LMFDB - Embedded newform 666.2.k.a.175.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] 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("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.2
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(-1.63169 + 0.581033i) q^{3} -1.00000 q^{4} -4.12550i q^{5} +(0.581033 + 1.63169i) q^{6} +(1.24300 - 2.15294i) q^{7} +1.00000i q^{8} +(2.32480 - 1.89613i) q^{9} -4.12550 q^{10} +(-0.302670 - 0.524240i) q^{11} +(1.63169 - 0.581033i) q^{12} -2.86241i q^{13} +(-2.15294 - 1.24300i) q^{14} +(2.39705 + 6.73152i) q^{15} +1.00000 q^{16} +(5.47905 + 3.16333i) q^{17} +(-1.89613 - 2.32480i) q^{18} +(-2.07794 + 1.19970i) q^{19} +4.12550i q^{20} +(-0.777258 + 4.23515i) q^{21} +(-0.524240 + 0.302670i) q^{22} +(-3.33371 - 1.92472i) q^{23} +(-0.581033 - 1.63169i) q^{24} -12.0198 q^{25} -2.86241 q^{26} +(-2.69163 + 4.44467i) q^{27} +(-1.24300 + 2.15294i) q^{28} +(8.47236 - 4.89152i) q^{29} +(6.73152 - 2.39705i) q^{30} +(-6.23125 - 3.59761i) q^{31} -1.00000i q^{32} +(0.798464 + 0.679534i) q^{33} +(3.16333 - 5.47905i) q^{34} +(-8.88196 - 5.12800i) q^{35} +(-2.32480 + 1.89613i) q^{36} +(-5.55330 + 2.48211i) q^{37} +(1.19970 + 2.07794i) q^{38} +(1.66315 + 4.67055i) q^{39} +4.12550 q^{40} +1.81248 q^{41} +(4.23515 + 0.777258i) q^{42} +(-4.05787 + 2.34281i) q^{43} +(0.302670 + 0.524240i) q^{44} +(-7.82248 - 9.59097i) q^{45} +(-1.92472 + 3.33371i) q^{46} +(0.873232 + 1.51248i) q^{47} +(-1.63169 + 0.581033i) q^{48} +(0.409896 + 0.709960i) q^{49} +12.0198i q^{50} +(-10.7781 - 1.97805i) q^{51} +2.86241i q^{52} +(1.48820 - 2.57764i) q^{53} +(4.44467 + 2.69163i) q^{54} +(-2.16275 + 1.24867i) q^{55} +(2.15294 + 1.24300i) q^{56} +(2.69348 - 3.16489i) q^{57} +(-4.89152 - 8.47236i) q^{58} +(-7.90047 + 4.56134i) q^{59} +(-2.39705 - 6.73152i) q^{60} +(-3.50551 - 2.02391i) q^{61} +(-3.59761 + 6.23125i) q^{62} +(-1.19252 - 7.36205i) q^{63} -1.00000 q^{64} -11.8089 q^{65} +(0.679534 - 0.798464i) q^{66} +1.15103 q^{67} +(-5.47905 - 3.16333i) q^{68} +(6.55790 + 1.20354i) q^{69} +(-5.12800 + 8.88196i) q^{70} +(3.34971 + 5.80188i) q^{71} +(1.89613 + 2.32480i) q^{72} +1.65116 q^{73} +(2.48211 + 5.55330i) q^{74} +(19.6125 - 6.98388i) q^{75} +(2.07794 - 1.19970i) q^{76} -1.50488 q^{77} +(4.67055 - 1.66315i) q^{78} +(1.91566 + 1.10601i) q^{79} -4.12550i q^{80} +(1.80940 - 8.81624i) q^{81} -1.81248i q^{82} +16.5261 q^{83} +(0.777258 - 4.23515i) q^{84} +(13.0503 - 22.6038i) q^{85} +(2.34281 + 4.05787i) q^{86} +(-10.9821 + 12.9041i) q^{87} +(0.524240 - 0.302670i) q^{88} +(8.11389 + 4.68456i) q^{89} +(-9.59097 + 7.82248i) q^{90} +(-6.16260 - 3.55798i) q^{91} +(3.33371 + 1.92472i) q^{92} +(12.2578 + 2.24961i) q^{93} +(1.51248 - 0.873232i) q^{94} +(4.94936 + 8.57255i) q^{95} +(0.581033 + 1.63169i) q^{96} +(-1.47331 + 0.850618i) q^{97} +(0.709960 - 0.409896i) q^{98} +(-1.69768 - 0.644853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.63169	+	0.581033i	−0.942055	+	0.335460i
$3$	−1.63169	+	0.581033i	−0.942055	+	0.335460i
$4$	−1.00000			−0.500000
$5$		−	4.12550i		−	1.84498i	−0.386021	−	0.922490i	$-0.626151\pi$
$5$		−	4.12550i		−	1.84498i	0.386021	−	0.922490i	$-0.373849\pi$
$6$	0.581033	+	1.63169i	0.237206	+	0.666133i
$7$	1.24300	−	2.15294i	0.469810	−	0.813735i	−0.529594	−	0.848251i	$-0.677656\pi$
$7$	1.24300	−	2.15294i	0.469810	−	0.813735i	0.999404	+	0.0345160i	$0.0109890\pi$
$8$			1.00000i			0.353553i
$9$	2.32480	−	1.89613i	0.774934	−	0.632043i
$10$	−4.12550			−1.30460
$11$	−0.302670	−	0.524240i	−0.0912585	−	0.158064i	0.816782	−	0.576946i	$-0.195756\pi$
$11$	−0.302670	−	0.524240i	−0.0912585	−	0.158064i	−0.908041	+	0.418881i	$0.862422\pi$
$12$	1.63169	−	0.581033i	0.471027	−	0.167730i
$13$		−	2.86241i		−	0.793889i	−0.917843	−	0.396945i	$-0.870071\pi$
$13$		−	2.86241i		−	0.793889i	0.917843	−	0.396945i	$-0.129929\pi$
$14$	−2.15294	−	1.24300i	−0.575398	−	0.332206i
$15$	2.39705	+	6.73152i	0.618916	+	1.73807i
$16$	1.00000			0.250000
$17$	5.47905	+	3.16333i	1.32886	+	0.767220i	0.985124	−	0.171844i	$-0.0549727\pi$
$17$	5.47905	+	3.16333i	1.32886	+	0.767220i	0.343740	+	0.939065i	$0.388306\pi$
$18$	−1.89613	−	2.32480i	−0.446922	−	0.547961i
$19$	−2.07794	+	1.19970i	−0.476712	+	0.275230i	−0.719045	−	0.694963i	$-0.755421\pi$
$19$	−2.07794	+	1.19970i	−0.476712	+	0.275230i	0.242333	+	0.970193i	$0.422087\pi$
$20$			4.12550i			0.922490i
$21$	−0.777258	+	4.23515i	−0.169612	+	0.924186i
$22$	−0.524240	+	0.302670i	−0.111768	+	0.0645295i
$23$	−3.33371	−	1.92472i	−0.695127	−	0.401332i	0.110403	−	0.993887i	$-0.464786\pi$
$23$	−3.33371	−	1.92472i	−0.695127	−	0.401332i	−0.805530	+	0.592555i	$0.798119\pi$
$24$	−0.581033	−	1.63169i	−0.118603	−	0.333067i
$25$	−12.0198			−2.40395
$26$	−2.86241			−0.561364
$27$	−2.69163	+	4.44467i	−0.518005	+	0.855378i
$28$	−1.24300	+	2.15294i	−0.234905	+	0.406868i
$29$	8.47236	−	4.89152i	1.57328	−	0.908332i	0.577513	−	0.816381i	$-0.304023\pi$
$29$	8.47236	−	4.89152i	1.57328	−	0.908332i	0.995764	−	0.0919506i	$-0.0293102\pi$
$30$	6.73152	−	2.39705i	1.22900	−	0.437640i
$31$	−6.23125	−	3.59761i	−1.11917	−	0.646151i	−0.177978	−	0.984034i	$-0.556956\pi$
$31$	−6.23125	−	3.59761i	−1.11917	−	0.646151i	−0.941188	+	0.337884i	$0.890289\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.798464	+	0.679534i	0.138995	+	0.118292i
$34$	3.16333	−	5.47905i	0.542507	−	0.939649i
$35$	−8.88196	−	5.12800i	−1.50133	−	0.866791i
$36$	−2.32480	+	1.89613i	−0.387467	+	0.316021i
$37$	−5.55330	+	2.48211i	−0.912957	+	0.408056i
$37$	−5.55330	+	2.48211i	−0.912957	+	0.408056i
$38$	1.19970	+	2.07794i	0.194617	+	0.337086i
$39$	1.66315	+	4.67055i	0.266318	+	0.747887i
$40$	4.12550			0.652299
$41$	1.81248			0.283063			0.141531	−	0.989934i	$-0.454797\pi$
$41$	1.81248			0.283063			0.141531	+	0.989934i	$0.454797\pi$
$42$	4.23515	+	0.777258i	0.653498	+	0.119933i
$43$	−4.05787	+	2.34281i	−0.618820	+	0.357276i	−0.776409	−	0.630229i	$-0.782961\pi$
$43$	−4.05787	+	2.34281i	−0.618820	+	0.357276i	0.157589	+	0.987505i	$0.449628\pi$
$44$	0.302670	+	0.524240i	0.0456293	+	0.0790322i
$45$	−7.82248	−	9.59097i	−1.16611	−	1.42974i
$46$	−1.92472	+	3.33371i	−0.283784	+	0.491529i
$47$	0.873232	+	1.51248i	0.127374	+	0.220618i	0.922658	−	0.385618i	$-0.126012\pi$
$47$	0.873232	+	1.51248i	0.127374	+	0.220618i	−0.795284	+	0.606236i	$0.792679\pi$
$48$	−1.63169	+	0.581033i	−0.235514	+	0.0838649i
$49$	0.409896	+	0.709960i	0.0585565	+	0.101423i
$50$			12.0198i			1.69985i
$51$	−10.7781	−	1.97805i	−1.50923	−	0.276983i
$52$			2.86241i			0.396945i
$53$	1.48820	−	2.57764i	0.204420	−	0.354066i	−0.745528	−	0.666475i	$-0.767803\pi$
$53$	1.48820	−	2.57764i	0.204420	−	0.354066i	0.949948	+	0.312409i	$0.101136\pi$
$54$	4.44467	+	2.69163i	0.604843	+	0.366285i
$55$	−2.16275	+	1.24867i	−0.291626	+	0.168370i
$56$	2.15294	+	1.24300i	0.287699	+	0.166103i
$57$	2.69348	−	3.16489i	0.356760	−	0.419199i
$58$	−4.89152	−	8.47236i	−0.642288	−	1.11247i
$59$	−7.90047	+	4.56134i	−1.02855	+	0.593836i	−0.916570	−	0.399874i	$-0.869054\pi$
$59$	−7.90047	+	4.56134i	−1.02855	+	0.593836i	−0.111984	+	0.993710i	$0.535721\pi$
$60$	−2.39705	−	6.73152i	−0.309458	−	0.869036i
$61$	−3.50551	−	2.02391i	−0.448834	−	0.259135i	0.258503	−	0.966010i	$-0.416771\pi$
$61$	−3.50551	−	2.02391i	−0.448834	−	0.259135i	−0.707338	+	0.706876i	$0.750104\pi$
$62$	−3.59761	+	6.23125i	−0.456898	+	0.791370i
$63$	−1.19252	−	7.36205i	−0.150244	−	0.927531i
$64$	−1.00000			−0.125000
$65$	−11.8089			−1.46471
$66$	0.679534	−	0.798464i	0.0836449	−	0.0982841i
$67$	1.15103			0.140620			0.0703101	−	0.997525i	$-0.477601\pi$
$67$	1.15103			0.140620			0.0703101	+	0.997525i	$0.477601\pi$
$68$	−5.47905	−	3.16333i	−0.664432	−	0.383610i
$69$	6.55790	+	1.20354i	0.789478	+	0.144889i
$70$	−5.12800	+	8.88196i	−0.612914	+	1.06160i
$71$	3.34971	+	5.80188i	0.397538	+	0.688556i	0.993422	−	0.114515i	$-0.0365313\pi$
$71$	3.34971	+	5.80188i	0.397538	+	0.688556i	−0.595884	+	0.803071i	$0.703198\pi$
$72$	1.89613	+	2.32480i	0.223461	+	0.273980i
$73$	1.65116			0.193254			0.0966268	−	0.995321i	$-0.469195\pi$
$73$	1.65116			0.193254			0.0966268	+	0.995321i	$0.469195\pi$
$74$	2.48211	+	5.55330i	0.288539	+	0.645558i
$75$	19.6125	−	6.98388i	2.26465	−	0.806429i
$76$	2.07794	−	1.19970i	0.238356	−	0.137615i
$77$	−1.50488			−0.171497
$78$	4.67055	−	1.66315i	0.528836	−	0.188315i
$79$	1.91566	+	1.10601i	0.215529	+	0.124436i	0.603878	−	0.797077i	$-0.293621\pi$
$79$	1.91566	+	1.10601i	0.215529	+	0.124436i	−0.388349	+	0.921512i	$0.626955\pi$
$80$		−	4.12550i		−	0.461245i
$81$	1.80940	−	8.81624i	0.201044	−	0.979582i
$82$		−	1.81248i		−	0.200155i
$83$	16.5261			1.81398			0.906989	−	0.421155i	$-0.138375\pi$
$83$	16.5261			1.81398			0.906989	+	0.421155i	$0.138375\pi$
$84$	0.777258	−	4.23515i	0.0848058	−	0.462093i
$85$	13.0503	−	22.6038i	1.41551	−	2.45173i
$86$	2.34281	+	4.05787i	0.252632	+	0.437572i
$87$	−10.9821	+	12.9041i	−1.17740	+	1.38347i
$88$	0.524240	−	0.302670i	0.0558842	−	0.0322648i
$89$	8.11389	+	4.68456i	0.860071	+	0.496562i	0.864036	−	0.503430i	$-0.167929\pi$
$89$	8.11389	+	4.68456i	0.860071	+	0.496562i	−0.00396519	+	0.999992i	$0.501262\pi$
$90$	−9.59097	+	7.82248i	−1.01098	+	0.824562i
$91$	−6.16260	−	3.55798i	−0.646016	−	0.372977i
$92$	3.33371	+	1.92472i	0.347564	+	0.200666i
$93$	12.2578	+	2.24961i	1.27107	+	0.233274i
$94$	1.51248	−	0.873232i	0.156001	−	0.0900670i
$95$	4.94936	+	8.57255i	0.507794	+	0.879525i
$96$	0.581033	+	1.63169i	0.0593015	+	0.166533i
$97$	−1.47331	+	0.850618i	−0.149592	+	0.0863672i	−0.572928	−	0.819606i	$-0.694192\pi$
$97$	−1.47331	+	0.850618i	−0.149592	+	0.0863672i	0.423336	+	0.905973i	$0.360859\pi$
$98$	0.709960	−	0.409896i	0.0717168	−	0.0414057i
$99$	−1.69768	−	0.644853i	−0.170623	−	0.0648101i
$100$	12.0198			1.20198
$101$	−6.03643	−	10.4554i	−0.600647	−	1.04035i	−0.992723	−	0.120418i	$-0.961576\pi$
$101$	−6.03643	−	10.4554i	−0.600647	−	1.04035i	0.392076	−	0.919933i	$-0.371757\pi$
$102$	−1.97805	+	10.7781i	−0.195856	+	1.06719i
$103$	13.9924	+	8.07850i	1.37871	+	0.795998i	0.992004	−	0.126205i	$-0.0402797\pi$
$103$	13.9924	+	8.07850i	1.37871	+	0.795998i	0.386705	+	0.922203i	$0.373613\pi$
$104$	2.86241			0.280682
$105$	17.4721	+	3.20658i	1.70510	+	0.312930i
$106$	−2.57764	−	1.48820i	−0.250362	−	0.144547i
$107$	−6.78135	−	11.7456i	−0.655578	−	1.13549i	−0.981749	−	0.190183i	$-0.939092\pi$
$107$	−6.78135	−	11.7456i	−0.655578	−	1.13549i	0.326171	−	0.945311i	$-0.394241\pi$
$108$	2.69163	−	4.44467i	0.259002	−	0.427689i
$109$	−5.09721	−	2.94287i	−0.488224	−	0.281876i	0.235613	−	0.971847i	$-0.424290\pi$
$109$	−5.09721	−	2.94287i	−0.488224	−	0.281876i	−0.723837	+	0.689971i	$0.757623\pi$
$110$	1.24867	+	2.16275i	0.119056	+	0.206211i
$111$	7.61905	−	7.27668i	0.723169	−	0.690672i
$112$	1.24300	−	2.15294i	0.117453	−	0.203434i
$113$	−18.0930	+	10.4460i	−1.70205	+	0.982677i	−0.758361	+	0.651835i	$0.774000\pi$
$113$	−18.0930	+	10.4460i	−1.70205	+	0.982677i	−0.943686	+	0.330843i	$0.892667\pi$
$114$	−3.16489	−	2.69348i	−0.296419	−	0.252268i
$115$	−7.94043	+	13.7532i	−0.740449	+	1.28250i
$116$	−8.47236	+	4.89152i	−0.786638	+	0.454166i
$117$	−5.42749	−	6.65453i	−0.501772	−	0.615211i
$118$	4.56134	+	7.90047i	0.419905	+	0.727298i
$119$	13.6209	−	7.86405i	1.24863	−	0.720896i
$120$	−6.73152	+	2.39705i	−0.614501	+	0.218820i
$121$	5.31678	−	9.20894i	0.483344	−	0.837176i
$122$	−2.02391	+	3.50551i	−0.183236	+	0.317374i
$123$	−2.95741	+	1.05311i	−0.266660	+	0.0949561i
$124$	6.23125	+	3.59761i	0.559583	+	0.323075i
$125$			28.9600i			2.59026i
$126$	−7.36205	+	1.19252i	−0.655863	+	0.106238i
$127$	1.95417	−	3.38472i	0.173404	−	0.300345i	−0.766204	−	0.642598i	$-0.777857\pi$
$127$	1.95417	−	3.38472i	0.173404	−	0.300345i	0.939608	+	0.342253i	$0.111190\pi$
$128$			1.00000i			0.0883883i
$129$	5.25992	−	6.18050i	0.463111	−	0.544163i
$130$			11.8089i			1.03571i
$131$	14.2253	−	8.21296i	1.24287	−	0.717570i	0.273190	−	0.961960i	$-0.411921\pi$
$131$	14.2253	−	8.21296i	1.24287	−	0.717570i	0.969677	+	0.244390i	$0.0785878\pi$
$132$	−0.798464	−	0.679534i	−0.0694974	−	0.0591459i
$133$			5.96491i			0.517224i
$134$		−	1.15103i		−	0.0994335i
$135$	18.3365	+	11.1043i	1.57815	+	0.955709i
$136$	−3.16333	+	5.47905i	−0.271253	+	0.469825i
$137$	5.96292	+	10.3281i	0.509447	+	0.882388i	0.999940	+	0.0109431i	$0.00348335\pi$
$137$	5.96292	+	10.3281i	0.509447	+	0.882388i	−0.490493	+	0.871445i	$0.663183\pi$
$138$	1.20354	−	6.55790i	0.102452	−	0.558246i
$139$	3.70014	+	6.40883i	0.313842	+	0.543590i	0.979191	−	0.202943i	$-0.0650505\pi$
$139$	3.70014	+	6.40883i	0.313842	+	0.543590i	−0.665349	+	0.746533i	$0.731717\pi$
$140$	8.88196	+	5.12800i	0.750663	+	0.433395i
$141$	−2.30364	−	1.96052i	−0.194002	−	0.165106i
$142$	5.80188	−	3.34971i	0.486883	−	0.281102i
$143$	−1.50059	+	0.866366i	−0.125486	+	0.0724492i
$144$	2.32480	−	1.89613i	0.193733	−	0.158011i
$145$	−20.1800	−	34.9527i	−1.67585	−	2.90266i
$146$		−	1.65116i		−	0.136651i
$147$	−1.08133	−	0.920269i	−0.0891867	−	0.0759025i
$148$	5.55330	−	2.48211i	0.456478	−	0.204028i
$149$	10.1249	−	17.5368i	0.829463	−	1.43667i	−0.0689968	−	0.997617i	$-0.521980\pi$
$149$	10.1249	−	17.5368i	0.829463	−	1.43667i	0.898460	−	0.439055i	$-0.144687\pi$
$150$	−6.98388	−	19.6125i	−0.570231	−	1.60135i
$151$	5.13849	−	8.90013i	0.418165	−	0.724282i	−0.577590	−	0.816327i	$-0.696007\pi$
$151$	5.13849	−	8.90013i	0.418165	−	0.724282i	0.995755	+	0.0920446i	$0.0293402\pi$
$152$	−1.19970	−	2.07794i	−0.0973085	−	0.168543i
$153$	18.7358	−	3.03486i	1.51470	−	0.245354i
$154$			1.50488i			0.121267i
$155$	−14.8420	+	25.7070i	−1.19214	+	2.06484i
$156$	−1.66315	−	4.67055i	−0.133159	−	0.373943i
$157$	7.03781	+	12.1898i	0.561678	+	0.972855i	0.997350	+	0.0727499i	$0.0231775\pi$
$157$	7.03781	+	12.1898i	0.561678	+	0.972855i	−0.435672	+	0.900106i	$0.643489\pi$
$158$	1.10601	−	1.91566i	0.0879892	−	0.152402i
$159$	−0.930582	+	5.07059i	−0.0738000	+	0.402124i
$160$	−4.12550			−0.326149
$161$	−8.28762	+	4.78486i	−0.653156	+	0.377100i
$162$	−8.81624	−	1.80940i	−0.692669	−	0.142160i
$163$	−14.1012	−	8.14132i	−1.10449	−	0.637678i	−0.167093	−	0.985941i	$-0.553438\pi$
$163$	−14.1012	−	8.14132i	−1.10449	−	0.637678i	−0.937397	+	0.348264i	$0.886771\pi$
$164$	−1.81248			−0.141531
$165$	2.80342	−	3.29406i	0.218246	−	0.256443i
$166$		−	16.5261i		−	1.28268i
$167$			8.34505i			0.645760i	0.946440	+	0.322880i	$0.104651\pi$
$167$			8.34505i			0.645760i	−0.946440	+	0.322880i	$0.895349\pi$
$168$	−4.23515	−	0.777258i	−0.326749	−	0.0599667i
$169$	4.80662			0.369740
$170$	−22.6038	−	13.0503i	−1.73363	−	1.00091i
$171$	−2.55601	+	6.72910i	−0.195463	+	0.514587i
$172$	4.05787	−	2.34281i	0.309410	−	0.178638i
$173$	−8.59165			−0.653211			−0.326605	−	0.945161i	$-0.605905\pi$
$173$	−8.59165			−0.653211			−0.326605	+	0.945161i	$0.605905\pi$
$174$	12.9041	+	10.9821i	0.978260	+	0.832550i
$175$	−14.9406	+	25.8778i	−1.12940	+	1.95618i
$176$	−0.302670	−	0.524240i	−0.0228146	−	0.0395161i
$177$	10.2408	−	12.0331i	0.769746	−	0.904464i
$178$	4.68456	−	8.11389i	0.351122	−	0.608162i
$179$		−	19.5696i		−	1.46270i	−0.682003	−	0.731349i	$-0.738891\pi$
$179$		−	19.5696i		−	1.46270i	0.682003	−	0.731349i	$-0.261109\pi$
$180$	7.82248	+	9.59097i	0.583053	+	0.714869i
$181$	−11.3299	−	19.6239i	−0.842143	−	1.45863i	−0.888080	−	0.459689i	$-0.847961\pi$
$181$	−11.3299	−	19.6239i	−0.842143	−	1.45863i	0.0459372	−	0.998944i	$-0.485373\pi$
$182$	−3.55798	+	6.16260i	−0.263735	+	0.456802i
$183$	6.89585	+	1.26556i	0.509756	+	0.0935532i
$184$	1.92472	−	3.33371i	0.141892	−	0.245765i
$185$	10.2399	+	22.9101i	0.752856	+	1.68439i
$186$	2.24961	−	12.2578i	0.164950	−	0.898784i
$187$		−	3.82978i		−	0.280062i
$188$	−0.873232	−	1.51248i	−0.0636870	−	0.110309i
$189$	6.22342	+	11.3197i	0.452687	+	0.823384i
$190$	8.57255	−	4.94936i	0.621918	−	0.359064i
$191$	6.29116	−	3.63220i	0.455212	−	0.262817i	−0.254817	−	0.966989i	$-0.582015\pi$
$191$	6.29116	−	3.63220i	0.455212	−	0.262817i	0.710029	+	0.704172i	$0.248682\pi$
$192$	1.63169	−	0.581033i	0.117757	−	0.0419325i
$193$	0.268129	+	0.154804i	0.0193003	+	0.0111431i	0.509619	−	0.860400i	$-0.329786\pi$
$193$	0.268129	+	0.154804i	0.0193003	+	0.0111431i	−0.490319	+	0.871543i	$0.663120\pi$
$194$	0.850618	+	1.47331i	0.0610708	+	0.105778i
$195$	19.2684	−	6.86134i	1.37984	−	0.491351i
$196$	−0.409896	−	0.709960i	−0.0292783	−	0.0507114i
$197$	7.41930	−	12.8506i	0.528604	−	0.915568i	−0.470840	−	0.882219i	$-0.656049\pi$
$197$	7.41930	−	12.8506i	0.528604	−	0.915568i	0.999444	−	0.0333497i	$-0.0106175\pi$
$198$	−0.644853	+	1.69768i	−0.0458277	+	0.120649i
$199$			16.7753i			1.18917i	0.804032	+	0.594586i	$0.202684\pi$
$199$			16.7753i			1.18917i	−0.804032	+	0.594586i	$0.797316\pi$
$200$		−	12.0198i		−	0.849925i
$201$	−1.87811	+	0.668784i	−0.132472	+	0.0471724i
$202$	−10.4554	+	6.03643i	−0.735639	+	0.424721i
$203$		−	24.3206i		−	1.70697i
$204$	10.7781	+	1.97805i	0.754617	+	0.138491i
$205$		−	7.47741i		−	0.522245i
$206$	8.07850	−	13.9924i	0.562856	−	0.974895i
$207$	−11.3997	+	1.84656i	−0.792336	+	0.128344i
$208$		−	2.86241i		−	0.198472i
$209$	1.25786	+	0.726227i	0.0870081	+	0.0502342i
$210$	3.20658	−	17.4721i	0.221275	−	1.20569i
$211$	1.45399	−	2.51838i	0.100097	−	0.173373i	−0.811628	−	0.584175i	$-0.801418\pi$
$211$	1.45399	−	2.51838i	0.100097	−	0.173373i	0.911724	+	0.410803i	$0.134751\pi$
$212$	−1.48820	+	2.57764i	−0.102210	+	0.177033i
$213$	−8.83677	−	7.52055i	−0.605485	−	0.515299i
$214$	−11.7456	+	6.78135i	−0.802915	+	0.463563i
$215$	9.66528	+	16.7408i	0.659167	+	1.14171i
$216$	−4.44467	−	2.69163i	−0.302422	−	0.183142i
$217$	−15.4909	+	8.94368i	−1.05159	+	0.607137i
$218$	−2.94287	+	5.09721i	−0.199317	+	0.345227i
$219$	−2.69417	+	0.959378i	−0.182055	+	0.0648288i
$220$	2.16275	−	1.24867i	0.145813	−	0.0841851i
$221$	9.05474	−	15.6833i	0.609088	−	1.05497i
$222$	−7.27668	−	7.61905i	−0.488379	−	0.511357i
$223$	−12.5979	−	21.8203i	−0.843621	−	1.46119i	−0.886813	−	0.462128i	$-0.847086\pi$
$223$	−12.5979	−	21.8203i	−0.843621	−	1.46119i	0.0431922	−	0.999067i	$-0.486247\pi$
$224$	−2.15294	−	1.24300i	−0.143849	−	0.0830515i
$225$	−27.9435	+	22.7910i	−1.86290	+	1.51940i
$226$	10.4460	+	18.0930i	0.694858	+	1.20353i
$227$	−11.4991	−	6.63903i	−0.763225	−	0.440648i	0.0672276	−	0.997738i	$-0.478585\pi$
$227$	−11.4991	−	6.63903i	−0.763225	−	0.440648i	−0.830452	+	0.557090i	$0.811918\pi$
$228$	−2.69348	+	3.16489i	−0.178380	+	0.209600i
$229$	6.91259			0.456797			0.228398	−	0.973568i	$-0.426651\pi$
$229$	6.91259			0.456797			0.228398	+	0.973568i	$0.426651\pi$
$230$	13.7532	+	7.94043i	0.906862	+	0.523577i
$231$	2.45549	−	0.874384i	0.161559	−	0.0575303i
$232$	4.89152	+	8.47236i	0.321144	+	0.556237i
$233$	−24.9882			−1.63703			−0.818515	−	0.574486i	$-0.805202\pi$
$233$	−24.9882			−1.63703			−0.818515	+	0.574486i	$0.805202\pi$
$234$	−6.65453	+	5.42749i	−0.435020	+	0.354806i
$235$	6.23975	−	3.60252i	0.407036	−	0.235002i
$236$	7.90047	−	4.56134i	0.514277	−	0.296918i
$237$	−3.76839	−	0.691595i	−0.244783	−	0.0449239i
$238$	−7.86405	−	13.6209i	−0.509750	−	0.882914i
$239$	3.28098	−	1.89428i	0.212229	−	0.122531i	−0.390118	−	0.920765i	$-0.627566\pi$
$239$	3.28098	−	1.89428i	0.212229	−	0.122531i	0.602347	+	0.798234i	$0.294232\pi$
$240$	2.39705	+	6.73152i	0.154729	+	0.434518i
$241$	−4.98462	−	2.87787i	−0.321088	−	0.185380i	0.330789	−	0.943705i	$-0.392685\pi$
$241$	−4.98462	−	2.87787i	−0.321088	−	0.185380i	−0.651877	+	0.758324i	$0.726018\pi$
$242$	−9.20894	−	5.31678i	−0.591973	−	0.341776i
$243$	2.17016	+	15.4367i	0.139216	+	0.990262i
$244$	3.50551	+	2.02391i	0.224417	+	0.129567i
$245$	2.92894	−	1.69102i	0.187123	−	0.108036i
$246$	1.05311	+	2.95741i	0.0671441	+	0.188557i
$247$	3.43403	+	5.94791i	0.218502	+	0.378457i
$248$	3.59761	−	6.23125i	0.228449	−	0.395685i
$249$	−26.9654	+	9.60222i	−1.70887	+	0.608516i
$250$	28.9600			1.83159
$251$			7.00459i			0.442126i	0.975260	+	0.221063i	$0.0709526\pi$
$251$			7.00459i			0.442126i	−0.975260	+	0.221063i	$0.929047\pi$
$252$	1.19252	+	7.36205i	0.0751218	+	0.463766i
$253$			2.33022i			0.146500i
$254$	−3.38472	−	1.95417i	−0.212376	−	0.122615i
$255$	−8.16046	+	44.4650i	−0.511028	+	2.78451i
$256$	1.00000			0.0625000
$257$	6.39759	−	3.69365i	0.399070	−	0.230403i	−0.287012	−	0.957927i	$-0.592662\pi$
$257$	6.39759	−	3.69365i	0.399070	−	0.230403i	0.686083	+	0.727523i	$0.259329\pi$
$258$	−6.18050	−	5.25992i	−0.384781	−	0.327469i
$259$	−1.55892	+	15.0412i	−0.0968667	+	0.934614i
$260$	11.8089			0.732355
$261$	10.4216	−	27.4365i	0.645081	−	1.69828i
$262$	−8.21296	−	14.2253i	−0.507398	−	0.878840i
$263$	13.2499	−	22.9496i	0.817026	−	1.41513i	−0.0908378	−	0.995866i	$-0.528954\pi$
$263$	13.2499	−	22.9496i	0.817026	−	1.41513i	0.907864	−	0.419265i	$-0.137712\pi$
$264$	−0.679534	+	0.798464i	−0.0418224	+	0.0491421i
$265$	−10.6340	−	6.13957i	−0.653244	−	0.377151i
$266$	5.96491			0.365732
$267$	−15.9612	−	2.92929i	−0.976810	−	0.179270i
$268$	−1.15103			−0.0703101
$269$	12.5852			0.767335			0.383667	−	0.923471i	$-0.374661\pi$
$269$	12.5852			0.767335			0.383667	+	0.923471i	$0.374661\pi$
$270$	11.1043	−	18.3365i	0.675788	−	1.11592i
$271$	−0.170960	+	0.296111i	−0.0103851	+	0.0179875i	−0.871171	−	0.490979i	$-0.836639\pi$
$271$	−0.170960	+	0.296111i	−0.0103851	+	0.0179875i	0.860786	+	0.508967i	$0.169972\pi$
$272$	5.47905	+	3.16333i	0.332216	+	0.191805i
$273$	12.1227	+	2.22483i	0.733701	+	0.134653i
$274$	10.3281	−	5.96292i	0.623943	−	0.360233i
$275$	3.63802	+	6.30124i	0.219381	+	0.379979i
$276$	−6.55790	−	1.20354i	−0.394739	−	0.0724447i
$277$	0.862047	+	0.497703i	0.0517954	+	0.0299041i	0.525674	−	0.850686i	$-0.323813\pi$
$277$	0.862047	+	0.497703i	0.0517954	+	0.0299041i	−0.473879	+	0.880590i	$0.657146\pi$
$278$	6.40883	−	3.70014i	0.384376	−	0.221920i
$279$	−21.3080	+	3.45151i	−1.27567	+	0.206637i
$280$	5.12800	−	8.88196i	0.306457	−	0.530799i
$281$			17.4908i			1.04342i	0.853124	+	0.521708i	$0.174705\pi$
$281$			17.4908i			1.04342i	−0.853124	+	0.521708i	$0.825295\pi$
$282$	−1.96052	+	2.30364i	−0.116747	+	0.137180i
$283$			20.2489i			1.20367i	0.798619	+	0.601837i	$0.205564\pi$
$283$			20.2489i			1.20367i	−0.798619	+	0.601837i	$0.794436\pi$
$284$	−3.34971	−	5.80188i	−0.198769	−	0.344278i
$285$	−13.0567	−	11.1120i	−0.773415	−	0.658216i
$286$	0.866366	+	1.50059i	0.0512293	+	0.0887317i
$287$	2.25292	−	3.90217i	0.132986	−	0.230338i
$288$	−1.89613	−	2.32480i	−0.111730	−	0.136990i
$289$	11.5133	+	19.9416i	0.677254	+	1.17304i
$290$	−34.9527	+	20.1800i	−2.05249	+	1.18501i
$291$	1.90975	−	2.24399i	0.111951	−	0.131545i
$292$	−1.65116			−0.0966268
$293$	−10.8016			−0.631039			−0.315519	−	0.948919i	$-0.602179\pi$
$293$	−10.8016			−0.631039			−0.315519	+	0.948919i	$0.602179\pi$
$294$	−0.920269	+	1.08133i	−0.0536712	+	0.0630645i
$295$	18.8178	+	32.5934i	1.09562	+	1.89766i
$296$	−2.48211	−	5.55330i	−0.144270	−	0.322779i
$297$	3.14475	+	0.0657919i	0.182477	+	0.00381763i
$298$	−17.5368	−	10.1249i	−1.01588	−	0.586519i
$299$	−5.50933	+	9.54245i	−0.318613	+	0.551854i
$300$	−19.6125	+	6.98388i	−1.13233	+	0.403214i
$301$			11.6485i			0.671408i
$302$	−8.90013	−	5.13849i	−0.512145	−	0.295687i
$303$	15.9245	+	13.5526i	0.914838	+	0.778574i
$304$	−2.07794	+	1.19970i	−0.119178	+	0.0688075i
$305$	−8.34963	+	14.4620i	−0.478098	+	0.828091i
$306$	−3.03486	−	18.7358i	−0.173492	−	1.07105i
$307$	8.74549			0.499131			0.249566	−	0.968358i	$-0.419712\pi$
$307$	8.74549			0.499131			0.249566	+	0.968358i	$0.419712\pi$
$308$	1.50488			0.0857484
$309$	−27.5250	−	5.05155i	−1.56584	−	0.287372i
$310$	25.7070	+	14.8420i	1.46006	+	0.842967i
$311$	9.17236	−	5.29566i	0.520117	−	0.300289i	−0.216866	−	0.976201i	$-0.569583\pi$
$311$	9.17236	−	5.29566i	0.520117	−	0.300289i	0.736982	+	0.675912i	$0.236250\pi$
$312$	−4.67055	+	1.66315i	−0.264418	+	0.0941576i
$313$		−	3.69272i		−	0.208725i	−0.994539	−	0.104362i	$-0.966720\pi$
$313$		−	3.69272i		−	0.208725i	0.994539	−	0.104362i	$-0.0332802\pi$
$314$	12.1898	−	7.03781i	0.687913	−	0.397167i
$315$	−30.3721	+	4.91975i	−1.71128	+	0.277197i
$316$	−1.91566	−	1.10601i	−0.107764	−	0.0622178i
$317$	−1.26106			−0.0708281			−0.0354140	−	0.999373i	$-0.511275\pi$
$317$	−1.26106			−0.0708281			−0.0354140	+	0.999373i	$0.511275\pi$
$318$	5.07059	+	0.930582i	0.284345	+	0.0521845i
$319$	−5.12866	−	2.96103i	−0.287150	−	0.165786i
$320$			4.12550i			0.230623i
$321$	17.8896	+	15.2250i	0.998502	+	0.849777i
$322$	4.78486	+	8.28762i	0.266650	+	0.461851i
$323$	−15.1802			−0.844648
$324$	−1.80940	+	8.81624i	−0.100522	+	0.489791i
$325$			34.4055i			1.90847i
$326$	−8.14132	+	14.1012i	−0.450906	+	0.780992i
$327$	10.0270	+	1.84020i	0.554492	+	0.101763i
$328$			1.81248i			0.100078i
$329$	4.34171			0.239366
$330$	−3.29406	−	2.80342i	−0.181332	−	0.154323i
$331$			8.64270i			0.475046i	0.971382	+	0.237523i	$0.0763354\pi$
$331$			8.64270i			0.475046i	−0.971382	+	0.237523i	$0.923665\pi$
$332$	−16.5261			−0.906989
$333$	−8.20392	+	16.3002i	−0.449572	+	0.893244i
$334$	8.34505			0.456621
$335$		−	4.74856i		−	0.259441i
$336$	−0.777258	+	4.23515i	−0.0424029	+	0.231046i
$337$	−3.85309			−0.209891			−0.104946	−	0.994478i	$-0.533467\pi$
$337$	−3.85309			−0.209891			−0.104946	+	0.994478i	$0.533467\pi$
$338$		−	4.80662i		−	0.261446i
$339$	23.4526	−	27.5572i	1.27377	−	1.49670i
$340$	−13.0503	+	22.6038i	−0.707753	+	1.22586i
$341$			4.35556i			0.235867i
$342$	6.72910	+	2.55601i	0.363868	+	0.138213i
$343$	19.4400			1.04966
$344$	−2.34281	−	4.05787i	−0.126316	−	0.218786i
$345$	4.96521	−	27.0546i	0.267318	−	1.45657i
$346$			8.59165i			0.461890i
$347$	−20.7963	−	12.0067i	−1.11640	−	0.644555i	−0.175922	−	0.984404i	$-0.556291\pi$
$347$	−20.7963	−	12.0067i	−1.11640	−	0.644555i	−0.940480	+	0.339849i	$0.889624\pi$
$348$	10.9821	−	12.9041i	0.588702	−	0.691735i
$349$	27.6423			1.47966			0.739830	−	0.672794i	$-0.234906\pi$
$349$	27.6423			1.47966			0.739830	+	0.672794i	$0.234906\pi$
$350$	25.8778	+	14.9406i	1.38323	+	0.798607i
$351$	12.7225	+	7.70455i	0.679075	+	0.411238i
$352$	−0.524240	+	0.302670i	−0.0279421	+	0.0161324i
$353$			8.56018i			0.455613i	0.973706	+	0.227806i	$0.0731553\pi$
$353$			8.56018i			0.455613i	−0.973706	+	0.227806i	$0.926845\pi$
$354$	−12.0331	−	10.2408i	−0.639553	−	0.544293i
$355$	23.9356	−	13.8193i	1.27037	−	0.733450i
$356$	−8.11389	−	4.68456i	−0.430035	−	0.248281i
$357$	−17.6558	+	20.7459i	−0.934445	+	1.09799i
$358$	−19.5696			−1.03428
$359$	20.0102			1.05610			0.528048	−	0.849215i	$-0.322924\pi$
$359$	20.0102			1.05610			0.528048	+	0.849215i	$0.322924\pi$
$360$	9.59097	−	7.82248i	0.505488	−	0.412281i
$361$	−6.62144	+	11.4687i	−0.348497	+	0.603614i
$362$	−19.6239	+	11.3299i	−1.03141	+	0.595485i
$363$	−3.32462	+	18.1153i	−0.174497	+	0.950808i
$364$	6.16260	+	3.55798i	0.323008	+	0.186489i
$365$		−	6.81186i		−	0.356549i
$366$	1.26556	−	6.89585i	0.0661521	−	0.360452i
$367$	−12.6372	+	21.8883i	−0.659657	+	1.14256i	0.321047	+	0.947063i	$0.395965\pi$
$367$	−12.6372	+	21.8883i	−0.659657	+	1.14256i	−0.980704	+	0.195496i	$0.937368\pi$
$368$	−3.33371	−	1.92472i	−0.173782	−	0.100333i
$369$	4.21367	−	3.43670i	0.219355	−	0.178908i
$370$	22.9101	−	10.2399i	1.19104	−	0.532349i
$371$	−3.69967	−	6.40802i	−0.192077	−	0.332688i
$372$	−12.2578	−	2.24961i	−0.635536	−	0.116637i
$373$	−12.2537			−0.634473			−0.317237	−	0.948346i	$-0.602755\pi$
$373$	−12.2537			−0.634473			−0.317237	+	0.948346i	$0.602755\pi$
$374$	−3.82978			−0.198033
$375$	−16.8267	−	47.2537i	−0.868929	−	2.44017i
$376$	−1.51248	+	0.873232i	−0.0780003	+	0.0450335i
$377$	−14.0015	−	24.2513i	−0.721115	−	1.24901i
$378$	11.3197	−	6.22342i	0.582221	−	0.320098i
$379$	15.4180	−	26.7048i	0.791970	−	1.37173i	−0.132776	−	0.991146i	$-0.542389\pi$
$379$	15.4180	−	26.7048i	0.791970	−	1.37173i	0.924745	−	0.380586i	$-0.124278\pi$
$380$	−4.94936	−	8.57255i	−0.253897	−	0.439762i
$381$	−1.22196	+	6.65823i	−0.0626027	+	0.341112i
$382$	−3.63220	−	6.29116i	−0.185840	−	0.321884i
$383$		−	15.3582i		−	0.784766i	−0.919802	−	0.392383i	$-0.871651\pi$
$383$		−	15.3582i		−	0.784766i	0.919802	−	0.392383i	$-0.128349\pi$
$384$	−0.581033	−	1.63169i	−0.0296507	−	0.0832666i
$385$			6.20838i			0.316408i
$386$	0.154804	−	0.268129i	0.00787933	−	0.0136474i
$387$	−4.99147	+	13.1408i	−0.253731	+	0.667986i
$388$	1.47331	−	0.850618i	0.0747962	−	0.0431836i
$389$	4.39589	+	2.53797i	0.222881	+	0.128680i	0.607283	−	0.794485i	$-0.292259\pi$
$389$	4.39589	+	2.53797i	0.222881	+	0.128680i	−0.384403	+	0.923165i	$0.625593\pi$
$390$	−6.86134	−	19.2684i	−0.347438	−	0.975692i
$391$	−12.1770	−	21.0913i	−0.615820	−	1.06663i
$392$	−0.709960	+	0.409896i	−0.0358584	+	0.0207029i
$393$	−18.4392	+	21.6663i	−0.930133	+	1.09292i
$394$	−12.8506	−	7.41930i	−0.647405	−	0.373779i
$395$	4.56284	−	7.90306i	0.229581	−	0.397646i
$396$	1.69768	+	0.644853i	0.0853114	+	0.0324051i
$397$	36.0842			1.81101			0.905507	−	0.424331i	$-0.139491\pi$
$397$	36.0842			1.81101			0.905507	+	0.424331i	$0.139491\pi$
$398$	16.7753			0.840872
$399$	−3.46581	−	9.73287i	−0.173508	−	0.487253i
$400$	−12.0198			−0.600988
$401$	−26.6967	−	15.4133i	−1.33317	−	0.769705i	−0.347384	−	0.937723i	$-0.612930\pi$
$401$	−26.6967	−	15.4133i	−1.33317	−	0.769705i	−0.985784	+	0.168018i	$0.946263\pi$
$402$	0.668784	+	1.87811i	0.0333559	+	0.0936718i
$403$	−10.2978	+	17.8364i	−0.512972	+	0.888494i
$404$	6.03643	+	10.4554i	0.300323	+	0.520175i
$405$	−36.3714	−	7.46467i	−1.80731	−	0.370922i
$406$	−24.3206			−1.20701
$407$	2.98204	+	2.16000i	0.147814	+	0.107067i
$408$	1.97805	−	10.7781i	0.0979282	−	0.533595i
$409$	20.9301	−	12.0840i	1.03493	−	0.597515i	0.116535	−	0.993187i	$-0.462821\pi$
$409$	20.9301	−	12.0840i	1.03493	−	0.597515i	0.918392	+	0.395671i	$0.129488\pi$
$410$	−7.47741			−0.369283
$411$	−15.7306	−	13.3875i	−0.775933	−	0.660359i
$412$	−13.9924	−	8.07850i	−0.689355	−	0.397999i
$413$			22.6790i			1.11596i
$414$	1.84656	+	11.3997i	0.0907533	+	0.560266i
$415$		−	68.1785i		−	3.34675i
$416$	−2.86241			−0.140341
$417$	−9.76121	−	8.30730i	−0.478009	−	0.406810i
$418$	0.726227	−	1.25786i	0.0355209	−	0.0615240i
$419$	16.2454	+	28.1379i	0.793642	+	1.37463i	0.923698	+	0.383121i	$0.125151\pi$
$419$	16.2454	+	28.1379i	0.793642	+	1.37463i	−0.130057	+	0.991507i	$0.541516\pi$
$420$	−17.4721	−	3.20658i	−0.852552	−	0.156465i
$421$	−4.23360	+	2.44427i	−0.206333	+	0.119126i	−0.599606	−	0.800295i	$-0.704676\pi$
$421$	−4.23360	+	2.44427i	−0.206333	+	0.119126i	0.393273	+	0.919422i	$0.371343\pi$
$422$	−2.51838	−	1.45399i	−0.122593	−	0.0707791i
$423$	4.89795	+	1.86046i	0.238146	+	0.0904587i
$424$	2.57764	+	1.48820i	0.125181	+	0.0722734i
$425$	−65.8568	−	38.0225i	−3.19453	−	1.84436i
$426$	−7.52055	+	8.83677i	−0.364372	+	0.428143i
$427$	−8.71471	+	5.03144i	−0.421734	+	0.243488i
$428$	6.78135	+	11.7456i	0.327789	+	0.567747i
$429$	1.94510	−	2.28553i	0.0939105	−	0.110346i
$430$	16.7408	−	9.66528i	0.807311	−	0.466101i
$431$	3.95310	−	2.28233i	0.190414	−	0.109936i	−0.401762	−	0.915744i	$-0.631602\pi$
$431$	3.95310	−	2.28233i	0.190414	−	0.109936i	0.592176	+	0.805808i	$0.298269\pi$
$432$	−2.69163	+	4.44467i	−0.129501	+	0.213844i
$433$	−20.1711			−0.969362			−0.484681	−	0.874691i	$-0.661064\pi$
$433$	−20.1711			−0.969362			−0.484681	+	0.874691i	$0.661064\pi$
$434$	8.94368	+	15.4909i	0.429310	+	0.743587i
$435$	53.2360	+	45.3066i	2.55247	+	2.17229i
$436$	5.09721	+	2.94287i	0.244112	+	0.140938i
$437$	9.23634			0.441834
$438$	0.959378	+	2.69417i	0.0458409	+	0.128733i
$439$	−21.3528	−	12.3280i	−1.01911	−	0.588385i	−0.105266	−	0.994444i	$-0.533570\pi$
$439$	−21.3528	−	12.3280i	−1.01911	−	0.588385i	−0.913847	+	0.406059i	$0.866903\pi$
$440$	−1.24867	−	2.16275i	−0.0595278	−	0.103105i
$441$	2.29910	+	0.873301i	0.109481	+	0.0415858i
$442$	−15.6833	−	9.05474i	−0.745977	−	0.430690i
$443$	15.6754	+	27.1505i	0.744759	+	1.28996i	0.950307	+	0.311313i	$0.100769\pi$
$443$	15.6754	+	27.1505i	0.744759	+	1.28996i	−0.205549	+	0.978647i	$0.565898\pi$
$444$	−7.61905	+	7.27668i	−0.361584	+	0.345336i
$445$	19.3261	−	33.4739i	0.916147	−	1.58681i
$446$	−21.8203	+	12.5979i	−1.03322	+	0.596530i
$447$	−6.33117	+	34.4975i	−0.299454	+	1.63168i
$448$	−1.24300	+	2.15294i	−0.0587263	+	0.101717i
$449$	33.1427	−	19.1350i	1.56410	−	0.903035i	0.567267	−	0.823534i	$-0.308001\pi$
$449$	33.1427	−	19.1350i	1.56410	−	0.903035i	0.996835	−	0.0795010i	$-0.0253327\pi$
$450$	22.7910	+	27.9435i	1.07438	+	1.31727i
$451$	−0.548585	−	0.950178i	−0.0258319	−	0.0447421i
$452$	18.0930	−	10.4460i	0.851024	−	0.491339i
$453$	−3.21314	+	17.5079i	−0.150966	+	0.822591i
$454$	−6.63903	+	11.4991i	−0.311585	+	0.539681i
$455$	−14.6784	+	25.4238i	−0.688136	+	1.19189i
$456$	3.16489	+	2.69348i	0.148209	+	0.126134i
$457$	2.81600	+	1.62582i	0.131727	+	0.0760525i	0.564415	−	0.825491i	$-0.309102\pi$
$457$	2.81600	+	1.62582i	0.131727	+	0.0760525i	−0.432689	+	0.901543i	$0.642435\pi$
$458$		−	6.91259i		−	0.323004i
$459$	−28.8076	+	15.8381i	−1.34462	+	0.739257i
$460$	7.94043	−	13.7532i	0.370225	−	0.641248i
$461$		−	2.38678i		−	0.111163i	−0.998454	−	0.0555817i	$-0.982299\pi$
$461$		−	2.38678i		−	0.111163i	0.998454	−	0.0555817i	$-0.0177013\pi$
$462$	−0.874384	−	2.45549i	−0.0406800	−	0.114240i
$463$		−	5.06685i		−	0.235477i	−0.993045	−	0.117738i	$-0.962436\pi$
$463$		−	5.06685i		−	0.235477i	0.993045	−	0.117738i	$-0.0375644\pi$
$464$	8.47236	−	4.89152i	0.393319	−	0.227083i
$465$	9.28079	−	50.5695i	0.430386	−	2.34510i
$466$			24.9882i			1.15755i
$467$		−	11.0299i		−	0.510405i	−0.966888	−	0.255203i	$-0.917858\pi$
$467$		−	11.0299i		−	0.510405i	0.966888	−	0.255203i	$-0.0821422\pi$
$468$	5.42749	+	6.65453i	0.250886	+	0.307606i
$469$	1.43073	−	2.47809i	0.0660648	−	0.114428i
$470$	−3.60252	−	6.23975i	−0.166172	−	0.287818i
$471$	−18.5662	−	15.8008i	−0.855485	−	0.728062i
$472$	−4.56134	−	7.90047i	−0.209953	−	0.363649i
$473$	2.45640	+	1.41820i	0.112945	+	0.0652089i
$474$	−0.691595	+	3.76839i	−0.0317660	+	0.173088i
$475$	24.9763	−	14.4201i	1.14599	−	0.661639i
$476$	−13.6209	+	7.86405i	−0.624314	+	0.360448i
$477$	−1.42776	−	8.81431i	−0.0653728	−	0.403580i
$478$	−1.89428	−	3.28098i	−0.0866422	−	0.150069i
$479$		−	28.3060i		−	1.29333i	−0.762772	−	0.646667i	$-0.776162\pi$
$479$		−	28.3060i		−	1.29333i	0.762772	−	0.646667i	$-0.223838\pi$
$480$	6.73152	−	2.39705i	0.307251	−	0.109410i
$481$	7.10481	+	15.8958i	0.323951	+	0.724786i
$482$	−2.87787	+	4.98462i	−0.131084	+	0.227043i
$483$	10.7426	−	12.6228i	0.488807	−	0.574356i
$484$	−5.31678	+	9.20894i	−0.241672	+	0.418588i
$485$	3.50923	+	6.07816i	0.159346	+	0.275995i
$486$	15.4367	−	2.17016i	0.700221	−	0.0984404i
$487$			28.7296i			1.30186i	0.759137	+	0.650930i	$0.225621\pi$
$487$			28.7296i			1.30186i	−0.759137	+	0.650930i	$0.774379\pi$
$488$	2.02391	−	3.50551i	0.0916180	−	0.158687i
$489$	27.7391	+	5.09083i	1.25440	+	0.230215i
$490$	−1.69102	−	2.92894i	−0.0763927	−	0.132316i
$491$	4.23594	−	7.33687i	0.191166	−	0.331108i	−0.754471	−	0.656333i	$-0.772107\pi$
$491$	4.23594	−	7.33687i	0.191166	−	0.331108i	0.945637	+	0.325225i	$0.105440\pi$
$492$	2.95741	−	1.05311i	0.133330	−	0.0474780i
$493$	61.8939			2.78756
$494$	5.94791	−	3.43403i	0.267609	−	0.154504i
$495$	−2.66034	+	7.00376i	−0.119573	+	0.314796i
$496$	−6.23125	−	3.59761i	−0.279791	−	0.161538i
$497$	16.6548			0.747070
$498$	9.60222	+	26.9654i	0.430286	+	1.20835i
$499$		−	1.32342i		−	0.0592444i	−0.999561	−	0.0296222i	$-0.990570\pi$
$499$		−	1.32342i		−	0.0592444i	0.999561	−	0.0296222i	$-0.00943042\pi$
$500$		−	28.9600i		−	1.29513i
$501$	−4.84875	−	13.6165i	−0.216626	−	0.608341i
$502$	7.00459			0.312630
$503$	−5.97983	−	3.45246i	−0.266628	−	0.153937i	0.360727	−	0.932672i	$-0.382529\pi$
$503$	−5.97983	−	3.45246i	−0.266628	−	0.153937i	−0.627354	+	0.778734i	$0.715862\pi$
$504$	7.36205	−	1.19252i	0.327932	−	0.0531192i
$505$	−43.1337	+	24.9033i	−1.91943	+	1.10818i
$506$	2.33022			0.103591
$507$	−7.84290	+	2.79281i	−0.348315	+	0.124033i
$508$	−1.95417	+	3.38472i	−0.0867022	+	0.150173i
$509$	−8.55195	−	14.8124i	−0.379058	−	0.656549i	0.611867	−	0.790961i	$-0.290419\pi$
$509$	−8.55195	−	14.8124i	−0.379058	−	0.656549i	−0.990926	+	0.134412i	$0.957085\pi$
$510$	44.4650	+	8.16046i	1.96894	+	0.361351i
$511$	2.05239	−	3.55485i	0.0907925	−	0.157257i
$512$		−	1.00000i		−	0.0441942i
$513$	0.260780	−	12.4649i	0.0115137	−	0.550339i
$514$	−3.69365	−	6.39759i	−0.162920	−	0.282185i
$515$	33.3279	−	57.7255i	1.46860	−	2.54369i
$516$	−5.25992	+	6.18050i	−0.231555	+	0.272081i
$517$	0.528603	−	0.915567i	0.0232479	−	0.0402666i
$518$	15.0412	+	1.55892i	0.660872	+	0.0684951i
$519$	14.0189	−	4.99203i	0.615360	−	0.219126i
$520$		−	11.8089i		−	0.517853i
$521$	4.87121	+	8.43719i	0.213412	+	0.369640i	0.952780	−	0.303661i	$-0.0982091\pi$
$521$	4.87121	+	8.43719i	0.213412	+	0.369640i	−0.739368	+	0.673301i	$0.764876\pi$
$522$	−27.4365	−	10.4216i	−1.20086	−	0.456141i
$523$	−32.4156	+	18.7152i	−1.41744	+	0.818357i	−0.996073	−	0.0885347i	$-0.971782\pi$
$523$	−32.4156	+	18.7152i	−1.41744	+	0.818357i	−0.421363	+	0.906892i	$0.638448\pi$
$524$	−14.2253	+	8.21296i	−0.621434	+	0.358785i
$525$	9.34245	−	50.9055i	0.407738	−	2.22170i
$526$	−22.9496	−	13.2499i	−1.00065	−	0.577725i
$527$	−22.7609	−	39.4230i	−0.991480	−	1.71729i
$528$	0.798464	+	0.679534i	0.0347487	+	0.0295729i
$529$	−4.09091	−	7.08566i	−0.177865	−	0.308072i
$530$	−6.13957	+	10.6340i	−0.266686	+	0.461914i
$531$	−9.71814	+	25.5845i	−0.421731	+	1.11027i
$532$		−	5.96491i		−	0.258612i
$533$		−	5.18807i		−	0.224720i
$534$	−2.92929	+	15.9612i	−0.126763	+	0.690709i
$535$	−48.4566	+	27.9765i	−2.09496	+	1.20953i
$536$			1.15103i			0.0497167i
$537$	11.3706	+	31.9314i	0.490677	+	1.37794i
$538$		−	12.5852i		−	0.542588i
$539$	0.248126	−	0.429768i	0.0106876	−	0.0185114i
$540$	−18.3365	−	11.1043i	−0.789077	−	0.477854i
$541$			34.2078i			1.47071i	0.677683	+	0.735355i	$0.262984\pi$
$541$			34.2078i			1.47071i	−0.677683	+	0.735355i	$0.737016\pi$
$542$	0.296111	+	0.170960i	0.0127191	+	0.00734336i
$543$	29.8889	+	25.4370i	1.28266	+	1.09161i
$544$	3.16333	−	5.47905i	0.135627	−	0.234912i
$545$	−12.1408	+	21.0285i	−0.520056	+	0.900764i
$546$	2.22483	−	12.1227i	0.0952139	−	0.518805i
$547$	−14.8414	+	8.56867i	−0.634571	+	0.366370i	−0.782520	−	0.622625i	$-0.786066\pi$
$547$	−14.8414	+	8.56867i	−0.634571	+	0.366370i	0.147949	+	0.988995i	$0.452733\pi$
$548$	−5.96292	−	10.3281i	−0.254724	−	0.441194i
$549$	−11.9872	+	1.94171i	−0.511601	+	0.0828704i
$550$	6.30124	−	3.63802i	0.268686	−	0.155126i
$551$	−11.7367	+	20.3286i	−0.500000	+	0.866026i
$552$	−1.20354	+	6.55790i	−0.0512261	+	0.279123i
$553$	4.76234	−	2.74954i	0.202515	−	0.116922i
$554$	0.497703	−	0.862047i	0.0211454	−	0.0366249i
$555$	−30.0199	−	31.4324i	−1.27428	−	1.33423i
$556$	−3.70014	−	6.40883i	−0.156921	−	0.271795i
$557$	1.53311	+	0.885143i	0.0649601	+	0.0375047i	0.532128	−	0.846664i	$-0.321392\pi$
$557$	1.53311	+	0.885143i	0.0649601	+	0.0375047i	−0.467168	+	0.884168i	$0.654726\pi$
$558$	3.45151	+	21.3080i	0.146114	+	0.902038i
$559$	6.70609	+	11.6153i	0.283637	+	0.491274i
$560$	−8.88196	−	5.12800i	−0.375331	−	0.216698i
$561$	2.22523	+	6.24901i	0.0939494	+	0.263833i
$562$	17.4908			0.737807
$563$	8.77097	+	5.06392i	0.369652	+	0.213419i	0.673307	−	0.739363i	$-0.264873\pi$
$563$	8.77097	+	5.06392i	0.369652	+	0.213419i	−0.303654	+	0.952782i	$0.598207\pi$
$564$	2.30364	+	1.96052i	0.0970009	+	0.0825528i
$565$	43.0950	+	74.6427i	1.81302	+	3.14024i
$566$	20.2489			0.851126
$567$	−16.7318	−	14.8541i	−0.702668	−	0.623815i
$568$	−5.80188	+	3.34971i	−0.243441	+	0.140551i
$569$	24.7799	−	14.3067i	1.03883	−	0.599768i	0.119327	−	0.992855i	$-0.461926\pi$
$569$	24.7799	−	14.3067i	1.03883	−	0.599768i	0.919501	+	0.393087i	$0.128593\pi$
$570$	−11.1120	+	13.0567i	−0.465429	+	0.546887i
$571$	−14.3909	−	24.9258i	−0.602241	−	1.04311i	−0.992481	−	0.122398i	$-0.960941\pi$
$571$	−14.3909	−	24.9258i	−0.602241	−	1.04311i	0.390241	−	0.920713i	$-0.372392\pi$
$572$	1.50059	−	0.866366i	0.0627428	−	0.0362246i
$573$	−8.15477	+	9.58199i	−0.340670	+	0.400293i
$574$	−3.90217	−	2.25292i	−0.162874	−	0.0940351i
$575$	40.0704	+	23.1347i	1.67105	+	0.964782i
$576$	−2.32480	+	1.89613i	−0.0968667	+	0.0790053i
$577$	18.2753	+	10.5513i	0.760812	+	0.439255i	0.829587	−	0.558377i	$-0.188576\pi$
$577$	18.2753	+	10.5513i	0.760812	+	0.439255i	−0.0687750	+	0.997632i	$0.521909\pi$
$578$	19.9416	−	11.5133i	0.829463	−	0.478891i
$579$	−0.527449	−	0.0968002i	−0.0219200	−	0.00402288i
$580$	20.1800	+	34.9527i	0.837927	+	1.45133i
$581$	20.5420	−	35.5798i	0.852225	−	1.47610i
$582$	−2.24399	−	1.90975i	−0.0930162	−	0.0791616i
$583$	−1.80174			−0.0746203
$584$			1.65116i			0.0683255i
$585$	−27.4533	+	22.3911i	−1.13505	+	0.925759i
$586$			10.8016i			0.446212i
$587$	−1.23464	−	0.712820i	−0.0509591	−	0.0294212i	0.474304	−	0.880361i	$-0.342700\pi$
$587$	−1.23464	−	0.712820i	−0.0509591	−	0.0294212i	−0.525263	+	0.850940i	$0.676033\pi$
$588$	1.08133	+	0.920269i	0.0445933	+	0.0379513i
$589$	17.2642			0.711360
$590$	32.5934	−	18.8178i	1.34185	−	0.774717i
$591$	−4.63935	+	25.2790i	−0.190837	+	1.03984i
$592$	−5.55330	+	2.48211i	−0.228239	+	0.102014i
$593$	35.9950			1.47814			0.739069	−	0.673630i	$-0.235266\pi$
$593$	35.9950			1.47814			0.739069	+	0.673630i	$0.235266\pi$
$594$	0.0657919	−	3.14475i	0.00269947	−	0.129031i
$595$	−32.4431	−	56.1932i	−1.33004	−	2.30369i
$596$	−10.1249	+	17.5368i	−0.414732	+	0.718336i
$597$	−9.74703	−	27.3721i	−0.398919	−	1.12027i
$598$	9.54245	+	5.50933i	0.390220	+	0.225293i
$599$	−10.0713			−0.411502			−0.205751	−	0.978604i	$-0.565964\pi$
$599$	−10.0713			−0.411502			−0.205751	+	0.978604i	$0.565964\pi$
$600$	6.98388	+	19.6125i	0.285116	+	0.800676i
$601$	4.67461			0.190681			0.0953406	−	0.995445i	$-0.469606\pi$
$601$	4.67461			0.190681			0.0953406	+	0.995445i	$0.469606\pi$
$602$	11.6485			0.474757
$603$	2.67591	−	2.18249i	0.108971	−	0.0888780i
$604$	−5.13849	+	8.90013i	−0.209082	+	0.362141i
$605$	−37.9915	−	21.9344i	−1.54457	−	0.891760i
$606$	13.5526	−	15.9245i	0.550535	−	0.646888i
$607$	−14.6090	+	8.43454i	−0.592963	+	0.342347i	−0.766268	−	0.642521i	$-0.777889\pi$
$607$	−14.6090	+	8.43454i	−0.592963	+	0.342347i	0.173305	+	0.984868i	$0.444555\pi$
$608$	1.19970	+	2.07794i	0.0486542	+	0.0842716i
$609$	14.1311	+	39.6837i	0.572621	+	1.60806i
$610$	14.4620	+	8.34963i	0.585549	+	0.338067i
$611$	4.32934	−	2.49955i	0.175146	−	0.101121i
$612$	−18.7358	+	3.03486i	−0.757349	+	0.122677i
$613$	−1.50842	+	2.61266i	−0.0609244	+	0.105524i	−0.894879	−	0.446309i	$-0.852738\pi$
$613$	−1.50842	+	2.61266i	−0.0609244	+	0.105524i	0.833954	+	0.551833i	$0.186072\pi$
$614$		−	8.74549i		−	0.352939i
$615$	4.34462	+	12.2008i	0.175192	+	0.491983i
$616$		−	1.50488i		−	0.0606333i
$617$	−0.224530	−	0.388898i	−0.00903925	−	0.0156564i	0.861470	−	0.507808i	$-0.169544\pi$
$617$	−0.224530	−	0.388898i	−0.00903925	−	0.0156564i	−0.870510	+	0.492151i	$0.836211\pi$
$618$	−5.05155	+	27.5250i	−0.203203	+	1.10722i
$619$	−5.72174	−	9.91034i	−0.229976	−	0.398330i	0.727825	−	0.685763i	$-0.240531\pi$
$619$	−5.72174	−	9.91034i	−0.229976	−	0.398330i	−0.957801	+	0.287433i	$0.907198\pi$
$620$	14.8420	−	25.7070i	0.596068	−	1.03242i
$621$	17.5279	−	9.63662i	0.703370	−	0.386704i
$622$	−5.29566	−	9.17236i	−0.212337	−	0.367778i
$623$	20.1712	−	11.6458i	0.808140	−	0.466580i
$624$	1.66315	+	4.67055i	0.0665795	+	0.186972i
$625$	59.3758			2.37503
$626$	−3.69272			−0.147591
$627$	−2.47440	−	0.454115i	−0.0988179	−	0.0181356i
$628$	−7.03781	−	12.1898i	−0.280839	−	0.486428i
$629$	−38.2785	−	3.96732i	−1.52626	−	0.158187i
$630$	4.91975	+	30.3721i	0.196008	+	1.21006i
$631$	2.21908	+	1.28118i	0.0883400	+	0.0510031i	0.543519	−	0.839397i	$-0.317091\pi$
$631$	2.21908	+	1.28118i	0.0883400	+	0.0510031i	−0.455179	+	0.890400i	$0.650425\pi$
$632$	−1.10601	+	1.91566i	−0.0439946	+	0.0762009i
$633$	−0.909190	+	4.95403i	−0.0361371	+	0.196905i
$634$			1.26106i			0.0500830i
$635$	−13.9637	−	8.06192i	−0.554131	−	0.319928i
$636$	0.930582	−	5.07059i	0.0369000	−	0.201062i
$637$	2.03219	−	1.17329i	0.0805185	−	0.0464874i
$638$	−2.96103	+	5.12866i	−0.117228	+	0.203046i
$639$	18.7885	+	7.13672i	0.743262	+	0.282324i
$640$	4.12550			0.163075
$641$	20.2591			0.800187			0.400094	−	0.916474i	$-0.368978\pi$
$641$	20.2591			0.800187			0.400094	+	0.916474i	$0.368978\pi$
$642$	15.2250	−	17.8896i	0.600883	−	0.706048i
$643$	−24.6651	−	14.2404i	−0.972698	−	0.561588i	−0.0726405	−	0.997358i	$-0.523143\pi$
$643$	−24.6651	−	14.2404i	−0.972698	−	0.561588i	−0.900058	+	0.435771i	$0.856476\pi$
$644$	8.28762	−	4.78486i	0.326578	−	0.188550i
$645$	−25.4977	−	21.6998i	−1.00397	−	0.854430i
$646$			15.1802i			0.597256i
$647$	−14.3995	+	8.31354i	−0.566102	+	0.326839i	−0.755591	−	0.655044i	$-0.772650\pi$
$647$	−14.3995	+	8.31354i	−0.566102	+	0.326839i	0.189489	+	0.981883i	$0.439317\pi$
$648$	8.81624	+	1.80940i	0.346335	+	0.0710798i
$649$	4.78248	+	2.76116i	0.187729	+	0.108385i
$650$	34.4055			1.34949
$651$	20.0797	−	23.5940i	0.786987	−	0.924722i
$652$	14.1012	+	8.14132i	0.552245	+	0.318839i
$653$		−	33.1663i		−	1.29790i	−0.760833	−	0.648948i	$-0.775209\pi$
$653$		−	33.1663i		−	1.29790i	0.760833	−	0.648948i	$-0.224791\pi$
$654$	1.84020	−	10.0270i	0.0719576	−	0.392085i
$655$	−33.8826	−	58.6864i	−1.32390	−	2.29307i
$656$	1.81248			0.0707656
$657$	3.83862	−	3.13081i	0.149759	−	0.122145i
$658$		−	4.34171i		−	0.169258i
$659$	9.39936	−	16.2802i	0.366147	−	0.634185i	−0.622813	−	0.782371i	$-0.714010\pi$
$659$	9.39936	−	16.2802i	0.366147	−	0.634185i	0.988960	+	0.148186i	$0.0473434\pi$
$660$	−2.80342	+	3.29406i	−0.109123	+	0.128221i
$661$			12.1566i			0.472837i	0.971651	+	0.236418i	$0.0759736\pi$
$661$			12.1566i			0.472837i	−0.971651	+	0.236418i	$0.924026\pi$
$662$	8.64270			0.335908
$663$	−5.66200	+	30.8513i	−0.219894	+	1.19816i
$664$			16.5261i			0.641338i
$665$	24.6083			0.954267
$666$	16.3002	+	8.20392i	0.631619	+	0.317895i
$667$	−37.6592			−1.45817
$668$		−	8.34505i		−	0.322880i
$669$	33.2342	+	28.2840i	1.28491	+	1.09352i
$670$	−4.74856			−0.183453
$671$			2.45031i			0.0945930i
$672$	4.23515	+	0.777258i	0.163374	+	0.0299834i
$673$	−7.74664	+	13.4176i	−0.298611	+	0.517210i	−0.975818	−	0.218583i	$-0.929857\pi$
$673$	−7.74664	+	13.4176i	−0.298611	+	0.517210i	0.677207	+	0.735792i	$0.263190\pi$
$674$			3.85309i			0.148415i
$675$	32.3528	−	53.4239i	1.24526	−	2.05629i
$676$	−4.80662			−0.184870
$677$	17.3613	+	30.0707i	0.667249	+	1.15571i	0.978670	+	0.205437i	$0.0658617\pi$
$677$	17.3613	+	30.0707i	0.667249	+	1.15571i	−0.311421	+	0.950272i	$0.600805\pi$
$678$	−27.5572	−	23.4526i	−1.05833	−	0.900693i
$679$			4.22928i			0.162305i
$680$	22.6038	+	13.0503i	0.866817	+	0.500457i
$681$	22.6205	+	4.15144i	0.866819	+	0.159083i
$682$	4.35556			0.166783
$683$	36.3425	+	20.9823i	1.39061	+	0.802867i	0.993382	−	0.114855i	$-0.0366403\pi$
$683$	36.3425	+	20.9823i	1.39061	+	0.802867i	0.397224	+	0.917722i	$0.369974\pi$
$684$	2.55601	−	6.72910i	0.0977316	−	0.257294i
$685$	42.6085	−	24.6001i	1.62799	−	0.939920i
$686$		−	19.4400i		−	0.742223i
$687$	−11.2792	+	4.01644i	−0.430327	+	0.153237i
$688$	−4.05787	+	2.34281i	−0.154705	+	0.0893190i
$689$	−7.37825	−	4.25984i	−0.281089	−	0.162287i
$690$	−27.0546	−	4.96521i	−1.02995	−	0.189022i
$691$	−9.35087			−0.355724			−0.177862	−	0.984055i	$-0.556918\pi$
$691$	−9.35087			−0.355724			−0.177862	+	0.984055i	$0.556918\pi$
$692$	8.59165			0.326605
$693$	−3.49854	+	2.85344i	−0.132899	+	0.108393i
$694$	−12.0067	+	20.7963i	−0.455769	+	0.789415i
$695$	26.4396	−	15.2649i	1.00291	−	0.579032i
$696$	−12.9041	−	10.9821i	−0.489130	−	0.416275i
$697$	9.93069	+	5.73349i	0.376152	+	0.217171i
$698$		−	27.6423i		−	1.04628i
$699$	40.7728	−	14.5190i	1.54217	−	0.549157i
$700$	14.9406	−	25.8778i	0.564701	−	0.978090i
$701$	−0.124833	−	0.0720722i	−0.00471486	−	0.00272213i	0.497641	−	0.867383i	$-0.334200\pi$
$701$	−0.124833	−	0.0720722i	−0.00471486	−	0.00272213i	−0.502356	+	0.864661i	$0.667533\pi$
$702$	7.70455	−	12.7225i	0.290789	−	0.480179i
$703$	8.56164	−	11.8200i	0.322908	−	0.445799i
$704$	0.302670	+	0.524240i	0.0114073	+	0.0197581i
$705$	−8.08812	+	9.50368i	−0.304616	+	0.357929i
$706$	8.56018			0.322167
$707$	−30.0131			−1.12876
$708$	−10.2408	+	12.0331i	−0.384873	+	0.452232i
$709$	24.2810	−	14.0186i	0.911891	−	0.526480i	0.0308516	−	0.999524i	$-0.490178\pi$
$709$	24.2810	−	14.0186i	0.911891	−	0.526480i	0.881039	+	0.473044i	$0.156845\pi$
$710$	−13.8193	−	23.9356i	−0.518627	−	0.898289i
$711$	6.55066	−	1.06109i	0.245669	−	0.0397940i
$712$	−4.68456	+	8.11389i	−0.175561	+	0.304081i
$713$	13.8488	+	23.9868i	0.518642	+	0.898314i
$714$	20.7459	+	17.6558i	0.776395	+	0.660752i
$715$	3.57419	+	6.19068i	0.133667	+	0.231518i
$716$			19.5696i			0.731349i
$717$	−4.25290	+	4.99723i	−0.158827	+	0.186625i
$718$		−	20.0102i		−	0.746772i
$719$	−20.1693	+	34.9342i	−0.752187	+	1.30283i	0.194573	+	0.980888i	$0.437668\pi$
$719$	−20.1693	+	34.9342i	−0.752187	+	1.30283i	−0.946760	+	0.321939i	$0.895665\pi$
$720$	−7.82248	−	9.59097i	−0.291527	−	0.357434i
$721$	34.7851	−	20.0832i	1.29546	−	0.747936i
$722$	11.4687	+	6.62144i	0.426820	+	0.246425i
$723$	9.80548	+	1.79956i	0.364670	+	0.0669262i
$724$	11.3299	+	19.6239i	0.421071	+	0.729317i
$725$	−101.836	+	58.7948i	−3.78208	+	2.18359i
$726$	18.1153	+	3.32462i	0.672323	+	0.123388i
$727$	25.3195	+	14.6182i	0.939049	+	0.542160i	0.889662	−	0.456620i	$-0.150940\pi$
$727$	25.3195	+	14.6182i	0.939049	+	0.542160i	0.0493867	+	0.998780i	$0.484273\pi$
$728$	3.55798	−	6.16260i	0.131867	−	0.228401i
$729$	−12.5102	−	23.9268i	−0.463342	−	0.886180i
$730$	−6.81186			−0.252118
$731$	−29.6444			−1.09644
$732$	−6.89585	−	1.26556i	−0.254878	−	0.0467766i
$733$	−24.6939			−0.912088			−0.456044	−	0.889957i	$-0.650734\pi$
$733$	−24.6939			−0.912088			−0.456044	+	0.889957i	$0.650734\pi$
$734$	21.8883	+	12.6372i	0.807912	+	0.466448i
$735$	−3.79657	+	4.46103i	−0.140039	+	0.164548i
$736$	−1.92472	+	3.33371i	−0.0709461	+	0.122882i
$737$	−0.348381	−	0.603414i	−0.0128328	−	0.0222270i
$738$	−3.43670	−	4.21367i	−0.126507	−	0.155107i
$739$	51.9399			1.91064			0.955319	−	0.295576i	$-0.0955116\pi$
$739$	51.9399			1.91064			0.955319	+	0.295576i	$0.0955116\pi$
$740$	−10.2399	−	22.9101i	−0.376428	−	0.842194i
$741$	−9.05919	−	7.70984i	−0.332798	−	0.283228i
$742$	−6.40802	+	3.69967i	−0.235246	+	0.135819i
$743$	29.5873			1.08545			0.542726	−	0.839910i	$-0.317392\pi$
$743$	29.5873			1.08545			0.542726	+	0.839910i	$0.317392\pi$
$744$	−2.24961	+	12.2578i	−0.0824749	+	0.449392i
$745$	−72.3482	−	41.7702i	−2.65063	−	1.53034i
$746$			12.2537i			0.448640i
$747$	38.4199	−	31.3356i	1.40571	−	1.14651i
$748$			3.82978i			0.140031i
$749$	−33.7169			−1.23199
$750$	−47.2537	+	16.8267i	−1.72546	+	0.614425i
$751$	5.43236	−	9.40913i	0.198230	−	0.343344i	−0.749725	−	0.661750i	$-0.769814\pi$
$751$	5.43236	−	9.40913i	0.198230	−	0.343344i	0.947955	+	0.318406i	$0.103147\pi$
$752$	0.873232	+	1.51248i	0.0318435	+	0.0551545i
$753$	−4.06990	−	11.4293i	−0.148315	−	0.416507i
$754$	−24.2513	+	14.0015i	−0.883182	+	0.509905i
$755$	−36.7175	−	21.1989i	−1.33629	−	0.771505i
$756$	−6.22342	−	11.3197i	−0.226343	−	0.411692i
$757$	−25.6528	−	14.8107i	−0.932368	−	0.538303i	−0.0448084	−	0.998996i	$-0.514268\pi$
$757$	−25.6528	−	14.8107i	−0.932368	−	0.538303i	−0.887560	+	0.460693i	$0.847601\pi$
$758$	−26.7048	−	15.4180i	−0.969961	−	0.560007i
$759$	−1.35394	−	3.80219i	−0.0491448	−	0.138011i
$760$	−8.57255	+	4.94936i	−0.310959	+	0.179532i
$761$	26.2118	+	45.4001i	0.950176	+	1.64575i	0.745040	+	0.667020i	$0.232430\pi$
$761$	26.2118	+	45.4001i	0.950176	+	1.64575i	0.205136	+	0.978733i	$0.434236\pi$
$762$	6.65823	+	1.22196i	0.241202	+	0.0442668i
$763$	−12.6717	+	7.31599i	−0.458745	+	0.264857i
$764$	−6.29116	+	3.63220i	−0.227606	+	0.131408i
$765$	−12.5203	−	77.2945i	−0.452674	−	2.79459i
$766$	−15.3582			−0.554913
$767$	13.0564	+	22.6144i	0.471440	+	0.816558i
$768$	−1.63169	+	0.581033i	−0.0588784	+	0.0209662i
$769$	−10.8810	−	6.28216i	−0.392379	−	0.226540i	0.290811	−	0.956780i	$-0.406075\pi$
$769$	−10.8810	−	6.28216i	−0.392379	−	0.226540i	−0.683191	+	0.730240i	$0.739408\pi$
$770$	6.20838			0.223734
$771$	−8.29272	+	9.74409i	−0.298655	+	0.350925i
$772$	−0.268129	−	0.154804i	−0.00965017	−	0.00557153i
$773$	17.3339	+	30.0232i	0.623457	+	1.07986i	0.988837	+	0.149000i	$0.0476055\pi$
$773$	17.3339	+	30.0232i	0.623457	+	1.07986i	−0.365381	+	0.930858i	$0.619061\pi$
$774$	13.1408	+	4.99147i	0.472337	+	0.179415i
$775$	74.8981	+	43.2425i	2.69042	+	1.55331i
$776$	−0.850618	−	1.47331i	−0.0305354	−	0.0528889i
$777$	−6.19576	−	25.4483i	−0.222272	−	0.912952i
$778$	2.53797	−	4.39589i	0.0909907	−	0.157600i
$779$	−3.76624	+	2.17444i	−0.134939	+	0.0779073i
$780$	−19.2684	+	6.86134i	−0.689918	+	0.245676i
$781$	2.02772	−	3.51211i	0.0725575	−	0.125673i
$782$	−21.0913	+	12.1770i	−0.754222	+	0.435450i
$783$	−1.06328	+	50.8230i	−0.0379984	+	1.81627i
$784$	0.409896	+	0.709960i	0.0146391	+	0.0253557i
$785$	50.2892	−	29.0345i	1.79490	−	1.03629i
$786$	21.6663	+	18.4392i	0.772812	+	0.657703i
$787$	10.3612	−	17.9462i	0.369338	−	0.639713i	−0.620124	−	0.784504i	$-0.712918\pi$
$787$	10.3612	−	17.9462i	0.369338	−	0.639713i	0.989462	+	0.144791i	$0.0462510\pi$
$788$	−7.41930	+	12.8506i	−0.264302	+	0.457784i
$789$	−8.28528	+	45.1451i	−0.294964	+	1.60721i
$790$	−7.90306	−	4.56284i	−0.281178	−	0.162338i
$791$			51.9376i			1.84669i
$792$	0.644853	−	1.69768i	0.0229138	−	0.0603243i
$793$	−5.79325	+	10.0342i	−0.205724	+	0.356325i
$794$		−	36.0842i		−	1.28058i
$795$	20.9187	+	3.83912i	0.741911	+	0.136160i
$796$		−	16.7753i		−	0.594586i
$797$	−45.0615	+	26.0163i	−1.59616	+	0.921544i	−0.603943	+	0.797027i	$0.706405\pi$
$797$	−45.0615	+	26.0163i	−1.59616	+	0.921544i	−0.992218	+	0.124517i	$0.960262\pi$
$798$	−9.73287	+	3.46581i	−0.344540	+	0.122688i
$799$			11.0493i			0.390896i
$800$			12.0198i			0.424963i
$801$	27.7457	−	4.49431i	0.980346	−	0.158799i
$802$	−15.4133	+	26.6967i	−0.544264	+	0.942692i
$803$	−0.499757	−	0.865604i	−0.0176360	−	0.0305465i
$804$	1.87811	−	0.668784i	0.0662359	−	0.0235862i
$805$	19.7399	+	34.1906i	0.695741	+	1.20506i
$806$	17.8364	+	10.2978i	0.628260	+	0.362726i
$807$	−20.5351	+	7.31244i	−0.722871	+	0.257410i
$808$	10.4554	−	6.03643i	0.367820	−	0.212361i
$809$	30.9772	−	17.8847i	1.08910	−	0.628792i	0.155763	−	0.987794i	$-0.450216\pi$
$809$	30.9772	−	17.8847i	1.08910	−	0.628792i	0.933337	+	0.359003i	$0.116883\pi$
$810$	−7.46467	+	36.3714i	−0.262282	+	1.27796i
$811$	13.6185	+	23.5880i	0.478212	+	0.828287i	0.999688	−	0.0249787i	$-0.00795179\pi$
$811$	13.6185	+	23.5880i	0.478212	+	0.828287i	−0.521476	+	0.853266i	$0.674618\pi$
$812$			24.3206i			0.853487i
$813$	0.106903	−	0.582494i	0.00374924	−	0.0204290i
$814$	2.16000	−	2.98204i	0.0757081	−	0.104520i
$815$	−33.5870	+	58.1744i	−1.17650	+	2.03776i
$816$	−10.7781	−	1.97805i	−0.377309	−	0.0692457i
$817$	5.62135	−	9.73646i	0.196666	−	0.340636i
$818$	−12.0840	−	20.9301i	−0.422507	−	0.731804i
$819$	−21.0732	+	3.41348i	−0.736357	+	0.119277i
$820$			7.47741i			0.261122i
$821$	−18.9202	+	32.7708i	−0.660321	+	1.14371i	0.320210	+	0.947347i	$0.396246\pi$
$821$	−18.9202	+	32.7708i	−0.660321	+	1.14371i	−0.980531	+	0.196363i	$0.937087\pi$
$822$	−13.3875	+	15.7306i	−0.466944	+	0.548667i
$823$	−12.7271	−	22.0440i	−0.443640	−	0.768406i	0.554317	−	0.832306i	$-0.312980\pi$
$823$	−12.7271	−	22.0440i	−0.443640	−	0.768406i	−0.997956	+	0.0638995i	$0.979646\pi$
$824$	−8.07850	+	13.9924i	−0.281428	+	0.487447i
$825$	−9.59735	−	8.16784i	−0.334137	−	0.284368i
$826$	22.6790			0.789104
$827$	37.0494	−	21.3905i	1.28833	−	0.743820i	0.309978	−	0.950744i	$-0.399678\pi$
$827$	37.0494	−	21.3905i	1.28833	−	0.743820i	0.978357	+	0.206923i	$0.0663451\pi$
$828$	11.3997	−	1.84656i	0.396168	−	0.0641722i
$829$	−32.3114	−	18.6550i	−1.12222	−	0.647915i	−0.180254	−	0.983620i	$-0.557692\pi$
$829$	−32.3114	−	18.6550i	−1.12222	−	0.647915i	−0.941967	+	0.335705i	$0.891025\pi$
$830$	−68.1785			−2.36651
$831$	−1.69577	−	0.311218i	−0.0588257	−	0.0107960i
$832$			2.86241i			0.0992361i
$833$			5.18654i			0.179703i
$834$	−8.30730	+	9.76121i	−0.287658	+	0.338003i
$835$	34.4275			1.19141
$836$	−1.25786	−	0.726227i	−0.0435041	−	0.0251171i
$837$	32.7625	−	18.0124i	1.13244	−	0.622600i
$838$	28.1379	−	16.2454i	0.972008	−	0.561189i
$839$	−53.9012			−1.86087			−0.930437	−	0.366451i	$-0.880573\pi$
$839$	−53.9012			−1.86087			−0.930437	+	0.366451i	$0.880573\pi$
$840$	−3.20658	+	17.4721i	−0.110637	+	0.602845i
$841$	33.3539	−	57.7706i	1.15013	−	1.99209i
$842$	2.44427	+	4.23360i	0.0842350	+	0.145899i
$843$	−10.1628	−	28.5396i	−0.350024	−	0.982955i
$844$	−1.45399	+	2.51838i	−0.0500484	+	0.0866863i
$845$		−	19.8297i		−	0.682163i
$846$	1.86046	−	4.89795i	0.0639639	−	0.168395i
$847$	−13.2175	−	22.8934i	−0.454160	−	0.786628i
$848$	1.48820	−	2.57764i	0.0511050	−	0.0885165i
$849$	−11.7653	−	33.0399i	−0.403784	−	1.13393i
$850$	−38.0225	+	65.8568i	−1.30416	+	2.25887i
$851$	23.2905	+	2.41390i	0.798387	+	0.0827476i
$852$	8.83677	+	7.52055i	0.302743	+	0.257650i
$853$			7.34096i			0.251350i	0.992071	+	0.125675i	$0.0401096\pi$
$853$			7.34096i			0.251350i	−0.992071	+	0.125675i	$0.959890\pi$
$854$	5.03144	+	8.71471i	0.172172	+	0.298211i
$855$	27.7609	+	10.5448i	0.949404	+	0.360626i
$856$	11.7456	−	6.78135i	0.401458	−	0.231782i
$857$	14.7608	−	8.52218i	0.504221	−	0.291112i	−0.226234	−	0.974073i	$-0.572641\pi$
$857$	14.7608	−	8.52218i	0.504221	−	0.291112i	0.730455	+	0.682961i	$0.239308\pi$
$858$	−2.28553	−	1.94510i	−0.0780267	−	0.0664048i
$859$	11.2707	+	6.50714i	0.384551	+	0.222021i	0.679797	−	0.733401i	$-0.262068\pi$
$859$	11.2707	+	6.50714i	0.384551	+	0.222021i	−0.295245	+	0.955421i	$0.595401\pi$
$860$	−9.66528	−	16.7408i	−0.329583	−	0.570855i
$861$	−1.40877	+	7.67614i	−0.0480107	+	0.261602i
$862$	−2.28233	−	3.95310i	−0.0777363	−	0.134643i
$863$	−23.6154	+	40.9031i	−0.803879	+	1.39236i	0.113167	+	0.993576i	$0.463901\pi$
$863$	−23.6154	+	40.9031i	−0.803879	+	1.39236i	−0.917046	+	0.398783i	$0.869433\pi$
$864$	4.44467	+	2.69163i	0.151211	+	0.0915712i
$865$			35.4449i			1.20516i
$866$			20.1711i			0.685442i
$867$	−30.3729	−	25.8489i	−1.03152	−	0.877874i
$868$	15.4909	−	8.94368i	0.525796	−	0.303568i
$869$		−	1.33902i		−	0.0454232i
$870$	45.3066	−	53.2360i	1.53604	−	1.80487i
$871$		−	3.29471i		−	0.111637i
$872$	2.94287	−	5.09721i	0.0996583	−	0.172613i
$873$	−1.81228	+	4.77111i	−0.0613364	+	0.161478i
$874$		−	9.23634i		−	0.312424i
$875$	62.3492	+	35.9973i	2.10779	+	1.21693i
$876$	2.69417	−	0.959378i	0.0910277	−	0.0324144i
$877$	−16.6836	+	28.8969i	−0.563366	+	0.975779i	0.433833	+	0.900993i	$0.357161\pi$
$877$	−16.6836	+	28.8969i	−0.563366	+	0.975779i	−0.997200	+	0.0747860i	$0.976173\pi$
$878$	−12.3280	+	21.3528i	−0.416051	+	0.720622i
$879$	17.6249	−	6.27611i	0.594473	−	0.211688i
$880$	−2.16275	+	1.24867i	−0.0729064	+	0.0420925i
$881$	−4.32602	−	7.49288i	−0.145747	−	0.252441i	0.783904	−	0.620882i	$-0.213225\pi$
$881$	−4.32602	−	7.49288i	−0.145747	−	0.252441i	−0.929651	+	0.368440i	$0.879892\pi$
$882$	0.873301	−	2.29910i	0.0294056	−	0.0774147i
$883$	−1.30842	+	0.755415i	−0.0440318	+	0.0254217i	−0.521854	−	0.853035i	$-0.674760\pi$
$883$	−1.30842	+	0.755415i	−0.0440318	+	0.0254217i	0.477823	+	0.878456i	$0.341426\pi$
$884$	−9.05474	+	15.6833i	−0.304544	+	0.527486i
$885$	−49.6426	−	42.2484i	−1.66872	−	1.42017i
$886$	27.1505	−	15.6754i	0.912139	−	0.526624i
$887$	−0.0315682	+	0.0546777i	−0.00105996	+	0.00183590i	−0.866555	−	0.499082i	$-0.833671\pi$
$887$	−0.0315682	+	0.0546777i	−0.00105996	+	0.00183590i	0.865495	+	0.500918i	$0.167004\pi$
$888$	7.27668	+	7.61905i	0.244189	+	0.255679i
$889$	−4.85807	−	8.41442i	−0.162934	−	0.282210i
$890$	−33.4739	−	19.3261i	−1.12205	−	0.647814i
$891$	−5.16948	+	1.71985i	−0.173184	+	0.0576173i
$892$	12.5979	+	21.8203i	0.421811	+	0.730597i
$893$	−3.62905	−	2.09523i	−0.121441	−	0.0701143i
$894$	34.4975	+	6.33117i	1.15377	+	0.211746i
$895$	−80.7343			−2.69865
$896$	2.15294	+	1.24300i	0.0719247	+	0.0415258i
$897$	3.44503	−	18.7714i	0.115026	−	0.626758i
$898$	−19.1350	−	33.1427i	−0.638542	−	1.10599i
$899$	−70.3912			−2.34768
$900$	27.9435	−	22.7910i	0.931451	−	0.759700i
$901$	16.3078	−	9.41534i	0.543293	−	0.313670i
$902$	−0.950178	+	0.548585i	−0.0316375	+	0.0182659i
$903$	−6.76816	−	19.0067i	−0.225230	−	0.632503i
$904$	−10.4460	−	18.0930i	−0.347429	−	0.601764i
$905$	−80.9585	+	46.7414i	−2.69115	+	1.55374i
$906$	17.5079	+	3.21314i	0.581659	+	0.106749i
$907$	2.88151	+	1.66364i	0.0956790	+	0.0552403i	0.547076	−	0.837083i	$-0.315741\pi$
$907$	2.88151	+	1.66364i	0.0956790	+	0.0552403i	−0.451397	+	0.892323i	$0.649074\pi$
$908$	11.4991	+	6.63903i	0.381612	+	0.220324i
$909$	−33.8583	−	12.8609i	−1.12301	−	0.426568i
$910$	25.4238	+	14.6784i	0.842791	+	0.486585i
$911$	−18.5335	+	10.7003i	−0.614043	+	0.354518i	−0.774546	−	0.632518i	$-0.782022\pi$
$911$	−18.5335	+	10.7003i	−0.614043	+	0.354518i	0.160503	+	0.987035i	$0.448688\pi$
$912$	2.69348	−	3.16489i	0.0891901	−	0.104800i
$913$	−5.00197	−	8.66366i	−0.165541	−	0.286725i
$914$	1.62582	−	2.81600i	0.0537772	−	0.0931449i
$915$	5.22108	−	28.4488i	0.172604	−	0.940489i
$916$	−6.91259			−0.228398
$917$		−	40.8349i		−	1.34849i
$918$	15.8381	+	28.8076i	0.522734	+	0.950791i
$919$			15.8634i			0.523286i	0.965165	+	0.261643i	$0.0842643\pi$
$919$			15.8634i			0.523286i	−0.965165	+	0.261643i	$0.915736\pi$
$920$	−13.7532	−	7.94043i	−0.453431	−	0.261788i
$921$	−14.2699	+	5.08142i	−0.470209	+	0.167438i
$922$	−2.38678			−0.0786044
$923$	16.6073	−	9.58825i	0.546637	−	0.315601i
$924$	−2.45549	+	0.874384i	−0.0807797	+	0.0287651i
$925$	66.7493	−	29.8344i	2.19470	−	0.980948i
$926$	−5.06685			−0.166507
$927$	47.8474	−	7.75043i	1.57151	−	0.254557i
$928$	−4.89152	−	8.47236i	−0.160572	−	0.278119i
$929$	−26.9546	+	46.6867i	−0.884351	+	1.53174i	−0.0378943	+	0.999282i	$0.512065\pi$
$929$	−26.9546	+	46.6867i	−0.884351	+	1.53174i	−0.846456	+	0.532458i	$0.821268\pi$
$930$	−50.5695	−	9.28079i	−1.65824	−	0.304329i
$931$	−1.70348	−	0.983503i	−0.0558292	−	0.0322330i
$932$	24.9882			0.818515
$933$	−11.8895	+	13.9703i	−0.389243	+	0.457367i
$934$	−11.0299			−0.360911
$935$	−15.7998			−0.516708
$936$	6.65453	−	5.42749i	0.217510	−	0.177403i
$937$	−16.6169	+	28.7812i	−0.542849	+	0.940242i	0.455890	+	0.890036i	$0.349321\pi$
$937$	−16.6169	+	28.7812i	−0.542849	+	0.940242i	−0.998739	+	0.0502059i	$0.984012\pi$
$938$	−2.47809	−	1.43073i	−0.0809125	−	0.0467149i
$939$	2.14559	+	6.02536i	0.0700188	+	0.196630i
$940$	−6.23975	+	3.60252i	−0.203518	+	0.117501i
$941$	6.41666	+	11.1140i	0.209177	+	0.362305i	0.951456	−	0.307786i	$-0.0995881\pi$
$941$	6.41666	+	11.1140i	0.209177	+	0.362305i	−0.742278	+	0.670092i	$0.766255\pi$
$942$	−15.8008	+	18.5662i	−0.514818	+	0.604920i
$943$	−6.04230	−	3.48853i	−0.196764	−	0.113602i
$944$	−7.90047	+	4.56134i	−0.257139	+	0.148459i
$945$	46.6993	−	25.6747i	1.51913	−	0.835198i
$946$	1.41820	−	2.45640i	0.0461097	−	0.0798643i
$947$		−	43.7609i		−	1.42204i	−0.703172	−	0.711020i	$-0.748234\pi$
$947$		−	43.7609i		−	1.42204i	0.703172	−	0.711020i	$-0.251766\pi$
$948$	3.76839	+	0.691595i	0.122391	+	0.0224619i
$949$		−	4.72629i		−	0.153422i
$950$	−14.4201	−	24.9763i	−0.467850	−	0.810340i
$951$	2.05765	−	0.732717i	0.0667239	−	0.0237600i
$952$	7.86405	+	13.6209i	0.254875	+	0.441457i
$953$	23.1853	−	40.1581i	0.751045	−	1.30085i	−0.196272	−	0.980550i	$-0.562883\pi$
$953$	23.1853	−	40.1581i	0.751045	−	1.30085i	0.947317	−	0.320299i	$-0.103783\pi$
$954$	−8.81431	+	1.42776i	−0.285374	+	0.0462255i
$955$	−14.9847	−	25.9542i	−0.484892	−	0.839857i
$956$	−3.28098	+	1.89428i	−0.106115	+	0.0612653i
$957$	10.0888	+	1.85156i	0.326125	+	0.0598523i
$958$	−28.3060			−0.914525
$959$	29.6477			0.957374
$960$	−2.39705	−	6.73152i	−0.0773646	−	0.217259i
$961$	10.3857	+	17.9885i	0.335021	+	0.580274i
$962$	15.8958	−	7.10481i	0.512501	−	0.229068i
$963$	−38.0365	−	14.4480i	−1.22571	−	0.465579i
$964$	4.98462	+	2.87787i	0.160544	+	0.0926901i
$965$	0.638645	−	1.10617i	0.0205587	−	0.0356087i
$966$	−12.6228	−	10.7426i	−0.406131	−	0.345639i
$967$			15.7860i			0.507644i	0.967251	+	0.253822i	$0.0816877\pi$
$967$			15.7860i			0.507644i	−0.967251	+	0.253822i	$0.918312\pi$
$968$	9.20894	+	5.31678i	0.295986	+	0.170888i
$969$	24.7693	−	8.82019i	0.795704	−	0.283345i
$970$	6.07816	−	3.50923i	0.195158	−	0.112674i
$971$	−16.9504	+	29.3589i	−0.543963	+	0.942172i	0.454708	+	0.890640i	$0.349744\pi$
$971$	−16.9504	+	29.3589i	−0.543963	+	0.942172i	−0.998671	+	0.0515314i	$0.983590\pi$
$972$	−2.17016	−	15.4367i	−0.0696079	−	0.495131i
$973$	18.3971			0.589784
$974$	28.7296			0.920555
$975$	−19.9907	−	56.1389i	−0.640215	−	1.79788i
$976$	−3.50551	−	2.02391i	−0.112209	−	0.0647837i
$977$	−29.5011	+	17.0325i	−0.943825	+	0.544918i	−0.891157	−	0.453694i	$-0.850106\pi$
$977$	−29.5011	+	17.0325i	−0.943825	+	0.544918i	−0.0526679	+	0.998612i	$0.516772\pi$
$978$	5.09083	−	27.7391i	0.162787	−	0.886998i
$979$		−	5.67151i		−	0.181262i
$980$	−2.92894	+	1.69102i	−0.0935616	+	0.0540178i
$981$	−17.4301	+	2.82336i	−0.556499	+	0.0901430i
$982$	−7.33687	−	4.23594i	−0.234129	−	0.135174i
$983$	−12.9942			−0.414452			−0.207226	−	0.978293i	$-0.566444\pi$
$983$	−12.9942			−0.414452			−0.207226	+	0.978293i	$0.566444\pi$
$984$	−1.05311	−	2.95741i	−0.0335720	−	0.0942787i
$985$	−53.0152	−	30.6083i	−1.68921	−	0.975263i
$986$		−	61.8939i		−	1.97110i
$987$	−7.08431	+	2.52268i	−0.225496	+	0.0802978i
$988$	−3.43403	−	5.94791i	−0.109251	−	0.189228i
$989$	18.0370			0.573545
$990$	7.00376	+	2.66034i	0.222594	+	0.0845512i
$991$		−	36.1067i		−	1.14697i	−0.819217	−	0.573483i	$-0.805592\pi$
$991$		−	36.1067i		−	1.14697i	0.819217	−	0.573483i	$-0.194408\pi$
$992$	−3.59761	+	6.23125i	−0.114224	+	0.197842i
$993$	−5.02169	−	14.1022i	−0.159359	−	0.447519i
$994$		−	16.6548i		−	0.528258i
$995$	69.2067			2.19400
$996$	26.9654	−	9.60222i	0.854433	−	0.304258i
$997$		−	47.2837i		−	1.49749i	−0.662858	−	0.748745i	$-0.730657\pi$
$997$		−	47.2837i		−	1.49749i	0.662858	−	0.748745i	$-0.269343\pi$
$998$	−1.32342			−0.0418921
$999$	3.91527	−	31.3635i	0.123874	−	0.992298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.2	✓	76
3.2	odd	2		1998.2.k.a.1063.21		76
9.2	odd	6		1998.2.t.a.397.21		76
9.7	even	3		666.2.t.a.619.14	yes	76
37.11	even	6		666.2.t.a.85.14	yes	76
111.11	odd	6		1998.2.t.a.307.21		76
333.11	odd	6		1998.2.k.a.1639.18		76
333.196	even	6	inner	666.2.k.a.529.21	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.2	✓	76	1.1	even	1	trivial
666.2.k.a.529.21	yes	76	333.196	even	6	inner
666.2.t.a.85.14	yes	76	37.11	even	6
666.2.t.a.619.14	yes	76	9.7	even	3
1998.2.k.a.1063.21		76	3.2	odd	2
1998.2.k.a.1639.18		76	333.11	odd	6
1998.2.t.a.307.21		76	111.11	odd	6
1998.2.t.a.397.21		76	9.2	odd	6

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.63169 + 0.581033i) q^{3} -1.00000 q^{4} -4.12550i q^{5} +(0.581033 + 1.63169i) q^{6} +(1.24300 - 2.15294i) q^{7} +1.00000i q^{8} +(2.32480 - 1.89613i) q^{9} -4.12550 q^{10} +(-0.302670 - 0.524240i) q^{11} +(1.63169 - 0.581033i) q^{12} -2.86241i q^{13} +(-2.15294 - 1.24300i) q^{14} +(2.39705 + 6.73152i) q^{15} +1.00000 q^{16} +(5.47905 + 3.16333i) q^{17} +(-1.89613 - 2.32480i) q^{18} +(-2.07794 + 1.19970i) q^{19} +4.12550i q^{20} +(-0.777258 + 4.23515i) q^{21} +(-0.524240 + 0.302670i) q^{22} +(-3.33371 - 1.92472i) q^{23} +(-0.581033 - 1.63169i) q^{24} -12.0198 q^{25} -2.86241 q^{26} +(-2.69163 + 4.44467i) q^{27} +(-1.24300 + 2.15294i) q^{28} +(8.47236 - 4.89152i) q^{29} +(6.73152 - 2.39705i) q^{30} +(-6.23125 - 3.59761i) q^{31} -1.00000i q^{32} +(0.798464 + 0.679534i) q^{33} +(3.16333 - 5.47905i) q^{34} +(-8.88196 - 5.12800i) q^{35} +(-2.32480 + 1.89613i) q^{36} +(-5.55330 + 2.48211i) q^{37} +(1.19970 + 2.07794i) q^{38} +(1.66315 + 4.67055i) q^{39} +4.12550 q^{40} +1.81248 q^{41} +(4.23515 + 0.777258i) q^{42} +(-4.05787 + 2.34281i) q^{43} +(0.302670 + 0.524240i) q^{44} +(-7.82248 - 9.59097i) q^{45} +(-1.92472 + 3.33371i) q^{46} +(0.873232 + 1.51248i) q^{47} +(-1.63169 + 0.581033i) q^{48} +(0.409896 + 0.709960i) q^{49} +12.0198i q^{50} +(-10.7781 - 1.97805i) q^{51} +2.86241i q^{52} +(1.48820 - 2.57764i) q^{53} +(4.44467 + 2.69163i) q^{54} +(-2.16275 + 1.24867i) q^{55} +(2.15294 + 1.24300i) q^{56} +(2.69348 - 3.16489i) q^{57} +(-4.89152 - 8.47236i) q^{58} +(-7.90047 + 4.56134i) q^{59} +(-2.39705 - 6.73152i) q^{60} +(-3.50551 - 2.02391i) q^{61} +(-3.59761 + 6.23125i) q^{62} +(-1.19252 - 7.36205i) q^{63} -1.00000 q^{64} -11.8089 q^{65} +(0.679534 - 0.798464i) q^{66} +1.15103 q^{67} +(-5.47905 - 3.16333i) q^{68} +(6.55790 + 1.20354i) q^{69} +(-5.12800 + 8.88196i) q^{70} +(3.34971 + 5.80188i) q^{71} +(1.89613 + 2.32480i) q^{72} +1.65116 q^{73} +(2.48211 + 5.55330i) q^{74} +(19.6125 - 6.98388i) q^{75} +(2.07794 - 1.19970i) q^{76} -1.50488 q^{77} +(4.67055 - 1.66315i) q^{78} +(1.91566 + 1.10601i) q^{79} -4.12550i q^{80} +(1.80940 - 8.81624i) q^{81} -1.81248i q^{82} +16.5261 q^{83} +(0.777258 - 4.23515i) q^{84} +(13.0503 - 22.6038i) q^{85} +(2.34281 + 4.05787i) q^{86} +(-10.9821 + 12.9041i) q^{87} +(0.524240 - 0.302670i) q^{88} +(8.11389 + 4.68456i) q^{89} +(-9.59097 + 7.82248i) q^{90} +(-6.16260 - 3.55798i) q^{91} +(3.33371 + 1.92472i) q^{92} +(12.2578 + 2.24961i) q^{93} +(1.51248 - 0.873232i) q^{94} +(4.94936 + 8.57255i) q^{95} +(0.581033 + 1.63169i) q^{96} +(-1.47331 + 0.850618i) q^{97} +(0.709960 - 0.409896i) q^{98} +(-1.69768 - 0.644853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Introduction

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