LMFDB - Embedded newform 840.2.u.e.629.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [840,2,Mod(629,840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(840, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 1, 1]))

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

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

chi := DirichletCharacter("840.629");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.u (of order $2$, degree $1$, 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$160$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			629.5
Character	$\chi$	$=$	840.629
Dual form			840.2.u.e.629.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37073 + 0.347977i) q^{2} +(-0.973146 - 1.43282i) q^{3} +(1.75782 - 0.953969i) q^{4} +(1.31834 + 1.80610i) q^{5} +(1.83252 + 1.62539i) q^{6} +(-2.61441 + 0.406058i) q^{7} +(-2.07755 + 1.91932i) q^{8} +(-1.10597 + 2.78870i) q^{9} +O(q^{10})$	\(q+(-1.37073 + 0.347977i) q^{2} +(-0.973146 - 1.43282i) q^{3} +(1.75782 - 0.953969i) q^{4} +(1.31834 + 1.80610i) q^{5} +(1.83252 + 1.62539i) q^{6} +(-2.61441 + 0.406058i) q^{7} +(-2.07755 + 1.91932i) q^{8} +(-1.10597 + 2.78870i) q^{9} +(-2.43557 - 2.01693i) q^{10} -2.00814 q^{11} +(-3.07749 - 1.59030i) q^{12} -1.33017i q^{13} +(3.44236 - 1.46635i) q^{14} +(1.30489 - 3.64654i) q^{15} +(2.17989 - 3.35382i) q^{16} -4.12882i q^{17} +(0.545590 - 4.20741i) q^{18} +2.33202 q^{19} +(4.04036 + 1.91715i) q^{20} +(3.12601 + 3.35083i) q^{21} +(2.75262 - 0.698786i) q^{22} -0.0975649 q^{23} +(4.77181 + 1.10898i) q^{24} +(-1.52398 + 4.76209i) q^{25} +(0.462871 + 1.82332i) q^{26} +(5.07198 - 1.12915i) q^{27} +(-4.20830 + 3.20784i) q^{28} +7.56166 q^{29} +(-0.519740 + 5.45251i) q^{30} -9.48706i q^{31} +(-1.82099 + 5.35574i) q^{32} +(1.95421 + 2.87731i) q^{33} +(1.43674 + 5.65952i) q^{34} +(-4.18005 - 4.18655i) q^{35} +(0.716226 + 5.95710i) q^{36} +6.19728 q^{37} +(-3.19658 + 0.811490i) q^{38} +(-1.90591 + 1.29445i) q^{39} +(-6.20539 - 1.22195i) q^{40} -5.88262 q^{41} +(-5.45094 - 3.50532i) q^{42} +3.65928 q^{43} +(-3.52995 + 1.91570i) q^{44} +(-6.49470 + 1.67894i) q^{45} +(0.133736 - 0.0339504i) q^{46} -7.79115i q^{47} +(-6.92678 + 0.140362i) q^{48} +(6.67023 - 2.12320i) q^{49} +(0.431874 - 7.05787i) q^{50} +(-5.91588 + 4.01795i) q^{51} +(-1.26895 - 2.33821i) q^{52} +2.49399i q^{53} +(-6.55942 + 3.31270i) q^{54} +(-2.64740 - 3.62689i) q^{55} +(4.65220 - 5.86149i) q^{56} +(-2.26939 - 3.34137i) q^{57} +(-10.3650 + 2.63129i) q^{58} -1.86318i q^{59} +(-1.18493 - 7.65480i) q^{60} +11.3191 q^{61} +(3.30128 + 13.0042i) q^{62} +(1.75909 - 7.73987i) q^{63} +(0.632417 - 7.97496i) q^{64} +(2.40243 - 1.75362i) q^{65} +(-3.67994 - 3.26400i) q^{66} -7.33230 q^{67} +(-3.93877 - 7.25774i) q^{68} +(0.0949450 + 0.139793i) q^{69} +(7.18656 + 4.28409i) q^{70} -8.88677i q^{71} +(-3.05469 - 7.91637i) q^{72} +6.85080 q^{73} +(-8.49482 + 2.15651i) q^{74} +(8.30629 - 2.45061i) q^{75} +(4.09928 - 2.22467i) q^{76} +(5.25008 - 0.815421i) q^{77} +(2.16205 - 2.43757i) q^{78} +10.9789 q^{79} +(8.93115 - 0.484370i) q^{80} +(-6.55365 - 6.16844i) q^{81} +(8.06351 - 2.04702i) q^{82} +10.1647 q^{83} +(8.69156 + 2.90805i) q^{84} +(7.45706 - 5.44318i) q^{85} +(-5.01590 + 1.27335i) q^{86} +(-7.35861 - 10.8345i) q^{87} +(4.17200 - 3.85426i) q^{88} -13.4335 q^{89} +(8.31827 - 4.56140i) q^{90} +(0.540128 + 3.47762i) q^{91} +(-0.171502 + 0.0930739i) q^{92} +(-13.5933 + 9.23230i) q^{93} +(2.71114 + 10.6796i) q^{94} +(3.07438 + 4.21185i) q^{95} +(9.44593 - 2.60276i) q^{96} +9.65918 q^{97} +(-8.40429 + 5.23144i) q^{98} +(2.22094 - 5.60008i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 24 q^{4} - 32 q^{9}+O(q^{10}) $ 160 * q - 24 * q^4 - 32 * q^9	$ 160 q - 24 q^{4} - 32 q^{9} - 48 q^{15} - 104 q^{16} - 16 q^{25} - 32 q^{30} + 48 q^{36} - 64 q^{39} - 64 q^{46} + 144 q^{49} + 16 q^{60} - 72 q^{64} + 8 q^{70} - 96 q^{79} + 16 q^{81} - 72 q^{84}+O(q^{100}) $ 160 * q - 24 * q^4 - 32 * q^9 - 48 * q^15 - 104 * q^16 - 16 * q^25 - 32 * q^30 + 48 * q^36 - 64 * q^39 - 64 * q^46 + 144 * q^49 + 16 * q^60 - 72 * q^64 + 8 * q^70 - 96 * q^79 + 16 * q^81 - 72 * q^84

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.37073	+	0.347977i	−0.969255	+	0.246057i
$2$	−1.37073	+	0.347977i	−0.969255	+	0.246057i
$3$	−0.973146	−	1.43282i	−0.561846	−	0.827242i
$3$	−0.973146	−	1.43282i	−0.561846	−	0.827242i
$4$	1.75782	−	0.953969i	0.878912	−	0.476984i
$5$	1.31834	+	1.80610i	0.589578	+	0.807712i
$5$	1.31834	+	1.80610i	0.589578	+	0.807712i
$6$	1.83252	+	1.62539i	0.748121	+	0.663562i
$7$	−2.61441	+	0.406058i	−0.988152	+	0.153476i
$7$	−2.61441	+	0.406058i	−0.988152	+	0.153476i
$8$	−2.07755	+	1.91932i	−0.734524	+	0.678582i
$9$	−1.10597	+	2.78870i	−0.368657	+	0.929565i
$10$	−2.43557	−	2.01693i	−0.770195	−	0.637809i
$11$	−2.00814			−0.605476			−0.302738	−	0.953074i	$-0.597901\pi$
$11$	−2.00814			−0.605476			−0.302738	+	0.953074i	$0.597901\pi$
$12$	−3.07749	−	1.59030i	−0.888395	−	0.459080i
$13$		−	1.33017i		−	0.368924i	−0.982840	−	0.184462i	$-0.940946\pi$
$13$		−	1.33017i		−	0.368924i	0.982840	−	0.184462i	$-0.0590543\pi$
$14$	3.44236	−	1.46635i	0.920008	−	0.391899i
$15$	1.30489	−	3.64654i	0.336921	−	0.941533i
$16$	2.17989	−	3.35382i	0.544972	−	0.838455i
$17$		−	4.12882i		−	1.00139i	−0.865625	−	0.500693i	$-0.833078\pi$
$17$		−	4.12882i		−	1.00139i	0.865625	−	0.500693i	$-0.166922\pi$
$18$	0.545590	−	4.20741i	0.128597	−	0.991697i
$19$	2.33202			0.535002			0.267501	−	0.963558i	$-0.413802\pi$
$19$	2.33202			0.535002			0.267501	+	0.963558i	$0.413802\pi$
$20$	4.04036	+	1.91715i	0.903453	+	0.428688i
$21$	3.12601	+	3.35083i	0.682151	+	0.731211i
$22$	2.75262	−	0.698786i	0.586861	−	0.148982i
$23$	−0.0975649			−0.0203437			−0.0101718	−	0.999948i	$-0.503238\pi$
$23$	−0.0975649			−0.0203437			−0.0101718	+	0.999948i	$0.503238\pi$
$24$	4.77181	+	1.10898i	0.974041	+	0.226370i
$25$	−1.52398	+	4.76209i	−0.304796	+	0.952418i
$26$	0.462871	+	1.82332i	0.0907764	+	0.357582i
$27$	5.07198	−	1.12915i	0.976104	−	0.217304i
$28$	−4.20830	+	3.20784i	−0.795293	+	0.606225i
$29$	7.56166			1.40417			0.702083	−	0.712095i	$-0.252254\pi$
$29$	7.56166			1.40417			0.702083	+	0.712095i	$0.252254\pi$
$30$	−0.519740	+	5.45251i	−0.0948911	+	0.995488i
$31$		−	9.48706i		−	1.70393i	−0.523602	−	0.851963i	$-0.675412\pi$
$31$		−	9.48706i		−	1.70393i	0.523602	−	0.851963i	$-0.324588\pi$
$32$	−1.82099	+	5.35574i	−0.321909	+	0.946771i
$33$	1.95421	+	2.87731i	0.340184	+	0.500875i
$34$	1.43674	+	5.65952i	0.246398	+	0.970600i
$35$	−4.18005	−	4.18655i	−0.706557	−	0.707656i
$36$	0.716226	+	5.95710i	0.119371	+	0.992850i
$37$	6.19728			1.01883			0.509413	−	0.860522i	$-0.329863\pi$
$37$	6.19728			1.01883			0.509413	+	0.860522i	$0.329863\pi$
$38$	−3.19658	+	0.811490i	−0.518553	+	0.131641i
$39$	−1.90591	+	1.29445i	−0.305189	+	0.207279i
$40$	−6.20539	−	1.22195i	−0.981158	−	0.193207i
$41$	−5.88262			−0.918711			−0.459355	−	0.888253i	$-0.651920\pi$
$41$	−5.88262			−0.918711			−0.459355	+	0.888253i	$0.651920\pi$
$42$	−5.45094	−	3.50532i	−0.841099	−	0.540882i
$43$	3.65928			0.558035			0.279017	−	0.960286i	$-0.409991\pi$
$43$	3.65928			0.558035			0.279017	+	0.960286i	$0.409991\pi$
$44$	−3.52995	+	1.91570i	−0.532160	+	0.288803i
$45$	−6.49470	+	1.67894i	−0.968173	+	0.250282i
$46$	0.133736	−	0.0339504i	0.0197182	−	0.00500571i
$47$		−	7.79115i		−	1.13646i	−0.822871	−	0.568228i	$-0.807629\pi$
$47$		−	7.79115i		−	1.13646i	0.822871	−	0.568228i	$-0.192371\pi$
$48$	−6.92678	+	0.140362i	−0.999795	+	0.0202595i
$49$	6.67023	−	2.12320i	0.952890	−	0.303315i
$50$	0.431874	−	7.05787i	0.0610762	−	0.998133i
$51$	−5.91588	+	4.01795i	−0.828389	+	0.562626i
$52$	−1.26895	−	2.33821i	−0.175971	−	0.324252i
$53$			2.49399i			0.342576i	0.985221	+	0.171288i	$0.0547928\pi$
$53$			2.49399i			0.342576i	−0.985221	+	0.171288i	$0.945207\pi$
$54$	−6.55942	+	3.31270i	−0.892625	+	0.450801i
$55$	−2.64740	−	3.62689i	−0.356975	−	0.489050i
$56$	4.65220	−	5.86149i	0.621676	−	0.783274i
$57$	−2.26939	−	3.34137i	−0.300589	−	0.442576i
$58$	−10.3650	+	2.63129i	−1.36100	+	0.345505i
$59$		−	1.86318i		−	0.242565i	−0.992618	−	0.121282i	$-0.961299\pi$
$59$		−	1.86318i		−	0.242565i	0.992618	−	0.121282i	$-0.0387007\pi$
$60$	−1.18493	−	7.65480i	−0.152973	−	0.988230i
$61$	11.3191			1.44926			0.724632	−	0.689136i	$-0.242010\pi$
$61$	11.3191			1.44926			0.724632	+	0.689136i	$0.242010\pi$
$62$	3.30128	+	13.0042i	0.419263	+	1.65154i
$63$	1.75909	−	7.73987i	0.221624	−	0.975132i
$64$	0.632417	−	7.97496i	0.0790521	−	0.996870i
$65$	2.40243	−	1.75362i	0.297984	−	0.217509i
$66$	−3.67994	−	3.26400i	−0.452969	−	0.401771i
$67$	−7.33230			−0.895783			−0.447892	−	0.894088i	$-0.647825\pi$
$67$	−7.33230			−0.895783			−0.447892	+	0.894088i	$0.647825\pi$
$68$	−3.93877	−	7.25774i	−0.477646	−	0.880131i
$69$	0.0949450	+	0.139793i	0.0114300	+	0.0168291i
$70$	7.18656	+	4.28409i	0.858958	+	0.512046i
$71$		−	8.88677i		−	1.05467i	−0.849659	−	0.527333i	$-0.823192\pi$
$71$		−	8.88677i		−	1.05467i	0.849659	−	0.527333i	$-0.176808\pi$
$72$	−3.05469	−	7.91637i	−0.359999	−	0.932953i
$73$	6.85080			0.801825			0.400913	−	0.916116i	$-0.368693\pi$
$73$	6.85080			0.801825			0.400913	+	0.916116i	$0.368693\pi$
$74$	−8.49482	+	2.15651i	−0.987503	+	0.250690i
$75$	8.30629	−	2.45061i	0.959128	−	0.282972i
$76$	4.09928	−	2.22467i	0.470219	−	0.255187i
$77$	5.25008	−	0.815421i	0.598303	−	0.0929258i
$78$	2.16205	−	2.43757i	0.244804	−	0.276000i
$79$	10.9789			1.23522			0.617612	−	0.786483i	$-0.288100\pi$
$79$	10.9789			1.23522			0.617612	+	0.786483i	$0.288100\pi$
$80$	8.93115	−	0.484370i	0.998533	−	0.0541542i
$81$	−6.55365	−	6.16844i	−0.728184	−	0.685382i
$82$	8.06351	−	2.04702i	0.890465	−	0.226055i
$83$	10.1647			1.11572			0.557858	−	0.829936i	$-0.311623\pi$
$83$	10.1647			1.11572			0.557858	+	0.829936i	$0.311623\pi$
$84$	8.69156	+	2.90805i	0.948327	+	0.317294i
$85$	7.45706	−	5.44318i	0.808832	−	0.590395i
$86$	−5.01590	+	1.27335i	−0.540878	+	0.137308i
$87$	−7.35861	−	10.8345i	−0.788925	−	1.16158i
$88$	4.17200	−	3.85426i	0.444737	−	0.410865i
$89$	−13.4335			−1.42395			−0.711974	−	0.702206i	$-0.752198\pi$
$89$	−13.4335			−1.42395			−0.711974	+	0.702206i	$0.752198\pi$
$90$	8.31827	−	4.56140i	0.876823	−	0.480813i
$91$	0.540128	+	3.47762i	0.0566209	+	0.364553i
$92$	−0.171502	+	0.0930739i	−0.0178803	+	0.00970363i
$93$	−13.5933	+	9.23230i	−1.40956	+	0.957345i
$94$	2.71114	+	10.6796i	0.279633	+	1.10152i
$95$	3.07438	+	4.21185i	0.315425	+	0.432127i
$96$	9.44593	−	2.60276i	0.964071	−	0.265643i
$97$	9.65918			0.980742			0.490371	−	0.871514i	$-0.336861\pi$
$97$	9.65918			0.980742			0.490371	+	0.871514i	$0.336861\pi$
$98$	−8.40429	+	5.23144i	−0.848961	+	0.528455i
$99$	2.22094	−	5.60008i	0.223213	−	0.562829i
$100$	1.86399	+	9.82474i	0.186399	+	0.982474i
$101$		−	15.6655i		−	1.55878i	−0.626539	−	0.779390i	$-0.715529\pi$
$101$		−	15.6655i		−	1.55878i	0.626539	−	0.779390i	$-0.284471\pi$
$102$	6.71094	−	7.56613i	0.664482	−	0.749159i
$103$	−8.59402			−0.846794			−0.423397	−	0.905944i	$-0.639162\pi$
$103$	−8.59402			−0.846794			−0.423397	+	0.905944i	$0.639162\pi$
$104$	2.55303	+	2.76350i	0.250345	+	0.270984i
$105$	−1.93080	+	10.0634i	−0.188427	+	0.982087i
$106$	−0.867851	−	3.41859i	−0.0842932	−	0.332043i
$107$			2.50519i			0.242186i	0.992641	+	0.121093i	$0.0386399\pi$
$107$			2.50519i			0.242186i	−0.992641	+	0.121093i	$0.961360\pi$
$108$	7.83848	−	6.82336i	0.754258	−	0.656578i
$109$		−	14.4916i		−	1.38804i	−0.719954	−	0.694022i	$-0.755837\pi$
$109$		−	14.4916i		−	1.38804i	0.719954	−	0.694022i	$-0.244163\pi$
$110$	4.89096	+	4.05027i	0.466334	+	0.386178i
$111$	−6.03086	−	8.87961i	−0.572424	−	0.842815i
$112$	−4.33726	+	9.65340i	−0.409833	+	0.912161i
$113$	−14.2102			−1.33678			−0.668390	−	0.743811i	$-0.733016\pi$
$113$	−14.2102			−1.33678			−0.668390	+	0.743811i	$0.733016\pi$
$114$	4.27346	+	3.79043i	0.400246	+	0.355007i
$115$	−0.128623	−	0.176212i	−0.0119942	−	0.0164318i
$116$	13.2921	−	7.21359i	1.23414	−	0.669765i
$117$	3.70945	+	1.47114i	0.342939	+	0.136007i
$118$	0.648343	+	2.55392i	0.0596848	+	0.235107i
$119$	1.67654	+	10.7944i	0.153689	+	0.989523i
$120$	4.28792	+	10.0804i	0.391431	+	0.920207i
$121$	−6.96739			−0.633399
$122$	−15.5155	+	3.93880i	−1.40471	+	0.356602i
$123$	5.72465	+	8.42876i	0.516174	+	0.759996i
$124$	−9.05036	−	16.6766i	−0.812747	−	1.49760i
$125$	−10.6099	+	3.52557i	−0.948980	+	0.315337i
$126$	0.282062	+	11.2214i	0.0251281	+	0.999684i
$127$		−	1.45342i		−	0.128970i	−0.997919	−	0.0644849i	$-0.979460\pi$
$127$		−	1.45342i		−	0.128970i	0.997919	−	0.0644849i	$-0.0205404\pi$
$128$	1.90823	+	11.1516i	0.168665	+	0.985673i
$129$	−3.56101	−	5.24310i	−0.313530	−	0.461629i
$130$	−2.68287	+	3.23973i	−0.235303	+	0.284143i
$131$		−	1.87492i		−	0.163813i	−0.996640	−	0.0819064i	$-0.973899\pi$
$131$		−	1.87492i		−	0.163813i	0.996640	−	0.0819064i	$-0.0261009\pi$
$132$	6.18002	+	3.19354i	0.537902	+	0.277962i
$133$	−6.09684	+	0.946935i	−0.528663	+	0.0821097i
$134$	10.0506	−	2.55148i	0.868243	−	0.220414i
$135$	8.72593	+	7.67191i	0.751008	+	0.660293i
$136$	7.92454	+	8.57783i	0.679523	+	0.735543i
$137$	18.4986			1.58044			0.790222	−	0.612821i	$-0.209965\pi$
$137$	18.4986			1.58044			0.790222	+	0.612821i	$0.209965\pi$
$138$	−0.178789	−	0.158581i	−0.0152196	−	0.0134993i
$139$	0.685361			0.0581315			0.0290658	−	0.999578i	$-0.490747\pi$
$139$	0.685361			0.0581315			0.0290658	+	0.999578i	$0.490747\pi$
$140$	−11.3416	−	3.37158i	−0.958542	−	0.284951i
$141$	−11.1633	+	7.58193i	−0.940124	+	0.638514i
$142$	3.09240	+	12.1814i	0.259508	+	1.02224i
$143$			2.67117i			0.223375i
$144$	6.94189	+	9.78827i	0.578491	+	0.815689i
$145$	9.96881	+	13.6571i	0.827865	+	1.13416i
$146$	−9.39062	+	2.38392i	−0.777174	+	0.197295i
$147$	−9.53329	−	7.49109i	−0.786293	−	0.617854i
$148$	10.8937	−	5.91201i	0.895458	−	0.485964i
$149$	−2.34916			−0.192450			−0.0962252	−	0.995360i	$-0.530677\pi$
$149$	−2.34916			−0.192450			−0.0962252	+	0.995360i	$0.530677\pi$
$150$	−10.5330	+	6.24954i	−0.860013	+	0.510273i
$151$	−8.32682			−0.677627			−0.338814	−	0.940853i	$-0.610026\pi$
$151$	−8.32682			−0.677627			−0.338814	+	0.940853i	$0.610026\pi$
$152$	−4.84488	+	4.47589i	−0.392972	+	0.363043i
$153$	11.5140	+	4.56636i	0.930855	+	0.369169i
$154$	−6.91272	+	2.94464i	−0.557043	+	0.237285i
$155$	17.1346	−	12.5071i	1.37628	−	1.00460i
$156$	−2.11538	+	4.09360i	−0.169366	+	0.327750i
$157$			14.0657i			1.12256i	0.827625	+	0.561281i	$0.189691\pi$
$157$			14.0657i			1.12256i	−0.827625	+	0.561281i	$0.810309\pi$
$158$	−15.0492	+	3.82041i	−1.19725	+	0.303936i
$159$	3.57345	−	2.42702i	0.283393	−	0.192475i
$160$	−12.0737	+	3.77178i	−0.954508	+	0.298185i
$161$	0.255074	−	0.0396171i	0.0201027	−	0.00312226i
$162$	11.1298	+	6.17477i	0.874439	+	0.485135i
$163$	−10.6143			−0.831372			−0.415686	−	0.909508i	$-0.636459\pi$
$163$	−10.6143			−0.831372			−0.415686	+	0.909508i	$0.636459\pi$
$164$	−10.3406	+	5.61184i	−0.807466	+	0.438211i
$165$	−2.62039	+	7.32275i	−0.203997	+	0.570076i
$166$	−13.9330	+	3.53707i	−1.08141	+	0.274530i
$167$		−	0.462349i		−	0.0357776i	−0.999840	−	0.0178888i	$-0.994306\pi$
$167$		−	0.462349i		−	0.0357776i	0.999840	−	0.0178888i	$-0.00569449\pi$
$168$	−12.9258	−	0.961697i	−0.997244	−	0.0741965i
$169$	11.2306			0.863895
$170$	−8.32755	+	10.0560i	−0.638694	+	0.771263i
$171$	−2.57915	+	6.50329i	−0.197232	+	0.497319i
$172$	6.43236	−	3.49084i	0.490463	−	0.266174i
$173$	3.85404			0.293017			0.146508	−	0.989209i	$-0.453196\pi$
$173$	3.85404			0.293017			0.146508	+	0.989209i	$0.453196\pi$
$174$	13.8569	+	12.2906i	1.05049	+	0.931751i
$175$	2.05062	−	13.0689i	0.155012	−	0.987913i
$176$	−4.37751	+	6.73492i	−0.329967	+	0.507664i
$177$	−2.66960	+	1.81314i	−0.200660	+	0.136284i
$178$	18.4137	−	4.67455i	1.38017	−	0.350372i
$179$	13.7858			1.03040			0.515199	−	0.857070i	$-0.327718\pi$
$179$	13.7858			1.03040			0.515199	+	0.857070i	$0.327718\pi$
$180$	−9.81488	+	9.14703i	−0.731558	+	0.681779i
$181$	−23.4970			−1.74652			−0.873260	−	0.487254i	$-0.837999\pi$
$181$	−23.4970			−1.74652			−0.873260	+	0.487254i	$0.837999\pi$
$182$	−1.95050	−	4.57893i	−0.144581	−	0.339413i
$183$	−11.0152	−	16.2183i	−0.814264	−	1.19889i
$184$	0.202696	−	0.187258i	0.0149429	−	0.0138049i
$185$	8.17009	+	11.1929i	0.600677	+	0.822918i
$186$	15.4202	−	17.3852i	1.13066	−	1.27474i
$187$			8.29124i			0.606316i
$188$	−7.43251	−	13.6955i	−0.542072	−	0.998844i
$189$	−12.8017	+	5.01157i	−0.931189	+	0.364538i
$190$	−5.67979	−	4.70351i	−0.412055	−	0.341229i
$191$			13.7417i			0.994314i	0.867661	+	0.497157i	$0.165623\pi$
$191$			13.7417i			0.994314i	−0.867661	+	0.497157i	$0.834377\pi$
$192$	−12.0422	+	6.85467i	−0.869068	+	0.494693i
$193$		−	12.8635i		−	0.925933i	−0.886376	−	0.462967i	$-0.846785\pi$
$193$		−	12.8635i		−	0.925933i	0.886376	−	0.462967i	$-0.153215\pi$
$194$	−13.2402	+	3.36118i	−0.950589	+	0.241319i
$195$	−4.85054	−	1.73573i	−0.347354	−	0.124298i
$196$	9.69962	−	10.0954i	0.692830	−	0.721101i
$197$		−	25.5732i		−	1.82201i	−0.412392	−	0.911006i	$-0.635307\pi$
$197$		−	25.5732i		−	1.82201i	0.412392	−	0.911006i	$-0.364693\pi$
$198$	−1.09562	+	8.44906i	−0.0778623	+	0.600449i
$199$			17.1175i			1.21342i	0.794921	+	0.606712i	$0.207512\pi$
$199$			17.1175i			1.21342i	−0.794921	+	0.606712i	$0.792488\pi$
$200$	−5.97383	−	12.8185i	−0.422413	−	0.906403i
$201$	7.13540	+	10.5059i	0.503293	+	0.741029i
$202$	5.45126	+	21.4733i	0.383549	+	1.51086i
$203$	−19.7693	+	3.07048i	−1.38753	+	0.215505i
$204$	−6.56607	+	12.7064i	−0.459717	+	0.889627i
$205$	−7.75527	−	10.6246i	−0.541651	−	0.742053i
$206$	11.7801	−	2.99053i	0.820760	−	0.208360i
$207$	0.107904	−	0.272079i	0.00749985	−	0.0189108i
$208$	−4.46116	−	2.89963i	−0.309326	−	0.201053i
$209$	−4.68301			−0.323931
$210$	−0.855227	−	14.4661i	−0.0590163	−	0.998257i
$211$			17.3613i			1.19520i	0.801795	+	0.597599i	$0.203879\pi$
$211$			17.3613i			1.19520i	−0.801795	+	0.597599i	$0.796121\pi$
$212$	2.37919	+	4.38399i	0.163403	+	0.301094i
$213$	−12.7332	+	8.64813i	−0.872463	+	0.592560i
$214$	−0.871749	−	3.43395i	−0.0595915	−	0.234740i
$215$	4.82416	+	6.60901i	0.329005	+	0.450731i
$216$	−8.37010	+	12.0806i	−0.569513	+	0.821982i
$217$	3.85230	+	24.8030i	0.261511	+	1.68374i
$218$	5.04275	+	19.8641i	0.341538	+	1.34537i
$219$	−6.66683	−	9.81599i	−0.450503	−	0.663303i
$220$	−8.11360	−	3.84990i	−0.547019	−	0.259560i
$221$	−5.49206			−0.369436
$222$	11.3566	+	10.0730i	0.762206	+	0.676054i
$223$	−6.52959			−0.437253			−0.218627	−	0.975809i	$-0.570158\pi$
$223$	−6.52959			−0.437253			−0.218627	+	0.975809i	$0.570158\pi$
$224$	2.58607	−	14.7415i	0.172789	−	0.984959i
$225$	−11.5945	−	9.51666i	−0.772969	−	0.634444i
$226$	19.4784	−	4.94482i	1.29568	−	0.328924i
$227$	12.4592			0.826949			0.413474	−	0.910516i	$-0.364315\pi$
$227$	12.4592			0.826949			0.413474	+	0.910516i	$0.364315\pi$
$228$	−7.17676	−	3.70861i	−0.475293	−	0.245609i
$229$	3.65759			0.241701			0.120850	−	0.992671i	$-0.461438\pi$
$229$	3.65759			0.241701			0.120850	+	0.992671i	$0.461438\pi$
$230$	0.237626	+	0.196782i	0.0156686	+	0.0129754i
$231$	−6.27745	−	6.72892i	−0.413026	−	0.442731i
$232$	−15.7097	+	14.5133i	−1.03139	+	0.952842i
$233$	−1.23863			−0.0811454			−0.0405727	−	0.999177i	$-0.512918\pi$
$233$	−1.23863			−0.0811454			−0.0405727	+	0.999177i	$0.512918\pi$
$234$	−5.59659	−	0.725730i	−0.365861	−	0.0474424i
$235$	14.0716	−	10.2714i	0.917929	−	0.670029i
$236$	−1.77741	−	3.27513i	−0.115700	−	0.213193i
$237$	−10.6841	−	15.7309i	−0.694006	−	1.02183i
$238$	−6.05431	−	14.2129i	−0.392443	−	0.921284i
$239$		−	19.6091i		−	1.26841i	−0.773165	−	0.634205i	$-0.781328\pi$
$239$		−	19.6091i		−	1.26841i	0.773165	−	0.634205i	$-0.218672\pi$
$240$	−9.38533	−	12.3254i	−0.605821	−	0.795601i
$241$			24.2251i			1.56048i	0.625482	+	0.780239i	$0.284902\pi$
$241$			24.2251i			1.56048i	−0.625482	+	0.780239i	$0.715098\pi$
$242$	9.55043	−	2.42449i	0.613925	−	0.155852i
$243$	−2.46063	+	15.3930i	−0.157849	+	0.987463i
$244$	19.8970	−	10.7981i	1.27378	−	0.691277i
$245$	12.6283	+	9.24800i	0.806794	+	0.590833i
$246$	−10.7800	−	9.56154i	−0.687307	−	0.609621i
$247$		−	3.10199i		−	0.197375i
$248$	18.2087	+	19.7098i	1.15625	+	1.25158i
$249$	−9.89171	−	14.5642i	−0.626861	−	0.922967i
$250$	13.3166	−	8.52463i	0.842213	−	0.539145i
$251$			14.6425i			0.924229i	0.886820	+	0.462115i	$0.152909\pi$
$251$			14.6425i			0.924229i	−0.886820	+	0.462115i	$0.847091\pi$
$252$	−4.29144	−	15.2834i	−0.270335	−	0.962766i
$253$	0.195924			0.0123176
$254$	0.505756	+	1.99225i	0.0317339	+	0.125005i
$255$	−15.0559	−	5.38765i	−0.942839	−	0.337388i
$256$	−6.49619	−	14.6219i	−0.406012	−	0.913868i
$257$			15.8068i			0.986002i	0.870029	+	0.493001i	$0.164100\pi$
$257$			15.8068i			0.986002i	−0.870029	+	0.493001i	$0.835900\pi$
$258$	6.70568	+	5.94775i	0.417478	+	0.370291i
$259$	−16.2022	+	2.51646i	−1.00676	+	0.156365i
$260$	2.55014	−	5.37439i	0.158153	−	0.333305i
$261$	−8.36299	+	21.0872i	−0.517656	+	1.30526i
$262$	0.652431	+	2.57002i	0.0403073	+	0.158777i
$263$	14.2549			0.878997			0.439499	−	0.898243i	$-0.355156\pi$
$263$	14.2549			0.878997			0.439499	+	0.898243i	$0.355156\pi$
$264$	−9.58244	−	2.22699i	−0.589759	−	0.137062i
$265$	−4.50439	+	3.28791i	−0.276702	+	0.201975i
$266$	8.02763	−	3.41956i	0.492206	−	0.209667i
$267$	13.0728	+	19.2478i	0.800040	+	1.17795i
$268$	−12.8889	+	6.99479i	−0.787314	+	0.427275i
$269$		−	9.33525i		−	0.569180i	−0.958649	−	0.284590i	$-0.908142\pi$
$269$		−	9.33525i		−	0.569180i	0.958649	−	0.284590i	$-0.0918575\pi$
$270$	−14.6306	−	7.47972i	−0.890389	−	0.455201i
$271$			0.207201i			0.0125865i	0.999980	+	0.00629327i	$0.00200322\pi$
$271$			0.207201i			0.0125865i	−0.999980	+	0.00629327i	$0.997997\pi$
$272$	−13.8473	−	9.00037i	−0.839617	−	0.545727i
$273$	4.45719	−	4.15814i	0.269761	−	0.251662i
$274$	−25.3567	+	6.43710i	−1.53185	+	0.388880i
$275$	3.06036	−	9.56292i	0.184547	−	0.576666i
$276$	0.300255	+	0.155158i	0.0180732	+	0.00933939i
$277$	28.6571			1.72184			0.860918	−	0.508744i	$-0.169890\pi$
$277$	28.6571			1.72184			0.860918	+	0.508744i	$0.169890\pi$
$278$	−0.939447	+	0.238490i	−0.0563443	+	0.0143037i
$279$	26.4565	+	10.4924i	1.58391	+	0.628165i
$280$	16.7196	+	0.674917i	0.999186	+	0.0403340i
$281$			3.11015i			0.185536i	0.995688	+	0.0927681i	$0.0295715\pi$
$281$			3.11015i			0.185536i	−0.995688	+	0.0927681i	$0.970428\pi$
$282$	12.6636	−	14.2774i	0.754109	−	0.850207i
$283$		−	20.5801i		−	1.22336i	−0.791106	−	0.611679i	$-0.790495\pi$
$283$		−	20.5801i		−	1.22336i	0.791106	−	0.611679i	$-0.209505\pi$
$284$	−8.47770	−	15.6214i	−0.503059	−	0.926958i
$285$	3.04302	−	8.50380i	0.180253	−	0.503722i
$286$	−0.929508	−	3.66147i	−0.0549629	−	0.216507i
$287$	15.3796	−	2.38869i	0.907826	−	0.141000i
$288$	−12.9216	−	11.0015i	−0.761411	−	0.648269i
$289$	−0.0471902			−0.00277589
$290$	−18.4170	−	15.2513i	−1.08148	−	0.895589i
$291$	−9.39980	−	13.8399i	−0.551026	−	0.811310i
$292$	12.0425	−	6.53545i	0.704734	−	0.382458i
$293$	−11.9389			−0.697476			−0.348738	−	0.937220i	$-0.613390\pi$
$293$	−11.9389			−0.697476			−0.348738	+	0.937220i	$0.613390\pi$
$294$	15.6743	+	6.95092i	0.914146	+	0.405386i
$295$	3.36508	−	2.45629i	0.195922	−	0.143011i
$296$	−12.8751	+	11.8946i	−0.748353	+	0.691357i
$297$	−10.1852	+	2.26748i	−0.591007	+	0.131573i
$298$	3.22007	−	0.817453i	0.186534	−	0.0473538i
$299$			0.129778i			0.00750528i
$300$	12.2632	−	12.2317i	0.708016	−	0.706197i
$301$	−9.56684	+	1.48588i	−0.551423	+	0.0856447i
$302$	11.4139	−	2.89755i	0.656794	−	0.166735i
$303$	−22.4460	+	15.2449i	−1.28949	+	0.875795i
$304$	5.08353	−	7.82116i	0.291561	−	0.448574i
$305$	14.9224	+	20.4434i	0.854454	+	1.17059i
$306$	−17.3717	−	2.25265i	−0.993072	−	0.128775i
$307$		−	7.70581i		−	0.439794i	−0.975523	−	0.219897i	$-0.929428\pi$
$307$		−	7.70581i		−	0.439794i	0.975523	−	0.219897i	$-0.0705721\pi$
$308$	8.45083	−	6.44178i	0.481531	−	0.367055i
$309$	8.36324	+	12.3137i	0.475768	+	0.700503i
$310$	−19.1347	+	23.1064i	−1.08678	+	1.31236i
$311$	26.8427			1.52211			0.761054	−	0.648688i	$-0.224682\pi$
$311$	26.8427			1.52211			0.761054	+	0.648688i	$0.224682\pi$
$312$	1.47514	−	6.34734i	0.0835134	−	0.359347i
$313$	−8.20422			−0.463730			−0.231865	−	0.972748i	$-0.574483\pi$
$313$	−8.20422			−0.463730			−0.231865	+	0.972748i	$0.574483\pi$
$314$	−4.89454	−	19.2803i	−0.276215	−	1.08805i
$315$	16.2980	−	7.02667i	0.918290	−	0.395908i
$316$	19.2990	−	10.4735i	1.08565	−	0.589183i
$317$		−	30.7315i		−	1.72605i	−0.505159	−	0.863026i	$-0.668566\pi$
$317$		−	30.7315i		−	1.72605i	0.505159	−	0.863026i	$-0.331434\pi$
$318$	−4.05370	+	4.57027i	−0.227320	+	0.256288i
$319$	−15.1849			−0.850189
$320$	15.2373	−	9.37147i	0.851791	−	0.523881i
$321$	3.58949	−	2.43791i	0.200346	−	0.136071i
$322$	−0.335853	+	0.143065i	−0.0187164	+	0.00797267i
$323$		−	9.62849i		−	0.535744i
$324$	−17.4047	−	4.59105i	−0.966926	−	0.255058i
$325$	6.33441	+	2.02716i	0.351370	+	0.112447i
$326$	14.5493	−	3.69352i	0.805812	−	0.204565i
$327$	−20.7639	+	14.1025i	−1.14825	+	0.779867i
$328$	12.2214	−	11.2906i	0.674815	−	0.623421i
$329$	3.16366	+	20.3692i	0.174418	+	1.12299i
$330$	1.04371	−	10.9494i	0.0574543	−	0.602744i
$331$			20.3258i			1.11721i	0.829434	+	0.558604i	$0.188663\pi$
$331$			20.3258i			1.11721i	−0.829434	+	0.558604i	$0.811337\pi$
$332$	17.8677	−	9.69677i	0.980617	−	0.532180i
$333$	−6.85402	+	17.2823i	−0.375598	+	0.947066i
$334$	0.160887	+	0.633758i	0.00880335	+	0.0346777i
$335$	−9.66644	−	13.2429i	−0.528134	−	0.723535i
$336$	18.0524	−	3.17964i	0.984840	−	0.173464i
$337$			8.04781i			0.438392i	0.975681	+	0.219196i	$0.0703434\pi$
$337$			8.04781i			0.438392i	−0.975681	+	0.219196i	$0.929657\pi$
$338$	−15.3942	+	3.90801i	−0.837335	+	0.212568i
$339$	13.8286	+	20.3607i	0.751065	+	1.10584i
$340$	7.91558	−	16.6819i	0.429282	−	0.904706i
$341$			19.0513i			1.03169i
$342$	1.27233	−	9.81176i	0.0687995	−	0.530559i
$343$	−16.5766	+	8.25942i	−0.895050	+	0.445967i
$344$	−7.60233	+	7.02333i	−0.409890	+	0.378672i
$345$	−0.127311	+	0.355775i	−0.00685421	+	0.0191543i
$346$	−5.28286	+	1.34112i	−0.284008	+	0.0720989i
$347$			20.1082i			1.07946i	0.841837	+	0.539732i	$0.181475\pi$
$347$			20.1082i			1.07946i	−0.841837	+	0.539732i	$0.818525\pi$
$348$	−23.2709	−	12.0253i	−1.24745	−	0.644625i
$349$	2.29568			0.122885			0.0614423	−	0.998111i	$-0.480430\pi$
$349$	2.29568			0.122885			0.0614423	+	0.998111i	$0.480430\pi$
$350$	1.73681	+	18.6275i	0.0928365	+	0.995681i
$351$	−1.50196	−	6.74662i	−0.0801688	−	0.360108i
$352$	3.65680	−	10.7551i	0.194908	−	0.573247i
$353$			15.2039i			0.809221i	0.914489	+	0.404610i	$0.132593\pi$
$353$			15.2039i			0.809221i	−0.914489	+	0.404610i	$0.867407\pi$
$354$	3.02838	−	3.41430i	0.160957	−	0.181468i
$355$	16.0504	−	11.7157i	0.851866	−	0.621807i
$356$	−23.6137	+	12.8151i	−1.25152	+	0.679201i
$357$	13.8350	−	12.9067i	0.732225	−	0.683097i
$358$	−18.8967	+	4.79715i	−0.998719	+	0.253537i
$359$			29.0532i			1.53337i	0.642023	+	0.766685i	$0.278095\pi$
$359$			29.0532i			1.53337i	−0.642023	+	0.766685i	$0.721905\pi$
$360$	10.2706	−	15.9535i	0.541310	−	0.840823i
$361$	−13.5617			−0.713773
$362$	32.2082	−	8.17644i	1.69282	−	0.429744i
$363$	6.78029	+	9.98304i	0.355873	+	0.523974i
$364$	4.26699	+	5.59777i	0.223651	+	0.293403i
$365$	9.03165	+	12.3732i	0.472738	+	0.647644i
$366$	20.7425	+	18.3980i	1.08423	+	0.961677i
$367$	7.34446			0.383378			0.191689	−	0.981456i	$-0.438604\pi$
$367$	7.34446			0.383378			0.191689	+	0.981456i	$0.438604\pi$
$368$	−0.212680	+	0.327215i	−0.0110867	+	0.0170573i
$369$	6.50601	−	16.4048i	0.338689	−	0.854002i
$370$	−15.0939	−	12.4995i	−0.784694	−	0.649817i
$371$	−1.01270	−	6.52030i	−0.0525770	−	0.338517i
$372$	−15.0873	+	29.1963i	−0.782239	+	1.51376i
$373$	19.5085			1.01011			0.505056	−	0.863086i	$-0.331472\pi$
$373$	19.5085			1.01011			0.505056	+	0.863086i	$0.331472\pi$
$374$	−2.88517	−	11.3651i	−0.149188	−	0.587675i
$375$	15.3765	+	11.7713i	0.794041	+	0.607865i
$376$	14.9537	+	16.1865i	0.771179	+	0.834755i
$377$		−	10.0583i		−	0.518030i
$378$	15.8038	−	11.3242i	0.812862	−	0.582456i
$379$		−	3.57410i		−	0.183589i	−0.995778	−	0.0917945i	$-0.970740\pi$
$379$		−	3.57410i		−	0.183589i	0.995778	−	0.0917945i	$-0.0292603\pi$
$380$	9.42220	+	4.47083i	0.483349	+	0.229349i
$381$	−2.08249	+	1.41439i	−0.106689	+	0.0724612i
$382$	−4.78180	−	18.8362i	−0.244658	−	0.963744i
$383$		−	14.6339i		−	0.747757i	−0.927478	−	0.373878i	$-0.878028\pi$
$383$		−	14.6339i		−	0.747757i	0.927478	−	0.373878i	$-0.121972\pi$
$384$	14.1213	−	13.5863i	0.720626	−	0.693324i
$385$	8.39410	+	8.40717i	0.427803	+	0.428469i
$386$	4.47620	+	17.6324i	0.227833	+	0.897466i
$387$	−4.04706	+	10.2046i	−0.205724	+	0.518730i
$388$	16.9791	−	9.21456i	0.861985	−	0.467798i
$389$	13.4414			0.681507			0.340754	−	0.940153i	$-0.389318\pi$
$389$	13.4414			0.681507			0.340754	+	0.940153i	$0.389318\pi$
$390$	7.25279	+	0.691345i	0.367259	+	0.0350076i
$391$			0.402828i			0.0203719i
$392$	−9.78263	+	17.2134i	−0.494097	+	0.869407i
$393$	−2.68644	+	1.82458i	−0.135513	+	0.0920377i
$394$	8.89888	+	35.0540i	0.448319	+	1.76600i
$395$	14.4739	+	19.8290i	0.728260	+	0.997705i
$396$	−1.43828	−	11.9627i	−0.0722763	−	0.601147i
$397$			7.47449i			0.375134i	0.982252	+	0.187567i	$0.0600601\pi$
$397$			7.47449i			0.375134i	−0.982252	+	0.187567i	$0.939940\pi$
$398$	−5.95649	−	23.4635i	−0.298572	−	1.17612i
$399$	7.28991	+	7.81419i	0.364952	+	0.391199i
$400$	12.6491	+	15.4920i	0.632454	+	0.774598i
$401$		−	30.4076i		−	1.51848i	−0.650808	−	0.759242i	$-0.725570\pi$
$401$		−	30.4076i		−	1.51848i	0.650808	−	0.759242i	$-0.274430\pi$
$402$	−13.4366	−	11.9178i	−0.670155	−	0.594408i
$403$	−12.6194			−0.628619
$404$	−14.9444	−	27.5373i	−0.743514	−	1.37003i
$405$	2.50089	−	19.9686i	0.124270	−	0.992248i
$406$	26.0299	−	11.0881i	1.29184	−	0.550291i
$407$	−12.4450			−0.616875
$408$	4.57879	−	19.7020i	0.226684	−	0.975392i
$409$		−	24.7533i		−	1.22397i	−0.790868	−	0.611986i	$-0.790371\pi$
$409$		−	24.7533i		−	1.22397i	0.790868	−	0.611986i	$-0.209629\pi$
$410$	14.3275	+	11.8648i	0.707586	+	0.585962i
$411$	−18.0019	−	26.5053i	−0.887967	−	1.30741i
$412$	−15.1068	+	8.19843i	−0.744257	+	0.403908i
$413$	0.756558	+	4.87110i	0.0372278	+	0.239691i
$414$	−0.0532304	+	0.410496i	−0.00261613	+	0.0201748i
$415$	13.4004	+	18.3584i	0.657802	+	0.901177i
$416$	7.12407	+	2.42224i	0.349286	+	0.118760i
$417$	−0.666956	−	0.982002i	−0.0326610	−	0.0480888i
$418$	6.41916	−	1.62958i	0.313971	−	0.0797055i
$419$		−	11.5934i		−	0.566374i	−0.959065	−	0.283187i	$-0.908608\pi$
$419$		−	11.5934i		−	0.566374i	0.959065	−	0.283187i	$-0.0913918\pi$
$420$	6.20617	+	19.5316i	0.302830	+	0.953045i
$421$			12.7176i			0.619816i	0.950767	+	0.309908i	$0.100298\pi$
$421$			12.7176i			0.619816i	−0.950767	+	0.309908i	$0.899702\pi$
$422$	−6.04133	−	23.7977i	−0.294087	−	1.15845i
$423$	21.7271	+	8.61679i	1.05641	+	0.418963i
$424$	−4.78676	−	5.18138i	−0.232466	−	0.251630i
$425$	19.6618	+	6.29225i	0.953739	+	0.305219i
$426$	14.4445	−	16.2851i	0.699836	−	0.789018i
$427$	−29.5928	+	4.59622i	−1.43209	+	0.222427i
$428$	2.38987	+	4.40368i	0.115519	+	0.212860i
$429$	3.82732	−	2.59944i	0.184785	−	0.125502i
$430$	−8.91242	−	7.38050i	−0.429795	−	0.355919i
$431$		−	2.50836i		−	0.120823i	−0.998174	−	0.0604117i	$-0.980759\pi$
$431$		−	2.50836i		−	0.120823i	0.998174	−	0.0604117i	$-0.0192414\pi$
$432$	7.26940	−	19.4719i	0.349749	−	0.936843i
$433$	−24.6527			−1.18473			−0.592366	−	0.805669i	$-0.701806\pi$
$433$	−24.6527			−1.18473			−0.592366	+	0.805669i	$0.701806\pi$
$434$	−13.9114	−	32.6578i	−0.667767	−	1.56763i
$435$	9.86712	−	27.5739i	0.473092	−	1.32207i
$436$	−13.8245	−	25.4737i	−0.662075	−	1.21997i
$437$	−0.227523			−0.0108839
$438$	12.5542	+	11.1352i	0.599863	+	0.532061i
$439$			5.50924i			0.262942i	0.991320	+	0.131471i	$0.0419700\pi$
$439$			5.50924i			0.262942i	−0.991320	+	0.131471i	$0.958030\pi$
$440$	12.4613	+	2.45384i	0.594068	+	0.116982i
$441$	−1.45612	+	20.9495i	−0.0693392	+	0.997593i
$442$	7.52815	−	1.91111i	0.358078	−	0.0909023i
$443$		−	13.1356i		−	0.624093i	−0.950067	−	0.312047i	$-0.898986\pi$
$443$		−	13.1356i		−	0.624093i	0.950067	−	0.312047i	$-0.101014\pi$
$444$	−19.0721	−	9.85554i	−0.905120	−	0.467723i
$445$	−17.7099	−	24.2622i	−0.839527	−	1.15014i
$446$	8.95033	−	2.27215i	0.423810	−	0.107589i
$447$	2.28607	+	3.36593i	0.108128	+	0.159203i
$448$	1.58491	+	21.1066i	0.0748798	+	0.997193i
$449$		−	10.4000i		−	0.490806i	−0.969421	−	0.245403i	$-0.921080\pi$
$449$		−	10.4000i		−	0.490806i	0.969421	−	0.245403i	$-0.0789203\pi$
$450$	19.2046	+	9.01017i	0.905314	+	0.424743i
$451$	11.8131			0.556257
$452$	−24.9790	+	13.5561i	−1.17491	+	0.637624i
$453$	8.10322	+	11.9309i	0.380722	+	0.560562i
$454$	−17.0783	+	4.33553i	−0.801524	+	0.203477i
$455$	−5.56884	+	5.56019i	−0.261071	+	0.260666i
$456$	11.1279	+	2.58617i	0.521114	+	0.121108i
$457$		−	40.4322i		−	1.89134i	−0.325129	−	0.945670i	$-0.605408\pi$
$457$		−	40.4322i		−	1.89134i	0.325129	−	0.945670i	$-0.394592\pi$
$458$	−5.01359	+	1.27276i	−0.234270	+	0.0594722i
$459$	−4.66205	−	20.9413i	−0.217606	−	0.977458i
$460$	−0.394198	−	0.187047i	−0.0183796	−	0.00872109i
$461$			18.2567i			0.850301i	0.905123	+	0.425151i	$0.139779\pi$
$461$			18.2567i			0.850301i	−0.905123	+	0.425151i	$0.860221\pi$
$462$	10.9462	+	7.03915i	0.509265	+	0.327491i
$463$		−	42.1208i		−	1.95752i	−0.205016	−	0.978759i	$-0.565725\pi$
$463$		−	42.1208i		−	1.95752i	0.205016	−	0.978759i	$-0.434275\pi$
$464$	16.4836	−	25.3604i	0.765230	−	1.17733i
$465$	−34.5950	−	12.3796i	−1.60430	−	0.574088i
$466$	1.69783	−	0.431015i	0.0786506	−	0.0199664i
$467$	−32.5243			−1.50504			−0.752521	−	0.658568i	$-0.771163\pi$
$467$	−32.5243			−1.50504			−0.752521	+	0.658568i	$0.771163\pi$
$468$	7.92398	−	0.952706i	0.366286	−	0.0440388i
$469$	19.1696	−	2.97734i	0.885170	−	0.137481i
$470$	−15.7142	+	18.9759i	−0.724842	+	0.875292i
$471$	20.1536	−	13.6880i	0.928631	−	0.630708i
$472$	3.57603	+	3.87084i	0.164600	+	0.178170i
$473$	−7.34833			−0.337877
$474$	20.1190	+	17.8450i	0.924097	+	0.819648i
$475$	−3.55395	+	11.1053i	−0.163066	+	0.509545i
$476$	13.2446	+	17.3753i	0.607066	+	0.796396i
$477$	−6.95497	−	2.75828i	−0.318446	−	0.126293i
$478$	6.82354	+	26.8789i	0.312101	+	1.22941i
$479$	−15.9517			−0.728852			−0.364426	−	0.931232i	$-0.618735\pi$
$479$	−15.9517			−0.728852			−0.364426	+	0.931232i	$0.618735\pi$
$480$	17.1538	+	13.6290i	0.782958	+	0.622074i
$481$		−	8.24346i		−	0.375869i
$482$	−8.42980	−	33.2062i	−0.383967	−	1.51250i
$483$	−0.304989	−	0.326923i	−0.0138775	−	0.0148755i
$484$	−12.2474	+	6.64667i	−0.556702	+	0.302121i
$485$	12.7340	+	17.4454i	0.578223	+	0.792156i
$486$	−1.98356	−	21.9560i	−0.0899762	−	0.995944i
$487$		−	8.42432i		−	0.381742i	−0.981615	−	0.190871i	$-0.938869\pi$
$487$		−	8.42432i		−	0.381742i	0.981615	−	0.190871i	$-0.0611313\pi$
$488$	−23.5160	+	21.7250i	−1.06452	+	0.983445i
$489$	10.3292	+	15.2084i	0.467104	+	0.687746i
$490$	−20.5282	−	8.28218i	−0.927368	−	0.374151i
$491$	−16.9685			−0.765777			−0.382888	−	0.923795i	$-0.625071\pi$
$491$	−16.9685			−0.765777			−0.382888	+	0.923795i	$0.625071\pi$
$492$	18.1037	+	9.35513i	0.816178	+	0.421762i
$493$		−	31.2208i		−	1.40611i
$494$	1.07942	+	4.25200i	0.0485655	+	0.191307i
$495$	13.0422	−	3.37155i	0.586205	−	0.151540i
$496$	−31.8179	−	20.6807i	−1.42866	−	0.928592i
$497$	3.60855	+	23.2336i	0.161865	+	1.04217i
$498$	18.6269	+	16.5215i	0.834692	+	0.740347i
$499$			34.6615i			1.55166i	0.630940	+	0.775831i	$0.282669\pi$
$499$			34.6615i			1.55166i	−0.630940	+	0.775831i	$0.717331\pi$
$500$	−15.2871	+	16.3189i	−0.683659	+	0.729802i
$501$	−0.662465	+	0.449933i	−0.0295968	+	0.0201015i
$502$	−5.09528	−	20.0710i	−0.227413	−	0.895814i
$503$			20.2162i			0.901396i	0.892676	+	0.450698i	$0.148825\pi$
$503$			20.2162i			0.901396i	−0.892676	+	0.450698i	$0.851175\pi$
$504$	11.2007	+	19.4562i	0.498919	+	0.866648i
$505$	28.2935	−	20.6524i	1.25904	−	0.919022i
$506$	−0.268559	+	0.0681770i	−0.0119389	+	0.00303084i
$507$	−10.9291	−	16.0915i	−0.485376	−	0.714650i
$508$	−1.38651	−	2.55485i	−0.0615166	−	0.113353i
$509$			2.33728i			0.103598i	0.998658	+	0.0517992i	$0.0164956\pi$
$509$			2.33728i			0.103598i	−0.998658	+	0.0517992i	$0.983504\pi$
$510$	22.5125	+	2.14591i	0.996868	+	0.0950227i
$511$	−17.9108	+	2.78182i	−0.792326	+	0.123061i
$512$	13.9926	+	17.7822i	0.618393	+	0.785869i
$513$	11.8280	−	2.63319i	0.522217	−	0.116258i
$514$	−5.50041	−	21.6669i	−0.242613	−	0.955687i
$515$	−11.3298	−	15.5216i	−0.499251	−	0.683966i
$516$	−11.2614	−	5.81935i	−0.495755	−	0.256183i
$517$			15.6457i			0.688097i
$518$	21.3332	−	9.08739i	0.937329	−	0.399277i
$519$	−3.75054	−	5.52216i	−0.164631	−	0.242396i
$520$	−1.62540	+	8.25425i	−0.0712787	+	0.361973i
$521$	18.0595			0.791203			0.395601	−	0.918422i	$-0.370536\pi$
$521$	18.0595			0.791203			0.395601	+	0.918422i	$0.370536\pi$
$522$	4.12557	−	31.8150i	0.180571	−	1.39251i
$523$		−	15.6316i		−	0.683522i	−0.939787	−	0.341761i	$-0.888977\pi$
$523$		−	15.6316i		−	0.683522i	0.939787	−	0.341761i	$-0.111023\pi$
$524$	−1.78862	−	3.29579i	−0.0781362	−	0.143977i
$525$	−20.7209	+	9.77973i	−0.904335	+	0.426822i
$526$	−19.5397	+	4.96040i	−0.851973	+	0.216284i
$527$	−39.1704			−1.70629
$528$	13.9099	−	0.281865i	0.605352	−	0.0122666i
$529$	−22.9905			−0.999586
$530$	5.03020	−	6.07428i	0.218498	−	0.263850i
$531$	5.19583	+	2.06062i	0.225480	+	0.0894233i
$532$	−9.81382	+	7.48074i	−0.425483	+	0.324331i
$533$			7.82491i			0.338934i
$534$	−24.6171	−	21.8346i	−1.06529	−	0.944877i
$535$	−4.52462	+	3.30268i	−0.195616	+	0.142787i
$536$	15.2332	−	14.0730i	0.657975	−	0.607863i
$537$	−13.4156	−	19.7526i	−0.578926	−	0.852389i
$538$	3.24846	+	12.7961i	0.140051	+	0.551681i
$539$	−13.3947	+	4.26368i	−0.576952	+	0.183650i
$540$	22.6574	+	5.16160i	0.975019	+	0.222120i
$541$		−	14.7905i		−	0.635895i	−0.948108	−	0.317948i	$-0.897006\pi$
$541$		−	14.7905i		−	0.635895i	0.948108	−	0.317948i	$-0.102994\pi$
$542$	−0.0721011	−	0.284017i	−0.00309701	−	0.0121996i
$543$	22.8661	+	33.6671i	0.981276	+	1.44479i
$544$	22.1129	+	7.51855i	0.948084	+	0.322355i
$545$	26.1733	−	19.1048i	1.12114	−	0.818360i
$546$	−4.66268	+	7.25070i	−0.199544	+	0.310301i
$547$	−35.5600			−1.52043			−0.760217	−	0.649669i	$-0.774908\pi$
$547$	−35.5600			−1.52043			−0.760217	+	0.649669i	$0.774908\pi$
$548$	32.5173	−	17.6471i	1.38907	−	0.753847i
$549$	−12.5186	+	31.5656i	−0.534282	+	1.34719i
$550$	−0.867262	+	14.1732i	−0.0369802	+	0.604346i
$551$	17.6339			0.751231
$552$	−0.465561	−	0.108198i	−0.0198156	−	0.00460520i
$553$	−28.7033	+	4.45808i	−1.22059	+	0.189577i
$554$	−39.2812	+	9.97201i	−1.66890	+	0.423670i
$555$	8.08675	−	22.5986i	0.343264	−	0.959259i
$556$	1.20474	−	0.653813i	0.0510925	−	0.0277278i
$557$			1.35270i			0.0573158i	0.999589	+	0.0286579i	$0.00912334\pi$
$557$			1.35270i			0.0573158i	−0.999589	+	0.0286579i	$0.990877\pi$
$558$	−39.9160	−	5.17605i	−1.68978	−	0.219119i
$559$		−	4.86748i		−	0.205872i
$560$	−23.1530	+	4.89291i	−0.978391	+	0.206763i
$561$	11.8799	−	8.06859i	0.501570	−	0.340656i
$562$	−1.08226	−	4.26319i	−0.0456525	−	0.179832i
$563$	30.5252			1.28649			0.643243	−	0.765662i	$-0.277589\pi$
$563$	30.5252			1.28649			0.643243	+	0.765662i	$0.277589\pi$
$564$	−12.3903	+	23.9772i	−0.521725	+	1.00962i
$565$	−18.7338	−	25.6650i	−0.788136	−	1.07973i
$566$	7.16140	+	28.2098i	0.301016	+	1.18575i
$567$	19.6387	+	13.4656i	0.824746	+	0.565504i
$568$	17.0566	+	18.4627i	0.715677	+	0.774678i
$569$		−	15.3875i		−	0.645079i	−0.946556	−	0.322539i	$-0.895464\pi$
$569$		−	15.3875i		−	0.645079i	0.946556	−	0.322539i	$-0.104536\pi$
$570$	−1.21204	+	12.7154i	−0.0507669	+	0.532587i
$571$			42.4541i			1.77665i	0.459217	+	0.888324i	$0.348130\pi$
$571$			42.4541i			1.77665i	−0.459217	+	0.888324i	$0.651870\pi$
$572$	2.54822	+	4.69545i	0.106546	+	0.196327i
$573$	19.6894	−	13.3727i	0.822538	−	0.558652i
$574$	−20.2501	+	8.62599i	−0.845221	+	0.360042i
$575$	0.148687	−	0.464613i	0.00620068	−	0.0193757i
$576$	21.5403	+	10.5837i	0.897513	+	0.440988i
$577$	0.806615			0.0335798			0.0167899	−	0.999859i	$-0.494655\pi$
$577$	0.806615			0.0335798			0.0167899	+	0.999859i	$0.494655\pi$
$578$	0.0646852	−	0.0164211i	0.00269055	−	0.000683028i
$579$	−18.4311	+	12.5180i	−0.765971	+	0.520232i
$580$	30.5519	+	14.4968i	1.26860	+	0.601949i
$581$	−26.5746	+	4.12745i	−1.10250	+	0.171235i
$582$	17.7006	+	15.6999i	0.733714	+	0.650783i
$583$		−	5.00827i		−	0.207421i
$584$	−14.2329	+	13.1489i	−0.588960	+	0.544105i
$585$	2.23329	+	8.63909i	0.0923351	+	0.357182i
$586$	16.3650	−	4.15446i	0.676033	−	0.171619i
$587$	−2.83907			−0.117181			−0.0585905	−	0.998282i	$-0.518661\pi$
$587$	−2.83907			−0.117181			−0.0585905	+	0.998282i	$0.518661\pi$
$588$	−23.9041	−	4.07354i	−0.985789	−	0.167990i
$589$		−	22.1240i		−	0.911603i
$590$	−3.75789	+	4.53789i	−0.154710	+	0.186822i
$591$	−36.6419	+	24.8864i	−1.50724	+	1.02369i
$592$	13.5094	−	20.7845i	0.555231	−	0.854239i
$593$		−	32.6365i		−	1.34022i	−0.742262	−	0.670110i	$-0.766247\pi$
$593$		−	32.6365i		−	1.34022i	0.742262	−	0.670110i	$-0.233753\pi$
$594$	13.1722	−	6.65234i	0.540463	−	0.272949i
$595$	−17.2855	+	17.2587i	−0.708638	+	0.707537i
$596$	−4.12940	+	2.24102i	−0.169147	+	0.0917958i
$597$	24.5263	−	16.6578i	1.00380	−	0.681758i
$598$	−0.0451599	−	0.177892i	−0.00184673	−	0.00727453i
$599$		−	38.2058i		−	1.56105i	−0.625128	−	0.780523i	$-0.714953\pi$
$599$		−	38.2058i		−	1.56105i	0.625128	−	0.780523i	$-0.285047\pi$
$600$	−12.5532	+	21.0337i	−0.512483	+	0.858697i
$601$		−	36.9925i		−	1.50896i	−0.656325	−	0.754479i	$-0.727890\pi$
$601$		−	36.9925i		−	1.50896i	0.656325	−	0.754479i	$-0.272110\pi$
$602$	12.5965	−	5.36579i	0.513396	−	0.218693i
$603$	8.10932	−	20.4476i	0.330237	−	0.832689i
$604$	−14.6371	+	7.94353i	−0.595575	+	0.323218i
$605$	−9.18536	−	12.5838i	−0.373438	−	0.511604i
$606$	25.4626	−	28.7074i	1.03435	−	1.16616i
$607$	29.2308			1.18644			0.593220	−	0.805041i	$-0.297857\pi$
$607$	29.2308			1.18644			0.593220	+	0.805041i	$0.297857\pi$
$608$	−4.24658	+	12.4897i	−0.172222	+	0.506524i
$609$	23.6378	+	25.3378i	0.957853	+	1.02674i
$610$	−27.5685	−	22.8299i	−1.11622	−	0.924354i
$611$	−10.3636			−0.419266
$612$	24.5958	−	2.95717i	0.994227	−	0.119537i
$613$	−1.66640			−0.0673052			−0.0336526	−	0.999434i	$-0.510714\pi$
$613$	−1.66640			−0.0673052			−0.0336526	+	0.999434i	$0.510714\pi$
$614$	2.68145	+	10.5626i	0.108214	+	0.426273i
$615$	−7.67616	+	21.4512i	−0.309533	+	0.864997i
$616$	−9.34225	+	11.7707i	−0.376410	+	0.474254i
$617$	−21.0418			−0.847111			−0.423556	−	0.905870i	$-0.639218\pi$
$617$	−21.0418			−0.847111			−0.423556	+	0.905870i	$0.639218\pi$
$618$	−15.7487	−	13.9686i	−0.633505	−	0.561900i
$619$	−8.07998			−0.324762			−0.162381	−	0.986728i	$-0.551917\pi$
$619$	−8.07998			−0.324762			−0.162381	+	0.986728i	$0.551917\pi$
$620$	18.1881	−	38.3312i	0.730453	−	1.53942i
$621$	−0.494848	+	0.110165i	−0.0198576	+	0.00442077i
$622$	−36.7942	+	9.34065i	−1.47531	+	0.374526i
$623$	35.1206	−	5.45478i	1.40708	−	0.218541i
$624$	0.186706	+	9.21383i	0.00747420	+	0.368848i
$625$	−20.3550	−	14.5147i	−0.814198	−	0.580587i
$626$	11.2458	−	2.85488i	0.449473	−	0.114104i
$627$	4.55725	+	6.70993i	0.181999	+	0.267969i
$628$	13.4182	+	24.7250i	0.535445	+	0.986634i
$629$		−	25.5875i		−	1.02024i
$630$	−19.8951	+	15.3030i	−0.792642	+	0.609688i
$631$	−27.5940			−1.09850			−0.549250	−	0.835658i	$-0.685087\pi$
$631$	−27.5940			−1.09850			−0.549250	+	0.835658i	$0.685087\pi$
$632$	−22.8092	+	21.0720i	−0.907302	+	0.838201i
$633$	24.8756	−	16.8951i	0.988718	−	0.671518i
$634$	10.6939	+	42.1247i	0.424708	+	1.67299i
$635$	2.62501	−	1.91609i	0.104170	−	0.0760377i
$636$	3.96619	−	7.67522i	0.157270	−	0.304342i
$637$	−2.82423	−	8.87257i	−0.111900	−	0.351544i
$638$	20.8144	−	5.28399i	0.824050	−	0.209195i
$639$	24.7825	+	9.82852i	0.980381	+	0.388810i
$640$	−17.6252	+	18.1480i	−0.696698	+	0.717364i
$641$			26.2441i			1.03658i	0.855205	+	0.518290i	$0.173431\pi$
$641$			26.2441i			1.03658i	−0.855205	+	0.518290i	$0.826569\pi$
$642$	−4.07190	+	4.59080i	−0.160705	+	0.181184i
$643$		−	10.0020i		−	0.394440i	−0.980359	−	0.197220i	$-0.936809\pi$
$643$		−	10.0020i		−	0.394440i	0.980359	−	0.197220i	$-0.0631913\pi$
$644$	0.410582	−	0.312973i	0.0161792	−	0.0123329i
$645$	4.77495	−	13.3437i	0.188013	−	0.525408i
$646$	3.35050	+	13.1981i	0.131824	+	0.519272i
$647$			39.2518i			1.54315i	0.636140	+	0.771573i	$0.280530\pi$
$647$			39.2518i			1.54315i	−0.636140	+	0.771573i	$0.719470\pi$
$648$	25.4547	+	0.236673i	0.999957	+	0.00929738i
$649$			3.74151i			0.146867i
$650$	−9.38819	−	0.574468i	−0.368235	−	0.0225325i
$651$	31.7895	−	29.6566i	1.24593	−	1.16234i
$652$	−18.6580	+	10.1257i	−0.730703	+	0.396552i
$653$			14.4218i			0.564370i	0.959360	+	0.282185i	$0.0910592\pi$
$653$			14.4218i			0.564370i	−0.959360	+	0.282185i	$0.908941\pi$
$654$	23.5545	−	26.5561i	0.921053	−	1.03843i
$655$	3.38630	−	2.47178i	0.132314	−	0.0965804i
$656$	−12.8234	+	19.7292i	−0.500671	+	0.770297i
$657$	−7.57679	+	19.1048i	−0.295599	+	0.745349i
$658$	−11.4246	−	26.8199i	−0.445376	−	1.04555i
$659$	28.6527			1.11615			0.558075	−	0.829790i	$-0.311540\pi$
$659$	28.6527			1.11615			0.558075	+	0.829790i	$0.311540\pi$
$660$	2.37949	+	15.3719i	0.0926216	+	0.598350i
$661$	30.3370			1.17997			0.589987	−	0.807413i	$-0.299133\pi$
$661$	30.3370			1.17997			0.589987	+	0.807413i	$0.299133\pi$
$662$	−7.07293	−	27.8613i	−0.274897	−	1.08286i
$663$	5.34458	+	7.86915i	0.207566	+	0.305613i
$664$	−21.1176	+	19.5092i	−0.819521	+	0.757106i
$665$	−9.74794	−	9.76311i	−0.378009	−	0.378597i
$666$	3.38117	−	26.0745i	0.131018	−	1.01037i
$667$	−0.737753			−0.0285659
$668$	−0.441067	−	0.812728i	−0.0170654	−	0.0314454i
$669$	6.35424	+	9.35575i	0.245669	+	0.361714i
$670$	17.8583	+	14.7887i	0.689927	+	0.571339i
$671$	−22.7303			−0.877495
$672$	−23.6386	+	10.6403i	−0.911880	+	0.410458i
$673$			35.2784i			1.35988i	0.733267	+	0.679940i	$0.237994\pi$
$673$			35.2784i			1.35988i	−0.733267	+	0.679940i	$0.762006\pi$
$674$	−2.80046	−	11.0314i	−0.107870	−	0.424914i
$675$	−2.35252	+	25.8740i	−0.0905484	+	0.995892i
$676$	19.7415	−	10.7137i	0.759287	−	0.412065i
$677$	−19.1645			−0.736552			−0.368276	−	0.929717i	$-0.620052\pi$
$677$	−19.1645			−0.736552			−0.368276	+	0.929717i	$0.620052\pi$
$678$	−26.0404	−	23.0970i	−1.00007	−	0.887037i
$679$	−25.2530	+	3.92219i	−0.969122	+	0.150520i
$680$	−5.04521	+	25.6210i	−0.193475	+	0.982519i
$681$	−12.1247	−	17.8519i	−0.464618	−	0.684086i
$682$	−6.62943	−	26.1143i	−0.253854	−	0.999968i
$683$		−	13.2192i		−	0.505820i	−0.967490	−	0.252910i	$-0.918612\pi$
$683$		−	13.2192i		−	0.505820i	0.967490	−	0.252910i	$-0.0813877\pi$
$684$	1.67025	+	13.8921i	0.0638637	+	0.531176i
$685$	24.3874	+	33.4103i	0.931795	+	1.27654i
$686$	19.8480	−	17.0897i	0.757798	−	0.652489i
$687$	−3.55938	−	5.24069i	−0.135799	−	0.199945i
$688$	7.97681	−	12.2726i	0.304113	−	0.467887i
$689$	3.31744			0.126384
$690$	0.0507084	−	0.531974i	0.00193043	−	0.0202519i
$691$	−36.7836			−1.39931			−0.699657	−	0.714479i	$-0.746664\pi$
$691$	−36.7836			−1.39931			−0.699657	+	0.714479i	$0.746664\pi$
$692$	6.77472	−	3.67663i	0.257536	−	0.139765i
$693$	−3.53248	+	15.5427i	−0.134188	+	0.590419i
$694$	−6.99720	−	27.5630i	−0.265610	−	1.04628i
$695$	0.903535	+	1.23783i	0.0342731	+	0.0469535i
$696$	36.0828	+	8.38575i	1.36772	+	0.317861i
$697$			24.2883i			0.919985i
$698$	−3.14676	+	0.798843i	−0.119107	+	0.0302367i
$699$	1.20537	+	1.77474i	0.0455912	+	0.0671268i
$700$	−8.86265	−	24.9290i	−0.334977	−	0.942226i
$701$	−4.86743			−0.183840			−0.0919201	−	0.995766i	$-0.529300\pi$
$701$	−4.86743			−0.183840			−0.0919201	+	0.995766i	$0.529300\pi$
$702$	4.40646	+	8.72518i	0.166311	+	0.329311i
$703$	14.4522			0.545074
$704$	−1.26998	+	16.0148i	−0.0478642	+	0.603581i
$705$	−28.4108	−	10.1666i	−1.07001	−	0.382895i
$706$	−5.29061	−	20.8405i	−0.199115	−	0.784342i
$707$	6.36113	+	40.9561i	0.239235	+	1.54031i
$708$	−2.96301	+	5.73391i	−0.111357	+	0.215493i
$709$		−	0.768670i		−	0.0288680i	−0.999896	−	0.0144340i	$-0.995405\pi$
$709$		−	0.768670i		−	0.0288680i	0.999896	−	0.0144340i	$-0.00459465\pi$
$710$	−17.9240	+	21.6443i	−0.672675	+	0.812298i
$711$	−12.1424	+	30.6168i	−0.455374	+	1.14822i
$712$	27.9087	−	25.7832i	1.04592	−	0.966265i
$713$			0.925604i			0.0346642i
$714$	−14.4728	+	22.5060i	−0.541632	+	0.842265i
$715$	−4.82440	+	3.52150i	−0.180422	+	0.131697i
$716$	24.2330	−	13.1512i	0.905629	−	0.491484i
$717$	−28.0965	+	19.0826i	−1.04928	+	0.712651i
$718$	−10.1099	−	39.8242i	−0.377297	−	1.48623i
$719$	−45.3201			−1.69015			−0.845077	−	0.534644i	$-0.820446\pi$
$719$	−45.3201			−1.69015			−0.845077	+	0.534644i	$0.820446\pi$
$720$	−8.52684	+	25.4420i	−0.317776	+	0.948166i
$721$	22.4683	−	3.48968i	0.836762	−	0.129962i
$722$	18.5895	−	4.71916i	0.691829	−	0.175629i
$723$	34.7104	−	23.5746i	1.29089	−	0.876749i
$724$	−41.3036	+	22.4154i	−1.53504	+	0.833063i
$725$	−11.5238	+	36.0093i	−0.427984	+	1.33735i
$726$	−12.7678	−	11.3247i	−0.473859	−	0.420299i
$727$	19.4319			0.720688			0.360344	−	0.932819i	$-0.382659\pi$
$727$	19.4319			0.720688			0.360344	+	0.932819i	$0.382659\pi$
$728$	−7.79680	−	6.18824i	−0.288969	−	0.229351i
$729$	24.4501	−	11.4540i	0.905558	−	0.424223i
$730$	−16.6856	−	13.8176i	−0.617562	−	0.511411i
$731$		−	15.1085i		−	0.558809i
$732$	−34.8345	−	18.0008i	−1.28752	−	0.665329i
$733$		−	33.0895i		−	1.22219i	−0.791558	−	0.611094i	$-0.790730\pi$
$733$		−	33.0895i		−	1.22219i	0.791558	−	0.611094i	$-0.209270\pi$
$734$	−10.0673	+	2.55571i	−0.371591	+	0.0943329i
$735$	0.961559	−	27.0938i	0.0354676	−	0.999371i
$736$	0.177665	−	0.522533i	0.00654881	−	0.0192608i
$737$	14.7243			0.542375
$738$	−3.20950	+	24.7506i	−0.118143	+	0.911083i
$739$		−	12.9023i		−	0.474619i	−0.971434	−	0.237310i	$-0.923734\pi$
$739$		−	12.9023i		−	0.474619i	0.971434	−	0.237310i	$-0.0762656\pi$
$740$	25.0393	+	11.8811i	0.920461	+	0.436758i
$741$	−4.44461	+	3.01869i	−0.163277	+	0.110894i
$742$	3.65706	+	8.58519i	0.134255	+	0.315172i
$743$	−20.1716			−0.740025			−0.370012	−	0.929027i	$-0.620647\pi$
$743$	−20.1716			−0.740025			−0.370012	+	0.929027i	$0.620647\pi$
$744$	10.5210	−	45.2704i	0.385718	−	1.65969i
$745$	−3.09698	−	4.24281i	−0.113464	−	0.155444i
$746$	−26.7410	+	6.78852i	−0.979057	+	0.248545i
$747$	−11.2418	+	28.3462i	−0.411317	+	1.03713i
$748$	7.90959	+	14.5745i	0.289203	+	0.532898i
$749$	−1.01725	−	6.54958i	−0.0371696	−	0.239316i
$750$	−25.1733	−	10.7846i	−0.919197	−	0.393797i
$751$	15.5652			0.567982			0.283991	−	0.958827i	$-0.408341\pi$
$751$	15.5652			0.567982			0.283991	+	0.958827i	$0.408341\pi$
$752$	−26.1301	−	16.9838i	−0.952867	−	0.619336i
$753$	20.9802	−	14.2493i	0.764561	−	0.519275i
$754$	3.50007	+	13.7873i	0.127465	+	0.502104i
$755$	−10.9776	−	15.0391i	−0.399514	−	0.547327i
$756$	−17.7223	+	21.0219i	−0.644554	+	0.764559i
$757$	29.6612			1.07806			0.539028	−	0.842288i	$-0.318792\pi$
$757$	29.6612			1.07806			0.539028	+	0.842288i	$0.318792\pi$
$758$	1.24370	+	4.89914i	0.0451734	+	0.177945i
$759$	−0.190662	−	0.280724i	−0.00692061	−	0.0101896i
$760$	−14.4711	−	2.84960i	−0.524921	−	0.103366i
$761$	−41.8111			−1.51565			−0.757825	−	0.652457i	$-0.773738\pi$
$761$	−41.8111			−1.51565			−0.757825	+	0.652457i	$0.773738\pi$
$762$	2.36236	−	2.66341i	0.0855795	−	0.0964851i
$763$	5.88444	+	37.8869i	0.213031	+	1.37160i
$764$	13.1091	+	24.1555i	0.474272	+	0.873914i
$765$	6.93207	+	26.8155i	0.250629	+	0.969516i
$766$	5.09226	+	20.0592i	0.183991	+	0.724767i
$767$	−2.47835			−0.0894880
$768$	−14.6288	+	23.5371i	−0.527873	+	0.849323i
$769$			9.12224i			0.328956i	0.986381	+	0.164478i	$0.0525940\pi$
$769$			9.12224i			0.328956i	−0.986381	+	0.164478i	$0.947406\pi$
$770$	−14.4316	−	8.60303i	−0.520078	−	0.310032i
$771$	22.6484	−	15.3823i	0.815662	−	0.553982i
$772$	−12.2714	−	22.6117i	−0.441656	−	0.813814i
$773$	17.9114			0.644228			0.322114	−	0.946701i	$-0.395606\pi$
$773$	17.9114			0.644228			0.322114	+	0.946701i	$0.395606\pi$
$774$	1.99647	−	15.3961i	0.0717615	−	0.553401i
$775$	45.1782	+	14.4581i	1.62285	+	0.519350i
$776$	−20.0674	+	18.5391i	−0.720379	+	0.665514i
$777$	19.3728	+	20.7660i	0.694994	+	0.744977i
$778$	−18.4246	+	4.67731i	−0.660555	+	0.167690i
$779$	−13.7184			−0.491512
$780$	−10.1822	+	1.57616i	−0.364582	+	0.0564355i
$781$			17.8458i			0.638575i
$782$	−0.140175	−	0.552171i	−0.00501265	−	0.0197456i
$783$	38.3526	−	8.53822i	1.37061	−	0.305131i
$784$	7.41952	−	26.9991i	0.264983	−	0.964253i
$785$	−25.4040	+	18.5433i	−0.906707	+	0.661838i
$786$	3.04748	−	3.43583i	0.108700	−	0.122552i
$787$			36.9161i			1.31592i	0.753055	+	0.657958i	$0.228579\pi$
$787$			36.9161i			1.31592i	−0.753055	+	0.657958i	$0.771421\pi$
$788$	−24.3960	−	44.9531i	−0.869072	−	1.60139i
$789$	−13.8721	−	20.4248i	−0.493861	−	0.727143i
$790$	−26.7399	−	22.1437i	−0.951363	−	0.787837i
$791$	37.1512	−	5.77016i	1.32094	−	0.205163i
$792$	6.13424	+	15.8971i	0.217971	+	0.564880i
$793$		−	15.0564i		−	0.534668i
$794$	−2.60095	−	10.2455i	−0.0923044	−	0.363600i
$795$	9.09443	+	3.25437i	0.322546	+	0.115421i
$796$	16.3295	+	30.0895i	0.578785	+	1.06649i
$797$	29.7782			1.05480			0.527399	−	0.849618i	$-0.323167\pi$
$797$	29.7782			1.05480			0.527399	+	0.849618i	$0.323167\pi$
$798$	−12.7117	−	8.17446i	−0.449989	−	0.289373i
$799$	−32.1683			−1.13803
$800$	−22.7294	−	16.8338i	−0.803604	−	0.595164i
$801$	14.8571	−	37.4619i	0.524948	−	1.32365i
$802$	10.5812	+	41.6808i	0.373634	+	1.47180i
$803$	−13.7573			−0.485486
$804$	22.5651	+	11.6606i	0.795809	+	0.411236i
$805$	0.407826	+	0.408461i	0.0143740	+	0.0143963i
$806$	17.2979	−	4.39128i	0.609293	−	0.154676i
$807$	−13.3758	+	9.08457i	−0.470850	+	0.319792i
$808$	30.0672	+	32.5459i	1.05776	+	1.14496i
$809$		−	8.02026i		−	0.281977i	−0.990011	−	0.140989i	$-0.954972\pi$
$809$		−	8.02026i		−	0.281977i	0.990011	−	0.140989i	$-0.0450281\pi$
$810$	3.52057	+	28.2419i	0.123700	+	0.992320i
$811$	2.93155			0.102941			0.0514703	−	0.998675i	$-0.483609\pi$
$811$	2.93155			0.102941			0.0514703	+	0.998675i	$0.483609\pi$
$812$	−31.8217	+	24.2566i	−1.11672	+	0.851240i
$813$	0.296882	−	0.201636i	0.0104121	−	0.00707170i
$814$	17.0588	−	4.33057i	0.597909	−	0.151786i
$815$	−13.9931	−	19.1704i	−0.490159	−	0.671509i
$816$	0.579529	+	28.5995i	0.0202876	+	1.00118i
$817$	8.53350			0.298549
$818$	8.61360	+	33.9302i	0.301167	+	1.18634i
$819$	−10.2954	−	2.33989i	−0.359750	−	0.0817624i
$820$	−23.7679	−	11.2779i	−0.830012	−	0.393840i
$821$	28.8608			1.00725			0.503624	−	0.863923i	$-0.332000\pi$
$821$	28.8608			1.00725			0.503624	+	0.863923i	$0.332000\pi$
$822$	33.8990	+	30.0674i	1.18236	+	1.04872i
$823$			55.7417i			1.94303i	0.236970	+	0.971517i	$0.423846\pi$
$823$			55.7417i			1.94303i	−0.236970	+	0.971517i	$0.576154\pi$
$824$	17.8545	−	16.4947i	0.621991	−	0.574620i
$825$	−16.6802	+	4.92116i	−0.580729	+	0.171333i
$826$	−2.73207	−	6.41371i	−0.0950610	−	0.223162i
$827$			30.4567i			1.05908i	0.848284	+	0.529541i	$0.177636\pi$
$827$			30.4567i			1.05908i	−0.848284	+	0.529541i	$0.822364\pi$
$828$	−0.0698786	−	0.581204i	−0.00242845	−	0.0201982i
$829$	−25.9657			−0.901827			−0.450913	−	0.892568i	$-0.648902\pi$
$829$	−25.9657			−0.901827			−0.450913	+	0.892568i	$0.648902\pi$
$830$	−24.7567	−	20.5014i	−0.859319	−	0.711614i
$831$	−27.8875	−	41.0605i	−0.967407	−	1.42437i
$832$	−10.6081	−	0.841225i	−0.367769	−	0.0291642i
$833$	−8.76633	−	27.5402i	−0.303735	−	0.954212i
$834$	1.25593	+	1.11398i	0.0434894	+	0.0385739i
$835$	0.835048	−	0.609531i	0.0288980	−	0.0210937i
$836$	−8.23190	+	4.46745i	−0.284706	+	0.154510i
$837$	−10.7123	−	48.1182i	−0.370271	−	1.66321i
$838$	4.03424	+	15.8915i	0.139361	+	0.548961i
$839$	−2.14123			−0.0739234			−0.0369617	−	0.999317i	$-0.511768\pi$
$839$	−2.14123			−0.0739234			−0.0369617	+	0.999317i	$0.511768\pi$
$840$	−15.3036	−	24.6130i	−0.528023	−	0.849230i
$841$	28.1788			0.971681
$842$	−4.42542	−	17.4324i	−0.152510	−	0.600760i
$843$	4.45631	−	3.02664i	0.153483	−	0.104243i
$844$	16.5621	+	30.5180i	0.570091	+	1.05047i
$845$	14.8057	+	20.2836i	0.509333	+	0.697778i
$846$	−32.7806	−	4.25077i	−1.12702	−	0.146145i
$847$	18.2156	−	2.82917i	0.625895	−	0.0972113i
$848$	8.36438	+	5.43661i	0.287234	+	0.186694i
$849$	−29.4876	+	20.0274i	−1.01201	+	0.687339i
$850$	−29.1407	−	1.78313i	−0.999518	−	0.0611609i
$851$	−0.604637			−0.0207267
$852$	−14.1326	+	27.3489i	−0.484176	+	0.936959i
$853$			44.6580i			1.52906i	0.644587	+	0.764531i	$0.277029\pi$
$853$			44.6580i			1.52906i	−0.644587	+	0.764531i	$0.722971\pi$
$854$	38.9644	−	16.5978i	1.33333	−	0.567965i
$855$	−15.1458	+	3.91533i	−0.517974	+	0.133901i
$856$	−4.80826	−	5.20465i	−0.164343	−	0.177891i
$857$		−	23.0490i		−	0.787338i	−0.919252	−	0.393669i	$-0.871206\pi$
$857$		−	23.0490i		−	0.787338i	0.919252	−	0.393669i	$-0.128794\pi$
$858$	−4.34169	+	4.89496i	−0.148223	+	0.167111i
$859$	14.2677			0.486806			0.243403	−	0.969925i	$-0.421736\pi$
$859$	14.2677			0.486806			0.243403	+	0.969925i	$0.421736\pi$
$860$	14.7848	+	7.01539i	0.504158	+	0.239223i
$861$	−18.3891	−	19.7117i	−0.626700	−	0.671771i
$862$	0.872852	+	3.43829i	0.0297295	+	0.117109i
$863$	−0.233651			−0.00795357			−0.00397679	−	0.999992i	$-0.501266\pi$
$863$	−0.233651			−0.00795357			−0.00397679	+	0.999992i	$0.501266\pi$
$864$	−3.18862	+	29.2204i	−0.108479	+	0.994099i
$865$	5.08091	+	6.96077i	0.172756	+	0.236673i
$866$	33.7922	−	8.57857i	1.14831	−	0.291512i
$867$	0.0459230	+	0.0676152i	0.00155963	+	0.00229633i
$868$	30.4330	+	39.9244i	1.03296	+	1.35512i
$869$	−22.0471			−0.747898
$870$	−3.93010	+	41.2300i	−0.133243	+	1.39783i
$871$			9.75324i			0.330476i
$872$	27.8140	+	30.1070i	0.941902	+	1.01955i
$873$	−10.6828	+	26.9365i	−0.361558	+	0.911663i
$874$	0.311874	−	0.0791729i	0.0105493	−	0.00267806i
$875$	26.3070	−	13.5255i	0.889340	−	0.457246i
$876$	−21.0833	−	10.8948i	−0.712338	−	0.368102i
$877$	40.6170			1.37154			0.685770	−	0.727819i	$-0.259466\pi$
$877$	40.6170			1.37154			0.685770	+	0.727819i	$0.259466\pi$
$878$	−1.91709	−	7.55170i	−0.0646987	−	0.254858i
$879$	11.6183	+	17.1063i	0.391874	+	0.576981i
$880$	−17.9350	+	0.972681i	−0.604587	+	0.0327891i
$881$	−40.1040			−1.35114			−0.675569	−	0.737297i	$-0.736102\pi$
$881$	−40.1040			−1.35114			−0.675569	+	0.737297i	$0.736102\pi$
$882$	−5.29398	−	29.2228i	−0.178258	−	0.983984i
$883$	57.5009			1.93506			0.967530	−	0.252757i	$-0.0813374\pi$
$883$	57.5009			1.93506			0.967530	+	0.252757i	$0.0813374\pi$
$884$	−9.65407	+	5.23925i	−0.324701	+	0.176215i
$885$	−6.79415	−	2.43124i	−0.228383	−	0.0817251i
$886$	4.57091	+	18.0055i	0.153563	+	0.604905i
$887$		−	13.7551i		−	0.461850i	−0.972972	−	0.230925i	$-0.925825\pi$
$887$		−	13.7551i		−	0.461850i	0.972972	−	0.230925i	$-0.0741752\pi$
$888$	29.5722	+	6.87267i	0.992379	+	0.230632i
$889$	0.590172	+	3.79982i	0.0197937	+	0.127442i
$890$	32.7182	+	27.0944i	1.09672	+	0.908206i
$891$	13.1606	+	12.3871i	0.440898	+	0.414982i
$892$	−11.4779	+	6.22902i	−0.384307	+	0.208563i
$893$		−	18.1691i		−	0.608006i
$894$	−4.30486	−	3.81829i	−0.143976	−	0.127703i
$895$	18.1743	+	24.8985i	0.607500	+	0.832265i
$896$	−9.51710	−	28.3800i	−0.317944	−	0.948109i
$897$	0.185950	−	0.126293i	0.00620868	−	0.00421681i
$898$	3.61896	+	14.2556i	0.120766	+	0.475716i
$899$		−	71.7380i		−	2.39260i
$900$	−29.4597	−	5.66777i	−0.981991	−	0.188926i
$901$	10.2972			0.343051
$902$	−16.1926	+	4.11069i	−0.539155	+	0.136871i
$903$	11.4389	+	12.2616i	0.380664	+	0.408041i
$904$	29.5223	−	27.2739i	0.981898	−	0.907116i
$905$	−30.9770	−	42.4379i	−1.02971	−	1.41069i
$906$	−15.2590	−	13.5343i	−0.506947	−	0.449648i
$907$	−53.8251			−1.78723			−0.893617	−	0.448830i	$-0.851841\pi$
$907$	−53.8251			−1.78723			−0.893617	+	0.448830i	$0.851841\pi$
$908$	21.9011	−	11.8857i	0.726815	−	0.394442i
$909$	43.6864	+	17.3257i	1.44899	+	0.574656i
$910$	5.69858	−	9.55937i	0.188906	−	0.316890i
$911$		−	34.4197i		−	1.14038i	−0.821514	−	0.570188i	$-0.806870\pi$
$911$		−	34.4197i		−	1.14038i	0.821514	−	0.570188i	$-0.193130\pi$
$912$	−16.1534	+	0.327326i	−0.534892	+	0.0108388i
$913$	−20.4120			−0.675540
$914$	14.0695	+	55.4218i	0.465378	+	1.83319i
$915$	14.7702	−	41.2756i	0.488287	−	1.36453i
$916$	6.42941	−	3.48923i	0.212434	−	0.115287i
$917$	0.761329	+	4.90181i	0.0251413	+	0.161872i
$918$	13.6775	+	27.0827i	0.451426	+	0.893863i
$919$	56.8106			1.87401			0.937005	−	0.349316i	$-0.113586\pi$
$919$	56.8106			1.87401			0.937005	+	0.349316i	$0.113586\pi$
$920$	0.605428	+	0.119219i	0.0199604	+	0.00393054i
$921$	−11.0411	+	7.49888i	−0.363816	+	0.247097i
$922$	−6.35293	−	25.0251i	−0.209223	−	0.824159i
$923$	−11.8210			−0.389092
$924$	−17.4538	−	5.83976i	−0.574189	−	0.192114i
$925$	−9.44454	+	29.5120i	−0.310534	+	0.970348i
$926$	14.6571	+	57.7363i	0.481661	+	1.89733i
$927$	9.50475	−	23.9661i	0.312177	−	0.787151i
$928$	−13.7697	+	40.4983i	−0.452013	+	1.32942i
$929$	8.90906			0.292297			0.146148	−	0.989263i	$-0.453312\pi$
$929$	8.90906			0.292297			0.146148	+	0.989263i	$0.453312\pi$
$930$	51.7283	+	4.93080i	1.69624	+	0.161687i
$931$	15.5551	−	4.95135i	0.509798	−	0.162274i
$932$	−2.17729	+	1.18161i	−0.0713196	+	0.0387051i
$933$	−26.1219	−	38.4608i	−0.855191	−	1.25915i
$934$	44.5821	−	11.3177i	1.45877	−	0.370327i
$935$	−14.9748	+	10.9306i	−0.489728	+	0.357470i
$936$	−10.5301	+	4.06327i	−0.344189	+	0.132812i
$937$	−29.8344			−0.974647			−0.487323	−	0.873222i	$-0.662027\pi$
$937$	−29.8344			−0.974647			−0.487323	+	0.873222i	$0.662027\pi$
$938$	−25.2404	+	10.7517i	−0.824128	+	0.351057i
$939$	7.98391	+	11.7552i	0.260545	+	0.383617i
$940$	14.9368	−	31.4791i	0.487185	−	1.02673i
$941$		−	51.4975i		−	1.67877i	−0.543537	−	0.839385i	$-0.682915\pi$
$941$		−	51.4975i		−	1.67877i	0.543537	−	0.839385i	$-0.317085\pi$
$942$	−22.8622	+	25.7756i	−0.744890	+	0.839813i
$943$	0.573937			0.0186900
$944$	−6.24875	−	4.06151i	−0.203380	−	0.132191i
$945$	−25.9284	−	16.5142i	−0.843450	−	0.537208i
$946$	10.0726	−	2.55705i	0.327489	−	0.0831370i
$947$			8.19688i			0.266363i	0.991092	+	0.133181i	$0.0425193\pi$
$947$			8.19688i			0.266363i	−0.991092	+	0.133181i	$0.957481\pi$
$948$	−33.7875	−	17.4598i	−1.09737	−	0.567067i
$949$		−	9.11276i		−	0.295813i
$950$	1.00714	−	16.4591i	0.0326759	−	0.534003i
$951$	−44.0328	+	29.9062i	−1.42786	+	0.969777i
$952$	−24.2011	−	19.2081i	−0.784361	−	0.622538i
$953$	16.6673			0.539906			0.269953	−	0.962873i	$-0.412992\pi$
$953$	16.6673			0.539906			0.269953	+	0.962873i	$0.412992\pi$
$954$	10.4932	+	1.36069i	0.339731	+	0.0440541i
$955$	−24.8188	+	18.1162i	−0.803119	+	0.586225i
$956$	−18.7065	−	34.4694i	−0.605012	−	1.11482i
$957$	14.7771	+	21.7572i	0.477675	+	0.703311i
$958$	21.8656	−	5.55084i	0.706444	−	0.179339i
$959$	−48.3629	+	7.51152i	−1.56172	+	0.242560i
$960$	−28.2558	−	12.7126i	−0.911952	−	0.410296i
$961$	−59.0043			−1.90337
$962$	2.86854	+	11.2996i	0.0924854	+	0.364313i
$963$	−6.98621	−	2.77067i	−0.225127	−	0.0892835i
$964$	23.1100	+	42.5835i	0.744324	+	1.37152i
$965$	23.2327	−	16.9584i	0.747887	−	0.545910i
$966$	0.531821	+	0.341996i	0.0171110	+	0.0110035i
$967$		−	13.9782i		−	0.449509i	−0.974415	−	0.224754i	$-0.927842\pi$
$967$		−	13.9782i		−	0.449509i	0.974415	−	0.224754i	$-0.0721580\pi$
$968$	14.4751	−	13.3727i	0.465247	−	0.429813i
$969$	−13.7959	+	9.36993i	−0.443189	+	0.301006i
$970$	−23.5256	−	19.4819i	−0.755362	−	0.625526i
$971$			34.0060i			1.09130i	0.838012	+	0.545652i	$0.183718\pi$
$971$			34.0060i			1.09130i	−0.838012	+	0.545652i	$0.816282\pi$
$972$	10.3591	+	29.4056i	0.332269	+	0.943185i
$973$	−1.79181	+	0.278296i	−0.0574428	+	0.00892177i
$974$	2.93147	+	11.5475i	0.0939305	+	0.370006i
$975$	−3.25974	−	11.0488i	−0.104395	−	0.353845i
$976$	24.6744	−	37.9623i	0.789808	−	1.21514i
$977$	24.4774			0.783101			0.391550	−	0.920157i	$-0.371939\pi$
$977$	24.4774			0.783101			0.391550	+	0.920157i	$0.371939\pi$
$978$	−19.4508	−	17.2523i	−0.621967	−	0.551667i
$979$	26.9763			0.862166
$980$	31.0207	+	4.20933i	0.990919	+	0.134462i
$981$	40.4127	+	16.0273i	1.29028	+	0.511712i
$982$	23.2593	−	5.90465i	0.742233	−	0.188425i
$983$			27.1165i			0.864881i	0.901663	+	0.432440i	$0.142347\pi$
$983$			27.1165i			0.864881i	−0.901663	+	0.432440i	$0.857653\pi$
$984$	−28.0707	−	6.52372i	−0.894862	−	0.207969i
$985$	46.1876	−	33.7140i	1.47166	−	1.07422i
$986$	10.8641	+	42.7954i	0.345984	+	1.36288i
$987$	26.1068	−	24.3552i	0.830989	−	0.775235i
$988$	−2.95920	−	5.45275i	−0.0941448	−	0.173475i
$989$	−0.357017			−0.0113525
$990$	−16.7042	+	9.15990i	−0.530895	+	0.291121i
$991$	37.8179			1.20133			0.600663	−	0.799502i	$-0.294903\pi$
$991$	37.8179			1.20133			0.600663	+	0.799502i	$0.294903\pi$
$992$	50.8103	+	17.2759i	1.61323	+	0.548509i
$993$	29.1233	−	19.7800i	0.924202	−	0.627700i
$994$	−13.0311	−	30.5914i	−0.413323	−	0.970301i
$995$	−30.9158	+	22.5666i	−0.980097	+	0.715408i
$996$	−31.2816	−	16.1649i	−0.991197	−	0.512204i
$997$		−	28.4532i		−	0.901122i	−0.892746	−	0.450561i	$-0.851224\pi$
$997$		−	28.4532i		−	0.901122i	0.892746	−	0.450561i	$-0.148776\pi$
$998$	−12.0614	−	47.5117i	−0.381798	−	1.50396i
$999$	31.4325	−	6.99763i	0.994480	−	0.221395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.u.e.629.5	yes	160
3.2	odd	2	inner	840.2.u.e.629.155	yes	160
5.4	even	2	inner	840.2.u.e.629.156	yes	160
7.6	odd	2	inner	840.2.u.e.629.8	yes	160
8.5	even	2	inner	840.2.u.e.629.4	yes	160
15.14	odd	2	inner	840.2.u.e.629.6	yes	160
21.20	even	2	inner	840.2.u.e.629.154	yes	160
24.5	odd	2	inner	840.2.u.e.629.158	yes	160
35.34	odd	2	inner	840.2.u.e.629.153	yes	160
40.29	even	2	inner	840.2.u.e.629.157	yes	160
56.13	odd	2	inner	840.2.u.e.629.1	✓	160
105.104	even	2	inner	840.2.u.e.629.7	yes	160
120.29	odd	2	inner	840.2.u.e.629.3	yes	160
168.125	even	2	inner	840.2.u.e.629.159	yes	160
280.69	odd	2	inner	840.2.u.e.629.160	yes	160
840.629	even	2	inner	840.2.u.e.629.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.u.e.629.1	✓	160	56.13	odd	2	inner
840.2.u.e.629.2	yes	160	840.629	even	2	inner
840.2.u.e.629.3	yes	160	120.29	odd	2	inner
840.2.u.e.629.4	yes	160	8.5	even	2	inner
840.2.u.e.629.5	yes	160	1.1	even	1	trivial
840.2.u.e.629.6	yes	160	15.14	odd	2	inner
840.2.u.e.629.7	yes	160	105.104	even	2	inner
840.2.u.e.629.8	yes	160	7.6	odd	2	inner
840.2.u.e.629.153	yes	160	35.34	odd	2	inner
840.2.u.e.629.154	yes	160	21.20	even	2	inner
840.2.u.e.629.155	yes	160	3.2	odd	2	inner
840.2.u.e.629.156	yes	160	5.4	even	2	inner
840.2.u.e.629.157	yes	160	40.29	even	2	inner
840.2.u.e.629.158	yes	160	24.5	odd	2	inner
840.2.u.e.629.159	yes	160	168.125	even	2	inner
840.2.u.e.629.160	yes	160	280.69	odd	2	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.u (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37073 + 0.347977i) q^{2} +(-0.973146 - 1.43282i) q^{3} +(1.75782 - 0.953969i) q^{4} +(1.31834 + 1.80610i) q^{5} +(1.83252 + 1.62539i) q^{6} +(-2.61441 + 0.406058i) q^{7} +(-2.07755 + 1.91932i) q^{8} +(-1.10597 + 2.78870i) q^{9} +O(q^{10})\)	\(q+(-1.37073 + 0.347977i) q^{2} +(-0.973146 - 1.43282i) q^{3} +(1.75782 - 0.953969i) q^{4} +(1.31834 + 1.80610i) q^{5} +(1.83252 + 1.62539i) q^{6} +(-2.61441 + 0.406058i) q^{7} +(-2.07755 + 1.91932i) q^{8} +(-1.10597 + 2.78870i) q^{9} +(-2.43557 - 2.01693i) q^{10} -2.00814 q^{11} +(-3.07749 - 1.59030i) q^{12} -1.33017i q^{13} +(3.44236 - 1.46635i) q^{14} +(1.30489 - 3.64654i) q^{15} +(2.17989 - 3.35382i) q^{16} -4.12882i q^{17} +(0.545590 - 4.20741i) q^{18} +2.33202 q^{19} +(4.04036 + 1.91715i) q^{20} +(3.12601 + 3.35083i) q^{21} +(2.75262 - 0.698786i) q^{22} -0.0975649 q^{23} +(4.77181 + 1.10898i) q^{24} +(-1.52398 + 4.76209i) q^{25} +(0.462871 + 1.82332i) q^{26} +(5.07198 - 1.12915i) q^{27} +(-4.20830 + 3.20784i) q^{28} +7.56166 q^{29} +(-0.519740 + 5.45251i) q^{30} -9.48706i q^{31} +(-1.82099 + 5.35574i) q^{32} +(1.95421 + 2.87731i) q^{33} +(1.43674 + 5.65952i) q^{34} +(-4.18005 - 4.18655i) q^{35} +(0.716226 + 5.95710i) q^{36} +6.19728 q^{37} +(-3.19658 + 0.811490i) q^{38} +(-1.90591 + 1.29445i) q^{39} +(-6.20539 - 1.22195i) q^{40} -5.88262 q^{41} +(-5.45094 - 3.50532i) q^{42} +3.65928 q^{43} +(-3.52995 + 1.91570i) q^{44} +(-6.49470 + 1.67894i) q^{45} +(0.133736 - 0.0339504i) q^{46} -7.79115i q^{47} +(-6.92678 + 0.140362i) q^{48} +(6.67023 - 2.12320i) q^{49} +(0.431874 - 7.05787i) q^{50} +(-5.91588 + 4.01795i) q^{51} +(-1.26895 - 2.33821i) q^{52} +2.49399i q^{53} +(-6.55942 + 3.31270i) q^{54} +(-2.64740 - 3.62689i) q^{55} +(4.65220 - 5.86149i) q^{56} +(-2.26939 - 3.34137i) q^{57} +(-10.3650 + 2.63129i) q^{58} -1.86318i q^{59} +(-1.18493 - 7.65480i) q^{60} +11.3191 q^{61} +(3.30128 + 13.0042i) q^{62} +(1.75909 - 7.73987i) q^{63} +(0.632417 - 7.97496i) q^{64} +(2.40243 - 1.75362i) q^{65} +(-3.67994 - 3.26400i) q^{66} -7.33230 q^{67} +(-3.93877 - 7.25774i) q^{68} +(0.0949450 + 0.139793i) q^{69} +(7.18656 + 4.28409i) q^{70} -8.88677i q^{71} +(-3.05469 - 7.91637i) q^{72} +6.85080 q^{73} +(-8.49482 + 2.15651i) q^{74} +(8.30629 - 2.45061i) q^{75} +(4.09928 - 2.22467i) q^{76} +(5.25008 - 0.815421i) q^{77} +(2.16205 - 2.43757i) q^{78} +10.9789 q^{79} +(8.93115 - 0.484370i) q^{80} +(-6.55365 - 6.16844i) q^{81} +(8.06351 - 2.04702i) q^{82} +10.1647 q^{83} +(8.69156 + 2.90805i) q^{84} +(7.45706 - 5.44318i) q^{85} +(-5.01590 + 1.27335i) q^{86} +(-7.35861 - 10.8345i) q^{87} +(4.17200 - 3.85426i) q^{88} -13.4335 q^{89} +(8.31827 - 4.56140i) q^{90} +(0.540128 + 3.47762i) q^{91} +(-0.171502 + 0.0930739i) q^{92} +(-13.5933 + 9.23230i) q^{93} +(2.71114 + 10.6796i) q^{94} +(3.07438 + 4.21185i) q^{95} +(9.44593 - 2.60276i) q^{96} +9.65918 q^{97} +(-8.40429 + 5.23144i) q^{98} +(2.22094 - 5.60008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 24 q^{4} - 32 q^{9}+O(q^{10}) \) 160 * q - 24 * q^4 - 32 * q^9	\( 160 q - 24 q^{4} - 32 q^{9} - 48 q^{15} - 104 q^{16} - 16 q^{25} - 32 q^{30} + 48 q^{36} - 64 q^{39} - 64 q^{46} + 144 q^{49} + 16 q^{60} - 72 q^{64} + 8 q^{70} - 96 q^{79} + 16 q^{81} - 72 q^{84}+O(q^{100}) \) 160 * q - 24 * q^4 - 32 * q^9 - 48 * q^15 - 104 * q^16 - 16 * q^25 - 32 * q^30 + 48 * q^36 - 64 * q^39 - 64 * q^46 + 144 * q^49 + 16 * q^60 - 72 * q^64 + 8 * q^70 - 96 * q^79 + 16 * q^81 - 72 * q^84

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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