LMFDB - Embedded newform 342.2.w.a.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(43,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([12, 16]))

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

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

chi := DirichletCharacter("342.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	342.43
Dual form			342.2.w.a.175.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(1.39081 - 1.03230i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.183383 - 1.04002i) q^{5} +(0.775102 + 1.54894i) q^{6} +2.95323 q^{7} +(0.500000 - 0.866025i) q^{8} +(0.868725 - 2.87147i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(1.39081 - 1.03230i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.183383 - 1.04002i) q^{5} +(0.775102 + 1.54894i) q^{6} +2.95323 q^{7} +(0.500000 - 0.866025i) q^{8} +(0.868725 - 2.87147i) q^{9} +(0.992372 + 0.361194i) q^{10} +(-2.65793 - 4.60367i) q^{11} +(-1.66000 + 0.494356i) q^{12} +(-2.44484 + 2.05146i) q^{13} +(-0.512823 + 2.90836i) q^{14} +(-0.818555 - 1.63578i) q^{15} +(0.766044 + 0.642788i) q^{16} +(2.45056 - 0.891932i) q^{17} +(2.67699 + 1.35415i) q^{18} +(-3.42915 + 2.69090i) q^{19} +(-0.528030 + 0.914575i) q^{20} +(4.10739 - 3.04861i) q^{21} +(4.99527 - 1.81813i) q^{22} +(6.80143 + 2.47552i) q^{23} +(-0.198589 - 1.72063i) q^{24} +(3.65046 + 1.32866i) q^{25} +(-1.59575 - 2.76393i) q^{26} +(-1.75597 - 4.89046i) q^{27} +(-2.77513 - 1.01006i) q^{28} +(4.16851 - 3.49780i) q^{29} +(1.75306 - 0.522070i) q^{30} +(-4.67989 + 8.10581i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-8.44904 - 3.65907i) q^{33} +(0.452846 + 2.56821i) q^{34} +(0.541572 - 3.07141i) q^{35} +(-1.79843 + 2.40117i) q^{36} +4.80756 q^{37} +(-2.05455 - 3.84432i) q^{38} +(-1.28259 + 5.37700i) q^{39} +(-0.808989 - 0.678823i) q^{40} +(-10.6019 + 3.85878i) q^{41} +(2.28905 + 4.57438i) q^{42} +(7.52577 - 2.73915i) q^{43} +(0.923089 + 5.23510i) q^{44} +(-2.82706 - 1.43007i) q^{45} +(-3.61897 + 6.26823i) q^{46} +(-2.32373 + 1.94984i) q^{47} +(1.72897 + 0.103212i) q^{48} +1.72157 q^{49} +(-1.94237 + 3.36428i) q^{50} +(2.48754 - 3.77022i) q^{51} +(2.99904 - 1.09156i) q^{52} +(-5.67594 + 4.76268i) q^{53} +(5.12108 - 0.880077i) q^{54} +(-5.27531 + 1.92006i) q^{55} +(1.47661 - 2.55757i) q^{56} +(-1.99150 + 7.28244i) q^{57} +(2.72080 + 4.71257i) q^{58} +(0.610666 + 0.512409i) q^{59} +(0.209722 + 1.81709i) q^{60} +(0.781304 + 4.43100i) q^{61} +(-7.17001 - 6.01635i) q^{62} +(2.56554 - 8.48010i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.68521 + 2.91887i) q^{65} +(5.07064 - 7.68529i) q^{66} +(0.176594 + 1.00151i) q^{67} -2.60783 q^{68} +(12.0150 - 3.57811i) q^{69} +(2.93070 + 1.06669i) q^{70} +(-7.58026 - 6.36059i) q^{71} +(-2.05240 - 2.18807i) q^{72} +(-2.38965 + 13.5524i) q^{73} +(-0.834823 + 4.73452i) q^{74} +(6.44868 - 1.92044i) q^{75} +(4.14269 - 1.35578i) q^{76} +(-7.84948 - 13.5957i) q^{77} +(-5.07259 - 2.19681i) q^{78} +(-6.52637 - 5.47628i) q^{79} +(0.808989 - 0.678823i) q^{80} +(-7.49064 - 4.98903i) q^{81} +(-1.95916 - 11.1109i) q^{82} -5.75022 q^{83} +(-4.90237 + 1.45995i) q^{84} +(-0.478232 - 2.71219i) q^{85} +(1.39071 + 7.88708i) q^{86} +(2.18686 - 9.16793i) q^{87} -5.31586 q^{88} +(1.57241 + 8.91760i) q^{89} +(1.89925 - 2.53579i) q^{90} +(-7.22016 + 6.05844i) q^{91} +(-5.54458 - 4.65245i) q^{92} +(1.85875 + 16.1047i) q^{93} +(-1.51671 - 2.62701i) q^{94} +(2.16973 + 4.05984i) q^{95} +(-0.401877 + 1.68478i) q^{96} +(0.775292 - 4.39690i) q^{97} +(-0.298947 + 1.69541i) q^{98} +(-15.5283 + 3.63283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 24 q^{7} + 27 q^{8}+O(q^{10}) $ 54 * q - 24 * q^7 + 27 * q^8	$ 54 q - 24 q^{7} + 27 q^{8} - 3 q^{13} + 3 q^{14} + 9 q^{17} + 6 q^{18} + 15 q^{19} + 3 q^{22} - 12 q^{23} - 6 q^{25} - 27 q^{27} - 3 q^{28} + 9 q^{29} - 57 q^{33} + 18 q^{34} - 18 q^{35} - 6 q^{37} - 3 q^{38} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 6 q^{44} + 54 q^{45} - 18 q^{47} + 6 q^{49} - 3 q^{50} - 15 q^{51} - 3 q^{52} - 24 q^{53} - 54 q^{54} - 36 q^{55} - 12 q^{56} + 12 q^{57} + 18 q^{58} + 69 q^{59} - 27 q^{60} + 84 q^{61} - 15 q^{62} + 39 q^{63} - 27 q^{64} + 24 q^{65} + 21 q^{66} - 30 q^{67} - 6 q^{68} + 42 q^{69} + 18 q^{70} - 60 q^{71} - 45 q^{73} + 3 q^{74} - 9 q^{78} - 18 q^{79} - 36 q^{81} + 3 q^{82} - 24 q^{83} - 21 q^{84} - 72 q^{85} + 3 q^{86} + 66 q^{87} + 9 q^{89} - 15 q^{91} + 6 q^{92} - 3 q^{93} + 6 q^{94} - 30 q^{95} - 78 q^{97} + 12 q^{98} - 51 q^{99}+O(q^{100}) $ 54 * q - 24 * q^7 + 27 * q^8 - 3 * q^13 + 3 * q^14 + 9 * q^17 + 6 * q^18 + 15 * q^19 + 3 * q^22 - 12 * q^23 - 6 * q^25 - 27 * q^27 - 3 * q^28 + 9 * q^29 - 57 * q^33 + 18 * q^34 - 18 * q^35 - 6 * q^37 - 3 * q^38 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 6 * q^44 + 54 * q^45 - 18 * q^47 + 6 * q^49 - 3 * q^50 - 15 * q^51 - 3 * q^52 - 24 * q^53 - 54 * q^54 - 36 * q^55 - 12 * q^56 + 12 * q^57 + 18 * q^58 + 69 * q^59 - 27 * q^60 + 84 * q^61 - 15 * q^62 + 39 * q^63 - 27 * q^64 + 24 * q^65 + 21 * q^66 - 30 * q^67 - 6 * q^68 + 42 * q^69 + 18 * q^70 - 60 * q^71 - 45 * q^73 + 3 * q^74 - 9 * q^78 - 18 * q^79 - 36 * q^81 + 3 * q^82 - 24 * q^83 - 21 * q^84 - 72 * q^85 + 3 * q^86 + 66 * q^87 + 9 * q^89 - 15 * q^91 + 6 * q^92 - 3 * q^93 + 6 * q^94 - 30 * q^95 - 78 * q^97 + 12 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$

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
$3$	1.39081	−	1.03230i	0.802987	−	0.595997i
$3$	1.39081	−	1.03230i	0.802987	−	0.595997i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.183383	−	1.04002i	0.0820114	−	0.465110i	−0.915950	−	0.401292i	$-0.868561\pi$
$5$	0.183383	−	1.04002i	0.0820114	−	0.465110i	0.997962	−	0.0638177i	$-0.0203276\pi$
$6$	0.775102	+	1.54894i	0.316434	+	0.632352i
$7$	2.95323			1.11622			0.558108	−	0.829768i	$-0.311527\pi$
$7$	2.95323			1.11622			0.558108	+	0.829768i	$0.311527\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.868725	−	2.87147i	0.289575	−	0.957155i
$10$	0.992372	+	0.361194i	0.313816	+	0.114220i
$11$	−2.65793	−	4.60367i	−0.801396	−	1.38806i	−0.918697	−	0.394962i	$-0.870758\pi$
$11$	−2.65793	−	4.60367i	−0.801396	−	1.38806i	0.117301	−	0.993096i	$-0.462576\pi$
$12$	−1.66000	+	0.494356i	−0.479202	+	0.142708i
$13$	−2.44484	+	2.05146i	−0.678076	+	0.568973i	−0.915443	−	0.402447i	$-0.868160\pi$
$13$	−2.44484	+	2.05146i	−0.678076	+	0.568973i	0.237368	+	0.971420i	$0.423715\pi$
$14$	−0.512823	+	2.90836i	−0.137058	+	0.777293i
$15$	−0.818555	−	1.63578i	−0.211350	−	0.422355i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	2.45056	−	0.891932i	0.594349	−	0.216325i	−0.0272924	−	0.999627i	$-0.508689\pi$
$17$	2.45056	−	0.891932i	0.594349	−	0.216325i	0.621641	+	0.783302i	$0.286466\pi$
$18$	2.67699	+	1.35415i	0.630973	+	0.319177i
$19$	−3.42915	+	2.69090i	−0.786701	+	0.617335i
$19$	−3.42915	+	2.69090i	−0.786701	+	0.617335i
$20$	−0.528030	+	0.914575i	−0.118071	+	0.204505i
$21$	4.10739	−	3.04861i	0.896306	−	0.665261i
$22$	4.99527	−	1.81813i	1.06500	−	0.387627i
$23$	6.80143	+	2.47552i	1.41820	+	0.516181i	0.933524	−	0.358515i	$-0.116717\pi$
$23$	6.80143	+	2.47552i	1.41820	+	0.516181i	0.484672	+	0.874696i	$0.338939\pi$
$24$	−0.198589	−	1.72063i	−0.0405368	−	0.351222i
$25$	3.65046	+	1.32866i	0.730092	+	0.265732i
$26$	−1.59575	−	2.76393i	−0.312953	−	0.542051i
$27$	−1.75597	−	4.89046i	−0.337937	−	0.941169i
$28$	−2.77513	−	1.01006i	−0.524450	−	0.190884i
$29$	4.16851	−	3.49780i	0.774074	−	0.649525i	−0.167675	−	0.985842i	$-0.553626\pi$
$29$	4.16851	−	3.49780i	0.774074	−	0.649525i	0.941749	+	0.336317i	$0.109181\pi$
$30$	1.75306	−	0.522070i	0.320064	−	0.0953165i
$31$	−4.67989	+	8.10581i	−0.840533	+	1.45585i	0.0489110	+	0.998803i	$0.484425\pi$
$31$	−4.67989	+	8.10581i	−0.840533	+	1.45585i	−0.889444	+	0.457043i	$0.848908\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	−8.44904	−	3.65907i	−1.47079	−	0.636963i
$34$	0.452846	+	2.56821i	0.0776624	+	0.440445i
$35$	0.541572	−	3.07141i	0.0915424	−	0.519163i
$36$	−1.79843	+	2.40117i	−0.299739	+	0.400196i
$37$	4.80756			0.790357			0.395179	−	0.918604i	$-0.370683\pi$
$37$	4.80756			0.790357			0.395179	+	0.918604i	$0.370683\pi$
$38$	−2.05455	−	3.84432i	−0.333292	−	0.623631i
$39$	−1.28259	+	5.37700i	−0.205379	+	0.861009i
$40$	−0.808989	−	0.678823i	−0.127912	−	0.107331i
$41$	−10.6019	+	3.85878i	−1.65574	+	0.602641i	−0.989685	−	0.143260i	$-0.954242\pi$
$41$	−10.6019	+	3.85878i	−1.65574	+	0.602641i	−0.666057	+	0.745901i	$0.732019\pi$
$42$	2.28905	+	4.57438i	0.353209	+	0.705842i
$43$	7.52577	−	2.73915i	1.14767	−	0.417717i	0.302991	−	0.952993i	$-0.402015\pi$
$43$	7.52577	−	2.73915i	1.14767	−	0.417717i	0.844677	+	0.535276i	$0.179792\pi$
$44$	0.923089	+	5.23510i	0.139161	+	0.789221i
$45$	−2.82706	−	1.43007i	−0.421434	−	0.213182i
$46$	−3.61897	+	6.26823i	−0.533587	+	0.924200i
$47$	−2.32373	+	1.94984i	−0.338951	+	0.284414i	−0.796335	−	0.604855i	$-0.793231\pi$
$47$	−2.32373	+	1.94984i	−0.338951	+	0.284414i	0.457384	+	0.889269i	$0.348786\pi$
$48$	1.72897	+	0.103212i	0.249556	+	0.0148974i
$49$	1.72157			0.245938
$50$	−1.94237	+	3.36428i	−0.274692	+	0.475781i
$51$	2.48754	−	3.77022i	0.348325	−	0.527936i
$52$	2.99904	−	1.09156i	0.415891	−	0.151372i
$53$	−5.67594	+	4.76268i	−0.779650	+	0.654204i	−0.943160	−	0.332338i	$-0.892163\pi$
$53$	−5.67594	+	4.76268i	−0.779650	+	0.654204i	0.163511	+	0.986542i	$0.447718\pi$
$54$	5.12108	−	0.880077i	0.696891	−	0.119763i
$55$	−5.27531	+	1.92006i	−0.711323	+	0.258900i
$56$	1.47661	−	2.55757i	0.197321	−	0.341770i
$57$	−1.99150	+	7.28244i	−0.263781	+	0.964583i
$58$	2.72080	+	4.71257i	0.357259	+	0.618791i
$59$	0.610666	+	0.512409i	0.0795019	+	0.0667100i	0.681673	−	0.731657i	$-0.261253\pi$
$59$	0.610666	+	0.512409i	0.0795019	+	0.0667100i	−0.602171	+	0.798367i	$0.705697\pi$
$60$	0.209722	+	1.81709i	0.0270750	+	0.234585i
$61$	0.781304	+	4.43100i	0.100036	+	0.567331i	0.993087	+	0.117377i	$0.0374486\pi$
$61$	0.781304	+	4.43100i	0.100036	+	0.567331i	−0.893052	+	0.449954i	$0.851440\pi$
$62$	−7.17001	−	6.01635i	−0.910592	−	0.764078i
$63$	2.56554	−	8.48010i	0.323228	−	1.06839i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.68521	+	2.91887i	0.209025	+	0.362042i
$66$	5.07064	−	7.68529i	0.624153	−	0.945994i
$67$	0.176594	+	1.00151i	0.0215743	+	0.122354i	0.993693	−	0.112136i	$-0.0357691\pi$
$67$	0.176594	+	1.00151i	0.0215743	+	0.122354i	−0.972119	+	0.234490i	$0.924658\pi$
$68$	−2.60783			−0.316246
$69$	12.0150	−	3.57811i	1.44644	−	0.430754i
$70$	2.93070	+	1.06669i	0.350286	+	0.127494i
$71$	−7.58026	−	6.36059i	−0.899611	−	0.754864i	0.0705031	−	0.997512i	$-0.477540\pi$
$71$	−7.58026	−	6.36059i	−0.899611	−	0.754864i	−0.970114	+	0.242648i	$0.921984\pi$
$72$	−2.05240	−	2.18807i	−0.241878	−	0.257867i
$73$	−2.38965	+	13.5524i	−0.279687	+	1.58618i	0.443982	+	0.896036i	$0.353566\pi$
$73$	−2.38965	+	13.5524i	−0.279687	+	1.58618i	−0.723669	+	0.690148i	$0.757546\pi$
$74$	−0.834823	+	4.73452i	−0.0970463	+	0.550377i
$75$	6.44868	−	1.92044i	0.744629	−	0.221754i
$76$	4.14269	−	1.35578i	0.475199	−	0.155519i
$77$	−7.84948	−	13.5957i	−0.894531	−	1.54937i
$78$	−5.07259	−	2.19681i	−0.574358	−	0.248740i
$79$	−6.52637	−	5.47628i	−0.734274	−	0.616129i	0.197019	−	0.980400i	$-0.436874\pi$
$79$	−6.52637	−	5.47628i	−0.734274	−	0.616129i	−0.931293	+	0.364270i	$0.881318\pi$
$80$	0.808989	−	0.678823i	0.0904478	−	0.0758947i
$81$	−7.49064	−	4.98903i	−0.832293	−	0.554336i
$82$	−1.95916	−	11.1109i	−0.216353	−	1.22700i
$83$	−5.75022			−0.631168			−0.315584	−	0.948898i	$-0.602200\pi$
$83$	−5.75022			−0.631168			−0.315584	+	0.948898i	$0.602200\pi$
$84$	−4.90237	+	1.45995i	−0.534893	+	0.159293i
$85$	−0.478232	−	2.71219i	−0.0518716	−	0.294178i
$86$	1.39071	+	7.88708i	0.149964	+	0.850486i
$87$	2.18686	−	9.16793i	0.234456	−	0.982906i
$88$	−5.31586			−0.566673
$89$	1.57241	+	8.91760i	0.166675	+	0.945263i	0.947320	+	0.320288i	$0.103780\pi$
$89$	1.57241	+	8.91760i	0.166675	+	0.945263i	−0.780645	+	0.624975i	$0.785109\pi$
$90$	1.89925	−	2.53579i	0.200199	−	0.267295i
$91$	−7.22016	+	6.05844i	−0.756879	+	0.635097i
$92$	−5.54458	−	4.65245i	−0.578062	−	0.485052i
$93$	1.85875	+	16.1047i	0.192743	+	1.66998i
$94$	−1.51671	−	2.62701i	−0.156436	−	0.270956i
$95$	2.16973	+	4.05984i	0.222610	+	0.416531i
$96$	−0.401877	+	1.68478i	−0.0410164	+	0.171952i
$97$	0.775292	−	4.39690i	0.0787190	−	0.446438i	−0.919817	−	0.392348i	$-0.871663\pi$
$97$	0.775292	−	4.39690i	0.0787190	−	0.446438i	0.998536	−	0.0540902i	$-0.0172258\pi$
$98$	−0.298947	+	1.69541i	−0.0301982	+	0.171262i
$99$	−15.5283	+	3.63283i	−1.56065	+	0.365114i
$100$	−2.97588	−	2.49706i	−0.297588	−	0.249706i
$101$	5.91562	+	2.15311i	0.588626	+	0.214242i	0.619125	−	0.785292i	$-0.287487\pi$
$101$	5.91562	+	2.15311i	0.588626	+	0.214242i	−0.0304989	+	0.999535i	$0.509710\pi$
$102$	3.28098	+	3.10444i	0.324866	+	0.307385i
$103$	9.16581			0.903134			0.451567	−	0.892237i	$-0.350865\pi$
$103$	9.16581			0.903134			0.451567	+	0.892237i	$0.350865\pi$
$104$	0.554199	+	3.14302i	0.0543437	+	0.308199i
$105$	−2.41738	−	4.83082i	−0.235912	−	0.471440i
$106$	−3.70470	−	6.41673i	−0.359833	−	0.623248i
$107$	−1.81473	−	3.14320i	−0.175437	−	0.303865i	0.764876	−	0.644178i	$-0.222800\pi$
$107$	−1.81473	−	3.14320i	−0.175437	−	0.303865i	−0.940312	+	0.340313i	$0.889467\pi$
$108$	−0.0225597	+	5.19610i	−0.00217081	+	0.499995i
$109$	−5.41289	−	4.54195i	−0.518461	−	0.435040i	0.345634	−	0.938369i	$-0.387664\pi$
$109$	−5.41289	−	4.54195i	−0.518461	−	0.435040i	−0.864095	+	0.503329i	$0.832108\pi$
$110$	−0.974838	−	5.52858i	−0.0929472	−	0.527130i
$111$	6.68641	−	4.96283i	0.634646	−	0.471051i
$112$	2.26231	+	1.89830i	0.213768	+	0.179372i
$113$	5.64236	+	9.77285i	0.530788	+	0.919352i	0.999355	+	0.0359241i	$0.0114374\pi$
$113$	5.64236	+	9.77285i	0.530788	+	0.919352i	−0.468566	+	0.883428i	$0.655229\pi$
$114$	−6.82598	−	3.22583i	−0.639312	−	0.302126i
$115$	3.82185	−	6.61963i	0.356389	−	0.617284i
$116$	−5.11344	+	1.86114i	−0.474771	+	0.172803i
$117$	3.76681	+	8.80242i	0.348242	+	0.813784i
$118$	−0.610666	+	0.512409i	−0.0562163	+	0.0471711i
$119$	7.23707	−	2.63408i	0.663421	−	0.241466i
$120$	−1.82590	−	0.108998i	−0.166681	−	0.00995013i
$121$	−8.62918	+	14.9462i	−0.784471	+	1.35874i
$122$	−4.49935			−0.407352
$123$	−10.7619	+	16.3112i	−0.970367	+	1.47073i
$124$	7.17001	−	6.01635i	0.643886	−	0.540284i
$125$	4.69141	−	8.12576i	0.419612	−	0.726790i
$126$	7.90577	+	3.99912i	0.704302	+	0.356270i
$127$	−2.29255	−	13.0017i	−0.203431	−	1.15371i	−0.899890	−	0.436117i	$-0.856353\pi$
$127$	−2.29255	−	13.0017i	−0.203431	−	1.15371i	0.696459	−	0.717597i	$-0.254758\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	7.63931	−	11.5785i	0.672604	−	1.01943i
$130$	−3.16716	+	1.15275i	−0.277779	+	0.101103i
$131$	−15.6101	−	13.0984i	−1.36386	−	1.14441i	−0.974769	−	0.223215i	$-0.928345\pi$
$131$	−15.6101	−	13.0984i	−1.36386	−	1.14441i	−0.389091	−	0.921199i	$-0.627211\pi$
$132$	6.68802	+	6.32815i	0.582118	+	0.550794i
$133$	−10.1271	+	7.94684i	−0.878128	+	0.689079i
$134$	−1.01696			−0.0878522
$135$	−5.40817	+	0.929415i	−0.465461	+	0.0799913i
$136$	0.452846	−	2.56821i	0.0388312	−	0.220223i
$137$	2.21068	+	12.5374i	0.188871	+	1.07114i	0.920880	+	0.389846i	$0.127472\pi$
$137$	2.21068	+	12.5374i	0.188871	+	1.07114i	−0.732009	+	0.681295i	$0.761417\pi$
$138$	1.43737	+	12.4538i	0.122357	+	1.06014i
$139$	8.19861	−	6.87945i	0.695397	−	0.583507i	−0.225063	−	0.974344i	$-0.572259\pi$
$139$	8.19861	−	6.87945i	0.695397	−	0.583507i	0.920460	+	0.390837i	$0.127814\pi$
$140$	−1.55939	+	2.70095i	−0.131793	+	0.228272i
$141$	−1.21906	+	5.11065i	−0.102663	+	0.430394i
$142$	7.58026	−	6.36059i	0.636121	−	0.533769i
$143$	15.9425	+	5.80258i	1.33317	+	0.485236i
$144$	2.51122	−	1.64127i	0.209269	−	0.136772i
$145$	−2.87333	−	4.97676i	−0.238617	−	0.413298i
$146$	−12.9315	−	4.70668i	−1.07022	−	0.389528i
$147$	2.39438	−	1.77717i	0.197485	−	0.146578i
$148$	−4.51763	−	1.64428i	−0.371347	−	0.135159i
$149$	10.6827	−	3.88818i	0.875159	−	0.318532i	0.134905	−	0.990859i	$-0.456927\pi$
$149$	10.6827	−	3.88818i	0.875159	−	0.318532i	0.740255	+	0.672327i	$0.234705\pi$
$150$	0.771466	+	6.68419i	0.0629899	+	0.545762i
$151$	8.42753	−	14.5969i	0.685823	−	1.18788i	−0.287354	−	0.957824i	$-0.592776\pi$
$151$	8.42753	−	14.5969i	0.685823	−	1.18788i	0.973177	−	0.230056i	$-0.0738909\pi$
$152$	0.615812	+	4.31518i	0.0499490	+	0.350007i
$153$	−0.432288	−	7.81155i	−0.0349484	−	0.631526i
$154$	14.7522	−	5.36936i	1.18877	−	0.432675i
$155$	7.57197	+	6.35363i	0.608195	+	0.510336i
$156$	3.04429	−	4.61405i	0.243738	−	0.369420i
$157$	−2.68383	+	15.2207i	−0.214193	+	1.21475i	0.668109	+	0.744063i	$0.267104\pi$
$157$	−2.68383	+	15.2207i	−0.214193	+	1.21475i	−0.882302	+	0.470684i	$0.844007\pi$
$158$	6.52637	−	5.47628i	0.519210	−	0.435669i
$159$	−2.97767	+	12.4832i	−0.236145	+	0.989986i
$160$	0.528030	+	0.914575i	0.0417445	+	0.0723035i
$161$	20.0862	+	7.31077i	1.58301	+	0.576170i
$162$	6.21397	−	6.51050i	0.488215	−	0.511513i
$163$	7.36262	−	12.7524i	0.576685	−	0.998848i	−0.419171	−	0.907907i	$-0.637679\pi$
$163$	7.36262	−	12.7524i	0.576685	−	0.998848i	0.995856	−	0.0909407i	$-0.0289874\pi$
$164$	11.2823			0.881002
$165$	−5.35491	+	8.11613i	−0.416879	+	0.631840i
$166$	0.998514	−	5.66286i	0.0774997	−	0.439523i
$167$	11.0534	+	4.02311i	0.855339	+	0.311318i	0.732215	−	0.681074i	$-0.238487\pi$
$167$	11.0534	+	4.02311i	0.855339	+	0.311318i	0.123124	+	0.992391i	$0.460709\pi$
$168$	−0.586479	−	5.08141i	−0.0452478	−	0.392039i
$169$	−0.488695	+	2.77153i	−0.0375919	+	0.213194i
$170$	2.75403			0.211224
$171$	4.74784	+	12.1843i	0.363076	+	0.931759i
$172$	−8.00875			−0.610662
$173$	−0.392460	+	2.22575i	−0.0298382	+	0.169221i	−0.996085	−	0.0883957i	$-0.971826\pi$
$173$	−0.392460	+	2.22575i	−0.0298382	+	0.169221i	0.966247	+	0.257616i	$0.0829371\pi$
$174$	8.64891	+	3.74563i	0.655672	+	0.283955i
$175$	10.7806	+	3.92383i	0.814940	+	0.296614i
$176$	0.923089	−	5.23510i	0.0695805	−	0.394611i
$177$	1.37828	+	0.0822773i	0.103598	+	0.00618434i
$178$	−9.05517			−0.678713
$179$	−4.29955	+	7.44703i	−0.321363	+	0.556617i	−0.980770	−	0.195169i	$-0.937474\pi$
$179$	−4.29955	+	7.44703i	−0.321363	+	0.556617i	0.659406	+	0.751787i	$0.270808\pi$
$180$	2.16746	+	2.31074i	0.161553	+	0.172232i
$181$	3.64084	+	1.32516i	0.270622	+	0.0984982i	0.473767	−	0.880650i	$-0.342894\pi$
$181$	3.64084	+	1.32516i	0.270622	+	0.0984982i	−0.203145	+	0.979149i	$0.565116\pi$
$182$	−4.71263	−	8.16251i	−0.349323	−	0.605045i
$183$	5.66075	+	5.35615i	0.418455	+	0.395938i
$184$	5.54458	−	4.65245i	0.408752	−	0.342983i
$185$	0.881624	−	4.99994i	0.0648183	−	0.367603i
$186$	−16.1828	−	0.966043i	−1.18658	−	0.0708337i
$187$	−10.6196	−	8.91089i	−0.776581	−	0.651628i
$188$	2.85048	−	1.03749i	0.207892	−	0.0756667i
$189$	−5.18579	−	14.4426i	−0.377211	−	1.05055i
$190$	−4.37493	+	1.43179i	−0.317391	+	0.103873i
$191$	−3.12154	+	5.40667i	−0.225867	+	0.391213i	−0.956579	−	0.291473i	$-0.905855\pi$
$191$	−3.12154	+	5.40667i	−0.225867	+	0.391213i	0.730712	+	0.682686i	$0.239188\pi$
$192$	−1.58940	−	0.688331i	−0.114705	−	0.0496760i
$193$	−6.81517	+	2.48052i	−0.490567	+	0.178552i	−0.575446	−	0.817839i	$-0.695172\pi$
$193$	−6.81517	+	2.48052i	−0.490567	+	0.178552i	0.0848795	+	0.996391i	$0.472949\pi$
$194$	4.19547	+	1.52703i	0.301218	+	0.109634i
$195$	5.35696	+	2.31997i	0.383620	+	0.166136i
$196$	−1.61774	−	0.588810i	−0.115553	−	0.0420579i
$197$	−7.94082	−	13.7539i	−0.565760	−	0.979925i	−0.996979	−	0.0776777i	$-0.975249\pi$
$197$	−7.94082	−	13.7539i	−0.565760	−	0.979925i	0.431218	−	0.902248i	$-0.358084\pi$
$198$	−0.881185	−	15.9232i	−0.0626231	−	1.13161i
$199$	22.2173	+	8.08644i	1.57494	+	0.573232i	0.974097	−	0.226132i	$-0.0726081\pi$
$199$	22.2173	+	8.08644i	1.57494	+	0.573232i	0.600846	+	0.799365i	$0.294830\pi$
$200$	2.97588	−	2.49706i	0.210427	−	0.176569i
$201$	1.27947	+	1.21062i	0.0902467	+	0.0853905i
$202$	−3.14764	+	5.45186i	−0.221467	+	0.383592i
$203$	12.3106	−	10.3298i	0.864033	−	0.725010i
$204$	−3.62701	+	2.69206i	−0.253941	+	0.188482i
$205$	2.06899	+	11.7338i	0.144504	+	0.819525i
$206$	−1.59163	+	9.02656i	−0.110894	+	0.628910i
$207$	13.0169	−	17.3795i	0.904740	−	1.20796i
$208$	−3.19151			−0.221291
$209$	21.5024	+	8.63445i	1.48736	+	0.597257i
$210$	5.17720	−	1.54179i	0.357261	−	0.106394i
$211$	2.86048	+	2.40022i	0.196923	+	0.165238i	0.735918	−	0.677071i	$-0.236751\pi$
$211$	2.86048	+	2.40022i	0.196923	+	0.165238i	−0.538994	+	0.842309i	$0.681196\pi$
$212$	6.96257	−	2.53417i	0.478191	−	0.174047i
$213$	−17.1088	−	1.02132i	−1.17227	−	0.0699795i
$214$	3.41058	−	1.24135i	0.233142	−	0.0848568i
$215$	−1.46867	−	8.32924i	−0.100162	−	0.568049i
$216$	−5.11325	−	0.924511i	−0.347912	−	0.0629050i
$217$	−13.8208	+	23.9383i	−0.938217	+	1.62504i
$218$	5.41289	−	4.54195i	0.366607	−	0.307620i
$219$	10.6665	+	21.3156i	0.720776	+	1.44038i
$220$	5.61387			0.378487
$221$	−4.16146	+	7.20786i	−0.279930	+	0.484853i
$222$	3.72635	+	7.44662i	0.250096	+	0.499784i
$223$	−1.15616	+	0.420809i	−0.0774224	+	0.0281795i	−0.380441	−	0.924805i	$-0.624228\pi$
$223$	−1.15616	+	0.420809i	−0.0774224	+	0.0281795i	0.303019	+	0.952985i	$0.402006\pi$
$224$	−2.26231	+	1.89830i	−0.151157	+	0.126835i
$225$	6.98644	−	9.32793i	0.465763	−	0.621862i
$226$	−10.6042	+	3.85960i	−0.705379	+	0.256737i
$227$	−6.46164	+	11.1919i	−0.428874	+	0.742832i	−0.996773	−	0.0802660i	$-0.974423\pi$
$227$	−6.46164	+	11.1919i	−0.428874	+	0.742832i	0.567899	+	0.823098i	$0.307756\pi$
$228$	4.36214	−	6.16212i	0.288890	−	0.408097i
$229$	1.70891	+	2.95992i	0.112928	+	0.195597i	0.916950	−	0.399003i	$-0.130644\pi$
$229$	1.70891	+	2.95992i	0.112928	+	0.195597i	−0.804022	+	0.594600i	$0.797310\pi$
$230$	5.85541	+	4.91327i	0.386094	+	0.323972i
$231$	−24.9520	−	10.8061i	−1.64172	−	0.710988i
$232$	−0.944926	−	5.35894i	−0.0620374	−	0.351832i
$233$	0.963668	+	0.808614i	0.0631320	+	0.0529741i	0.673808	−	0.738907i	$-0.264658\pi$
$233$	0.963668	+	0.808614i	0.0631320	+	0.0529741i	−0.610676	+	0.791881i	$0.709102\pi$
$234$	−9.32279	+	2.18106i	−0.609450	+	0.142580i
$235$	1.60174	+	2.77429i	0.104486	+	0.180975i
$236$	−0.398584	−	0.690367i	−0.0259456	−	0.0449391i
$237$	−14.7301	−	0.879323i	−0.956824	−	0.0571182i
$238$	1.33736	+	7.58453i	0.0866880	+	0.491632i
$239$	−2.24736			−0.145370			−0.0726849	−	0.997355i	$-0.523157\pi$
$239$	−2.24736			−0.145370			−0.0726849	+	0.997355i	$0.523157\pi$
$240$	0.424407	−	1.77923i	0.0273953	−	0.114849i
$241$	−22.5360	−	8.20243i	−1.45167	−	0.528365i	−0.508613	−	0.860995i	$-0.669842\pi$
$241$	−22.5360	−	8.20243i	−1.45167	−	0.528365i	−0.943057	+	0.332630i	$0.892064\pi$
$242$	−13.2207	−	11.0935i	−0.849857	−	0.713115i
$243$	−15.5682	+	0.793757i	−0.998703	+	0.0509196i
$244$	0.781304	−	4.43100i	0.0500179	−	0.283666i
$245$	0.315706	−	1.79046i	0.0201697	−	0.114388i
$246$	−14.1946	−	13.4308i	−0.905015	−	0.856316i
$247$	2.86343	−	13.6136i	0.182196	−	0.866211i
$248$	4.67989	+	8.10581i	0.297173	+	0.514719i
$249$	−7.99748	+	5.93593i	−0.506820	+	0.376174i
$250$	7.18766	+	6.03116i	0.454587	+	0.381444i
$251$	7.98681	−	6.70173i	0.504123	−	0.423009i	−0.354932	−	0.934892i	$-0.615496\pi$
$251$	7.98681	−	6.70173i	0.504123	−	0.423009i	0.859055	+	0.511883i	$0.171052\pi$
$252$	−5.31119	+	7.09122i	−0.334573	+	0.446705i
$253$	−6.68126	−	37.8913i	−0.420047	−	2.38221i
$254$	13.2023			0.828384
$255$	−3.46492	−	3.27847i	−0.216982	−	0.205306i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−0.617509	−	3.50207i	−0.0385192	−	0.218453i	0.959472	−	0.281803i	$-0.0909326\pi$
$257$	−0.617509	−	3.50207i	−0.0385192	−	0.218453i	−0.997991	+	0.0633503i	$0.979821\pi$
$258$	10.0760	+	9.53384i	0.627306	+	0.593551i
$259$	14.1978			0.882210
$260$	−0.585268	−	3.31922i	−0.0362968	−	0.205849i
$261$	−6.42252	−	15.0084i	−0.397544	−	0.928995i
$262$	15.6101	−	13.0984i	0.964395	−	0.809223i
$263$	−10.7646	−	9.03257i	−0.663773	−	0.556972i	0.247442	−	0.968903i	$-0.420410\pi$
$263$	−10.7646	−	9.03257i	−0.663773	−	0.556972i	−0.911215	+	0.411931i	$0.864855\pi$
$264$	−7.39337	+	5.48755i	−0.455030	+	0.337735i
$265$	3.91239	+	6.77646i	0.240336	+	0.416275i
$266$	−6.06757	−	11.3532i	−0.372026	−	0.696107i
$267$	11.3925	+	10.7795i	0.697212	+	0.659696i
$268$	0.176594	−	1.00151i	0.0107872	−	0.0611771i
$269$	1.67736	−	9.51276i	0.102270	−	0.580003i	−0.890005	−	0.455950i	$-0.849300\pi$
$269$	1.67736	−	9.51276i	0.102270	−	0.580003i	0.992276	−	0.124053i	$-0.0395893\pi$
$270$	0.0238244	−	5.48740i	0.00144991	−	0.333953i
$271$	−12.8549	−	10.7865i	−0.780879	−	0.655235i	0.162591	−	0.986694i	$-0.448015\pi$
$271$	−12.8549	−	10.7865i	−0.780879	−	0.655235i	−0.943470	+	0.331458i	$0.892459\pi$
$272$	2.45056	+	0.891932i	0.148587	+	0.0540813i
$273$	−3.78779	+	15.8795i	−0.229248	+	0.961072i
$274$	−12.7308			−0.769095
$275$	−3.58596	−	20.3370i	−0.216241	−	1.22637i
$276$	−12.5142	−	0.747042i	−0.753266	−	0.0449666i
$277$	−0.660723	−	1.14441i	−0.0396990	−	0.0687607i	0.845493	−	0.533986i	$-0.179307\pi$
$277$	−0.660723	−	1.14441i	−0.0396990	−	0.0687607i	−0.885192	+	0.465226i	$0.845973\pi$
$278$	5.35126	+	9.26866i	0.320947	+	0.555897i
$279$	19.2100	+	20.4799i	1.15007	+	1.22610i
$280$	−2.38913	−	2.00472i	−0.142778	−	0.119805i
$281$	0.266893	+	1.51363i	0.0159215	+	0.0902955i	0.991733	−	0.128318i	$-0.0409578\pi$
$281$	0.266893	+	1.51363i	0.0159215	+	0.0902955i	−0.975812	+	0.218613i	$0.929847\pi$
$282$	−4.82132	−	2.08799i	−0.287105	−	0.124338i
$283$	−15.6648	−	13.1444i	−0.931178	−	0.781351i	0.0448508	−	0.998994i	$-0.485719\pi$
$283$	−15.6648	−	13.1444i	−0.931178	−	0.781351i	−0.976028	+	0.217643i	$0.930163\pi$
$284$	4.94766	+	8.56960i	0.293590	+	0.508512i
$285$	7.20865	+	3.40667i	0.427004	+	0.201794i
$286$	−8.48280	+	14.6926i	−0.501599	+	0.868794i
$287$	−31.3099	+	11.3959i	−1.84817	+	0.672677i
$288$	1.18026	+	2.75808i	0.0695476	+	0.162521i
$289$	−7.81304	+	6.55592i	−0.459591	+	0.385643i
$290$	5.40010	−	1.96548i	0.317105	−	0.115417i
$291$	−3.46062	−	6.91560i	−0.202865	−	0.405400i
$292$	6.88071	−	11.9177i	0.402663	−	0.697433i
$293$	−17.1457			−1.00167			−0.500833	−	0.865544i	$-0.666973\pi$
$293$	−17.1457			−1.00167			−0.500833	+	0.865544i	$0.666973\pi$
$294$	1.33439	+	2.66660i	0.0778232	+	0.155519i
$295$	0.644900	−	0.541135i	0.0375475	−	0.0315061i
$296$	2.40378	−	4.16347i	0.139717	−	0.241997i
$297$	−17.8468	+	21.0824i	−1.03558	+	1.22333i
$298$	1.97408	+	11.1956i	0.114355	+	0.648542i
$299$	−21.7068	+	7.90063i	−1.25534	+	0.456905i
$300$	−6.71660	−	0.400952i	−0.387783	−	0.0231490i
$301$	22.2253	−	8.08935i	1.28105	−	0.466263i
$302$	12.9117	+	10.8342i	0.742987	+	0.623440i
$303$	10.4502	−	3.11210i	0.600347	−	0.178786i
$304$	−4.35656	−	0.142866i	−0.249866	−	0.00819395i
$305$	4.75159			0.272075
$306$	7.76794	+	0.930741i	0.444064	+	0.0532069i
$307$	1.42049	−	8.05597i	0.0810714	−	0.459779i	−0.917064	−	0.398740i	$-0.869448\pi$
$307$	1.42049	−	8.05597i	0.0810714	−	0.459779i	0.998135	−	0.0610386i	$-0.0194413\pi$
$308$	2.72609	+	15.4605i	0.155334	+	0.880941i
$309$	12.7479	−	9.46184i	0.725204	−	0.538265i
$310$	−7.57197	+	6.35363i	−0.430059	+	0.360862i
$311$	3.30999	−	5.73307i	0.187692	−	0.325092i	−0.756788	−	0.653660i	$-0.773233\pi$
$311$	3.30999	−	5.73307i	0.187692	−	0.325092i	0.944480	+	0.328568i	$0.106566\pi$
$312$	4.01532	+	3.79926i	0.227323	+	0.215091i
$313$	15.6944	−	13.1691i	0.887098	−	0.744364i	−0.0805275	−	0.996752i	$-0.525660\pi$
$313$	15.6944	−	13.1691i	0.887098	−	0.744364i	0.967626	+	0.252388i	$0.0812161\pi$
$314$	−14.5235	−	5.28611i	−0.819606	−	0.298312i
$315$	−8.34897	−	4.22331i	−0.470411	−	0.237957i
$316$	4.25979	+	7.37817i	0.239632	+	0.415054i
$317$	16.7872	+	6.11003i	0.942861	+	0.343174i	0.767295	−	0.641294i	$-0.221602\pi$
$317$	16.7872	+	6.11003i	0.942861	+	0.343174i	0.175566	+	0.984468i	$0.443824\pi$
$318$	−11.7765	−	5.10013i	−0.660395	−	0.286001i
$319$	−27.1823	−	9.89356i	−1.52192	−	0.553933i
$320$	−0.992372	+	0.361194i	−0.0554753	+	0.0201914i
$321$	−5.76867	−	2.49827i	−0.321976	−	0.139440i
$322$	−10.6876	+	18.5115i	−0.595599	+	1.03161i
$323$	−6.00324	+	9.65278i	−0.334029	+	0.537095i
$324$	5.33255	+	7.25010i	0.296253	+	0.402783i
$325$	−11.6505	+	4.24042i	−0.646251	+	0.235216i
$326$	11.2802	+	9.46520i	0.624752	+	0.524229i
$327$	−12.2170	−	0.729299i	−0.675600	−	0.0403303i
$328$	−1.95916	+	11.1109i	−0.108176	+	0.613498i
$329$	−6.86251	+	5.75833i	−0.378343	+	0.317467i
$330$	−7.06296	−	6.68290i	−0.388803	−	0.367882i
$331$	15.3403	+	26.5703i	0.843181	+	1.46043i	0.887191	+	0.461402i	$0.152653\pi$
$331$	15.3403	+	26.5703i	0.843181	+	1.46043i	−0.0440096	+	0.999031i	$0.514013\pi$
$332$	5.40343	+	1.96669i	0.296552	+	0.107936i
$333$	4.17644	−	13.8047i	0.228868	−	0.756495i
$334$	−5.88140	+	10.1869i	−0.321816	+	0.557401i
$335$	1.07397			0.0586775
$336$	5.10605	+	0.304809i	0.278558	+	0.0166287i
$337$	−1.07632	+	6.10414i	−0.0586311	+	0.332513i	−0.999988	−	0.00489900i	$-0.998441\pi$
$337$	−1.07632	+	6.10414i	−0.0586311	+	0.332513i	0.941357	+	0.337412i	$0.109552\pi$
$338$	−2.64456	−	0.962541i	−0.143845	−	0.0523553i
$339$	17.9360	+	7.76762i	0.974147	+	0.421879i
$340$	−0.478232	+	2.71219i	−0.0259358	+	0.147089i
$341$	49.7553			2.69440
$342$	−12.8237	+	2.55992i	−0.693425	+	0.138425i
$343$	−15.5884			−0.841696
$344$	1.39071	−	7.88708i	0.0749818	−	0.425243i
$345$	−1.51795	−	13.1520i	−0.0817238	−	0.708078i
$346$	−2.12379	−	0.772995i	−0.114176	−	0.0415565i
$347$	2.80255	−	15.8941i	0.150449	−	0.853238i	−0.812380	−	0.583128i	$-0.801829\pi$
$347$	2.80255	−	15.8941i	0.150449	−	0.853238i	0.962829	−	0.270111i	$-0.0870603\pi$
$348$	−5.19059	+	7.86709i	−0.278245	+	0.421720i
$349$	24.4255			1.30746			0.653732	−	0.756726i	$-0.273202\pi$
$349$	24.4255			1.30746			0.653732	+	0.756726i	$0.273202\pi$
$350$	−5.73626	+	9.93549i	−0.306616	+	0.531074i
$351$	14.3256	+	8.35405i	0.764646	+	0.445906i
$352$	4.99527	+	1.81813i	0.266249	+	0.0969067i
$353$	−10.5856	−	18.3347i	−0.563413	−	0.975860i	−0.997195	−	0.0748424i	$-0.976155\pi$
$353$	−10.5856	−	18.3347i	−0.563413	−	0.975860i	0.433782	−	0.901018i	$-0.357179\pi$
$354$	−0.320363	+	1.34305i	−0.0170271	+	0.0713825i
$355$	−8.00521	+	6.71717i	−0.424873	+	0.356510i
$356$	1.57241	−	8.91760i	0.0833377	−	0.472632i
$357$	7.34627	−	11.1343i	0.388806	−	0.589291i
$358$	−6.58729	−	5.52739i	−0.348149	−	0.292132i
$359$	19.5836	−	7.12784i	1.03358	−	0.376193i	0.231139	−	0.972921i	$-0.425755\pi$
$359$	19.5836	−	7.12784i	1.03358	−	0.376193i	0.802444	+	0.596728i	$0.203533\pi$
$360$	−2.65201	+	1.73328i	−0.139773	+	0.0913516i
$361$	4.51813	−	18.4550i	0.237796	−	0.971315i
$362$	−1.93725	+	3.35542i	−0.101820	+	0.176357i
$363$	3.42732	+	29.6952i	0.179888	+	1.55860i
$364$	8.85684	−	3.22363i	0.464225	−	0.168964i
$365$	13.6565	+	4.97054i	0.714812	+	0.260170i
$366$	−6.25776	+	4.64467i	−0.327098	+	0.242781i
$367$	−1.32876	−	0.483628i	−0.0693605	−	0.0252452i	0.307107	−	0.951675i	$-0.400639\pi$
$367$	−1.32876	−	0.483628i	−0.0693605	−	0.0252452i	−0.376467	+	0.926430i	$0.622861\pi$
$368$	3.61897	+	6.26823i	0.188652	+	0.326754i
$369$	1.87022	+	33.7953i	0.0973597	+	1.75931i
$370$	4.77089	+	1.73646i	0.248027	+	0.0902743i
$371$	−16.7623	+	14.0653i	−0.870257	+	0.730233i
$372$	3.76148	−	15.7692i	0.195024	−	0.817595i
$373$	4.13398	−	7.16027i	0.214049	−	0.370745i	−0.738929	−	0.673784i	$-0.764668\pi$
$373$	4.13398	−	7.16027i	0.214049	−	0.370745i	0.952978	+	0.303039i	$0.0980013\pi$
$374$	10.6196	−	8.91089i	0.549125	−	0.460771i
$375$	−1.86332	−	16.1443i	−0.0962216	−	0.833690i
$376$	0.526747	+	2.98733i	0.0271649	+	0.154060i
$377$	−3.01574	+	17.1031i	−0.155318	+	0.880854i
$378$	15.1237	−	2.59907i	0.777881	−	0.133682i
$379$	−8.13253			−0.417740			−0.208870	−	0.977943i	$-0.566979\pi$
$379$	−8.13253			−0.417740			−0.208870	+	0.977943i	$0.566979\pi$
$380$	−0.650335	−	4.55709i	−0.0333615	−	0.233774i
$381$	−16.6101	−	15.7163i	−0.850963	−	0.805173i
$382$	−4.78248	−	4.01298i	−0.244693	−	0.205322i
$383$	9.73358	−	3.54273i	0.497363	−	0.181025i	−0.0811447	−	0.996702i	$-0.525858\pi$
$383$	9.73358	−	3.54273i	0.497363	−	0.181025i	0.578507	+	0.815677i	$0.303635\pi$
$384$	0.953871	−	1.44573i	0.0486770	−	0.0737770i
$385$	−15.5792	+	5.67037i	−0.793990	+	0.288989i
$386$	−1.25939	−	7.14237i	−0.0641014	−	0.363537i
$387$	−1.32757	−	23.9896i	−0.0674843	−	1.21946i
$388$	−2.23237	+	3.86657i	−0.113331	+	0.196295i
$389$	−19.4257	+	16.3001i	−0.984922	+	0.826448i	−0.984825	−	0.173552i	$-0.944475\pi$
$389$	−19.4257	+	16.3001i	−0.984922	+	0.826448i	−9.75622e−5		1.00000i	$0.500031\pi$
$390$	−3.21495	+	4.87272i	−0.162795	+	0.246740i
$391$	18.8753			0.954566
$392$	0.860783	−	1.49092i	0.0434761	−	0.0753028i
$393$	−35.2322	−	2.10321i	−1.77723	−	0.106093i
$394$	14.9239	−	5.43184i	0.751853	−	0.273652i
$395$	−6.89225	+	5.78328i	−0.346787	+	0.290988i
$396$	15.8343	+	1.89724i	0.795705	+	0.0953399i
$397$	−7.31690	+	2.66314i	−0.367225	+	0.133659i	−0.519040	−	0.854750i	$-0.673710\pi$
$397$	−7.31690	+	2.66314i	−0.367225	+	0.133659i	0.151815	+	0.988409i	$0.451488\pi$
$398$	−11.8216	+	20.4756i	−0.592562	+	1.02635i
$399$	−5.88135	+	21.5067i	−0.294436	+	1.07668i
$400$	1.94237	+	3.36428i	0.0971184	+	0.168214i
$401$	9.70653	+	8.14474i	0.484721	+	0.406729i	0.852130	−	0.523330i	$-0.175311\pi$
$401$	9.70653	+	8.14474i	0.484721	+	0.406729i	−0.367409	+	0.930059i	$0.619755\pi$
$402$	−1.41440	+	1.04981i	−0.0705441	+	0.0523596i
$403$	−5.18719	−	29.4180i	−0.258392	−	1.46541i
$404$	−4.82246	−	4.04652i	−0.239926	−	0.201322i
$405$	−6.56233	+	6.87548i	−0.326085	+	0.341645i
$406$	8.03516	+	13.9173i	0.398778	+	0.690704i
$407$	−12.7781	−	22.1324i	−0.633389	−	1.09706i
$408$	−2.02134	−	4.03938i	−0.100071	−	0.199979i
$409$	1.01456	+	5.75387i	0.0501669	+	0.284511i	0.999563	−	0.0295717i	$-0.00941434\pi$
$409$	1.01456	+	5.75387i	0.0501669	+	0.284511i	−0.949396	+	0.314082i	$0.898303\pi$
$410$	−11.9148			−0.588431
$411$	16.0169	+	15.1551i	0.790058	+	0.747545i
$412$	−8.61304	−	3.13489i	−0.424334	−	0.154445i
$413$	1.80344	+	1.51326i	0.0887413	+	0.0744628i
$414$	14.8551	+	15.8371i	0.730090	+	0.778351i
$415$	−1.05449	+	5.98032i	−0.0517630	+	0.293562i
$416$	0.554199	−	3.14302i	0.0271719	−	0.154099i
$417$	4.30110	−	18.0314i	0.210626	−	0.883003i
$418$	−12.2371	+	19.6764i	−0.598538	+	0.962405i
$419$	−1.74693	−	3.02577i	−0.0853431	−	0.147819i	0.820194	−	0.572085i	$-0.193865\pi$
$419$	−1.74693	−	3.02577i	−0.0853431	−	0.147819i	−0.905537	+	0.424267i	$0.860532\pi$
$420$	0.619357	+	5.36628i	0.0302215	+	0.261848i
$421$	−25.0137	−	20.9890i	−1.21909	−	1.02294i	−0.998872	−	0.0474901i	$-0.984878\pi$
$421$	−25.0137	−	20.9890i	−1.21909	−	1.02294i	−0.220221	−	0.975450i	$-0.570678\pi$
$422$	−2.86048	+	2.40022i	−0.139246	+	0.116841i
$423$	3.58022	+	8.36639i	0.174076	+	0.406788i
$424$	1.28663	+	7.29684i	0.0624843	+	0.354366i
$425$	10.1307			0.491413
$426$	3.97670	−	16.6715i	0.192672	−	0.807736i
$427$	2.30737	+	13.0858i	0.111662	+	0.633264i
$428$	0.630249	+	3.57432i	0.0304642	+	0.172771i
$429$	28.1630	−	8.38705i	1.35972	−	0.404930i
$430$	8.45773			0.407868
$431$	−0.948768	−	5.38073i	−0.0457006	−	0.259181i	0.953394	−	0.301729i	$-0.0975636\pi$
$431$	−0.948768	−	5.38073i	−0.0457006	−	0.259181i	−0.999094	+	0.0425478i	$0.986453\pi$
$432$	1.79837	−	4.87502i	0.0865242	−	0.234550i
$433$	20.9772	−	17.6020i	1.00810	−	0.845897i	0.0200143	−	0.999800i	$-0.493629\pi$
$433$	20.9772	−	17.6020i	1.00810	−	0.845897i	0.988086	+	0.153903i	$0.0491844\pi$
$434$	−21.1747	−	17.7677i	−1.01642	−	0.852876i
$435$	−9.13377	−	3.95561i	−0.437931	−	0.189657i
$436$	3.53301	+	6.11936i	0.169201	+	0.293064i
$437$	−29.9845	+	9.81304i	−1.43435	+	0.469421i
$438$	−22.8440	+	6.80304i	−1.09153	+	0.325062i
$439$	2.70897	−	15.3633i	0.129292	−	0.733252i	−0.849373	−	0.527792i	$-0.823020\pi$
$439$	2.70897	−	15.3633i	0.129292	−	0.733252i	0.978666	−	0.205460i	$-0.0658690\pi$
$440$	−0.974838	+	5.52858i	−0.0464736	+	0.263565i
$441$	1.49557	−	4.94342i	0.0712175	−	0.235401i
$442$	−6.37573	−	5.34987i	−0.303262	−	0.254467i
$443$	−31.8801	−	11.6034i	−1.51467	−	0.551295i	−0.554860	−	0.831944i	$-0.687228\pi$
$443$	−31.8801	−	11.6034i	−1.51467	−	0.551295i	−0.959811	+	0.280649i	$0.909450\pi$
$444$	−7.98056	+	2.37664i	−0.378741	+	0.112791i
$445$	9.56280			0.453320
$446$	−0.213650	−	1.21167i	−0.0101166	−	0.0573743i
$447$	10.8439	−	16.4354i	0.512897	−	0.777369i
$448$	−1.47661	−	2.55757i	−0.0697635	−	0.120834i
$449$	3.04950	+	5.28188i	0.143915	+	0.249267i	0.928967	−	0.370161i	$-0.120698\pi$
$449$	3.04950	+	5.28188i	0.143915	+	0.249267i	−0.785053	+	0.619429i	$0.787364\pi$
$450$	7.97303	+	8.50008i	0.375852	+	0.400697i
$451$	45.9437	+	38.5514i	2.16341	+	1.81531i
$452$	−1.95957	−	11.1133i	−0.0921704	−	0.522725i
$453$	−3.34723	−	29.0013i	−0.157267	−	1.36260i
$454$	−9.89981	−	8.30693i	−0.464621	−	0.389863i
$455$	4.97682	+	8.62010i	0.233317	+	0.404117i
$456$	5.31103	+	5.36591i	0.248712	+	0.251282i
$457$	−9.94442	+	17.2242i	−0.465180	+	0.805716i	−0.999210	−	0.0397500i	$-0.987344\pi$
$457$	−9.94442	+	17.2242i	−0.465180	+	0.805716i	0.534029	+	0.845466i	$0.320677\pi$
$458$	−3.21170	+	1.16896i	−0.150073	+	0.0546221i
$459$	−8.66507	−	10.4182i	−0.404451	−	0.486278i
$460$	−5.85541	+	4.91327i	−0.273010	+	0.229082i
$461$	3.92217	−	1.42755i	0.182674	−	0.0664877i	−0.249064	−	0.968487i	$-0.580123\pi$
$461$	3.92217	−	1.42755i	0.182674	−	0.0664877i	0.431737	+	0.901999i	$0.357901\pi$
$462$	14.9748	−	22.6964i	0.696690	−	1.05593i
$463$	12.5231	−	21.6907i	0.581999	−	1.00805i	−0.413243	−	0.910621i	$-0.635604\pi$
$463$	12.5231	−	21.6907i	0.581999	−	1.00805i	0.995242	−	0.0974312i	$-0.0310626\pi$
$464$	5.44161			0.252620
$465$	17.0900	+	1.02020i	0.792531	+	0.0473106i
$466$	−0.963668	+	0.808614i	−0.0446411	+	0.0374583i
$467$	−12.5949	+	21.8150i	−0.582821	+	1.00948i	0.412322	+	0.911038i	$0.364718\pi$
$467$	−12.5949	+	21.8150i	−0.582821	+	1.00948i	−0.995143	+	0.0984376i	$0.968616\pi$
$468$	−0.529041	−	9.55989i	−0.0244549	−	0.441906i
$469$	0.521522	+	2.95770i	0.0240816	+	0.136574i
$470$	−3.01028	+	1.09565i	−0.138854	+	0.0505386i
$471$	11.9796	+	23.9397i	0.551992	+	1.10308i
$472$	0.749092	−	0.272647i	0.0344798	−	0.0125496i
$473$	−32.6131	−	27.3657i	−1.49955	−	1.25827i
$474$	3.42382	−	14.3536i	0.157261	−	0.659284i
$475$	−16.0932	+	5.26685i	−0.738409	+	0.241659i
$476$	−7.70153			−0.352999
$477$	8.74504	+	20.4357i	0.400408	+	0.935687i
$478$	0.390250	−	2.21322i	0.0178496	−	0.101230i
$479$	−0.401361	−	2.27623i	−0.0183387	−	0.104004i	0.974265	−	0.225408i	$-0.0723714\pi$
$479$	−0.401361	−	2.27623i	−0.0183387	−	0.104004i	−0.992603	+	0.121404i	$0.961260\pi$
$480$	1.67851	+	0.726919i	0.0766129	+	0.0331792i
$481$	−11.7537	+	9.86252i	−0.535922	+	0.449692i
$482$	11.9912	−	20.7693i	0.546182	−	0.946015i
$483$	35.4830	−	10.5670i	1.61453	−	0.480815i
$484$	13.2207	−	11.0935i	0.600940	−	0.504248i
$485$	−4.43068	−	1.61263i	−0.201187	−	0.0732259i
$486$	1.92170	−	15.4696i	0.0871700	−	0.701713i
$487$	−2.27709	−	3.94403i	−0.103185	−	0.178721i	0.809810	−	0.586692i	$-0.199570\pi$
$487$	−2.27709	−	3.94403i	−0.103185	−	0.178721i	−0.912995	+	0.407971i	$0.866237\pi$
$488$	4.22801	+	1.53887i	0.191393	+	0.0696613i
$489$	−2.92427	−	25.3367i	−0.132240	−	1.14576i
$490$	1.70843	+	0.621819i	0.0771792	+	0.0280909i
$491$	−39.6616	+	14.4356i	−1.78990	+	0.651472i	−0.790673	+	0.612238i	$0.790269\pi$
$491$	−39.6616	+	14.4356i	−1.78990	+	0.651472i	−0.999230	+	0.0392335i	$0.987508\pi$
$492$	15.6916	−	11.6467i	0.707433	−	0.525075i
$493$	7.09541	−	12.2896i	0.319561	−	0.553496i
$494$	12.9095	+	5.18390i	0.580827	+	0.233235i
$495$	0.930584	+	16.8159i	0.0418267	+	0.755818i
$496$	−8.79532	+	3.20123i	−0.394922	+	0.143740i
$497$	−22.3862	−	18.7843i	−1.00416	−	0.842591i
$498$	−4.45700	−	8.90674i	−0.199723	−	0.399121i
$499$	5.87341	−	33.3098i	0.262930	−	1.49115i	−0.511936	−	0.859024i	$-0.671071\pi$
$499$	5.87341	−	33.3098i	0.262930	−	1.49115i	0.774866	−	0.632126i	$-0.217818\pi$
$500$	−7.18766	+	6.03116i	−0.321442	+	0.269722i
$501$	19.5263	−	5.81501i	0.872370	−	0.259795i
$502$	5.21302	+	9.02922i	0.232668	+	0.402994i
$503$	−7.96250	−	2.89811i	−0.355030	−	0.129220i	0.158347	−	0.987384i	$-0.449384\pi$
$503$	−7.96250	−	2.89811i	−0.355030	−	0.129220i	−0.513377	+	0.858163i	$0.671606\pi$
$504$	−6.06121	−	6.46188i	−0.269988	−	0.287835i
$505$	3.32409	−	5.75750i	0.147920	−	0.256205i
$506$	38.4758			1.71046
$507$	2.18136	+	4.35916i	0.0968774	+	0.193597i
$508$	−2.29255	+	13.0017i	−0.101715	+	0.576857i
$509$	13.6642	+	4.97334i	0.605653	+	0.220440i	0.626600	−	0.779341i	$-0.284446\pi$
$509$	13.6642	+	4.97334i	0.605653	+	0.220440i	−0.0209472	+	0.999781i	$0.506668\pi$
$510$	3.83034	−	2.84298i	0.169610	−	0.125889i
$511$	−7.05718	+	40.0232i	−0.312191	+	1.77052i
$512$	−1.00000			−0.0441942
$513$	19.1812	+	12.0450i	0.846871	+	0.531798i
$514$	3.55609			0.156853
$515$	1.68085	−	9.53259i	0.0740673	−	0.420056i
$516$	−11.1387	+	8.26741i	−0.490353	+	0.363953i
$517$	15.1527	+	5.51515i	0.666417	+	0.242556i
$518$	−2.46543	+	13.9821i	−0.108325	+	0.614339i
$519$	1.75180	+	3.50074i	0.0768954	+	0.153665i
$520$	3.37042			0.147803
$521$	19.1624	−	33.1903i	0.839520	−	1.45409i	−0.0507759	−	0.998710i	$-0.516169\pi$
$521$	19.1624	−	33.1903i	0.839520	−	1.45409i	0.890296	−	0.455382i	$-0.150497\pi$
$522$	15.8956	−	3.71877i	0.695732	−	0.162766i
$523$	3.94686	+	1.43654i	0.172584	+	0.0628155i	0.426867	−	0.904314i	$-0.359617\pi$
$523$	3.94686	+	1.43654i	0.172584	+	0.0628155i	−0.254283	+	0.967130i	$0.581839\pi$
$524$	10.1888	+	17.6475i	0.445098	+	0.770933i
$525$	19.0444	−	5.67151i	0.831167	−	0.247525i
$526$	10.7646	−	9.03257i	0.469359	−	0.393839i
$527$	−4.23854	+	24.0379i	−0.184634	+	1.04711i
$528$	−4.12033	−	8.23395i	−0.179315	−	0.358337i
$529$	22.5122	+	18.8900i	0.978793	+	0.821305i
$530$	−7.35289	+	2.67623i	−0.319389	+	0.116248i
$531$	2.00187	−	1.30836i	0.0868736	−	0.0567781i
$532$	12.2343	−	4.00393i	0.530425	−	0.173592i
$533$	18.0038	−	31.1835i	0.779832	−	1.35071i
$534$	−12.5940	+	9.34762i	−0.544998	+	0.404511i
$535$	−3.60178	+	1.31094i	−0.155718	+	0.0566768i
$536$	0.955632	+	0.347822i	0.0412770	+	0.0150236i
$537$	1.70768	+	14.7958i	0.0736920	+	0.638488i
$538$	9.07697	+	3.30375i	0.391336	+	0.142435i
$539$	−4.57580	−	7.92552i	−0.197094	−	0.341376i
$540$	5.39990	+	0.976340i	0.232375	+	0.0420150i
$541$	39.3732	+	14.3307i	1.69279	+	0.616124i	0.994972	−	0.100155i	$-0.0319338\pi$
$541$	39.3732	+	14.3307i	1.69279	+	0.616124i	0.697814	+	0.716279i	$0.254156\pi$
$542$	12.8549	−	10.7865i	0.552165	−	0.463321i
$543$	6.43169	−	1.91538i	0.276010	−	0.0821970i
$544$	−1.30392	+	2.25845i	−0.0559050	+	0.0968302i
$545$	−5.71634	+	4.79658i	−0.244861	+	0.205463i
$546$	−14.9805	−	6.48770i	−0.641107	−	0.277648i
$547$	3.95978	+	22.4570i	0.169308	+	0.960193i	0.944511	+	0.328480i	$0.106536\pi$
$547$	3.95978	+	22.4570i	0.169308	+	0.960193i	−0.775203	+	0.631712i	$0.782352\pi$
$548$	2.21068	−	12.5374i	0.0944355	−	0.535570i
$549$	13.4022	+	1.60583i	0.571992	+	0.0685350i
$550$	20.6507			0.880549
$551$	−4.88223	+	23.2115i	−0.207990	+	0.988844i
$552$	2.90876	−	12.1943i	0.123805	−	0.519026i
$553$	−19.2739	−	16.1727i	−0.819609	−	0.687733i
$554$	1.24175	−	0.451961i	0.0527570	−	0.0192020i
$555$	−3.93525	−	7.86408i	−0.167042	−	0.333812i
$556$	−10.0571	+	3.66048i	−0.426515	+	0.155239i
$557$	−0.803228	−	4.55533i	−0.0340339	−	0.193016i	0.963051	−	0.269320i	$-0.0867990\pi$
$557$	−0.803228	−	4.55533i	−0.0340339	−	0.193016i	−0.997085	+	0.0763045i	$0.975688\pi$
$558$	−23.5045	+	15.3619i	−0.995026	+	0.650321i
$559$	−12.7800	+	22.1356i	−0.540536	+	0.936236i
$560$	2.38913	−	2.00472i	0.100959	−	0.0847149i
$561$	−23.9685	−	1.43082i	−1.01195	−	0.0604091i
$562$	−1.53698			−0.0648335
$563$	−11.4525	+	19.8363i	−0.482665	+	0.836000i	−0.999802	−	0.0199023i	$-0.993664\pi$
$563$	−11.4525	+	19.8363i	−0.482665	+	0.836000i	0.517137	+	0.855903i	$0.326998\pi$
$564$	2.89349	−	4.38550i	0.121838	−	0.184663i
$565$	11.1986	−	4.07597i	0.471130	−	0.171477i
$566$	15.6648	−	13.1444i	0.658442	−	0.552498i
$567$	−22.1216	−	14.7337i	−0.929018	−	0.618759i
$568$	−9.29856	+	3.38440i	−0.390159	+	0.142006i
$569$	−1.14845	+	1.98918i	−0.0481457	+	0.0833908i	−0.889094	−	0.457725i	$-0.848665\pi$
$569$	−1.14845	+	1.98918i	−0.0481457	+	0.0833908i	0.840948	+	0.541116i	$0.181998\pi$
$570$	−4.60668	+	6.50757i	−0.192953	+	0.272572i
$571$	−11.7282	−	20.3138i	−0.490810	−	0.850107i	0.509135	−	0.860687i	$-0.329966\pi$
$571$	−11.7282	−	20.3138i	−0.490810	−	0.850107i	−0.999944	+	0.0105800i	$0.996632\pi$
$572$	−12.9964	−	10.9053i	−0.543407	−	0.455973i
$573$	1.23981	+	10.7420i	0.0517937	+	0.448755i
$574$	−5.78584	−	32.8131i	−0.241496	−	1.36959i
$575$	21.5392	+	18.0736i	0.898248	+	0.753719i
$576$	−2.92112	+	0.683396i	−0.121714	+	0.0284748i
$577$	1.63601	+	2.83365i	0.0681079	+	0.117966i	0.898068	−	0.439856i	$-0.144970\pi$
$577$	1.63601	+	2.83365i	0.0681079	+	0.117966i	−0.829960	+	0.557822i	$0.811637\pi$
$578$	−5.09960	−	8.83277i	−0.212115	−	0.367395i
$579$	−6.91800	+	10.4852i	−0.287502	+	0.435751i
$580$	0.997899	+	5.65936i	0.0414355	+	0.234992i
$581$	−16.9817			−0.704520
$582$	7.41147	−	2.20717i	0.307215	−	0.0914900i
$583$	37.0120	+	13.4713i	1.53288	+	0.557923i
$584$	10.5419	+	8.84567i	0.436225	+	0.366037i
$585$	9.84543	−	2.30333i	0.407059	−	0.0952311i
$586$	2.97733	−	16.8853i	0.122992	−	0.697524i
$587$	1.18943	−	6.74560i	0.0490930	−	0.278421i	−0.950372	−	0.311115i	$-0.899298\pi$
$587$	1.18943	−	6.74560i	0.0490930	−	0.278421i	0.999465	+	0.0326942i	$0.0104088\pi$
$588$	−2.85781	+	0.851066i	−0.117854	+	0.0350974i
$589$	−5.76387	−	40.3891i	−0.237496	−	1.66421i
$590$	0.420929	+	0.729070i	0.0173294	+	0.0300153i
$591$	−25.2423	−	10.9318i	−1.03833	−	0.449675i
$592$	3.68280	+	3.09024i	0.151362	+	0.127008i
$593$	2.59809	−	2.18006i	0.106691	−	0.0895244i	−0.587882	−	0.808947i	$-0.700038\pi$
$593$	2.59809	−	2.18006i	0.106691	−	0.0895244i	0.694573	+	0.719423i	$0.255593\pi$
$594$	−17.6631	−	21.2366i	−0.724724	−	0.871347i
$595$	−1.41233	−	8.00972i	−0.0578999	−	0.328367i
$596$	−11.3683			−0.465663
$597$	39.2477	−	11.6881i	1.60630	−	0.478364i
$598$	−4.01126	−	22.7490i	−0.164033	−	0.930275i
$599$	7.45930	+	42.3038i	0.304779	+	1.72849i	0.624544	+	0.780990i	$0.285285\pi$
$599$	7.45930	+	42.3038i	0.304779	+	1.72849i	−0.319765	+	0.947497i	$0.603604\pi$
$600$	1.56119	−	6.54494i	0.0637352	−	0.267196i
$601$	−40.5875			−1.65560			−0.827799	−	0.561024i	$-0.810408\pi$
$601$	−40.5875			−1.65560			−0.827799	+	0.561024i	$0.810408\pi$
$602$	4.10707	+	23.2924i	0.167392	+	0.949326i
$603$	3.02922	+	0.362956i	0.123359	+	0.0147807i
$604$	−12.9117	+	10.8342i	−0.525371	+	0.440839i
$605$	13.9618	+	11.7154i	0.567629	+	0.476298i
$606$	1.25017	+	10.8318i	0.0507847	+	0.440013i
$607$	6.99941	+	12.1233i	0.284097	+	0.492071i	0.972390	−	0.233362i	$-0.0749728\pi$
$607$	6.99941	+	12.1233i	0.284097	+	0.492071i	−0.688293	+	0.725433i	$0.741639\pi$
$608$	0.897204	−	4.26556i	0.0363864	−	0.172991i
$609$	6.45829	−	27.0750i	0.261703	−	1.09713i
$610$	−0.825105	+	4.67940i	−0.0334075	+	0.189463i
$611$	1.68112	−	9.53409i	0.0680107	−	0.385708i
$612$	−2.26549	+	7.48831i	−0.0915770	+	0.302697i
$613$	−14.5106	−	12.1758i	−0.586076	−	0.491776i	0.300860	−	0.953668i	$-0.402726\pi$
$613$	−14.5106	−	12.1758i	−0.586076	−	0.491776i	−0.886936	+	0.461892i	$0.847171\pi$
$614$	7.68692	+	2.79781i	0.310219	+	0.112910i
$615$	14.9904	+	14.1837i	0.604470	+	0.571943i
$616$	−15.6990			−0.632529
$617$	−1.54694	−	8.77312i	−0.0622774	−	0.353192i	−0.999983	−	0.00576277i	$-0.998166\pi$
$617$	−1.54694	−	8.77312i	−0.0622774	−	0.353192i	0.937706	−	0.347430i	$-0.112945\pi$
$618$	7.10444	+	14.1973i	0.285782	+	0.571099i
$619$	12.4299	+	21.5293i	0.499601	+	0.865334i	1.00000		0.000461103i	$-0.000146773\pi$
$619$	12.4299	+	21.5293i	0.499601	+	0.865334i	−0.500399	+	0.865795i	$0.666813\pi$
$620$	−4.94225	−	8.56023i	−0.198486	−	0.343787i
$621$	0.163286	−	37.6090i	0.00655243	−	1.50920i
$622$	5.07119	+	4.25524i	0.203336	+	0.170619i
$623$	4.64370	+	26.3357i	0.186046	+	1.05512i
$624$	−4.43879	+	3.29458i	−0.177694	+	0.131889i
$625$	7.28880	+	6.11603i	0.291552	+	0.244641i
$626$	10.2438	+	17.7427i	0.409424	+	0.709142i
$627$	38.8192	−	10.1880i	1.55029	−	0.406870i
$628$	7.72777	−	13.3849i	0.308372	−	0.534115i
$629$	11.7812	−	4.28801i	0.469748	−	0.170974i
$630$	5.60894	−	7.48876i	0.223465	−	0.298359i
$631$	−17.0957	+	14.3450i	−0.680569	+	0.571065i	−0.916173	−	0.400784i	$-0.868738\pi$
$631$	−17.0957	+	14.3450i	−0.680569	+	0.571065i	0.235603	+	0.971849i	$0.424293\pi$
$632$	−8.00578	+	2.91387i	−0.318453	+	0.115907i
$633$	6.45613	+	0.385403i	0.256608	+	0.0153184i
$634$	−8.93227	+	15.4711i	−0.354746	+	0.614437i
$635$	−13.9424			−0.553287
$636$	7.06762	−	10.7120i	0.280249	−	0.424758i
$637$	−4.20895	+	3.53173i	−0.166765	+	0.139932i
$638$	14.4634	−	25.0514i	0.572612	−	0.991793i
$639$	−24.8494	+	16.2409i	−0.983026	+	0.642478i
$640$	−0.183383	−	1.04002i	−0.00724885	−	0.0411103i
$641$	−43.8488	+	15.9596i	−1.73192	+	0.630368i	−0.998765	−	0.0496914i	$-0.984176\pi$
$641$	−43.8488	+	15.9596i	−1.73192	+	0.630368i	−0.733157	+	0.680059i	$0.761954\pi$
$642$	3.46204	−	5.24721i	0.136636	−	0.207091i
$643$	−7.10536	+	2.58614i	−0.280208	+	0.101987i	−0.478301	−	0.878196i	$-0.658747\pi$
$643$	−7.10536	+	2.58614i	−0.280208	+	0.101987i	0.198093	+	0.980183i	$0.436525\pi$
$644$	−16.3744	−	13.7398i	−0.645242	−	0.541422i
$645$	−10.6409	−	10.0683i	−0.418985	−	0.396439i
$646$	−8.46368	−	7.58823i	−0.332999	−	0.298555i
$647$	−48.9608			−1.92485			−0.962424	−	0.271552i	$-0.912463\pi$
$647$	−48.9608			−1.92485			−0.962424	+	0.271552i	$0.912463\pi$
$648$	−8.06594	+	3.99257i	−0.316860	+	0.156843i
$649$	0.735857	−	4.17325i	0.0288849	−	0.163814i
$650$	−2.15292	−	12.2098i	−0.0844444	−	0.478908i
$651$	5.48931	+	47.5609i	0.215143	+	1.86406i
$652$	−11.2802	+	9.46520i	−0.441766	+	0.370686i
$653$	3.86404	−	6.69271i	0.151211	−	0.261906i	−0.780462	−	0.625204i	$-0.785016\pi$
$653$	3.86404	−	6.69271i	0.151211	−	0.261906i	0.931673	+	0.363298i	$0.118349\pi$
$654$	2.83967	−	11.9047i	0.111040	−	0.465511i
$655$	−16.4852	+	13.8327i	−0.644130	+	0.540489i
$656$	−10.6019	−	3.85878i	−0.413936	−	0.150660i
$657$	36.8392	+	18.6351i	1.43723	+	0.727023i
$658$	−4.47919	−	7.75818i	−0.174617	−	0.302445i
$659$	4.30091	+	1.56540i	0.167539	+	0.0609794i	0.424428	−	0.905462i	$-0.360475\pi$
$659$	4.30091	+	1.56540i	0.167539	+	0.0609794i	−0.256889	+	0.966441i	$0.582697\pi$
$660$	7.80785	−	5.79518i	0.303920	−	0.225577i
$661$	8.38299	+	3.05116i	0.326060	+	0.118676i	0.499864	−	0.866104i	$-0.333383\pi$
$661$	8.38299	+	3.05116i	0.326060	+	0.118676i	−0.173803	+	0.984780i	$0.555606\pi$
$662$	−28.8304	+	10.4934i	−1.12053	+	0.407838i
$663$	1.65284	+	14.3207i	0.0641910	+	0.556168i
$664$	−2.87511	+	4.97983i	−0.111576	+	0.193255i
$665$	6.40772	+	11.9896i	0.248481	+	0.464938i
$666$	12.8698	+	6.51016i	0.498694	+	0.252264i
$667$	37.0107	−	13.4708i	1.43306	−	0.521592i
$668$	−9.01082	−	7.56098i	−0.348639	−	0.292543i
$669$	−1.17361	+	1.77877i	−0.0453743	+	0.0687713i
$670$	−0.186494	+	1.05766i	−0.00720488	+	0.0408609i
$671$	18.3222	−	15.3741i	0.707320	−	0.593512i
$672$	−1.18684	+	4.97555i	−0.0457832	+	0.191936i
$673$	16.2565	+	28.1571i	0.626642	+	1.08538i	0.988221	+	0.153034i	$0.0489044\pi$
$673$	16.2565	+	28.1571i	0.626642	+	1.08538i	−0.361579	+	0.932341i	$0.617762\pi$
$674$	−5.82450	−	2.11994i	−0.224351	−	0.0816572i
$675$	0.0876386	−	20.1855i	0.00337321	−	0.776940i
$676$	1.40714	−	2.43724i	0.0541208	−	0.0937400i
$677$	28.2604			1.08613			0.543067	−	0.839689i	$-0.317263\pi$
$677$	28.2604			1.08613			0.543067	+	0.839689i	$0.317263\pi$
$678$	−10.7642	+	16.3146i	−0.413395	+	0.626560i
$679$	2.28962	−	12.9851i	0.0878674	−	0.498321i
$680$	−2.58794	−	0.941934i	−0.0992430	−	0.0361215i
$681$	2.56642	+	22.2362i	0.0983455	+	0.852092i
$682$	−8.63992	+	48.9994i	−0.330840	+	1.87628i
$683$	−40.8054			−1.56137			−0.780687	−	0.624923i	$-0.785131\pi$
$683$	−40.8054			−1.56137			−0.780687	+	0.624923i	$0.785131\pi$
$684$	−0.294221	−	13.0734i	−0.0112498	−	0.499873i
$685$	13.4445			0.513687
$686$	2.70690	−	15.3516i	0.103350	−	0.586127i
$687$	5.43229	+	2.35259i	0.207255	+	0.0897570i
$688$	7.52577	+	2.73915i	0.286917	+	0.104429i
$689$	4.10629	−	23.2879i	0.156437	−	0.887199i
$690$	13.2157	+	0.788922i	0.503115	+	0.0300337i
$691$	−16.7787			−0.638292			−0.319146	−	0.947706i	$-0.603396\pi$
$691$	−16.7787			−0.638292			−0.319146	+	0.947706i	$0.603396\pi$
$692$	1.13004	−	1.95729i	0.0429578	−	0.0744051i
$693$	−45.8586	+	10.7286i	−1.74202	+	0.407546i
$694$	15.1659	+	5.51995i	0.575691	+	0.209535i
$695$	−5.65126	−	9.78826i	−0.214364	−	0.371290i
$696$	−6.84623	−	6.47784i	−0.259506	−	0.245542i
$697$	−22.5389	+	18.9124i	−0.853722	+	0.716358i
$698$	−4.24144	+	24.0544i	−0.160541	+	0.910472i
$699$	2.17501	+	0.129839i	0.0822665	+	0.00491095i
$700$	−8.78846	−	7.37439i	−0.332173	−	0.278726i
$701$	−20.8614	+	7.59294i	−0.787926	+	0.286782i	−0.704474	−	0.709730i	$-0.748817\pi$
$701$	−20.8614	+	7.59294i	−0.787926	+	0.286782i	−0.0834523	+	0.996512i	$0.526595\pi$
$702$	−10.7148	+	12.6573i	−0.404403	+	0.477721i
$703$	−16.4858	+	12.9366i	−0.621775	+	0.487915i
$704$	−2.65793	+	4.60367i	−0.100175	+	0.173507i
$705$	5.09160	+	2.20505i	0.191761	+	0.0830469i
$706$	19.8944	−	7.24096i	0.748734	−	0.272517i
$707$	17.4702	+	6.35863i	0.657034	+	0.239141i
$708$	−1.26702	−	0.548715i	−0.0476175	−	0.0206220i
$709$	−21.1147	−	7.68512i	−0.792979	−	0.288621i	−0.0864052	−	0.996260i	$-0.527538\pi$
$709$	−21.1147	−	7.68512i	−0.792979	−	0.288621i	−0.706574	+	0.707639i	$0.749760\pi$
$710$	−5.22503	−	9.05002i	−0.196092	−	0.339641i
$711$	−21.3946	+	13.9829i	−0.802359	+	0.524399i
$712$	8.50907	+	3.09705i	0.318891	+	0.116067i
$713$	−51.8960	+	43.5460i	−1.94352	+	1.63081i
$714$	9.68950	+	9.16811i	0.362620	+	0.343108i
$715$	8.95835	−	15.5163i	0.335023	−	0.580278i
$716$	6.58729	−	5.52739i	0.246178	−	0.206568i
$717$	−3.12566	+	2.31995i	−0.116730	+	0.0866400i
$718$	3.61890	+	20.5238i	0.135056	+	0.765942i
$719$	6.31736	−	35.8275i	0.235598	−	1.33614i	−0.605753	−	0.795652i	$-0.707128\pi$
$719$	6.31736	−	35.8275i	0.235598	−	1.33614i	0.841351	−	0.540489i	$-0.181761\pi$
$720$	−1.24643	−	2.91270i	−0.0464516	−	0.108550i
$721$	27.0687			1.00809
$722$	17.3900	+	7.65416i	0.647191	+	0.284858i
$723$	−39.8107	+	11.8558i	−1.48058	+	0.440922i
$724$	−2.96804	−	2.49048i	−0.110306	−	0.0925581i
$725$	19.8644	−	7.23004i	0.737744	−	0.268517i
$726$	−29.8392	−	1.78127i	−1.10744	−	0.0661092i
$727$	24.7119	−	8.99438i	0.916512	−	0.333583i	0.159662	−	0.987172i	$-0.448959\pi$
$727$	24.7119	−	8.99438i	0.916512	−	0.333583i	0.756850	+	0.653589i	$0.226737\pi$
$728$	1.63668	+	9.28206i	0.0606593	+	0.344016i
$729$	−20.8331	+	17.1750i	−0.771597	+	0.636112i
$730$	−7.26645	+	12.5859i	−0.268943	+	0.465824i
$731$	15.9992	−	13.4249i	0.591752	−	0.496539i
$732$	−3.48746	−	6.96923i	−0.128900	−	0.257590i
$733$	−25.9634			−0.958979			−0.479489	−	0.877548i	$-0.659178\pi$
$733$	−25.9634			−0.958979			−0.479489	+	0.877548i	$0.659178\pi$
$734$	0.707017	−	1.22459i	0.0260965	−	0.0452004i
$735$	−1.40920	−	2.81609i	−0.0519790	−	0.103873i
$736$	−6.80143	+	2.47552i	−0.250704	+	0.0912488i
$737$	4.14126	−	3.47493i	0.152545	−	0.128001i
$738$	−33.6066	−	4.02668i	−1.23708	−	0.148224i
$739$	49.6524	−	18.0720i	1.82649	−	0.664789i	0.832675	−	0.553762i	$-0.186808\pi$
$739$	49.6524	−	18.0720i	1.82649	−	0.664789i	0.993817	−	0.111027i	$-0.0354140\pi$
$740$	−2.53854	+	4.39687i	−0.0933184	+	0.161632i
$741$	−10.0708	−	21.8899i	−0.369958	−	0.804144i
$742$	−10.9408	−	18.9501i	−0.401651	−	0.695680i
$743$	13.7196	+	11.5121i	0.503322	+	0.422337i	0.858772	−	0.512358i	$-0.171228\pi$
$743$	13.7196	+	11.5121i	0.503322	+	0.422337i	−0.355450	+	0.934695i	$0.615672\pi$
$744$	14.8765	+	6.44263i	0.545398	+	0.236198i
$745$	−2.08475	−	11.8232i	−0.0763792	−	0.433168i
$746$	6.33363	+	5.31454i	0.231891	+	0.194579i
$747$	−4.99535	+	16.5115i	−0.182770	+	0.604126i
$748$	6.93144	+	12.0056i	0.253438	+	0.438968i
$749$	−5.35931	−	9.28260i	−0.195825	−	0.339179i
$750$	16.2226	+	0.968420i	0.592367	+	0.0353617i
$751$	−5.09273	−	28.8823i	−0.185836	−	1.05393i	−0.924876	−	0.380269i	$-0.875832\pi$
$751$	−5.09273	−	28.8823i	−0.185836	−	1.05393i	0.739040	−	0.673662i	$-0.235280\pi$
$752$	−3.03342			−0.110617
$753$	4.18999	−	17.5656i	0.152692	−	0.640127i
$754$	−16.3196	−	5.93984i	−0.594324	−	0.216316i
$755$	−13.6356	−	11.4416i	−0.496249	−	0.416403i
$756$	−0.0666240	+	15.3453i	−0.00242309	+	0.558103i
$757$	−6.54011	+	37.0908i	−0.237704	+	1.34809i	0.599138	+	0.800646i	$0.295510\pi$
$757$	−6.54011	+	37.0908i	−0.237704	+	1.34809i	−0.836843	+	0.547443i	$0.815601\pi$
$758$	1.41220	−	8.00898i	0.0512934	−	0.290899i
$759$	−48.4075	−	45.8027i	−1.75708	−	1.66253i
$760$	4.60079	+	0.150876i	0.166888	+	0.00547283i
$761$	10.2505	+	17.7544i	0.371581	+	0.643597i	0.989809	−	0.142402i	$-0.0454826\pi$
$761$	10.2505	+	17.7544i	0.371581	+	0.643597i	−0.618228	+	0.785999i	$0.712149\pi$
$762$	18.3619	−	13.6287i	0.665181	−	0.493714i
$763$	−15.9855	−	13.4134i	−0.578714	−	0.485599i
$764$	4.78248	−	4.01298i	0.173024	−	0.145184i
$765$	−8.20341	−	0.982918i	−0.296595	−	0.0355375i
$766$	1.79869	+	10.2009i	0.0649894	+	0.368573i
$767$	−2.54417			−0.0918645
$768$	1.25813	+	1.19043i	0.0453987	+	0.0429558i
$769$	4.24423	+	24.0703i	0.153051	+	0.867995i	0.960546	+	0.278121i	$0.0897116\pi$
$769$	4.24423	+	24.0703i	0.153051	+	0.867995i	−0.807495	+	0.589874i	$0.799177\pi$
$770$	−2.87892	−	16.3272i	−0.103749	−	0.588391i
$771$	−4.47402	−	4.23327i	−0.161128	−	0.152458i
$772$	7.25256			0.261025
$773$	−1.32693	−	7.52542i	−0.0477265	−	0.270670i	0.951601	−	0.307336i	$-0.0994375\pi$
$773$	−1.32693	−	7.52542i	−0.0477265	−	0.270670i	−0.999328	+	0.0366655i	$0.988326\pi$
$774$	23.8556	+	2.85834i	0.857473	+	0.102741i
$775$	−27.8536	+	23.3719i	−1.00053	+	0.839545i
$776$	−3.42018	−	2.86987i	−0.122777	−	0.103022i
$777$	19.7465	−	14.6564i	0.708402	−	0.525794i
$778$	−12.6792	−	21.9611i	−0.454572	−	0.787342i
$779$	25.9720	−	41.7611i	0.930543	−	1.49625i
$780$	−4.24042	−	4.01225i	−0.151831	−	0.143661i
$781$	−9.13427	+	51.8030i	−0.326850	+	1.85366i
$782$	−3.27766	+	18.5886i	−0.117209	+	0.664726i
$783$	−24.4256	−	14.2439i	−0.872901	−	0.509035i
$784$	1.31880	+	1.10660i	0.0470999	+	0.0395215i
$785$	15.3377	+	5.58245i	0.547424	+	0.199246i
$786$	8.18926	−	34.3317i	0.292101	−	1.22457i
$787$	−31.6668			−1.12880			−0.564400	−	0.825502i	$-0.690892\pi$
$787$	−31.6668			−1.12880			−0.564400	+	0.825502i	$0.690892\pi$
$788$	2.75782	+	15.6404i	0.0982432	+	0.557165i
$789$	−24.2958	−	1.45036i	−0.864955	−	0.0516340i
$790$	−4.49859	−	7.79179i	−0.160053	−	0.277220i
$791$	16.6632	+	28.8615i	0.592474	+	1.02620i
$792$	−4.61802	+	15.2643i	−0.164094	+	0.542394i
$793$	−11.0002	−	9.23025i	−0.390628	−	0.327776i
$794$	−1.35211	−	7.66819i	−0.0479846	−	0.272134i
$795$	12.4367	+	5.38604i	0.441085	+	0.191023i
$796$	−18.1117	−	15.1975i	−0.641953	−	0.538662i
$797$	−5.86203	−	10.1533i	−0.207644	−	0.359650i	0.743328	−	0.668927i	$-0.233246\pi$
$797$	−5.86203	−	10.1533i	−0.207644	−	0.359650i	−0.950972	+	0.309277i	$0.899913\pi$
$798$	−20.1587	−	9.52661i	−0.713610	−	0.337238i
$799$	−3.95532	+	6.85082i	−0.139929	+	0.242364i
$800$	−3.65046	+	1.32866i	−0.129063	+	0.0469752i
$801$	26.9726	+	3.23180i	0.953029	+	0.114190i
$802$	−9.70653	+	8.14474i	−0.342749	+	0.287601i
$803$	68.7421	−	25.0201i	2.42586	−	0.882939i
$804$	−0.788250	−	1.57521i	−0.0277994	−	0.0555535i
$805$	11.2868	−	19.5493i	0.397807	−	0.689022i
$806$	29.8718			1.05219
$807$	−7.48711	−	14.9620i	−0.263559	−	0.526687i
$808$	4.82246	−	4.04652i	0.169653	−	0.142356i
$809$	11.7373	−	20.3296i	0.412661	−	0.714749i	−0.582519	−	0.812817i	$-0.697933\pi$
$809$	11.7373	−	20.3296i	0.412661	−	0.714749i	0.995180	+	0.0980678i	$0.0312662\pi$
$810$	−5.63149	−	7.65654i	−0.197870	−	0.269024i
$811$	−7.71003	−	43.7258i	−0.270736	−	1.53542i	−0.752189	−	0.658947i	$-0.771002\pi$
$811$	−7.71003	−	43.7258i	−0.270736	−	1.53542i	0.481453	−	0.876472i	$-0.340109\pi$
$812$	−15.1012	+	5.49637i	−0.529947	+	0.192885i
$813$	−29.0137	−	1.73199i	−1.01755	−	0.0607435i
$814$	24.0151	−	8.74077i	0.841728	−	0.306364i
$815$	−11.9126	−	9.99583i	−0.417279	−	0.350139i
$816$	4.32901	−	1.28920i	0.151546	−	0.0451310i
$817$	−18.4362	+	29.6440i	−0.645000	+	1.03711i
$818$	−5.84263			−0.204283
$819$	11.1243	+	25.9956i	0.388713	+	0.908359i
$820$	2.06899	−	11.7338i	0.0722522	−	0.409763i
$821$	7.25286	+	41.1330i	0.253127	+	1.43555i	0.800836	+	0.598884i	$0.204389\pi$
$821$	7.25286	+	41.1330i	0.253127	+	1.43555i	−0.547709	+	0.836669i	$0.684500\pi$
$822$	−17.7062	+	13.1420i	−0.617573	+	0.458378i
$823$	−25.8210	+	21.6664i	−0.900065	+	0.755244i	−0.970203	−	0.242293i	$-0.922100\pi$
$823$	−25.8210	+	21.6664i	−0.900065	+	0.755244i	0.0701384	+	0.997537i	$0.477656\pi$
$824$	4.58290	−	7.93782i	0.159653	−	0.276527i
$825$	−25.9812	−	24.5832i	−0.904550	−	0.855876i
$826$	−1.80344	+	1.51326i	−0.0627496	+	0.0526531i
$827$	15.3728	+	5.59524i	0.534564	+	0.194565i	0.595175	−	0.803596i	$-0.297083\pi$
$827$	15.3728	+	5.59524i	0.534564	+	0.194565i	−0.0606110	+	0.998161i	$0.519305\pi$
$828$	−18.1761	+	11.8794i	−0.631662	+	0.412836i
$829$	−7.05906	−	12.2266i	−0.245171	−	0.424649i	0.717009	−	0.697064i	$-0.245511\pi$
$829$	−7.05906	−	12.2266i	−0.245171	−	0.424649i	−0.962180	+	0.272415i	$0.912177\pi$
$830$	−5.70635	−	2.07694i	−0.198070	−	0.0720918i
$831$	−2.10031	−	0.909592i	−0.0728589	−	0.0315534i
$832$	2.99904	+	1.09156i	0.103973	+	0.0378430i
$833$	4.21880	−	1.53552i	0.146173	−	0.0532026i
$834$	17.0106	+	7.36688i	0.589030	+	0.255094i
$835$	6.21111	−	10.7580i	0.214944	−	0.372295i
$836$	−17.2525	−	15.4680i	−0.596691	−	0.534972i
$837$	47.8589	+	8.65322i	1.65424	+	0.299099i
$838$	3.28315	−	1.19497i	0.113415	−	0.0412796i
$839$	24.7785	+	20.7916i	0.855447	+	0.717806i	0.960982	−	0.276610i	$-0.0892110\pi$
$839$	24.7785	+	20.7916i	0.855447	+	0.717806i	−0.105535	+	0.994416i	$0.533655\pi$
$840$	−5.39230	−	0.321897i	−0.186052	−	0.0111065i
$841$	0.106119	−	0.601831i	0.00365928	−	0.0207528i
$842$	25.0137	−	20.9890i	0.862029	−	0.723328i
$843$	1.93371	+	1.82966i	0.0666006	+	0.0630169i
$844$	−1.86704	−	3.23381i	−0.0642663	−	0.111312i
$845$	2.79282	+	1.01650i	0.0960758	+	0.0349687i
$846$	−8.86099	+	2.07302i	−0.304647	+	0.0712720i
$847$	−25.4840	+	44.1395i	−0.875639	+	1.51665i
$848$	−7.40941			−0.254440
$849$	−35.3557	−	2.11058i	−1.21341	−	0.0724350i
$850$	−1.75919	+	9.97684i	−0.0603396	+	0.342203i
$851$	32.6983	+	11.9012i	1.12088	+	0.407968i
$852$	15.7277	+	6.81126i	0.538821	+	0.233350i
$853$	2.65747	−	15.0713i	0.0909901	−	0.516030i	−0.904912	−	0.425598i	$-0.860064\pi$
$853$	2.65747	−	15.0713i	0.0909901	−	0.516030i	0.995903	−	0.0904328i	$-0.0288250\pi$
$854$	−13.2876			−0.454693
$855$	13.5426	−	2.70343i	0.463147	−	0.0924554i
$856$	−3.62946			−0.124052
$857$	7.97404	−	45.2230i	0.272388	−	1.54479i	−0.474750	−	0.880121i	$-0.657462\pi$
$857$	7.97404	−	45.2230i	0.272388	−	1.54479i	0.747138	−	0.664669i	$-0.231427\pi$
$858$	3.36918	+	29.1915i	0.115022	+	0.996581i
$859$	16.6627	+	6.06472i	0.568523	+	0.206926i	0.610257	−	0.792203i	$-0.291066\pi$
$859$	16.6627	+	6.06472i	0.568523	+	0.206926i	−0.0417341	+	0.999129i	$0.513288\pi$
$860$	−1.46867	+	8.32924i	−0.0500812	+	0.284025i
$861$	−31.7823	+	48.1707i	−1.08314	+	1.64165i
$862$	5.46374			0.186096
$863$	4.67025	−	8.08912i	0.158977	−	0.275357i	−0.775523	−	0.631319i	$-0.782514\pi$
$863$	4.67025	−	8.08912i	0.158977	−	0.275357i	0.934500	+	0.355963i	$0.115847\pi$
$864$	4.48868	+	2.61759i	0.152708	+	0.0890522i
$865$	2.24285	+	0.816330i	0.0762591	+	0.0277561i
$866$	13.6919	+	23.7151i	0.465270	+	0.805871i
$867$	−4.09883	+	17.1835i	−0.139203	+	0.583581i
$868$	21.1747	−	17.7677i	0.718716	−	0.603074i
$869$	−7.86433	+	44.6008i	−0.266779	+	1.51298i
$870$	5.48158	−	8.30812i	0.185843	−	0.281672i
$871$	−2.48631	−	2.08626i	−0.0842453	−	0.0706902i
$872$	−6.63989	+	2.41672i	−0.224855	+	0.0818405i
$873$	−11.9520	−	6.04592i	−0.404515	−	0.204623i
$874$	−4.45721	−	31.2330i	−0.150767	−	1.05647i
$875$	13.8548	−	23.9972i	0.468378	−	0.811255i
$876$	−2.73287	−	23.6783i	−0.0923350	−	0.800016i
$877$	22.2840	−	8.11072i	0.752478	−	0.273880i	0.0628299	−	0.998024i	$-0.479987\pi$
$877$	22.2840	−	8.11072i	0.752478	−	0.273880i	0.689648	+	0.724145i	$0.257765\pi$
$878$	14.6595	+	5.33563i	0.494735	+	0.180069i
$879$	−23.8465	+	17.6995i	−0.804324	+	0.596990i
$880$	−5.27531	−	1.92006i	−0.177831	−	0.0647251i
$881$	6.90123	+	11.9533i	0.232508	+	0.402716i	0.958546	−	0.284939i	$-0.0919734\pi$
$881$	6.90123	+	11.9533i	0.232508	+	0.402716i	−0.726037	+	0.687655i	$0.758640\pi$
$882$	4.60861	+	2.33126i	0.155180	+	0.0784976i
$883$	−2.67079	−	0.972088i	−0.0898792	−	0.0327134i	0.296689	−	0.954974i	$-0.404117\pi$
$883$	−2.67079	−	0.972088i	−0.0898792	−	0.0327134i	−0.386568	+	0.922261i	$0.626340\pi$
$884$	6.37573	−	5.34987i	0.214439	−	0.179936i
$885$	0.338323	−	1.41835i	0.0113726	−	0.0476772i
$886$	16.9631	−	29.3809i	0.569885	−	0.987070i
$887$	−5.70400	+	4.78623i	−0.191522	+	0.160706i	−0.733506	−	0.679683i	$-0.762118\pi$
$887$	−5.70400	+	4.78623i	−0.191522	+	0.160706i	0.541985	+	0.840388i	$0.317673\pi$
$888$	−0.954727	−	8.27202i	−0.0320386	−	0.277591i
$889$	−6.77043	−	38.3970i	−0.227073	−	1.28779i
$890$	−1.66056	+	9.41752i	−0.0556622	+	0.315676i
$891$	−3.05825	+	47.7449i	−0.102455	+	1.59951i
$892$	1.23036			0.0411956
$893$	2.72159	−	12.9392i	0.0910746	−	0.432995i
$894$	14.3027	+	13.5331i	0.478355	+	0.452615i
$895$	6.95657	+	5.83726i	0.232533	+	0.195118i
$896$	2.77513	−	1.01006i	0.0927105	−	0.0337439i
$897$	−22.0343	+	33.3962i	−0.735705	+	1.11507i
$898$	−5.73118	+	2.08598i	−0.191252	+	0.0696100i
$899$	8.84430	+	50.1585i	0.294974	+	1.67288i
$900$	−9.75544	+	6.37588i	−0.325181	+	0.212529i
$901$	−9.66125	+	16.7338i	−0.321863	+	0.557483i
$902$	−45.9437	+	38.5514i	−1.52976	+	1.28362i
$903$	22.5607	−	34.1939i	0.750771	−	1.13790i
$904$	11.2847			0.375324
$905$	2.04585	−	3.54352i	0.0680065	−	0.117791i
$906$	29.1420	+	1.73965i	0.968177	+	0.0577959i
$907$	53.6472	−	19.5260i	1.78132	−	0.648349i	0.781628	−	0.623745i	$-0.214390\pi$
$907$	53.6472	−	19.5260i	1.78132	−	0.648349i	0.999697	−	0.0246037i	$-0.00783240\pi$
$908$	9.89981	−	8.30693i	0.328537	−	0.275675i
$909$	11.3216	−	15.1160i	0.375515	−	0.501367i
$910$	−9.35336	+	3.40435i	−0.310061	+	0.112853i
$911$	27.7829	−	48.1214i	0.920488	−	1.59433i	0.121827	−	0.992551i	$-0.461125\pi$
$911$	27.7829	−	48.1214i	0.920488	−	1.59433i	0.798661	−	0.601781i	$-0.205542\pi$
$912$	−6.20664	+	4.29856i	−0.205522	+	0.142340i
$913$	15.2837	+	26.4721i	0.505816	+	0.876098i
$914$	−15.2357	−	12.7843i	−0.503953	−	0.422867i
$915$	6.60857	−	4.90505i	0.218473	−	0.162156i
$916$	−0.593498	−	3.36590i	−0.0196097	−	0.111212i
$917$	−46.1002	−	38.6827i	−1.52236	−	1.27741i
$918$	11.7646	−	6.72434i	0.388288	−	0.221936i
$919$	−16.8508	−	29.1865i	−0.555857	−	0.962773i	−0.997836	−	0.0657474i	$-0.979057\pi$
$919$	−16.8508	−	29.1865i	−0.555857	−	0.962773i	0.441979	−	0.897025i	$-0.354276\pi$
$920$	−3.82185	−	6.61963i	−0.126003	−	0.218243i
$921$	−6.34053	−	12.6707i	−0.208927	−	0.417514i
$922$	0.724787	+	4.11047i	0.0238696	+	0.135371i
$923$	31.5810			1.03950
$924$	19.7513	+	18.6885i	0.649769	+	0.614805i
$925$	17.5498	+	6.38760i	0.577033	+	0.210023i
$926$	19.1865	+	16.0994i	0.630509	+	0.529060i
$927$	7.96256	−	26.3193i	0.261525	−	0.864440i
$928$	−0.944926	+	5.35894i	−0.0310187	+	0.175916i
$929$	2.86194	−	16.2309i	0.0938973	−	0.532518i	−0.901182	−	0.433440i	$-0.857300\pi$
$929$	2.86194	−	16.2309i	0.0938973	−	0.532518i	0.995080	−	0.0990780i	$-0.0315893\pi$
$930$	−3.97235	+	16.6532i	−0.130259	+	0.546081i
$931$	−5.90351	+	4.63256i	−0.193480	+	0.151826i
$932$	−0.628990	−	1.08944i	−0.0206032	−	0.0356859i
$933$	−1.31465	−	11.3905i	−0.0430398	−	0.372909i
$934$	−19.2965	−	16.1917i	−0.631399	−	0.529807i
$935$	−11.2149	+	9.41043i	−0.366767	+	0.307754i
$936$	9.50652	+	1.13905i	0.310730	+	0.0372312i
$937$	0.0904762	+	0.513116i	0.00295573	+	0.0167628i	0.986250	−	0.165260i	$-0.0528465\pi$
$937$	0.0904762	+	0.513116i	0.00295573	+	0.0167628i	−0.983294	+	0.182023i	$0.941735\pi$
$938$	−3.00332			−0.0980620
$939$	8.23348	−	34.5171i	0.268689	−	1.12642i
$940$	−0.556277	−	3.15480i	−0.0181438	−	0.102898i
$941$	−6.55169	−	37.1565i	−0.213579	−	1.21127i	−0.883356	−	0.468704i	$-0.844721\pi$
$941$	−6.55169	−	37.1565i	−0.213579	−	1.21127i	0.669777	−	0.742563i	$-0.266390\pi$
$942$	−25.6563	+	7.64054i	−0.835926	+	0.248942i
$943$	−81.6607			−2.65924
$944$	0.138427	+	0.785057i	0.00450540	+	0.0255514i
$945$	−15.9716	+	2.74477i	−0.519555	+	0.0892875i
$946$	32.6131	−	27.3657i	1.06034	−	0.889734i
$947$	29.5851	+	24.8249i	0.961387	+	0.806700i	0.981178	−	0.193104i	$-0.0618556\pi$
$947$	29.5851	+	24.8249i	0.961387	+	0.806700i	−0.0197908	+	0.999804i	$0.506300\pi$
$948$	13.5410	+	5.86429i	0.439792	+	0.190463i
$949$	−21.9598	−	38.0356i	−0.712847	−	1.23469i
$950$	−2.39227	−	16.7633i	−0.0776154	−	0.543874i
$951$	29.6552	−	8.83144i	0.961635	−	0.286379i
$952$	1.33736	−	7.58453i	0.0433440	−	0.245816i
$953$	−5.17679	+	29.3590i	−0.167693	+	0.951033i	0.778552	+	0.627580i	$0.215955\pi$
$953$	−5.17679	+	29.3590i	−0.167693	+	0.951033i	−0.946244	+	0.323452i	$0.895156\pi$
$954$	−21.6438	+	5.06356i	−0.700744	+	0.163939i
$955$	5.05059	+	4.23795i	0.163433	+	0.137137i
$956$	2.11183	+	0.768643i	0.0683015	+	0.0248597i
$957$	−48.0187	+	14.3002i	−1.55222	+	0.462258i
$958$	2.31135			0.0746762
$959$	6.52864	+	37.0258i	0.210821	+	1.19562i
$960$	−1.00735	+	1.52678i	−0.0325119	+	0.0492765i
$961$	−28.3028	−	49.0219i	−0.912993	−	1.58135i
$962$	−7.67168	−	13.2877i	−0.247345	−	0.428414i
$963$	−10.6021	+	2.48036i	−0.341648	+	0.0799284i
$964$	18.3715	+	15.4155i	0.591706	+	0.496501i
$965$	1.33000	+	7.54278i	0.0428141	+	0.242811i
$966$	4.24489	+	36.7789i	0.136577	+	1.18334i
$967$	31.6877	+	26.5891i	1.01901	+	0.855048i	0.989502	−	0.144517i	$-0.0461627\pi$
$967$	31.6877	+	26.5891i	1.01901	+	0.855048i	0.0295042	+	0.999565i	$0.490607\pi$
$968$	8.62918	+	14.9462i	0.277352	+	0.480389i
$969$	1.61515	+	19.6224i	0.0518860	+	0.630361i
$970$	2.35751	−	4.08333i	0.0756952	−	0.131108i
$971$	−41.1074	+	14.9619i	−1.31920	+	0.480149i	−0.903201	−	0.429217i	$-0.858789\pi$
$971$	−41.1074	+	14.9619i	−1.31920	+	0.480149i	−0.415997	+	0.909366i	$0.636567\pi$
$972$	14.9008	+	4.57876i	0.477945	+	0.146864i
$973$	24.2124	−	20.3166i	0.776213	−	0.651320i
$974$	4.27952	−	1.55762i	0.137125	−	0.0499093i
$975$	−11.8262	+	17.9244i	−0.378743	+	0.574039i
$976$	−2.24968	+	3.89655i	−0.0720104	+	0.124726i
$977$	−41.5779			−1.33020			−0.665098	−	0.746756i	$-0.731610\pi$
$977$	−41.5779			−1.33020			−0.665098	+	0.746756i	$0.731610\pi$
$978$	25.4595	+	1.51982i	0.814107	+	0.0485986i
$979$	36.8743	−	30.9412i	1.17851	−	0.988886i
$980$	−0.909039	+	1.57450i	−0.0290382	+	0.0502956i
$981$	−17.7444	+	11.5972i	−0.566534	+	0.370271i
$982$	−7.32917	−	41.5658i	−0.233883	−	1.32642i
$983$	−2.24780	+	0.818132i	−0.0716936	+	0.0260944i	−0.377618	−	0.925961i	$-0.623257\pi$
$983$	−2.24780	+	0.818132i	−0.0716936	+	0.0260944i	0.305924	+	0.952056i	$0.401035\pi$
$984$	8.74496	+	17.4757i	0.278779	+	0.557104i
$985$	−15.7605	+	5.73635i	−0.502171	+	0.182775i
$986$	10.8708	+	9.12168i	0.346197	+	0.290493i
$987$	−3.60016	+	15.0929i	−0.114595	+	0.480413i
$988$	−7.34686	+	11.8132i	−0.233735	+	0.375829i
$989$	57.9668			1.84324
$990$	−16.7220	−	2.00360i	−0.531460	−	0.0636786i
$991$	7.47258	−	42.3791i	0.237374	−	1.34622i	−0.600181	−	0.799864i	$-0.704905\pi$
$991$	7.47258	−	42.3791i	0.237374	−	1.34622i	0.837555	−	0.546353i	$-0.183984\pi$
$992$	−1.62531	−	9.21759i	−0.0516036	−	0.292659i
$993$	48.7640	+	21.1185i	1.54748	+	0.670174i
$994$	22.3862	−	18.7843i	0.710049	−	0.595802i
$995$	12.4843	−	21.6235i	0.395779	−	0.685510i
$996$	9.54538	−	2.84265i	0.302457	−	0.0900729i
$997$	−47.2493	+	39.6468i	−1.49640	+	1.25563i	−0.610266	+	0.792197i	$0.708937\pi$
$997$	−47.2493	+	39.6468i	−1.49640	+	1.25563i	−0.886133	+	0.463431i	$0.846618\pi$
$998$	31.7838	+	11.5684i	1.00610	+	0.366190i
$999$	−8.44194	−	23.5111i	−0.267091	−	0.743860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.w.a.43.8	yes	54
9.4	even	3		342.2.v.a.157.3	yes	54
19.4	even	9		342.2.v.a.61.3	✓	54
171.4	even	9	inner	342.2.w.a.175.8	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.v.a.61.3	✓	54	19.4	even	9
342.2.v.a.157.3	yes	54	9.4	even	3
342.2.w.a.43.8	yes	54	1.1	even	1	trivial
342.2.w.a.175.8	yes	54	171.4	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(1.39081 - 1.03230i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.183383 - 1.04002i) q^{5} +(0.775102 + 1.54894i) q^{6} +2.95323 q^{7} +(0.500000 - 0.866025i) q^{8} +(0.868725 - 2.87147i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(1.39081 - 1.03230i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.183383 - 1.04002i) q^{5} +(0.775102 + 1.54894i) q^{6} +2.95323 q^{7} +(0.500000 - 0.866025i) q^{8} +(0.868725 - 2.87147i) q^{9} +(0.992372 + 0.361194i) q^{10} +(-2.65793 - 4.60367i) q^{11} +(-1.66000 + 0.494356i) q^{12} +(-2.44484 + 2.05146i) q^{13} +(-0.512823 + 2.90836i) q^{14} +(-0.818555 - 1.63578i) q^{15} +(0.766044 + 0.642788i) q^{16} +(2.45056 - 0.891932i) q^{17} +(2.67699 + 1.35415i) q^{18} +(-3.42915 + 2.69090i) q^{19} +(-0.528030 + 0.914575i) q^{20} +(4.10739 - 3.04861i) q^{21} +(4.99527 - 1.81813i) q^{22} +(6.80143 + 2.47552i) q^{23} +(-0.198589 - 1.72063i) q^{24} +(3.65046 + 1.32866i) q^{25} +(-1.59575 - 2.76393i) q^{26} +(-1.75597 - 4.89046i) q^{27} +(-2.77513 - 1.01006i) q^{28} +(4.16851 - 3.49780i) q^{29} +(1.75306 - 0.522070i) q^{30} +(-4.67989 + 8.10581i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-8.44904 - 3.65907i) q^{33} +(0.452846 + 2.56821i) q^{34} +(0.541572 - 3.07141i) q^{35} +(-1.79843 + 2.40117i) q^{36} +4.80756 q^{37} +(-2.05455 - 3.84432i) q^{38} +(-1.28259 + 5.37700i) q^{39} +(-0.808989 - 0.678823i) q^{40} +(-10.6019 + 3.85878i) q^{41} +(2.28905 + 4.57438i) q^{42} +(7.52577 - 2.73915i) q^{43} +(0.923089 + 5.23510i) q^{44} +(-2.82706 - 1.43007i) q^{45} +(-3.61897 + 6.26823i) q^{46} +(-2.32373 + 1.94984i) q^{47} +(1.72897 + 0.103212i) q^{48} +1.72157 q^{49} +(-1.94237 + 3.36428i) q^{50} +(2.48754 - 3.77022i) q^{51} +(2.99904 - 1.09156i) q^{52} +(-5.67594 + 4.76268i) q^{53} +(5.12108 - 0.880077i) q^{54} +(-5.27531 + 1.92006i) q^{55} +(1.47661 - 2.55757i) q^{56} +(-1.99150 + 7.28244i) q^{57} +(2.72080 + 4.71257i) q^{58} +(0.610666 + 0.512409i) q^{59} +(0.209722 + 1.81709i) q^{60} +(0.781304 + 4.43100i) q^{61} +(-7.17001 - 6.01635i) q^{62} +(2.56554 - 8.48010i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.68521 + 2.91887i) q^{65} +(5.07064 - 7.68529i) q^{66} +(0.176594 + 1.00151i) q^{67} -2.60783 q^{68} +(12.0150 - 3.57811i) q^{69} +(2.93070 + 1.06669i) q^{70} +(-7.58026 - 6.36059i) q^{71} +(-2.05240 - 2.18807i) q^{72} +(-2.38965 + 13.5524i) q^{73} +(-0.834823 + 4.73452i) q^{74} +(6.44868 - 1.92044i) q^{75} +(4.14269 - 1.35578i) q^{76} +(-7.84948 - 13.5957i) q^{77} +(-5.07259 - 2.19681i) q^{78} +(-6.52637 - 5.47628i) q^{79} +(0.808989 - 0.678823i) q^{80} +(-7.49064 - 4.98903i) q^{81} +(-1.95916 - 11.1109i) q^{82} -5.75022 q^{83} +(-4.90237 + 1.45995i) q^{84} +(-0.478232 - 2.71219i) q^{85} +(1.39071 + 7.88708i) q^{86} +(2.18686 - 9.16793i) q^{87} -5.31586 q^{88} +(1.57241 + 8.91760i) q^{89} +(1.89925 - 2.53579i) q^{90} +(-7.22016 + 6.05844i) q^{91} +(-5.54458 - 4.65245i) q^{92} +(1.85875 + 16.1047i) q^{93} +(-1.51671 - 2.62701i) q^{94} +(2.16973 + 4.05984i) q^{95} +(-0.401877 + 1.68478i) q^{96} +(0.775292 - 4.39690i) q^{97} +(-0.298947 + 1.69541i) q^{98} +(-15.5283 + 3.63283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 24 q^{7} + 27 q^{8}+O(q^{10}) \) 54 * q - 24 * q^7 + 27 * q^8	\( 54 q - 24 q^{7} + 27 q^{8} - 3 q^{13} + 3 q^{14} + 9 q^{17} + 6 q^{18} + 15 q^{19} + 3 q^{22} - 12 q^{23} - 6 q^{25} - 27 q^{27} - 3 q^{28} + 9 q^{29} - 57 q^{33} + 18 q^{34} - 18 q^{35} - 6 q^{37} - 3 q^{38} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 6 q^{44} + 54 q^{45} - 18 q^{47} + 6 q^{49} - 3 q^{50} - 15 q^{51} - 3 q^{52} - 24 q^{53} - 54 q^{54} - 36 q^{55} - 12 q^{56} + 12 q^{57} + 18 q^{58} + 69 q^{59} - 27 q^{60} + 84 q^{61} - 15 q^{62} + 39 q^{63} - 27 q^{64} + 24 q^{65} + 21 q^{66} - 30 q^{67} - 6 q^{68} + 42 q^{69} + 18 q^{70} - 60 q^{71} - 45 q^{73} + 3 q^{74} - 9 q^{78} - 18 q^{79} - 36 q^{81} + 3 q^{82} - 24 q^{83} - 21 q^{84} - 72 q^{85} + 3 q^{86} + 66 q^{87} + 9 q^{89} - 15 q^{91} + 6 q^{92} - 3 q^{93} + 6 q^{94} - 30 q^{95} - 78 q^{97} + 12 q^{98} - 51 q^{99}+O(q^{100}) \) 54 * q - 24 * q^7 + 27 * q^8 - 3 * q^13 + 3 * q^14 + 9 * q^17 + 6 * q^18 + 15 * q^19 + 3 * q^22 - 12 * q^23 - 6 * q^25 - 27 * q^27 - 3 * q^28 + 9 * q^29 - 57 * q^33 + 18 * q^34 - 18 * q^35 - 6 * q^37 - 3 * q^38 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 6 * q^44 + 54 * q^45 - 18 * q^47 + 6 * q^49 - 3 * q^50 - 15 * q^51 - 3 * q^52 - 24 * q^53 - 54 * q^54 - 36 * q^55 - 12 * q^56 + 12 * q^57 + 18 * q^58 + 69 * q^59 - 27 * q^60 + 84 * q^61 - 15 * q^62 + 39 * q^63 - 27 * q^64 + 24 * q^65 + 21 * q^66 - 30 * q^67 - 6 * q^68 + 42 * q^69 + 18 * q^70 - 60 * q^71 - 45 * q^73 + 3 * q^74 - 9 * q^78 - 18 * q^79 - 36 * q^81 + 3 * q^82 - 24 * q^83 - 21 * q^84 - 72 * q^85 + 3 * q^86 + 66 * q^87 + 9 * q^89 - 15 * q^91 + 6 * q^92 - 3 * q^93 + 6 * q^94 - 30 * q^95 - 78 * q^97 + 12 * q^98 - 51 * q^99

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