	−17.1552	−	14.3949i	−0.617031	−	0.517750i	−0.896869	+	0.442297i	$0.854164\pi$
$774$		0			0
$775$	−41.2686	+	15.0206i	−1.48241	+	0.539554i
$776$	−5.45858	+	4.58029i	−0.195952	+	0.164423i
$777$		0			0
$778$	1.31046			0.0469823
$779$	−2.32399	−	28.4752i	−0.0832655	−	1.02023i
$780$		0			0
$781$	−4.71436	−	26.7364i	−0.168693	−	0.956705i
$782$	−3.09627	+	2.59808i	−0.110722	+	0.0929070i
$783$		0			0
$784$	−15.7947	−	5.74881i	−0.564097	−	0.205315i
$785$	−16.3889	−	13.7520i	−0.584946	−	0.490828i
$786$		0			0
$787$	−16.8444	−	29.1753i	−0.600437	−	1.03999i	−0.992755	−	0.120157i	$-0.961660\pi$
$787$	−16.8444	−	29.1753i	−0.600437	−	1.03999i	0.392318	−	0.919830i	$-0.371673\pi$
$788$	−2.57991	+	14.6314i	−0.0919054	+	0.521221i
$789$		0			0
$790$	0.507741	+	0.879433i	0.0180646	+	0.0312888i
$791$	−4.73514	+	8.20150i	−0.168362	+	0.291612i
$792$		0			0
$793$	−17.6202	−	6.41323i	−0.625712	−	0.227740i
$794$	17.8662	−	6.50276i	0.634047	−	0.230774i
$795$		0			0
$796$	1.40121	+	7.94664i	0.0496645	+	0.281661i
$797$	47.8631			1.69540			0.847699	−	0.530478i	$-0.177988\pi$
$797$	47.8631			1.69540			0.847699	+	0.530478i	$0.177988\pi$
$798$		0			0
$799$	3.38507			0.119755
$800$	1.15270	+	6.53731i	0.0407542	+	0.231129i
$801$		0			0
$802$	33.7003	−	12.2659i	1.19000	−	0.433124i
$803$	40.8546	+	14.8699i	1.44173	+	0.524746i
$804$		0			0
$805$	−28.3935	+	49.1790i	−1.00074	+	1.73333i
$806$	−8.98726	−	15.5664i	−0.316563	−	0.548303i
$807$		0			0
$808$	0.806751	−	4.57531i	0.0283814	−	0.160959i
$809$	−1.83703	−	3.18183i	−0.0645865	−	0.111867i	0.831924	−	0.554890i	$-0.187240\pi$
$809$	−1.83703	−	3.18183i	−0.0645865	−	0.111867i	−0.896510	+	0.443022i	$0.853906\pi$
$810$		0			0
$811$	−14.3289	−	12.0234i	−0.503155	−	0.422197i	0.355558	−	0.934654i	$-0.384291\pi$
$811$	−14.3289	−	12.0234i	−0.503155	−	0.422197i	−0.858713	+	0.512457i	$0.828735\pi$
$812$	−17.3011	−	6.29710i	−0.607151	−	0.220985i
$813$		0			0
$814$	17.6630	−	14.8210i	0.619087	−	0.519476i
$815$	11.4324	+	64.8365i	0.400460	+	2.27112i
$816$		0			0
$817$	14.9508	−	10.3393i	0.523064	−	0.361725i
$818$	−29.1088			−1.01776
$819$		0			0
$820$	17.1288	−	14.3728i	0.598164	−	0.501920i
$821$	−20.9706	+	7.63267i	−0.731879	+	0.266382i	−0.680960	−	0.732321i	$-0.738437\pi$
$821$	−20.9706	+	7.63267i	−0.731879	+	0.266382i	−0.0509190	+	0.998703i	$0.516215\pi$
$822$		0			0
$823$	−20.2264	−	16.9720i	−0.705049	−	0.591606i	0.218156	−	0.975914i	$-0.429996\pi$
$823$	−20.2264	−	16.9720i	−0.705049	−	0.591606i	−0.923205	+	0.384307i	$0.874440\pi$
$824$	6.19119	−	10.7235i	0.215680	−	0.373569i
$825$		0			0
$826$	9.86097	−	55.9243i	0.343107	−	1.94586i
$827$	−5.15224	+	29.2198i	−0.179161	+	1.01607i	0.754070	+	0.656794i	$0.228088\pi$
$827$	−5.15224	+	29.2198i	−0.179161	+	1.01607i	−0.933231	+	0.359277i	$0.883023\pi$
$828$		0			0
$829$	−0.884133	+	1.53136i	−0.0307072	+	0.0531864i	−0.880971	−	0.473171i	$-0.843109\pi$
$829$	−0.884133	+	1.53136i	−0.0307072	+	0.0531864i	0.850263	+	0.526357i	$0.176443\pi$
$830$	40.7786	+	34.2173i	1.41545	+	1.18770i
$831$		0			0
$832$	−2.55303	+	0.929228i	−0.0885105	+	0.0322152i
$833$	−15.2554	+	12.8008i	−0.528567	+	0.443520i
$834$		0			0
$835$	−26.3432			−0.911643
$836$	−14.3858	+	3.76487i	−0.497543	+	0.130211i
$837$		0			0
$838$	−2.28493	−	12.9585i	−0.0789316	−	0.447643i
$839$	−20.4643	+	17.1716i	−0.706505	+	0.592828i	−0.923616	−	0.383319i	$-0.874781\pi$
$839$	−20.4643	+	17.1716i	−0.706505	+	0.592828i	0.217111	+	0.976147i	$0.430337\pi$
$840$		0			0
$841$	13.8718	+	5.04892i	0.478338	+	0.174101i
$842$	−0.115400	−	0.0968323i	−0.00397695	−	0.00333706i
$843$		0			0
$844$	−3.97178	−	6.87933i	−0.136714	−	0.236796i
$845$	3.32841	−	18.8764i	0.114501	−	0.649366i
$846$		0			0
$847$	1.55690	+	2.69664i	0.0534958	+	0.0926575i
$848$	0.315207	−	0.545955i	0.0108243	−	0.0187482i
$849$		0			0
$850$	7.39053	+	2.68993i	0.253493	+	0.0922639i
$851$	−21.6668	+	7.88609i	−0.742730	+	0.270332i
$852$		0			0
$853$	2.41828	+	13.7148i	0.0828004	+	0.469584i	0.997810	+	0.0661513i	$0.0210720\pi$
$853$	2.41828	+	13.7148i	0.0828004	+	0.469584i	−0.915009	+	0.403433i	$0.867817\pi$
$854$	−33.6759			−1.15237
$855$		0			0
$856$	−3.89899			−0.133265
$857$	3.41551	+	19.3703i	0.116671	+	0.661677i	0.985909	+	0.167282i	$0.0534991\pi$
$857$	3.41551	+	19.3703i	0.116671	+	0.661677i	−0.869238	+	0.494395i	$0.835390\pi$
$858$		0			0
$859$	40.7806	−	14.8429i	1.39142	−	0.506435i	0.465799	−	0.884891i	$-0.345767\pi$
$859$	40.7806	−	14.8429i	1.39142	−	0.506435i	0.925619	+	0.378456i	$0.123545\pi$
$860$	13.3687	+	4.86581i	0.455869	+	0.165923i
$861$		0			0
$862$	−15.3983	+	26.6706i	−0.524467	+	0.908404i
$863$	−14.7096	−	25.4778i	−0.500721	−	0.867274i	−1.00000		0.000832579i	$-0.999735\pi$
$863$	−14.7096	−	25.4778i	−0.500721	−	0.867274i	0.499279	−	0.866441i	$-0.333598\pi$
$864$		0			0
$865$	−8.58693	+	48.6989i	−0.291964	+	1.65581i
$866$	14.7169	+	25.4904i	0.500100	+	0.866199i
$867$		0			0
$868$	−24.7290	−	20.7501i	−0.839356	−	0.704303i
$869$	−0.954241	−	0.347315i	−0.0323704	−	0.0117819i
$870$		0			0
$871$	1.47590	−	1.23843i	0.0500090	−	0.0419625i
$872$	−2.01367	−	11.4201i	−0.0681915	−	0.386733i
$873$		0			0
$874$	14.8059	+	1.38241i	0.500816	+	0.0467606i
$875$	27.2686			0.921846
$876$		0			0
$877$	−20.0437	+	16.8187i	−0.676828	+	0.567926i	−0.915077	−	0.403278i	$-0.867871\pi$
$877$	−20.0437	+	16.8187i	−0.676828	+	0.567926i	0.238250	+	0.971204i	$0.423426\pi$
$878$	−18.6065	+	6.77222i	−0.627940	+	0.228552i
$879$		0			0
$880$	−8.91534	−	7.48086i	−0.300536	−	0.252180i
$881$	11.3143	−	19.5970i	0.381189	−	0.660240i	−0.610043	−	0.792368i	$-0.708848\pi$
$881$	11.3143	−	19.5970i	0.381189	−	0.660240i	0.991233	+	0.132129i	$0.0421812\pi$
$882$		0			0
$883$	−1.43810	+	8.15587i	−0.0483959	+	0.274467i	−0.999397	−	0.0347205i	$-0.988946\pi$
$883$	−1.43810	+	8.15587i	−0.0483959	+	0.274467i	0.951001	+	0.309187i	$0.100057\pi$
$884$	−0.558963	+	3.17004i	−0.0188000	+	0.106620i
$885$		0			0
$886$	−9.29339	+	16.0966i	−0.312217	+	0.540776i
$887$	−30.9152	−	25.9409i	−1.03803	−	0.871011i	−0.0462457	−	0.998930i	$-0.514726\pi$
$887$	−30.9152	−	25.9409i	−1.03803	−	0.871011i	−0.991785	+	0.127919i	$0.959170\pi$
$888$		0			0
$889$	−27.8949	+	10.1529i	−0.935564	+	0.340517i
$890$	17.7010	−	14.8529i	0.593339	−	0.497870i
$891$		0			0
$892$	11.9682			0.400726
$893$	−8.75465	−	8.85737i	−0.292963	−	0.296401i
$894$		0			0
$895$	−5.81908	−	33.0016i	−0.194510	−	1.10312i
$896$	−3.73783	+	3.13641i	−0.124872	+	0.104780i
$897$		0			0
$898$	3.17530	+	1.15571i	0.105961	+	0.0385667i
$899$	−19.1234	−	16.0464i	−0.637800	−	0.535178i
$900$		0			0
$901$	−0.373455	−	0.646844i	−0.0124416	−	0.0215495i
$902$	−3.88279	+	22.0204i	−0.129283	+	0.733199i
$903$		0			0
$904$	0.970437	+	1.68085i	0.0322763	+	0.0559041i
$905$	32.2631	−	55.8813i	1.07246	−	1.85756i
$906$		0			0
$907$	18.0903	+	6.58434i	0.600680	+	0.218630i	0.624420	−	0.781089i	$-0.285335\pi$
$907$	18.0903	+	6.58434i	0.600680	+	0.218630i	−0.0237404	+	0.999718i	$0.507558\pi$
$908$	24.9907	−	9.09586i	0.829344	−	0.301857i
$909$		0			0
$910$	7.85323	+	44.5379i	0.260332	+	1.47642i
$911$	58.7684			1.94708			0.973542	−	0.228510i	$-0.0733853\pi$
$911$	58.7684			1.94708			0.973542	+	0.228510i	$0.0733853\pi$
$912$		0			0
$913$	−53.2327			−1.76174
$914$	3.78400	+	21.4601i	0.125163	+	0.709837i
$915$		0			0
$916$	18.7023	−	6.80709i	0.617942	−	0.224913i
$917$	85.3016	+	31.0473i	2.81691	+	1.02527i
$918$		0			0
$919$	26.8714	−	46.5426i	0.886406	−	1.53530i	0.0423114	−	0.999104i	$-0.486528\pi$
$919$	26.8714	−	46.5426i	0.886406	−	1.53530i	0.844094	−	0.536195i	$-0.180139\pi$
$920$	5.81908	+	10.0789i	0.191849	+	0.332293i
$921$		0			0
$922$	−2.04277	+	11.5851i	−0.0672749	+	0.381535i
$923$	10.8106	+	18.7245i	0.355836	+	0.616326i
$924$		0			0
$925$	34.3692	+	28.8392i	1.13005	+	0.948226i
$926$	−15.9684	−	5.81201i	−0.524753	−	0.190995i
$927$		0			0
$928$	−2.89053	+	2.42544i	−0.0948863	+	0.0796190i
$929$	5.38981	+	30.5672i	0.176834	+	1.00288i	0.936006	+	0.351985i	$0.114493\pi$
$929$	5.38981	+	30.5672i	0.176834	+	1.00288i	−0.759171	+	0.650891i	$0.774396\pi$
$930$		0			0
$931$	72.9488	+	6.81115i	2.39080	+	0.223226i
$932$	4.31046			0.141194
$933$		0			0
$934$	8.96657	−	7.52384i	0.293395	−	0.246188i
$935$	−12.9572	+	4.71605i	−0.423747	+	0.154231i
$936$		0			0
$937$	−15.8899	−	13.3332i	−0.519100	−	0.435577i	0.345218	−	0.938523i	$-0.387805\pi$
$937$	−15.8899	−	13.3332i	−0.519100	−	0.435577i	−0.864318	+	0.502946i	$0.832250\pi$
$938$	1.73009	−	2.99660i	0.0564893	−	0.0978423i
$939$		0			0
$940$	1.69253	−	9.59883i	0.0552043	−	0.313079i
$941$	2.58095	−	14.6373i	0.0841365	−	0.477162i	−0.913403	−	0.407056i	$-0.866555\pi$
$941$	2.58095	−	14.6373i	0.0841365	−	0.477162i	0.997540	−	0.0701055i	$-0.0223336\pi$
$942$		0			0
$943$	11.1800	−	19.3644i	0.364072	−	0.630592i
$944$	−8.91534	−	7.48086i	−0.290170	−	0.243481i
$945$		0			0
$946$	−13.3687	+	4.86581i	−0.434654	+	0.158201i
$947$	19.3043	−	16.1982i	0.627305	−	0.526371i	−0.272785	−	0.962075i	$-0.587945\pi$
$947$	19.3043	−	16.1982i	0.627305	−	0.526371i	0.900090	+	0.435704i	$0.143500\pi$
$948$		0			0
$949$	−34.6245			−1.12396
$950$	−12.0753	−	26.2949i	−0.391775	−	0.853120i
$951$		0			0
$952$	1.00387	+	5.69323i	0.0325356	+	0.184519i
$953$	9.48751	−	7.96097i	0.307331	−	0.257881i	−0.476057	−	0.879414i	$-0.657934\pi$
$953$	9.48751	−	7.96097i	0.307331	−	0.257881i	0.783388	+	0.621533i	$0.213490\pi$
$954$		0			0
$955$	32.3508	+	11.7747i	1.04685	+	0.381021i
$956$	−0.218941	−	0.183713i	−0.00708105	−	0.00594171i
$957$		0			0
$958$	14.9898	+	25.9631i	0.484298	+	0.838829i
$959$	3.85235	−	21.8478i	0.124399	−	0.705501i
$960$		0			0
$961$	−6.38485	−	11.0589i	−0.205963	−	0.356738i
$962$	−9.18139	+	15.9026i	−0.296020	+	0.512721i
$963$		0			0
$964$	−8.98932	−	3.27185i	−0.289527	−	0.105379i
$965$	8.09240	−	2.94539i	0.260503	−	0.0948155i
$966$		0			0
$967$	−0.591929	−	3.35700i	−0.0190352	−	0.107954i	0.973810	−	0.227364i	$-0.0730107\pi$
$967$	−0.591929	−	3.35700i	−0.0190352	−	0.107954i	−0.992845	+	0.119410i	$0.961900\pi$
$968$	0.638156			0.0205111
$969$		0			0
$970$	24.3090			0.780516
$971$	2.41323	+	13.6861i	0.0774442	+	0.439208i	0.998733	+	0.0503282i	$0.0160267\pi$
$971$	2.41323	+	13.6861i	0.0774442	+	0.439208i	−0.921289	+	0.388880i	$0.872862\pi$
$972$		0			0
$973$	−13.8221	+	5.03082i	−0.443115	+	0.161281i
$974$	−13.6356	−	4.96296i	−0.436914	−	0.159024i
$975$		0			0
$976$	−3.45084	+	5.97702i	−0.110459	+	0.191320i
$977$	6.42009	+	11.1199i	0.205397	+	0.355758i	0.950259	−	0.311460i	$-0.100818\pi$
$977$	6.42009	+	11.1199i	0.205397	+	0.355758i	−0.744862	+	0.667218i	$0.767485\pi$
$978$		0			0
$979$	−4.01249	+	22.7560i	−0.128240	+	0.727283i
$980$	28.6707	+	49.6591i	0.915852	+	1.58630i
$981$		0			0
$982$	8.92855	+	7.49194i	0.284921	+	0.239077i
$983$	−0.814330	−	0.296392i	−0.0259731	−	0.00945343i	0.329001	−	0.944330i	$-0.393288\pi$
$983$	−0.814330	−	0.296392i	−0.0259731	−	0.00945343i	−0.354974	+	0.934876i	$0.615510\pi$
$984$		0			0
$985$	38.8267	−	32.5794i	1.23712	−	1.03807i
$986$	0.776311	+	4.40268i	0.0247228	+	0.140210i
$987$		0			0
$988$	9.74035	−	6.73595i	0.309882	−	0.214299i
$989$	14.2267			0.452382
$990$		0			0
$991$	−16.0646	+	13.4798i	−0.510310	+	0.428201i	−0.861238	−	0.508201i	$-0.830311\pi$
$991$	−16.0646	+	13.4798i	−0.510310	+	0.428201i	0.350928	+	0.936402i	$0.385866\pi$
$992$	−6.21688	+	2.26276i	−0.197386	+	0.0718427i
$993$		0			0
$994$	29.7460	+	24.9599i	0.943487	+	0.791680i
$995$	13.7640	−	23.8399i	0.436348	−	0.755776i
$996$		0			0
$997$	6.90208	−	39.1437i	0.218591	−	1.23969i	−0.655974	−	0.754784i	$-0.727742\pi$
$997$	6.90208	−	39.1437i	0.218591	−	1.23969i	0.874565	−	0.484909i	$-0.161147\pi$
$998$	−0.292919	+	1.66122i	−0.00927218	+	0.0525852i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.u.e.199.1		6
3.2	odd	2		114.2.i.a.85.1	yes	6
12.11	even	2		912.2.bo.a.769.1		6
19.6	even	9		6498.2.a.br.1.1		3
19.13	odd	18		6498.2.a.bm.1.1		3
19.17	even	9	inner	342.2.u.e.55.1		6
57.17	odd	18		114.2.i.a.55.1	✓	6
57.32	even	18		2166.2.a.s.1.3		3
57.44	odd	18		2166.2.a.q.1.3		3
228.131	even	18		912.2.bo.a.625.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.a.55.1	✓	6	57.17	odd	18
114.2.i.a.85.1	yes	6	3.2	odd	2
342.2.u.e.55.1		6	19.17	even	9	inner
342.2.u.e.199.1		6	1.1	even	1	trivial
912.2.bo.a.625.1		6	228.131	even	18
912.2.bo.a.769.1		6	12.11	even	2
2166.2.a.q.1.3		3	57.44	odd	18
2166.2.a.s.1.3		3	57.32	even	18
6498.2.a.bm.1.1		3	19.13	odd	18
6498.2.a.br.1.1		3	19.6	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(3.20574 + 1.16679i) q^{5} +(2.43969 - 4.22567i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.592396 + 3.35965i) q^{10} +(-1.70574 - 2.95442i) q^{11} +(2.08125 + 1.74638i) q^{13} +(4.58512 + 1.66885i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.205737 - 1.16679i) q^{17} +(-2.52094 + 3.55596i) q^{19} -3.41147 q^{20} +(2.61334 - 2.19285i) q^{22} +(-3.20574 + 1.16679i) q^{23} +(5.08512 + 4.26692i) q^{25} +(-1.35844 + 2.35289i) q^{26} +(-0.847296 + 4.80526i) q^{28} +(-0.655230 + 3.71599i) q^{29} +(-3.30793 + 5.72951i) q^{31} +(0.766044 + 0.642788i) q^{32} +(1.11334 - 0.405223i) q^{34} +(12.7515 - 10.6998i) q^{35} +6.75877 q^{37} +(-3.93969 - 1.86516i) q^{38} +(-0.592396 - 3.35965i) q^{40} +(-5.02094 + 4.21307i) q^{41} +(-3.91875 - 1.42631i) q^{43} +(2.61334 + 2.19285i) q^{44} +(-1.70574 - 2.95442i) q^{46} +(-0.496130 + 2.81369i) q^{47} +(-8.40420 - 14.5565i) q^{49} +(-3.31908 + 5.74881i) q^{50} +(-2.55303 - 0.929228i) q^{52} +(0.592396 - 0.215615i) q^{53} +(-2.02094 - 11.4613i) q^{55} -4.87939 q^{56} -3.77332 q^{58} +(-2.02094 - 11.4613i) q^{59} +(-6.48545 + 2.36051i) q^{61} +(-6.21688 - 2.26276i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(4.63429 + 8.02682i) q^{65} +(0.123141 - 0.698367i) q^{67} +(0.592396 + 1.02606i) q^{68} +(12.7515 + 10.6998i) q^{70} +(7.47818 + 2.72183i) q^{71} +(-9.76264 + 8.19183i) q^{73} +(1.17365 + 6.65609i) q^{74} +(1.15270 - 4.20372i) q^{76} -16.6459 q^{77} +(0.228026 - 0.191336i) q^{79} +(3.20574 - 1.16679i) q^{80} +(-5.02094 - 4.21307i) q^{82} +(7.80200 - 13.5135i) q^{83} +(0.701867 - 3.98048i) q^{85} +(0.724155 - 4.10689i) q^{86} +(-1.70574 + 2.95442i) q^{88} +(-5.18866 - 4.35381i) q^{89} +(12.4572 - 4.53406i) q^{91} +(2.61334 - 2.19285i) q^{92} -2.85710 q^{94} +(-12.2306 + 8.45805i) q^{95} +(-1.23736 - 7.01741i) q^{97} +(12.8760 - 10.8042i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{5} + 9 q^{7} - 3 q^{8} + 15 q^{13} + 6 q^{14} + 9 q^{17} - 12 q^{19} + 9 q^{22} - 9 q^{23} + 9 q^{25} - 3 q^{28} + 9 q^{29} - 9 q^{31} + 36 q^{35} + 18 q^{37} - 18 q^{38} - 27 q^{41} - 21 q^{43}+ \cdots + 24 q^{98}+O(q^{100}) \) 6 * q + 9 * q^5 + 9 * q^7 - 3 * q^8 + 15 * q^13 + 6 * q^14 + 9 * q^17 - 12 * q^19 + 9 * q^22 - 9 * q^23 + 9 * q^25 - 3 * q^28 + 9 * q^29 - 9 * q^31 + 36 * q^35 + 18 * q^37 - 18 * q^38 - 27 * q^41 - 21 * q^43 + 9 * q^44 - 27 * q^47 - 12 * q^49 - 3 * q^50 - 3 * q^52 - 9 * q^55 - 18 * q^56 - 36 * q^58 - 9 * q^59 - 3 * q^61 - 21 * q^62 - 3 * q^64 + 18 * q^65 - 3 * q^67 + 36 * q^70 - 9 * q^71 - 12 * q^73 + 6 * q^74 + 9 * q^76 - 18 * q^77 - 21 * q^79 + 9 * q^80 - 27 * q^82 + 9 * q^83 + 18 * q^85 + 6 * q^86 + 24 * q^91 + 9 * q^92 - 18 * q^94 - 36 * q^95 - 54 * q^97 + 24 * q^98

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