LMFDB - Embedded newform 572.2.j.a.463.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(463,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("572.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.j (of order $4$, degree $2$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.15
Character	$\chi$	$=$	572.463
Dual form			572.2.j.a.551.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11565 + 0.869100i) q^{2} -0.202427i q^{3} +(0.489330 - 1.93922i) q^{4} +(-1.00276 - 1.00276i) q^{5} +(0.175929 + 0.225836i) q^{6} +(0.926254 + 0.926254i) q^{7} +(1.13945 + 2.58875i) q^{8} +2.95902 q^{9} +O(q^{10})$	\(q+(-1.11565 + 0.869100i) q^{2} -0.202427i q^{3} +(0.489330 - 1.93922i) q^{4} +(-1.00276 - 1.00276i) q^{5} +(0.175929 + 0.225836i) q^{6} +(0.926254 + 0.926254i) q^{7} +(1.13945 + 2.58875i) q^{8} +2.95902 q^{9} +(1.99022 + 0.247225i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-0.392549 - 0.0990534i) q^{12} +(-3.34209 - 1.35294i) q^{13} +(-1.83838 - 0.228364i) q^{14} +(-0.202985 + 0.202985i) q^{15} +(-3.52111 - 1.89783i) q^{16} -2.50950i q^{17} +(-3.30122 + 2.57169i) q^{18} +(-1.33024 + 1.33024i) q^{19} +(-2.43524 + 1.45388i) q^{20} +(0.187499 - 0.187499i) q^{21} +(-1.40343 - 0.174334i) q^{22} +6.79920 q^{23} +(0.524033 - 0.230656i) q^{24} -2.98896i q^{25} +(4.90442 - 1.39522i) q^{26} -1.20627i q^{27} +(2.24945 - 1.34296i) q^{28} +5.87626 q^{29} +(0.0500449 - 0.402873i) q^{30} +(4.35176 - 4.35176i) q^{31} +(5.57772 - 0.942893i) q^{32} +(0.143137 - 0.143137i) q^{33} +(2.18100 + 2.79971i) q^{34} -1.85761i q^{35} +(1.44794 - 5.73818i) q^{36} +(2.60377 - 2.60377i) q^{37} +(0.327964 - 2.64019i) q^{38} +(-0.273870 + 0.676528i) q^{39} +(1.45329 - 3.73848i) q^{40} +(1.68231 + 1.68231i) q^{41} +(-0.0462269 + 0.372137i) q^{42} -7.31241 q^{43} +(1.71724 - 1.02522i) q^{44} +(-2.96718 - 2.96718i) q^{45} +(-7.58550 + 5.90919i) q^{46} +(6.08062 + 6.08062i) q^{47} +(-0.384172 + 0.712767i) q^{48} -5.28411i q^{49} +(2.59771 + 3.33462i) q^{50} -0.507989 q^{51} +(-4.25902 + 5.81900i) q^{52} +7.95211 q^{53} +(1.04837 + 1.34576i) q^{54} -1.41811i q^{55} +(-1.34242 + 3.45327i) q^{56} +(0.269276 + 0.269276i) q^{57} +(-6.55582 + 5.10706i) q^{58} +(-4.24939 - 4.24939i) q^{59} +(0.294304 + 0.492957i) q^{60} +6.72879 q^{61} +(-1.07291 + 8.63713i) q^{62} +(2.74081 + 2.74081i) q^{63} +(-5.40329 + 5.89953i) q^{64} +(1.99464 + 4.70796i) q^{65} +(-0.0352898 + 0.284091i) q^{66} +(-5.14443 + 5.14443i) q^{67} +(-4.86645 - 1.22797i) q^{68} -1.37634i q^{69} +(1.61445 + 2.07244i) q^{70} +(3.76978 - 3.76978i) q^{71} +(3.37167 + 7.66018i) q^{72} +(4.32502 - 4.32502i) q^{73} +(-0.641947 + 5.16782i) q^{74} -0.605045 q^{75} +(1.92869 + 3.23054i) q^{76} +1.30992i q^{77} +(-0.282429 - 0.992786i) q^{78} -10.0181i q^{79} +(1.62776 + 5.43388i) q^{80} +8.63289 q^{81} +(-3.33896 - 0.414766i) q^{82} +(-7.24721 + 7.24721i) q^{83} +(-0.271851 - 0.455349i) q^{84} +(-2.51641 + 2.51641i) q^{85} +(8.15806 - 6.35522i) q^{86} -1.18951i q^{87} +(-1.02481 + 2.63624i) q^{88} +(0.716716 - 0.716716i) q^{89} +(5.88909 + 0.731544i) q^{90} +(-1.84246 - 4.34879i) q^{91} +(3.32705 - 13.1851i) q^{92} +(-0.880912 - 0.880912i) q^{93} +(-12.0685 - 1.49915i) q^{94} +2.66781 q^{95} +(-0.190867 - 1.12908i) q^{96} +(-8.88136 - 8.88136i) q^{97} +(4.59242 + 5.89519i) q^{98} +(2.09235 + 2.09235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.11565	+	0.869100i	−0.788880	+	0.614547i
$2$	−1.11565	+	0.869100i	−0.788880	+	0.614547i
$3$		−	0.202427i		−	0.116871i	−0.998291	−	0.0584356i	$-0.981389\pi$
$3$		−	0.202427i		−	0.116871i	0.998291	−	0.0584356i	$-0.0186112\pi$
$4$	0.489330	−	1.93922i	0.244665	−	0.969608i
$5$	−1.00276	−	1.00276i	−0.448446	−	0.448446i	0.446392	−	0.894838i	$-0.352709\pi$
$5$	−1.00276	−	1.00276i	−0.448446	−	0.448446i	−0.894838	+	0.446392i	$0.852709\pi$
$6$	0.175929	+	0.225836i	0.0718227	+	0.0921973i
$7$	0.926254	+	0.926254i	0.350091	+	0.350091i	0.860143	−	0.510052i	$-0.170374\pi$
$7$	0.926254	+	0.926254i	0.350091	+	0.350091i	−0.510052	+	0.860143i	$0.670374\pi$
$8$	1.13945	+	2.58875i	0.402858	+	0.915263i
$9$	2.95902			0.986341
$10$	1.99022	+	0.247225i	0.629361	+	0.0781793i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	−0.392549	−	0.0990534i	−0.113319	−	0.0285942i
$13$	−3.34209	−	1.35294i	−0.926929	−	0.375237i
$13$	−3.34209	−	1.35294i	−0.926929	−	0.375237i
$14$	−1.83838	−	0.228364i	−0.491327	−	0.0610327i
$15$	−0.202985	+	0.202985i	−0.0524104	+	0.0524104i
$16$	−3.52111	−	1.89783i	−0.880278	−	0.474458i
$17$		−	2.50950i		−	0.608642i	−0.952570	−	0.304321i	$-0.901570\pi$
$17$		−	2.50950i		−	0.608642i	0.952570	−	0.304321i	$-0.0984295\pi$
$18$	−3.30122	+	2.57169i	−0.778105	+	0.606153i
$19$	−1.33024	+	1.33024i	−0.305178	+	0.305178i	−0.843036	−	0.537858i	$-0.819234\pi$
$19$	−1.33024	+	1.33024i	−0.305178	+	0.305178i	0.537858	+	0.843036i	$0.319234\pi$
$20$	−2.43524	+	1.45388i	−0.544536	+	0.325098i
$21$	0.187499	−	0.187499i	0.0409155	−	0.0409155i
$22$	−1.40343	−	0.174334i	−0.299212	−	0.0371681i
$23$	6.79920			1.41773			0.708865	−	0.705344i	$-0.249207\pi$
$23$	6.79920			1.41773			0.708865	+	0.705344i	$0.249207\pi$
$24$	0.524033	−	0.230656i	0.106968	−	0.0470824i
$25$		−	2.98896i		−	0.597792i
$26$	4.90442	−	1.39522i	0.961837	−	0.273624i
$27$		−	1.20627i		−	0.232146i
$28$	2.24945	−	1.34296i	0.425106	−	0.253796i
$29$	5.87626			1.09119			0.545597	−	0.838048i	$-0.316303\pi$
$29$	5.87626			1.09119			0.545597	+	0.838048i	$0.316303\pi$
$30$	0.0500449	−	0.402873i	0.00913690	−	0.0735542i
$31$	4.35176	−	4.35176i	0.781599	−	0.781599i	−0.198502	−	0.980101i	$-0.563608\pi$
$31$	4.35176	−	4.35176i	0.781599	−	0.781599i	0.980101	+	0.198502i	$0.0636076\pi$
$32$	5.57772	−	0.942893i	0.986011	−	0.166682i
$33$	0.143137	−	0.143137i	0.0249170	−	0.0249170i
$34$	2.18100	+	2.79971i	0.374039	+	0.480146i
$35$		−	1.85761i		−	0.313994i
$36$	1.44794	−	5.73818i	0.241323	−	0.956364i
$37$	2.60377	−	2.60377i	0.428057	−	0.428057i	−0.459909	−	0.887966i	$-0.652118\pi$
$37$	2.60377	−	2.60377i	0.428057	−	0.428057i	0.887966	+	0.459909i	$0.152118\pi$
$38$	0.327964	−	2.64019i	0.0532028	−	0.428295i
$39$	−0.273870	+	0.676528i	−0.0438543	+	0.108331i
$40$	1.45329	−	3.73848i	0.229786	−	0.591106i
$41$	1.68231	+	1.68231i	0.262733	+	0.262733i	0.826164	−	0.563430i	$-0.190519\pi$
$41$	1.68231	+	1.68231i	0.262733	+	0.262733i	−0.563430	+	0.826164i	$0.690519\pi$
$42$	−0.0462269	+	0.372137i	−0.00713296	+	0.0574220i
$43$	−7.31241			−1.11513			−0.557566	−	0.830132i	$-0.688265\pi$
$43$	−7.31241			−1.11513			−0.557566	+	0.830132i	$0.688265\pi$
$44$	1.71724	−	1.02522i	0.258884	−	0.154558i
$45$	−2.96718	−	2.96718i	−0.442321	−	0.442321i
$46$	−7.58550	+	5.90919i	−1.11842	+	0.871262i
$47$	6.08062	+	6.08062i	0.886949	+	0.886949i	0.994229	−	0.107280i	$-0.0342141\pi$
$47$	6.08062	+	6.08062i	0.886949	+	0.886949i	−0.107280	+	0.994229i	$0.534214\pi$
$48$	−0.384172	+	0.712767i	−0.0554504	+	0.102879i
$49$		−	5.28411i		−	0.754872i
$50$	2.59771	+	3.33462i	0.367371	+	0.471587i
$51$	−0.507989			−0.0711327
$52$	−4.25902	+	5.81900i	−0.590619	+	0.806950i
$53$	7.95211			1.09231			0.546153	−	0.837685i	$-0.316092\pi$
$53$	7.95211			1.09231			0.546153	+	0.837685i	$0.316092\pi$
$54$	1.04837	+	1.34576i	0.142664	+	0.183135i
$55$		−	1.41811i		−	0.191218i
$56$	−1.34242	+	3.45327i	−0.179388	+	0.461462i
$57$	0.269276	+	0.269276i	0.0356664	+	0.0356664i
$58$	−6.55582	+	5.10706i	−0.860822	+	0.670590i
$59$	−4.24939	−	4.24939i	−0.553224	−	0.553224i	0.374146	−	0.927370i	$-0.377936\pi$
$59$	−4.24939	−	4.24939i	−0.553224	−	0.553224i	−0.927370	+	0.374146i	$0.877936\pi$
$60$	0.294304	+	0.492957i	0.0379945	+	0.0636405i
$61$	6.72879			0.861534			0.430767	−	0.902463i	$-0.358243\pi$
$61$	6.72879			0.861534			0.430767	+	0.902463i	$0.358243\pi$
$62$	−1.07291	+	8.63713i	−0.136259	+	1.09692i
$63$	2.74081	+	2.74081i	0.345309	+	0.345309i
$64$	−5.40329	+	5.89953i	−0.675411	+	0.737441i
$65$	1.99464	+	4.70796i	0.247404	+	0.583951i
$66$	−0.0352898	+	0.284091i	−0.00434388	+	0.0349692i
$67$	−5.14443	+	5.14443i	−0.628493	+	0.628493i	−0.947689	−	0.319196i	$-0.896587\pi$
$67$	−5.14443	+	5.14443i	−0.628493	+	0.628493i	0.319196	+	0.947689i	$0.396587\pi$
$68$	−4.86645	−	1.22797i	−0.590144	−	0.148913i
$69$		−	1.37634i		−	0.165692i
$70$	1.61445	+	2.07244i	0.192964	+	0.247704i
$71$	3.76978	−	3.76978i	0.447391	−	0.447391i	−0.447095	−	0.894486i	$-0.647542\pi$
$71$	3.76978	−	3.76978i	0.447391	−	0.447391i	0.894486	+	0.447095i	$0.147542\pi$
$72$	3.37167	+	7.66018i	0.397355	+	0.902761i
$73$	4.32502	−	4.32502i	0.506206	−	0.506206i	−0.407154	−	0.913360i	$-0.633479\pi$
$73$	4.32502	−	4.32502i	0.506206	−	0.506206i	0.913360	+	0.407154i	$0.133479\pi$
$74$	−0.641947	+	5.16782i	−0.0746249	+	0.600747i
$75$	−0.605045			−0.0698646
$76$	1.92869	+	3.23054i	0.221236	+	0.370569i
$77$			1.30992i			0.149279i
$78$	−0.282429	−	0.992786i	−0.0319788	−	0.112411i
$79$		−	10.0181i		−	1.12712i	−0.826074	−	0.563562i	$-0.809430\pi$
$79$		−	10.0181i		−	1.12712i	0.826074	−	0.563562i	$-0.190570\pi$
$80$	1.62776	+	5.43388i	0.181989	+	0.607526i
$81$	8.63289			0.959210
$82$	−3.33896	−	0.414766i	−0.368727	−	0.0458033i
$83$	−7.24721	+	7.24721i	−0.795484	+	0.795484i	−0.982380	−	0.186895i	$-0.940157\pi$
$83$	−7.24721	+	7.24721i	−0.795484	+	0.795484i	0.186895	+	0.982380i	$0.440157\pi$
$84$	−0.271851	−	0.455349i	−0.0296614	−	0.0496826i
$85$	−2.51641	+	2.51641i	−0.272943	+	0.272943i
$86$	8.15806	−	6.35522i	0.879706	−	0.685301i
$87$		−	1.18951i		−	0.127529i
$88$	−1.02481	+	2.63624i	−0.109245	+	0.281024i
$89$	0.716716	−	0.716716i	0.0759717	−	0.0759717i	−0.668100	−	0.744072i	$-0.732892\pi$
$89$	0.716716	−	0.716716i	0.0759717	−	0.0759717i	0.744072	+	0.668100i	$0.232892\pi$
$90$	5.88909	+	0.731544i	0.620765	+	0.0771115i
$91$	−1.84246	−	4.34879i	−0.193143	−	0.455877i
$92$	3.32705	−	13.1851i	0.346869	−	1.37464i
$93$	−0.880912	−	0.880912i	−0.0913463	−	0.0913463i
$94$	−12.0685	−	1.49915i	−1.24477	−	0.154625i
$95$	2.66781			0.273711
$96$	−0.190867	−	1.12908i	−0.0194803	−	0.115236i
$97$	−8.88136	−	8.88136i	−0.901765	−	0.901765i	0.0938236	−	0.995589i	$-0.470091\pi$
$97$	−8.88136	−	8.88136i	−0.901765	−	0.901765i	−0.995589	+	0.0938236i	$0.970091\pi$
$98$	4.59242	+	5.89519i	0.463904	+	0.595504i
$99$	2.09235	+	2.09235i	0.210289	+	0.210289i
$100$	−5.79624	−	1.46259i	−0.579624	−	0.146259i
$101$			4.15143i			0.413083i	0.978438	+	0.206541i	$0.0662208\pi$
$101$			4.15143i			0.413083i	−0.978438	+	0.206541i	$0.933779\pi$
$102$	0.566735	−	0.441493i	0.0561152	−	0.0437143i
$103$	−2.49053			−0.245399			−0.122699	−	0.992444i	$-0.539155\pi$
$103$	−2.49053			−0.245399			−0.122699	+	0.992444i	$0.539155\pi$
$104$	−0.305743	−	10.1935i	−0.0299806	−	0.999550i
$105$	−0.376031			−0.0366968
$106$	−8.87173	+	6.91118i	−0.861699	+	0.671273i
$107$			6.95039i			0.671920i	0.941876	+	0.335960i	$0.109061\pi$
$107$			6.95039i			0.671920i	−0.941876	+	0.335960i	$0.890939\pi$
$108$	−2.33921	−	0.590261i	−0.225090	−	0.0567979i
$109$	12.8711	+	12.8711i	1.23283	+	1.23283i	0.962872	+	0.269959i	$0.0870100\pi$
$109$	12.8711	+	12.8711i	1.23283	+	1.23283i	0.269959	+	0.962872i	$0.412990\pi$
$110$	1.23248	+	1.58211i	0.117512	+	0.150848i
$111$	−0.527073	−	0.527073i	−0.0500275	−	0.0500275i
$112$	−1.50357	−	5.01932i	−0.142074	−	0.474281i
$113$	−0.712320			−0.0670095			−0.0335047	−	0.999439i	$-0.510667\pi$
$113$	−0.712320			−0.0670095			−0.0335047	+	0.999439i	$0.510667\pi$
$114$	−0.534444	−	0.0663887i	−0.0500553	−	0.00621787i
$115$	−6.81794	−	6.81794i	−0.635776	−	0.635776i
$116$	2.87543	−	11.3953i	0.266977	−	1.05803i
$117$	−9.88932	−	4.00337i	−0.914268	−	0.370111i
$118$	8.43397	+	1.04767i	0.776410	+	0.0964457i
$119$	2.32443	−	2.32443i	0.213080	−	0.213080i
$120$	−0.756769	−	0.294185i	−0.0690832	−	0.0268553i
$121$			1.00000i			0.0909091i
$122$	−7.50695	+	5.84800i	−0.679647	+	0.529453i
$123$	0.340545	−	0.340545i	0.0307059	−	0.0307059i
$124$	−6.30955	−	10.5684i	−0.566614	−	0.949074i
$125$	−8.01098	+	8.01098i	−0.716524	+	0.716524i
$126$	−5.43981	−	0.675733i	−0.484616	−	0.0601991i
$127$	−20.5404			−1.82266			−0.911331	−	0.411674i	$-0.864944\pi$
$127$	−20.5404			−1.82266			−0.911331	+	0.411674i	$0.864944\pi$
$128$	0.900870	−	11.2778i	0.0796264	−	0.996825i
$129$			1.48023i			0.130327i
$130$	−6.31700	−	3.51888i	−0.554038	−	0.308626i
$131$		−	7.57563i		−	0.661886i	−0.943651	−	0.330943i	$-0.892633\pi$
$131$		−	7.57563i		−	0.661886i	0.943651	−	0.330943i	$-0.107367\pi$
$132$	−0.207533	−	0.347615i	−0.0180634	−	0.0302560i
$133$	−2.46428			−0.213680
$134$	1.26834	−	10.2104i	0.109568	−	0.882044i
$135$	−1.20959	+	1.20959i	−0.104105	+	0.104105i
$136$	6.49646	−	2.85945i	0.557067	−	0.245196i
$137$	−14.0399	+	14.0399i	−1.19951	+	1.19951i	−0.225200	+	0.974312i	$0.572304\pi$
$137$	−14.0399	+	14.0399i	−1.19951	+	1.19951i	−0.974312	+	0.225200i	$0.927696\pi$
$138$	1.19618	+	1.53551i	0.101825	+	0.130711i
$139$			1.83889i			0.155973i	0.996954	+	0.0779865i	$0.0248491\pi$
$139$			1.83889i			0.155973i	−0.996954	+	0.0779865i	$0.975151\pi$
$140$	−3.60231	−	0.908985i	−0.304451	−	0.0768233i
$141$	1.23088	−	1.23088i	0.103659	−	0.103659i
$142$	−0.929422	+	7.48206i	−0.0779954	+	0.627881i
$143$	−1.40655	−	3.31988i	−0.117621	−	0.277623i
$144$	−10.4191	−	5.61573i	−0.868255	−	0.467977i
$145$	−5.89245	−	5.89245i	−0.489342	−	0.489342i
$146$	−1.06631	+	8.58407i	−0.0882488	+	0.710423i
$147$	−1.06964			−0.0882228
$148$	−3.77517	−	6.32337i	−0.310317	−	0.519778i
$149$	−11.4076	−	11.4076i	−0.934550	−	0.934550i	0.0634362	−	0.997986i	$-0.479794\pi$
$149$	−11.4076	−	11.4076i	−0.934550	−	0.934550i	−0.997986	+	0.0634362i	$0.979794\pi$
$150$	0.675016	−	0.525845i	0.0551148	−	0.0429351i
$151$	12.8440	+	12.8440i	1.04523	+	1.04523i	0.998928	+	0.0462984i	$0.0147425\pi$
$151$	12.8440	+	12.8440i	1.04523	+	1.04523i	0.0462984	+	0.998928i	$0.485257\pi$
$152$	−4.95941	−	1.92791i	−0.402261	−	0.156374i
$153$		−	7.42565i		−	0.600329i
$154$	−1.13845	−	1.46141i	−0.0917391	−	0.117764i
$155$	−8.72750			−0.701010
$156$	1.17792	+	0.862139i	0.0943092	+	0.0690263i
$157$	−6.75652			−0.539229			−0.269615	−	0.962968i	$-0.586896\pi$
$157$	−6.75652			−0.539229			−0.269615	+	0.962968i	$0.586896\pi$
$158$	8.70674	+	11.1767i	0.692671	+	0.889167i
$159$		−	1.60972i		−	0.127659i
$160$	−6.53858	−	4.64760i	−0.516920	−	0.367425i
$161$	6.29779	+	6.29779i	0.496335	+	0.496335i
$162$	−9.63124	+	7.50285i	−0.756702	+	0.589479i
$163$	5.54407	+	5.54407i	0.434245	+	0.434245i	0.890070	−	0.455825i	$-0.150656\pi$
$163$	5.54407	+	5.54407i	0.434245	+	0.434245i	−0.455825	+	0.890070i	$0.650656\pi$
$164$	4.08557	−	2.43916i	0.319030	−	0.190467i
$165$	−0.287064			−0.0223479
$166$	1.78676	−	14.3839i	0.138680	−	1.11640i
$167$	−1.19263	−	1.19263i	−0.0922886	−	0.0922886i	0.659455	−	0.751744i	$-0.270787\pi$
$167$	−1.19263	−	1.19263i	−0.0922886	−	0.0922886i	−0.751744	+	0.659455i	$0.770787\pi$
$168$	0.699033	+	0.271741i	0.0539316	+	0.0209653i
$169$	9.33913	+	9.04326i	0.718395	+	0.695636i
$170$	0.620409	−	4.99444i	0.0475832	−	0.383056i
$171$	−3.93621	+	3.93621i	−0.301009	+	0.301009i
$172$	−3.57818	+	14.1803i	−0.272834	+	1.08124i
$173$			8.36093i			0.635670i	0.948146	+	0.317835i	$0.102956\pi$
$173$			8.36093i			0.635670i	−0.948146	+	0.317835i	$0.897044\pi$
$174$	1.03380	+	1.32707i	0.0783725	+	0.100605i
$175$	2.76854	−	2.76854i	0.209282	−	0.209282i
$176$	−1.14783	−	3.83177i	−0.0865212	−	0.288831i
$177$	−0.860191	+	0.860191i	−0.0646559	+	0.0646559i
$178$	−0.176703	+	1.42250i	−0.0132444	+	0.106621i
$179$	−5.52344			−0.412841			−0.206421	−	0.978463i	$-0.566181\pi$
$179$	−5.52344			−0.412841			−0.206421	+	0.978463i	$0.566181\pi$
$180$	−7.20593	+	4.30207i	−0.537098	+	0.320657i
$181$		−	22.6859i		−	1.68623i	−0.537732	−	0.843116i	$-0.680719\pi$
$181$		−	22.6859i		−	1.68623i	0.537732	−	0.843116i	$-0.319281\pi$
$182$	5.83507	+	3.25042i	0.432524	+	0.240937i
$183$		−	1.36209i		−	0.100688i
$184$	7.74738	+	17.6014i	0.571144	+	1.29760i
$185$	−5.22189			−0.383921
$186$	1.74839	+	0.217185i	0.128198	+	0.0159247i
$187$	1.77448	−	1.77448i	0.129763	−	0.129763i
$188$	14.7671	−	8.81620i	1.07700	−	0.642987i
$189$	1.11731	−	1.11731i	0.0812722	−	0.0812722i
$190$	−2.97633	+	2.31859i	−0.215926	+	0.168208i
$191$			8.77267i			0.634768i	0.948297	+	0.317384i	$0.102804\pi$
$191$			8.77267i			0.634768i	−0.948297	+	0.317384i	$0.897196\pi$
$192$	1.19422	+	1.09377i	0.0861856	+	0.0789360i
$193$	1.99961	−	1.99961i	0.143935	−	0.143935i	−0.631467	−	0.775403i	$-0.717547\pi$
$193$	1.99961	−	1.99961i	0.143935	−	0.143935i	0.775403	+	0.631467i	$0.217547\pi$
$194$	17.6272	+	2.18966i	1.26556	+	0.157208i
$195$	0.953018	−	0.403768i	0.0682470	−	0.0289144i
$196$	−10.2470	−	2.58567i	−0.731930	−	0.184691i
$197$	7.04022	+	7.04022i	0.501595	+	0.501595i	0.911933	−	0.410338i	$-0.134589\pi$
$197$	7.04022	+	7.04022i	0.501595	+	0.501595i	−0.410338	+	0.911933i	$0.634589\pi$
$198$	−4.15277	−	0.515858i	−0.295125	−	0.0366604i
$199$	−23.0433			−1.63350			−0.816749	−	0.576993i	$-0.804226\pi$
$199$	−23.0433			−1.63350			−0.816749	+	0.576993i	$0.804226\pi$
$200$	7.73768	−	3.40578i	0.547137	−	0.240825i
$201$	1.04137	+	1.04137i	0.0734526	+	0.0734526i
$202$	−3.60801	−	4.63153i	−0.253859	−	0.325873i
$203$	5.44291	+	5.44291i	0.382017	+	0.382017i
$204$	−0.248574	+	0.985100i	−0.0174037	+	0.0689708i
$205$		−	3.37390i		−	0.235643i
$206$	2.77854	−	2.16452i	0.193590	−	0.150809i
$207$	20.1190			1.39837
$208$	9.20023	+	11.1066i	0.637922	+	0.770101i
$209$	−1.88124			−0.130128
$210$	0.419517	−	0.326808i	0.0289494	−	0.0225519i
$211$		−	0.539925i		−	0.0371700i	−0.999827	−	0.0185850i	$-0.994084\pi$
$211$		−	0.539925i		−	0.0371700i	0.999827	−	0.0185850i	$-0.00591613\pi$
$212$	3.89120	−	15.4209i	0.267249	−	1.05911i
$213$	−0.763105	−	0.763105i	−0.0522871	−	0.0522871i
$214$	−6.04059	−	7.75418i	−0.412926	−	0.530065i
$215$	7.33257	+	7.33257i	0.500077	+	0.500077i
$216$	3.12272	−	1.37448i	0.212474	−	0.0935218i
$217$	8.06166			0.547261
$218$	−25.5459	−	3.17332i	−1.73019	−	0.214924i
$219$	−0.875500	−	0.875500i	−0.0591608	−	0.0591608i
$220$	−2.75002	−	0.693924i	−0.185407	−	0.0467843i
$221$	−3.39518	+	8.38696i	−0.228385	+	0.564168i
$222$	1.04611	+	0.129947i	0.0702100	+	0.00872149i
$223$	−14.8991	+	14.8991i	−0.997717	+	0.997717i	−0.999997	−	0.00228004i	$-0.999274\pi$
$223$	−14.8991	+	14.8991i	−0.997717	+	0.997717i	0.00228004	+	0.999997i	$0.499274\pi$
$224$	6.03974	+	4.29303i	0.403547	+	0.286840i
$225$		−	8.84440i		−	0.589627i
$226$	0.794697	−	0.619078i	0.0528625	−	0.0411804i
$227$	0.389800	−	0.389800i	0.0258719	−	0.0258719i	−0.694052	−	0.719924i	$-0.744176\pi$
$227$	0.389800	−	0.389800i	0.0258719	−	0.0258719i	0.719924	+	0.694052i	$0.244176\pi$
$228$	0.653948	−	0.390419i	0.0433088	−	0.0258561i
$229$	−6.99833	+	6.99833i	−0.462462	+	0.462462i	−0.899462	−	0.436999i	$-0.856041\pi$
$229$	−6.99833	+	6.99833i	−0.462462	+	0.462462i	0.436999	+	0.899462i	$0.356041\pi$
$230$	13.5319	+	1.68093i	0.892265	+	0.110837i
$231$	0.265163			0.0174464
$232$	6.69573	+	15.2122i	0.439596	+	0.998729i
$233$		−	12.2438i		−	0.802118i	−0.916052	−	0.401059i	$-0.868642\pi$
$233$		−	12.2438i		−	0.802118i	0.916052	−	0.401059i	$-0.131358\pi$
$234$	14.5123	−	4.12848i	0.948699	−	0.269887i
$235$		−	12.1947i		−	0.795498i
$236$	−10.3198	+	6.16114i	−0.671765	+	0.401056i
$237$	−2.02793			−0.131728
$238$	−0.573077	+	4.61340i	−0.0371471	+	0.299042i
$239$	16.1909	−	16.1909i	1.04730	−	1.04730i	0.0484764	−	0.998824i	$-0.484563\pi$
$239$	16.1909	−	16.1909i	1.04730	−	1.04730i	0.998824	−	0.0484764i	$-0.0154366\pi$
$240$	1.09996	−	0.329501i	0.0710022	−	0.0212692i
$241$	−18.2706	+	18.2706i	−1.17691	+	1.17691i	−0.196386	+	0.980527i	$0.562921\pi$
$241$	−18.2706	+	18.2706i	−1.17691	+	1.17691i	−0.980527	+	0.196386i	$0.937079\pi$
$242$	−0.869100	−	1.11565i	−0.0558679	−	0.0717164i
$243$		−	5.36632i		−	0.344250i
$244$	3.29260	−	13.0486i	0.210787	−	0.835350i
$245$	−5.29867	+	5.29867i	−0.338520	+	0.338520i
$246$	−0.0839598	+	0.675896i	−0.00535308	+	0.0430935i
$247$	6.24550	−	2.64605i	0.397392	−	0.168364i
$248$	16.2243	+	6.30700i	1.03024	+	0.400495i
$249$	1.46703	+	1.46703i	0.0929691	+	0.0929691i
$250$	1.97507	−	15.8998i	0.124914	−	1.00559i
$251$	22.5957			1.42623			0.713116	−	0.701047i	$-0.247283\pi$
$251$	22.5957			1.42623			0.713116	+	0.701047i	$0.247283\pi$
$252$	6.65617	−	3.97386i	0.419300	−	0.250329i
$253$	4.80776	+	4.80776i	0.302261	+	0.302261i
$254$	22.9158	−	17.8516i	1.43786	−	1.12011i
$255$	0.509389	+	0.509389i	0.0318992	+	0.0318992i
$256$	8.79647	+	13.3650i	0.549780	+	0.835310i
$257$			24.6849i			1.53980i	0.638162	+	0.769902i	$0.279695\pi$
$257$			24.6849i			1.53980i	−0.638162	+	0.769902i	$0.720305\pi$
$258$	−1.28647	−	1.65141i	−0.0800919	−	0.102812i
$259$	4.82351			0.299718
$260$	10.1058	−	1.56428i	0.626735	−	0.0970128i
$261$	17.3880			1.07629
$262$	6.58398	+	8.45172i	0.406760	+	0.522149i
$263$			5.64916i			0.348342i	0.984715	+	0.174171i	$0.0557246\pi$
$263$			5.64916i			0.348342i	−0.984715	+	0.174171i	$0.944275\pi$
$264$	0.533645	+	0.207449i	0.0328436	+	0.0127676i
$265$	−7.97402	−	7.97402i	−0.489840	−	0.489840i
$266$	2.74926	−	2.14170i	0.168568	−	0.131316i
$267$	−0.145082	−	0.145082i	−0.00887890	−	0.00887890i
$268$	7.45884	+	12.4935i	0.455621	+	0.763161i
$269$	−27.7598			−1.69255			−0.846273	−	0.532750i	$-0.821159\pi$
$269$	−27.7598			−1.69255			−0.846273	+	0.532750i	$0.821159\pi$
$270$	0.298219	−	2.40073i	0.0181490	−	0.146104i
$271$	9.12941	+	9.12941i	0.554572	+	0.554572i	0.927757	−	0.373185i	$-0.121734\pi$
$271$	9.12941	+	9.12941i	0.554572	+	0.554572i	−0.373185	+	0.927757i	$0.621734\pi$
$272$	−4.76260	+	8.83622i	−0.288775	+	0.535774i
$273$	−0.880310	+	0.372964i	−0.0532788	+	0.0225728i
$274$	3.46148	−	27.8657i	0.209116	−	1.68343i
$275$	2.11351	−	2.11351i	0.127450	−	0.127450i
$276$	−2.66902	−	0.673484i	−0.160656	−	0.0405389i
$277$			14.8945i			0.894927i	0.894302	+	0.447463i	$0.147672\pi$
$277$			14.8945i			0.894927i	−0.894302	+	0.447463i	$0.852328\pi$
$278$	−1.59818	−	2.05155i	−0.0958527	−	0.123044i
$279$	12.8770	−	12.8770i	0.770923	−	0.770923i
$280$	4.80890	−	2.11667i	0.287387	−	0.126495i
$281$	−9.62151	+	9.62151i	−0.573971	+	0.573971i	−0.933236	−	0.359265i	$-0.883028\pi$
$281$	−9.62151	+	9.62151i	−0.573971	+	0.573971i	0.359265	+	0.933236i	$0.383028\pi$
$282$	−0.303467	+	2.44298i	−0.0180712	+	0.145477i
$283$	10.1763			0.604919			0.302460	−	0.953162i	$-0.402192\pi$
$283$	10.1763			0.604919			0.302460	+	0.953162i	$0.402192\pi$
$284$	−5.46575	−	9.15509i	−0.324333	−	0.543254i
$285$		−	0.540036i		−	0.0319890i
$286$	4.45452	+	2.48139i	0.263401	+	0.146727i
$287$			3.11650i			0.183961i
$288$	16.5046	−	2.79004i	0.972543	−	0.164405i
$289$	10.7024			0.629555
$290$	11.6950	+	1.45276i	0.686755	+	0.0853088i
$291$	−1.79782	+	1.79782i	−0.105390	+	0.105390i
$292$	−6.27079	−	10.5035i	−0.366970	−	0.614672i
$293$	−9.19403	+	9.19403i	−0.537121	+	0.537121i	−0.922682	−	0.385561i	$-0.874008\pi$
$293$	−9.19403	+	9.19403i	−0.537121	+	0.537121i	0.385561	+	0.922682i	$0.374008\pi$
$294$	1.19334	−	0.929628i	0.0695972	−	0.0542170i
$295$			8.52221i			0.496182i
$296$	9.70740	+	3.77364i	0.564231	+	0.219339i
$297$	0.852958	−	0.852958i	0.0494937	−	0.0494937i
$298$	22.6412	+	2.81250i	1.31157	+	0.162924i
$299$	−22.7235	−	9.19887i	−1.31414	−	0.531985i
$300$	−0.296067	+	1.17331i	−0.0170934	+	0.0677413i
$301$	−6.77315	−	6.77315i	−0.390398	−	0.390398i
$302$	−25.4920	−	3.16662i	−1.46690	−	0.182218i
$303$	0.840361			0.0482775
$304$	7.20849	−	2.15935i	0.413435	−	0.123847i
$305$	−6.74734	−	6.74734i	−0.386352	−	0.386352i
$306$	6.45364	+	8.28440i	0.368930	+	0.473588i
$307$	−12.4046	−	12.4046i	−0.707969	−	0.707969i	0.258139	−	0.966108i	$-0.416891\pi$
$307$	−12.4046	−	12.4046i	−0.707969	−	0.707969i	−0.966108	+	0.258139i	$0.916891\pi$
$308$	2.54022	+	0.640983i	0.144742	+	0.0365234i
$309$			0.504149i			0.0286800i
$310$	9.73680	−	7.58507i	0.553013	−	0.430803i
$311$	29.4514			1.67004			0.835019	−	0.550221i	$-0.185457\pi$
$311$	29.4514			1.67004			0.835019	+	0.550221i	$0.185457\pi$
$312$	−2.06343	+	0.0618906i	−0.116819	+	0.00350386i
$313$	−2.42084			−0.136834			−0.0684171	−	0.997657i	$-0.521795\pi$
$313$	−2.42084			−0.136834			−0.0684171	+	0.997657i	$0.521795\pi$
$314$	7.53789	−	5.87210i	0.425387	−	0.331382i
$315$		−	5.49672i		−	0.309705i
$316$	−19.4273	−	4.90215i	−1.09287	−	0.275768i
$317$	8.11559	+	8.11559i	0.455817	+	0.455817i	0.897280	−	0.441463i	$-0.145540\pi$
$317$	8.11559	+	8.11559i	0.455817	+	0.455817i	−0.441463	+	0.897280i	$0.645540\pi$
$318$	1.39901	+	1.79588i	0.0784524	+	0.100708i
$319$	4.15514	+	4.15514i	0.232643	+	0.232643i
$320$	11.3340	−	0.497611i	0.633588	−	0.0278173i
$321$	1.40695			0.0785280
$322$	−12.4995	−	1.55269i	−0.696570	−	0.0865280i
$323$	3.33823	+	3.33823i	0.185744	+	0.185744i
$324$	4.22433	−	16.7410i	0.234685	−	0.930057i
$325$	−4.04387	+	9.98938i	−0.224314	+	0.554111i
$326$	−11.0036	−	1.36686i	−0.609431	−	0.0757036i
$327$	2.60546	−	2.60546i	0.144082	−	0.144082i
$328$	−2.43818	+	6.27201i	−0.134626	+	0.346314i
$329$			11.2644i			0.621026i
$330$	0.320261	−	0.249487i	0.0176298	−	0.0137338i
$331$	−21.1540	+	21.1540i	−1.16273	+	1.16273i	−0.178853	+	0.983876i	$0.557239\pi$
$331$	−21.1540	+	21.1540i	−1.16273	+	1.16273i	−0.983876	+	0.178853i	$0.942761\pi$
$332$	10.5076	+	17.6002i	0.576681	+	0.965935i
$333$	7.70462	−	7.70462i	0.422210	−	0.422210i
$334$	2.36707	+	0.294038i	0.129520	+	0.0160890i
$335$	10.3172			0.563690
$336$	−1.01604	+	0.304363i	−0.0554297	+	0.0166044i
$337$			9.22301i			0.502409i	0.967934	+	0.251205i	$0.0808267\pi$
$337$			9.22301i			0.502409i	−0.967934	+	0.251205i	$0.919173\pi$
$338$	−18.2787	−	1.97243i	−0.994228	−	0.107286i
$339$			0.144193i			0.00783147i
$340$	3.64851	+	6.11122i	0.197868	+	0.331427i
$341$	6.15431			0.333275
$342$	0.970453	−	7.81237i	0.0524761	−	0.422445i
$343$	11.3782	−	11.3782i	0.614365	−	0.614365i
$344$	−8.33216	−	18.9300i	−0.449240	−	1.02064i
$345$	−1.38013	+	1.38013i	−0.0743038	+	0.0743038i
$346$	−7.26648	−	9.32783i	−0.390649	−	0.501467i
$347$			1.21276i			0.0651044i	0.999470	+	0.0325522i	$0.0103635\pi$
$347$			1.21276i			0.0651044i	−0.999470	+	0.0325522i	$0.989636\pi$
$348$	−2.30672	−	0.582063i	−0.123653	−	0.0312019i
$349$	20.0278	−	20.0278i	1.07207	−	1.07207i	0.0748724	−	0.997193i	$-0.476145\pi$
$349$	20.0278	−	20.0278i	1.07207	−	1.07207i	0.997193	−	0.0748724i	$-0.0238550\pi$
$350$	−0.682570	+	5.49484i	−0.0364849	+	0.293712i
$351$	−1.63200	+	4.03145i	−0.0871096	+	0.215183i
$352$	4.61077	+	3.27732i	0.245755	+	0.174682i
$353$	−20.6211	−	20.6211i	−1.09755	−	1.09755i	−0.994697	−	0.102853i	$-0.967203\pi$
$353$	−20.6211	−	20.6211i	−1.09755	−	1.09755i	−0.102853	−	0.994697i	$-0.532797\pi$
$354$	0.212076	−	1.70726i	0.0112717	−	0.0907399i
$355$	−7.56034			−0.401261
$356$	−1.03916	−	1.74058i	−0.0550751	−	0.0922503i
$357$	−0.470527	−	0.470527i	−0.0249029	−	0.0249029i
$358$	6.16220	−	4.80042i	0.325682	−	0.253710i
$359$	−0.721526	−	0.721526i	−0.0380807	−	0.0380807i	0.687810	−	0.725891i	$-0.258572\pi$
$359$	−0.721526	−	0.721526i	−0.0380807	−	0.0380807i	−0.725891	+	0.687810i	$0.758572\pi$
$360$	4.30033	−	11.0623i	0.226647	−	0.583032i
$361$			15.4609i			0.813733i
$362$	19.7163	+	25.3095i	1.03627	+	1.33024i
$363$	0.202427			0.0106246
$364$	−9.33480	+	1.44494i	−0.489277	+	0.0757356i
$365$	−8.67389			−0.454012
$366$	1.18379	+	1.51961i	0.0618777	+	0.0794311i
$367$			10.2398i			0.534512i	0.963626	+	0.267256i	$0.0861169\pi$
$367$			10.2398i			0.534512i	−0.963626	+	0.267256i	$0.913883\pi$
$368$	−23.9407	−	12.9037i	−1.24800	−	0.672654i
$369$	4.97801	+	4.97801i	0.259145	+	0.259145i
$370$	5.82578	−	4.53835i	0.302868	−	0.235938i
$371$	7.36567	+	7.36567i	0.382407	+	0.382407i
$372$	−2.13933	+	1.27722i	−0.110919	+	0.0662208i
$373$	18.9052			0.978877			0.489438	−	0.872038i	$-0.337202\pi$
$373$	18.9052			0.978877			0.489438	+	0.872038i	$0.337202\pi$
$374$	−0.437490	+	3.52189i	−0.0226221	+	0.182113i
$375$	1.62164	+	1.62164i	0.0837409	+	0.0837409i
$376$	−8.81263	+	22.6698i	−0.454477	+	1.16911i
$377$	−19.6390	−	7.95020i	−1.01146	−	0.409456i
$378$	−0.275467	+	2.21757i	−0.0141685	+	0.114060i
$379$	−0.138107	+	0.138107i	−0.00709410	+	0.00709410i	−0.710645	−	0.703551i	$-0.751597\pi$
$379$	−0.138107	+	0.138107i	−0.00709410	+	0.00709410i	0.703551	+	0.710645i	$0.251597\pi$
$380$	1.30544	−	5.17346i	0.0669676	−	0.265393i
$381$			4.15792i			0.213017i
$382$	−7.62433	−	9.78718i	−0.390094	−	0.500756i
$383$	8.73513	−	8.73513i	0.446344	−	0.446344i	−0.447793	−	0.894137i	$-0.647790\pi$
$383$	8.73513	−	8.73513i	0.446344	−	0.446344i	0.894137	+	0.447793i	$0.147790\pi$
$384$	−2.28292	−	0.182360i	−0.116500	−	0.00930603i
$385$	1.31353	−	1.31353i	0.0669437	−	0.0669437i
$386$	−0.492995	+	3.96873i	−0.0250928	+	0.202003i
$387$	−21.6376			−1.09990
$388$	−21.5688	+	12.8770i	−1.09499	+	0.653728i
$389$		−	13.9588i		−	0.707737i	−0.935295	−	0.353868i	$-0.884866\pi$
$389$		−	13.9588i		−	0.707737i	0.935295	−	0.353868i	$-0.115134\pi$
$390$	−0.712315	+	1.27873i	−0.0360695	+	0.0647510i
$391$		−	17.0626i		−	0.862891i
$392$	13.6793	−	6.02100i	0.690906	−	0.304106i
$393$	−1.53351			−0.0773553
$394$	−13.9731	−	1.73573i	−0.703952	−	0.0874450i
$395$	−10.0457	+	10.0457i	−0.505455	+	0.505455i
$396$	5.08136	−	3.03366i	0.255348	−	0.152447i
$397$	10.6366	−	10.6366i	0.533837	−	0.533837i	−0.387875	−	0.921712i	$-0.626791\pi$
$397$	10.6366	−	10.6366i	0.533837	−	0.533837i	0.921712	+	0.387875i	$0.126791\pi$
$398$	25.7082	−	20.0270i	1.28864	−	1.00386i
$399$			0.498836i			0.0249730i
$400$	−5.67254	+	10.5245i	−0.283627	+	0.526223i
$401$	22.9911	−	22.9911i	1.14812	−	1.14812i	0.161198	−	0.986922i	$-0.448464\pi$
$401$	22.9911	−	22.9911i	1.14812	−	1.14812i	0.986922	−	0.161198i	$-0.0515357\pi$
$402$	−2.06686	−	0.256745i	−0.103085	−	0.0128053i
$403$	−20.4316	+	8.65632i	−1.01777	+	0.431202i
$404$	8.05052	+	2.03142i	0.400528	+	0.101067i
$405$	−8.65668	−	8.65668i	−0.430154	−	0.430154i
$406$	−10.8028	−	1.34192i	−0.536133	−	0.0665985i
$407$	3.68229			0.182524
$408$	−0.578830	−	1.31506i	−0.0286564	−	0.0651051i
$409$	9.53938	+	9.53938i	0.471692	+	0.471692i	0.902462	−	0.430770i	$-0.141758\pi$
$409$	9.53938	+	9.53938i	0.471692	+	0.471692i	−0.430770	+	0.902462i	$0.641758\pi$
$410$	2.93226	+	3.76408i	0.144814	+	0.185894i
$411$	2.84206	+	2.84206i	0.140188	+	0.140188i
$412$	−1.21869	+	4.82967i	−0.0600405	+	0.237941i
$413$		−	7.87204i		−	0.387358i
$414$	−22.4457	+	17.4854i	−1.10314	+	0.859361i
$415$	14.5344			0.713464
$416$	−19.9169	−	4.39506i	−0.976507	−	0.215485i
$417$	0.372241			0.0182287
$418$	2.09880	−	1.63499i	0.102656	−	0.0799698i
$419$		−	35.6344i		−	1.74085i	−0.492299	−	0.870426i	$-0.663843\pi$
$419$		−	35.6344i		−	1.74085i	0.492299	−	0.870426i	$-0.336157\pi$
$420$	−0.184003	+	0.729204i	−0.00897842	+	0.0355815i
$421$	−4.09278	−	4.09278i	−0.199470	−	0.199470i	0.600303	−	0.799773i	$-0.295047\pi$
$421$	−4.09278	−	4.09278i	−0.199470	−	0.199470i	−0.799773	+	0.600303i	$0.795047\pi$
$422$	0.469249	+	0.602365i	0.0228427	+	0.0293227i
$423$	17.9927	+	17.9927i	0.874834	+	0.874834i
$424$	9.06106	+	20.5860i	0.440044	+	0.999747i
$425$	−7.50078			−0.363841
$426$	1.51457	+	0.188140i	0.0733811	+	0.00911540i
$427$	6.23257	+	6.23257i	0.301615	+	0.301615i
$428$	13.4783	+	3.40103i	0.651499	+	0.164395i
$429$	−0.672033	+	0.284722i	−0.0324461	+	0.0137465i
$430$	−14.5533	−	1.80781i	−0.701821	−	0.0871803i
$431$	−25.5223	+	25.5223i	−1.22936	+	1.22936i	−0.265160	+	0.964204i	$0.585425\pi$
$431$	−25.5223	+	25.5223i	−1.22936	+	1.22936i	−0.964204	+	0.265160i	$0.914575\pi$
$432$	−2.28929	+	4.24740i	−0.110143	+	0.204353i
$433$			14.7784i			0.710204i	0.934828	+	0.355102i	$0.115554\pi$
$433$			14.7784i			0.710204i	−0.934828	+	0.355102i	$0.884446\pi$
$434$	−8.99396	+	7.00639i	−0.431724	+	0.336318i
$435$	−1.19279	+	1.19279i	−0.0571899	+	0.0571899i
$436$	31.2581	−	18.6617i	1.49699	−	0.893732i
$437$	−9.04456	+	9.04456i	−0.432660	+	0.432660i
$438$	1.73764	+	0.215850i	0.0830279	+	0.0103137i
$439$	−23.8661			−1.13907			−0.569534	−	0.821968i	$-0.692876\pi$
$439$	−23.8661			−1.13907			−0.569534	+	0.821968i	$0.692876\pi$
$440$	3.67114	−	1.61587i	0.175015	−	0.0770337i
$441$		−	15.6358i		−	0.744562i
$442$	−3.50129	−	12.3076i	−0.166539	−	0.585414i
$443$			4.79777i			0.227949i	0.993484	+	0.113974i	$0.0363582\pi$
$443$			4.79777i			0.227949i	−0.993484	+	0.113974i	$0.963642\pi$
$444$	−1.28002	+	0.764195i	−0.0607470	+	0.0362671i
$445$	−1.43738			−0.0681384
$446$	3.67330	−	29.5709i	0.173936	−	1.40022i
$447$	−2.30921	+	2.30921i	−0.109222	+	0.109222i
$448$	−10.4693	+	0.459647i	−0.494627	+	0.0217163i
$449$	0.875430	−	0.875430i	0.0413141	−	0.0413141i	−0.686148	−	0.727462i	$-0.740700\pi$
$449$	0.875430	−	0.875430i	0.0413141	−	0.0413141i	0.727462	+	0.686148i	$0.240700\pi$
$450$	7.68667	+	9.86722i	0.362353	+	0.465145i
$451$			2.37915i			0.112030i
$452$	−0.348559	+	1.38134i	−0.0163949	+	0.0649729i
$453$	2.59996	−	2.59996i	0.122157	−	0.122157i
$454$	−0.0961032	+	0.773653i	−0.00451035	+	0.0363093i
$455$	−2.51323	+	6.20831i	−0.117822	+	0.291050i
$456$	−0.390261	+	1.00392i	−0.0182757	+	0.0470127i
$457$	−13.9862	−	13.9862i	−0.654246	−	0.654246i	0.299767	−	0.954012i	$-0.403091\pi$
$457$	−13.9862	−	13.9862i	−0.654246	−	0.654246i	−0.954012	+	0.299767i	$0.903091\pi$
$458$	1.72540	−	13.8899i	0.0806228	−	0.649032i
$459$	−3.02712			−0.141294
$460$	−16.5577	+	9.88523i	−0.772005	+	0.460901i
$461$	12.2601	+	12.2601i	0.571010	+	0.571010i	0.932411	−	0.361401i	$-0.117701\pi$
$461$	12.2601	+	12.2601i	0.571010	+	0.571010i	−0.361401	+	0.932411i	$0.617701\pi$
$462$	−0.295828	+	0.230453i	−0.0137632	+	0.0107217i
$463$	−10.0377	−	10.0377i	−0.466489	−	0.466489i	0.434286	−	0.900775i	$-0.357001\pi$
$463$	−10.0377	−	10.0377i	−0.466489	−	0.466489i	−0.900775	+	0.434286i	$0.857001\pi$
$464$	−20.6910	−	11.1521i	−0.960554	−	0.517725i
$465$			1.76668i			0.0819278i
$466$	10.6411	+	13.6597i	0.492939	+	0.632775i
$467$	3.03103			0.140259			0.0701297	−	0.997538i	$-0.477659\pi$
$467$	3.03103			0.140259			0.0701297	+	0.997538i	$0.477659\pi$
$468$	−12.6025	+	17.2186i	−0.582552	+	0.795928i
$469$	−9.53011			−0.440059
$470$	10.5985	+	13.6050i	0.488870	+	0.627553i
$471$			1.36770i			0.0630203i
$472$	6.15864	−	15.8426i	0.283475	−	0.729216i
$473$	−5.17066	−	5.17066i	−0.237747	−	0.237747i
$474$	2.26245	−	1.76248i	0.103918	−	0.0809532i
$475$	3.97603	+	3.97603i	0.182433	+	0.182433i
$476$	−3.37016	−	5.64498i	−0.154471	−	0.258737i
$477$	23.5305			1.07739
$478$	−3.99178	+	32.1348i	−0.182580	+	1.46981i
$479$	−11.3739	−	11.3739i	−0.519688	−	0.519688i	0.397789	−	0.917477i	$-0.369778\pi$
$479$	−11.3739	−	11.3739i	−0.519688	−	0.519688i	−0.917477	+	0.397789i	$0.869778\pi$
$480$	−0.940798	+	1.32358i	−0.0429414	+	0.0604131i
$481$	−12.2248	+	5.17930i	−0.557401	+	0.236156i
$482$	4.50453	−	36.2625i	0.205176	−	1.65171i
$483$	1.27484	−	1.27484i	0.0580072	−	0.0580072i
$484$	1.93922	+	0.489330i	0.0881462	+	0.0222423i
$485$			17.8117i			0.808786i
$486$	4.66387	+	5.98691i	0.211558	+	0.271572i
$487$	14.0464	−	14.0464i	0.636502	−	0.636502i	−0.313189	−	0.949691i	$-0.601397\pi$
$487$	14.0464	−	14.0464i	0.636502	−	0.636502i	0.949691	+	0.313189i	$0.101397\pi$
$488$	7.66715	+	17.4192i	0.347076	+	0.788530i
$489$	1.12227	−	1.12227i	0.0507507	−	0.0507507i
$490$	1.30636	−	10.5165i	0.0590154	−	0.475088i
$491$	−20.9435			−0.945168			−0.472584	−	0.881286i	$-0.656679\pi$
$491$	−20.9435			−0.945168			−0.472584	+	0.881286i	$0.656679\pi$
$492$	−0.493752	−	0.827029i	−0.0222600	−	0.0372854i
$493$		−	14.7464i		−	0.664146i
$494$	−4.66808	+	8.38002i	−0.210027	+	0.377035i
$495$		−	4.19622i		−	0.188606i
$496$	−23.5819	+	7.06413i	−1.05886	+	0.317189i
$497$	6.98355			0.313255
$498$	−2.91168	−	0.361689i	−0.130475	−	0.0162077i
$499$	9.44475	−	9.44475i	0.422805	−	0.422805i	−0.463363	−	0.886168i	$-0.653358\pi$
$499$	9.44475	−	9.44475i	0.422805	−	0.422805i	0.886168	+	0.463363i	$0.153358\pi$
$500$	11.6150	+	19.4550i	0.519439	+	0.870055i
$501$	−0.241420	+	0.241420i	−0.0107859	+	0.0107859i
$502$	−25.2088	+	19.6380i	−1.12513	+	0.876486i
$503$			4.65334i			0.207482i	0.994604	+	0.103741i	$0.0330813\pi$
$503$			4.65334i			0.207482i	−0.994604	+	0.103741i	$0.966919\pi$
$504$	−3.97225	+	10.2183i	−0.176938	+	0.455159i
$505$	4.16287	−	4.16287i	0.185245	−	0.185245i
$506$	−9.54218	−	1.18533i	−0.424202	−	0.0526944i
$507$	1.83060	−	1.89049i	0.0812997	−	0.0839596i
$508$	−10.0510	+	39.8322i	−0.445941	+	1.76727i
$509$	−20.3107	−	20.3107i	−0.900257	−	0.900257i	0.0952011	−	0.995458i	$-0.469651\pi$
$509$	−20.3107	−	20.3107i	−0.900257	−	0.900257i	−0.995458	+	0.0952011i	$0.969651\pi$
$510$	−1.01101	−	0.125587i	−0.0447682	−	0.00556110i
$511$	8.01214			0.354436
$512$	−21.4292	−	7.26554i	−0.947047	−	0.321094i
$513$	1.60462	+	1.60462i	0.0708457	+	0.0708457i
$514$	−21.4537	−	27.5396i	−0.946282	−	1.21472i
$515$	2.49739	+	2.49739i	0.110048	+	0.110048i
$516$	2.87048	+	0.724319i	0.126366	+	0.0318864i
$517$			8.59929i			0.378196i
$518$	−5.38132	+	4.19211i	−0.236442	+	0.184191i
$519$	1.69247			0.0742914
$520$	−9.91496	+	10.5281i	−0.434800	+	0.461689i
$521$	10.0920			0.442139			0.221069	−	0.975258i	$-0.429045\pi$
$521$	10.0920			0.442139			0.221069	+	0.975258i	$0.429045\pi$
$522$	−19.3988	+	15.1119i	−0.849064	+	0.661430i
$523$		−	4.24454i		−	0.185601i	−0.995685	−	0.0928005i	$-0.970418\pi$
$523$		−	4.24454i		−	0.185601i	0.995685	−	0.0928005i	$-0.0295819\pi$
$524$	−14.6908	−	3.70698i	−0.641770	−	0.161940i
$525$	−0.560426	−	0.560426i	−0.0244590	−	0.0244590i
$526$	−4.90969	−	6.30246i	−0.214073	−	0.274800i
$527$	−10.9207	−	10.9207i	−0.475714	−	0.475714i
$528$	−0.775653	+	0.232352i	−0.0337560	+	0.0101118i
$529$	23.2291			1.00996
$530$	15.8264	+	1.96596i	0.687455	+	0.0853958i
$531$	−12.5741	−	12.5741i	−0.545668	−	0.545668i
$532$	−1.20584	+	4.77877i	−0.0522800	+	0.207186i
$533$	−3.34638	−	7.89850i	−0.144948	−	0.342122i
$534$	0.287952	+	0.0357694i	0.0124609	+	0.00154789i
$535$	6.96955	−	6.96955i	0.301320	−	0.301320i
$536$	−19.1795	−	7.45582i	−0.828429	−	0.322043i
$537$			1.11809i			0.0482492i
$538$	30.9701	−	24.1261i	1.33522	−	1.04015i
$539$	3.73643	−	3.73643i	0.160939	−	0.160939i
$540$	1.75377	+	2.93754i	0.0754701	+	0.126412i
$541$	11.7803	−	11.7803i	0.506475	−	0.506475i	−0.406968	−	0.913442i	$-0.633414\pi$
$541$	11.7803	−	11.7803i	0.506475	−	0.506475i	0.913442	+	0.406968i	$0.133414\pi$
$542$	−18.1196	−	2.25081i	−0.778302	−	0.0966807i
$543$	−4.59224			−0.197072
$544$	−2.36619	−	13.9973i	−0.101449	−	0.600128i
$545$		−	25.8132i		−	1.10572i
$546$	0.657971	−	1.18117i	0.0281586	−	0.0505495i
$547$		−	41.2238i		−	1.76260i	−0.472554	−	0.881302i	$-0.656668\pi$
$547$		−	41.2238i		−	1.76260i	0.472554	−	0.881302i	$-0.343332\pi$
$548$	20.3563	+	34.0966i	0.869578	+	1.45654i
$549$	19.9107			0.849766
$550$	−0.521077	+	4.19479i	−0.0222188	+	0.178866i
$551$	−7.81683	+	7.81683i	−0.333008	+	0.333008i
$552$	3.56300	−	1.56828i	0.151651	−	0.0667502i
$553$	9.27931	−	9.27931i	0.394596	−	0.394596i
$554$	−12.9449	−	16.6170i	−0.549974	−	0.705990i
$555$			1.05705i			0.0448693i
$556$	3.56601	+	0.899825i	0.151233	+	0.0381611i
$557$	8.65617	−	8.65617i	0.366774	−	0.366774i	−0.499526	−	0.866299i	$-0.666492\pi$
$557$	8.65617	−	8.65617i	0.366774	−	0.366774i	0.866299	+	0.499526i	$0.166492\pi$
$558$	−3.17475	+	25.5575i	−0.134398	+	1.08193i
$559$	24.4387	+	9.89322i	1.03365	+	0.418439i
$560$	−3.52544	+	6.54087i	−0.148977	+	0.276402i
$561$	−0.359202	−	0.359202i	−0.0151655	−	0.0151655i
$562$	2.37214	−	19.0962i	0.100063	−	0.805527i
$563$	−42.7641			−1.80229			−0.901145	−	0.433517i	$-0.857272\pi$
$563$	−42.7641			−1.80229			−0.901145	+	0.433517i	$0.857272\pi$
$564$	−1.78463	−	2.98924i	−0.0751466	−	0.125870i
$565$	0.714284	+	0.714284i	0.0300501	+	0.0300501i
$566$	−11.3532	+	8.84424i	−0.477209	+	0.371751i
$567$	7.99625	+	7.99625i	0.335811	+	0.335811i
$568$	14.0545	+	5.46354i	0.589715	+	0.229245i
$569$		−	14.0794i		−	0.590241i	−0.955460	−	0.295120i	$-0.904640\pi$
$569$		−	14.0794i		−	0.590241i	0.955460	−	0.295120i	$-0.0953598\pi$
$570$	0.469345	+	0.602489i	0.0196587	+	0.0252355i
$571$	−47.6494			−1.99407			−0.997033	−	0.0769725i	$-0.975475\pi$
$571$	−47.6494			−1.99407			−0.997033	+	0.0769725i	$0.975475\pi$
$572$	−7.12623	+	1.10308i	−0.297963	+	0.0461219i
$573$	1.77582			0.0741860
$574$	−2.70855	−	3.47691i	−0.113053	−	0.145123i
$575$		−	20.3225i		−	0.847508i
$576$	−15.9885	+	17.4569i	−0.666186	+	0.727369i
$577$	15.4559	+	15.4559i	0.643437	+	0.643437i	0.951399	−	0.307961i	$-0.0996468\pi$
$577$	15.4559	+	15.4559i	0.643437	+	0.643437i	−0.307961	+	0.951399i	$0.599647\pi$
$578$	−11.9401	+	9.30149i	−0.496644	+	0.386891i
$579$	−0.404775	−	0.404775i	−0.0168219	−	0.0168219i
$580$	−14.3101	+	8.54339i	−0.594194	+	0.354745i
$581$	−13.4255			−0.556984
$582$	0.443245	−	3.56822i	0.0183731	−	0.147908i
$583$	5.62299	+	5.62299i	0.232880	+	0.232880i
$584$	16.1246	+	6.26825i	0.667240	+	0.259382i
$585$	5.90218	+	13.9310i	0.244025	+	0.575975i
$586$	2.26674	−	18.2478i	0.0936383	−	0.753810i
$587$	−16.1904	+	16.1904i	−0.668248	+	0.668248i	−0.957310	−	0.289062i	$-0.906657\pi$
$587$	−16.1904	+	16.1904i	−0.668248	+	0.668248i	0.289062	+	0.957310i	$0.406657\pi$
$588$	−0.523409	+	2.07427i	−0.0215850	+	0.0855415i
$589$			11.5778i			0.477053i
$590$	−7.40666	−	9.50777i	−0.304927	−	0.391429i
$591$	1.42513	−	1.42513i	0.0586220	−	0.0586220i
$592$	−14.1097	+	4.22665i	−0.579905	+	0.173714i
$593$	2.44426	−	2.44426i	0.100374	−	0.100374i	−0.655137	−	0.755510i	$-0.727389\pi$
$593$	2.44426	−	2.44426i	0.100374	−	0.100374i	0.755510	+	0.655137i	$0.227389\pi$
$594$	−0.210293	+	1.69291i	−0.00862842	+	0.0694608i
$595$	−4.66167			−0.191110
$596$	−27.7039	+	16.5398i	−1.13480	+	0.677495i
$597$			4.66459i			0.190909i
$598$	33.3462	−	9.48635i	1.36363	−	0.387926i
$599$			19.1093i			0.780785i	0.920649	+	0.390393i	$0.127661\pi$
$599$			19.1093i			0.780785i	−0.920649	+	0.390393i	$0.872339\pi$
$600$	−0.689421	−	1.56631i	−0.0281455	−	0.0639445i
$601$	41.0075			1.67273			0.836366	−	0.548171i	$-0.184676\pi$
$601$	41.0075			1.67273			0.836366	+	0.548171i	$0.184676\pi$
$602$	13.4430	+	1.66989i	0.547895	+	0.0680596i
$603$	−15.2225	+	15.2225i	−0.619908	+	0.619908i
$604$	31.1921	−	18.6223i	1.26919	−	0.757729i
$605$	1.00276	−	1.00276i	0.0407678	−	0.0407678i
$606$	−0.937544	+	0.730358i	−0.0380851	+	0.0296687i
$607$			45.7263i			1.85597i	0.372615	+	0.927986i	$0.378461\pi$
$607$			45.7263i			1.85597i	−0.372615	+	0.927986i	$0.621539\pi$
$608$	−6.16542	+	8.67397i	−0.250041	+	0.351776i
$609$	1.10179	−	1.10179i	0.0446468	−	0.0446468i
$610$	13.3918	+	1.66352i	0.542216	+	0.0673541i
$611$	−12.0953	−	28.5486i	−0.489323	−	1.15495i
$612$	−14.3999	−	3.63359i	−0.582083	−	0.146879i
$613$	0.0665917	+	0.0665917i	0.00268961	+	0.00268961i	0.708450	−	0.705761i	$-0.249395\pi$
$613$	0.0665917	+	0.0665917i	0.00268961	+	0.00268961i	−0.705761	+	0.708450i	$0.749395\pi$
$614$	24.6200	+	3.05830i	0.993583	+	0.123423i
$615$	−0.682967			−0.0275399
$616$	−3.39106	+	1.49259i	−0.136630	+	0.0601384i
$617$	20.6988	+	20.6988i	0.833303	+	0.833303i	0.987967	−	0.154664i	$-0.0494297\pi$
$617$	20.6988	+	20.6988i	0.833303	+	0.833303i	−0.154664	+	0.987967i	$0.549430\pi$
$618$	−0.438156	−	0.562452i	−0.0176252	−	0.0226251i
$619$	13.5383	+	13.5383i	0.544150	+	0.544150i	0.924743	−	0.380593i	$-0.124280\pi$
$619$	13.5383	+	13.5383i	0.544150	+	0.544150i	−0.380593	+	0.924743i	$0.624280\pi$
$620$	−4.27063	+	16.9245i	−0.171512	+	0.679705i
$621$		−	8.20164i		−	0.329120i
$622$	−32.8574	+	25.5963i	−1.31746	+	1.02632i
$623$	1.32772			0.0531940
$624$	2.24826	−	1.86237i	0.0900026	−	0.0745546i
$625$	1.12131			0.0448524
$626$	2.70080	−	2.10396i	0.107946	−	0.0840910i
$627$			0.380813i			0.0152082i
$628$	−3.30617	+	13.1024i	−0.131930	+	0.522841i
$629$	−6.53415	−	6.53415i	−0.260534	−	0.260534i
$630$	4.77720	+	6.13239i	0.190328	+	0.244320i
$631$	−31.5677	−	31.5677i	−1.25669	−	1.25669i	−0.952664	−	0.304027i	$-0.901669\pi$
$631$	−31.5677	−	31.5677i	−1.25669	−	1.25669i	−0.304027	−	0.952664i	$-0.598331\pi$
$632$	25.9344	−	11.4152i	1.03161	−	0.454071i
$633$	−0.109295			−0.00434410
$634$	−16.1074	−	2.00086i	−0.639706	−	0.0794643i
$635$	20.5970	+	20.5970i	0.817366	+	0.817366i
$636$	−3.12159	−	0.787683i	−0.123779	−	0.0312337i
$637$	−7.14905	+	17.6600i	−0.283256	+	0.699713i
$638$	−8.24690	−	1.02443i	−0.326498	−	0.0405576i
$639$	11.1549	−	11.1549i	0.441280	−	0.441280i
$640$	−12.2122	+	10.4055i	−0.482730	+	0.411314i
$641$			33.2761i			1.31433i	0.753747	+	0.657164i	$0.228244\pi$
$641$			33.2761i			1.31433i	−0.753747	+	0.657164i	$0.771756\pi$
$642$	−1.56965	+	1.22278i	−0.0619492	+	0.0482591i
$643$	2.19867	−	2.19867i	0.0867070	−	0.0867070i	−0.662423	−	0.749130i	$-0.730472\pi$
$643$	2.19867	−	2.19867i	0.0867070	−	0.0867070i	0.749130	+	0.662423i	$0.230472\pi$
$644$	15.2945	−	9.13107i	0.602686	−	0.359815i
$645$	1.48431	−	1.48431i	0.0584445	−	0.0584445i
$646$	−6.62553	−	0.823024i	−0.260678	−	0.0323814i
$647$	40.8314			1.60525			0.802623	−	0.596486i	$-0.203437\pi$
$647$	40.8314			1.60525			0.802623	+	0.596486i	$0.203437\pi$
$648$	9.83678	+	22.3484i	0.386425	+	0.877929i
$649$		−	6.00955i		−	0.235896i
$650$	−4.17024	−	14.6591i	−0.163570	−	0.574978i
$651$		−	1.63190i		−	0.0639590i
$652$	13.4640	−	8.03827i	0.527292	−	0.314803i
$653$	−3.31839			−0.129859			−0.0649293	−	0.997890i	$-0.520682\pi$
$653$	−3.31839			−0.129859			−0.0649293	+	0.997890i	$0.520682\pi$
$654$	−0.642364	+	5.17118i	−0.0251184	+	0.202209i
$655$	−7.59651	+	7.59651i	−0.296820	+	0.296820i
$656$	−2.73087	−	9.11636i	−0.106623	−	0.355934i
$657$	12.7978	−	12.7978i	0.499291	−	0.499291i
$658$	−9.78988	−	12.5671i	−0.381649	−	0.489915i
$659$		−	13.2542i		−	0.516310i	−0.966103	−	0.258155i	$-0.916885\pi$
$659$		−	13.2542i		−	0.516310i	0.966103	−	0.258155i	$-0.0831146\pi$
$660$	−0.140469	+	0.556678i	−0.00546774	+	0.0216687i
$661$	−8.39383	+	8.39383i	−0.326482	+	0.326482i	−0.851247	−	0.524765i	$-0.824153\pi$
$661$	−8.39383	+	8.39383i	−0.326482	+	0.326482i	0.524765	+	0.851247i	$0.324153\pi$
$662$	5.21542	−	41.9853i	0.202703	−	1.63181i
$663$	1.69774	+	0.687276i	0.0659349	+	0.0266916i
$664$	−27.0191	−	10.5034i	−1.04854	−	0.407610i
$665$	2.47107	+	2.47107i	0.0958240	+	0.0958240i
$666$	−1.89954	+	15.2917i	−0.0736056	+	0.592542i
$667$	39.9539			1.54702
$668$	−2.89636	+	1.72918i	−0.112064	+	0.0669040i
$669$	3.01597	+	3.01597i	0.116604	+	0.116604i
$670$	−11.5104	+	8.96670i	−0.444684	+	0.346414i
$671$	4.75798	+	4.75798i	0.183680	+	0.183680i
$672$	0.869023	−	1.22261i	0.0335233	−	0.0471630i
$673$		−	13.2992i		−	0.512645i	−0.966591	−	0.256322i	$-0.917489\pi$
$673$		−	13.2992i		−	0.512645i	0.966591	−	0.256322i	$-0.0825108\pi$
$674$	−8.01572	−	10.2896i	−0.308754	−	0.396341i
$675$	−3.60548			−0.138775
$676$	22.1067	−	13.6855i	0.850260	−	0.526364i
$677$	5.37562			0.206602			0.103301	−	0.994650i	$-0.467060\pi$
$677$	5.37562			0.206602			0.103301	+	0.994650i	$0.467060\pi$
$678$	−0.125318	−	0.160868i	−0.00481280	−	0.00617809i
$679$		−	16.4528i		−	0.631400i
$680$	−9.38170	−	3.64703i	−0.359772	−	0.139857i
$681$	−0.0789058	−	0.0789058i	−0.00302368	−	0.00302368i
$682$	−6.86603	+	5.34872i	−0.262914	+	0.204813i
$683$	13.0070	+	13.0070i	0.497698	+	0.497698i	0.910721	−	0.413023i	$-0.135527\pi$
$683$	13.0070	+	13.0070i	0.497698	+	0.497698i	−0.413023	+	0.910721i	$0.635527\pi$
$684$	5.70705	+	9.55926i	0.218215	+	0.365507i
$685$	28.1573			1.07583
$686$	−2.80524	+	22.5828i	−0.107105	+	0.862217i
$687$	1.41665	+	1.41665i	0.0540485	+	0.0540485i
$688$	25.7478	+	13.8777i	0.981627	+	0.529083i
$689$	−26.5767	−	10.7587i	−1.01249	−	0.409873i
$690$	0.340265	−	2.73921i	0.0129537	−	0.104280i
$691$	8.19265	−	8.19265i	0.311663	−	0.311663i	−0.533891	−	0.845554i	$-0.679271\pi$
$691$	8.19265	−	8.19265i	0.311663	−	0.311663i	0.845554	+	0.533891i	$0.179271\pi$
$692$	16.2136	+	4.09125i	0.616350	+	0.155526i
$693$			3.87609i			0.147240i
$694$	−1.05401	−	1.35301i	−0.0400097	−	0.0513596i
$695$	1.84396	−	1.84396i	0.0699455	−	0.0699455i
$696$	3.07935	−	1.35539i	0.116723	−	0.0513761i
$697$	4.22176	−	4.22176i	0.159910	−	0.159910i
$698$	−4.93777	+	39.7502i	−0.186897	+	1.50457i
$699$	−2.47847			−0.0937444
$700$	−4.01406	−	6.72352i	−0.151717	−	0.254125i
$701$			34.7785i			1.31356i	0.754080	+	0.656782i	$0.228083\pi$
$701$			34.7785i			1.31356i	−0.754080	+	0.656782i	$0.771917\pi$
$702$	−1.68300	−	5.91604i	−0.0635207	−	0.223286i
$703$			6.92727i			0.261267i
$704$	−7.99230	+	0.350897i	−0.301221	+	0.0132249i
$705$	−2.46854			−0.0929707
$706$	40.9276	+	5.08403i	1.54033	+	0.191340i
$707$	−3.84528	+	3.84528i	−0.144617	+	0.144617i
$708$	1.24718	+	2.08901i	0.0468718	+	0.0785099i
$709$	10.9678	−	10.9678i	0.411906	−	0.411906i	−0.470496	−	0.882402i	$-0.655925\pi$
$709$	10.9678	−	10.9678i	0.411906	−	0.411906i	0.882402	+	0.470496i	$0.155925\pi$
$710$	8.43466	−	6.57070i	0.316547	−	0.246594i
$711$		−	29.6438i		−	1.11173i
$712$	2.67206	+	1.03874i	0.100140	+	0.0389283i
$713$	29.5885	−	29.5885i	1.10810	−	1.10810i
$714$	0.933876	+	0.116006i	0.0349494	+	0.00434142i
$715$	−1.91861	+	4.73946i	−0.0717520	+	0.177246i
$716$	−2.70278	+	10.7111i	−0.101008	+	0.400294i
$717$	−3.27747	−	3.27747i	−0.122399	−	0.122399i
$718$	1.43205	+	0.177889i	0.0534434	+	0.00663875i
$719$	29.8478			1.11313			0.556567	−	0.830803i	$-0.312118\pi$
$719$	29.8478			1.11313			0.556567	+	0.830803i	$0.312118\pi$
$720$	4.81657	+	16.0790i	0.179503	+	0.599228i
$721$	−2.30686	−	2.30686i	−0.0859120	−	0.0859120i
$722$	−13.4371	−	17.2489i	−0.500077	−	0.641938i
$723$	3.69846	+	3.69846i	0.137547	+	0.137547i
$724$	−43.9929	−	11.1009i	−1.63498	−	0.412562i
$725$		−	17.5639i		−	0.652307i
$726$	−0.225836	+	0.175929i	−0.00838158	+	0.00652934i
$727$	−4.47370			−0.165920			−0.0829602	−	0.996553i	$-0.526437\pi$
$727$	−4.47370			−0.165920			−0.0829602	+	0.996553i	$0.526437\pi$
$728$	9.15853	−	9.72492i	0.339438	−	0.360430i
$729$	24.8124			0.918977
$730$	9.67698	−	7.53848i	0.358161	−	0.279011i
$731$			18.3505i			0.678716i
$732$	−2.64138	−	0.666510i	−0.0976283	−	0.0246349i
$733$	−16.3359	−	16.3359i	−0.603378	−	0.603378i	0.337829	−	0.941207i	$-0.390307\pi$
$733$	−16.3359	−	16.3359i	−0.603378	−	0.603378i	−0.941207	+	0.337829i	$0.890307\pi$
$734$	−8.89939	−	11.4240i	−0.328482	−	0.421666i
$735$	1.07259	+	1.07259i	0.0395632	+	0.0395632i
$736$	37.9240	−	6.41092i	1.39790	−	0.236310i
$737$	−7.27533			−0.267990
$738$	−9.88007	−	1.22730i	−0.363691	−	0.0451777i
$739$	−2.71185	−	2.71185i	−0.0997571	−	0.0997571i	0.655467	−	0.755224i	$-0.272472\pi$
$739$	−2.71185	−	2.71185i	−0.0997571	−	0.0997571i	−0.755224	+	0.655467i	$0.772472\pi$
$740$	−2.55523	+	10.1264i	−0.0939320	+	0.372253i
$741$	−0.535631	−	1.26426i	−0.0196769	−	0.0464436i
$742$	−14.6190	−	1.81597i	−0.536680	−	0.0666664i
$743$	−17.4996	+	17.4996i	−0.641997	+	0.641997i	−0.951046	−	0.309049i	$-0.899989\pi$
$743$	−17.4996	+	17.4996i	−0.641997	+	0.641997i	0.309049	+	0.951046i	$0.399989\pi$
$744$	1.27670	−	3.28422i	0.0468063	−	0.120405i
$745$			22.8781i			0.838190i
$746$	−21.0916	+	16.4306i	−0.772217	+	0.601565i
$747$	−21.4447	+	21.4447i	−0.784619	+	0.784619i
$748$	−2.57279	−	4.30941i	−0.0940707	−	0.157568i
$749$	−6.43783	+	6.43783i	−0.235233	+	0.235233i
$750$	−3.21853	−	0.399807i	−0.117524	−	0.0145989i
$751$	−6.38937			−0.233151			−0.116576	−	0.993182i	$-0.537192\pi$
$751$	−6.38937			−0.233151			−0.116576	+	0.993182i	$0.537192\pi$
$752$	−9.87055	−	32.9505i	−0.359942	−	1.20158i
$753$		−	4.57398i		−	0.166685i
$754$	28.8197	−	8.19865i	1.04955	−	0.298577i
$755$		−	25.7587i		−	0.937455i
$756$	−1.61997	−	2.71343i	−0.0589177	−	0.0986866i
$757$	42.0627			1.52879			0.764397	−	0.644745i	$-0.223037\pi$
$757$	42.0627			1.52879			0.764397	+	0.644745i	$0.223037\pi$
$758$	0.0340497	−	0.274108i	0.00123674	−	0.00995605i
$759$	0.973219	−	0.973219i	0.0353256	−	0.0353256i
$760$	3.03985	+	6.90630i	0.110267	+	0.250518i
$761$	−25.9339	+	25.9339i	−0.940105	+	0.940105i	−0.998305	−	0.0582001i	$-0.981464\pi$
$761$	−25.9339	+	25.9339i	−0.940105	+	0.940105i	0.0582001	+	0.998305i	$0.481464\pi$
$762$	−3.61365	−	4.63876i	−0.130909	−	0.168045i
$763$			23.8439i			0.863206i
$764$	17.0121	+	4.29273i	0.615476	+	0.155305i
$765$	−7.44612	+	7.44612i	−0.269215	+	0.269215i
$766$	−2.15361	+	17.3370i	−0.0778129	+	0.626412i
$767$	8.45271	+	19.9510i	0.305209	+	0.720389i
$768$	2.70542	−	1.78064i	0.0976236	−	0.0642533i
$769$	−31.1703	−	31.1703i	−1.12403	−	1.12403i	−0.991129	−	0.132901i	$-0.957571\pi$
$769$	−31.1703	−	31.1703i	−1.12403	−	1.12403i	−0.132901	−	0.991129i	$-0.542429\pi$
$770$	−0.323845	+	2.60703i	−0.0116706	+	0.0939507i
$771$	4.99689			0.179959
$772$	−2.89921	−	4.85615i	−0.104345	−	0.174777i
$773$	−31.6240	−	31.6240i	−1.13744	−	1.13744i	−0.988908	−	0.148529i	$-0.952546\pi$
$773$	−31.6240	−	31.6240i	−1.13744	−	1.13744i	−0.148529	−	0.988908i	$-0.547454\pi$
$774$	24.1399	−	18.8052i	0.867690	−	0.675940i
$775$	−13.0072	−	13.0072i	−0.467234	−	0.467234i
$776$	12.8717	−	33.1115i	0.462069	−	1.18864i
$777$		−	0.976406i		−	0.0350284i
$778$	12.1316	+	15.5730i	0.434937	+	0.558320i
$779$	−4.47576			−0.160361
$780$	−0.316653	−	2.04568i	−0.0113380	−	0.0732472i
$781$	5.33128			0.190768
$782$	14.8291	+	19.0358i	0.530286	+	0.680717i
$783$		−	7.08833i		−	0.253316i
$784$	−10.0283	+	18.6059i	−0.358155	+	0.664498i
$785$	6.77515	+	6.77515i	0.241815	+	0.241815i
$786$	1.71085	−	1.33277i	0.0610241	−	0.0475385i
$787$	−27.4432	−	27.4432i	−0.978246	−	0.978246i	0.0215228	−	0.999768i	$-0.493149\pi$
$787$	−27.4432	−	27.4432i	−0.978246	−	0.978246i	−0.999768	+	0.0215228i	$0.993149\pi$
$788$	17.0975	−	10.2075i	0.609073	−	0.363628i
$789$	1.14354			0.0407111
$790$	2.47672	−	19.9382i	0.0881178	−	0.709369i
$791$	−0.659790	−	0.659790i	−0.0234594	−	0.0234594i
$792$	−3.03243	+	7.80070i	−0.107753	+	0.277186i
$793$	−22.4882	−	9.10362i	−0.798581	−	0.323279i
$794$	−2.62241	+	21.1110i	−0.0930659	+	0.749202i
$795$	−1.61416	+	1.61416i	−0.0572482	+	0.0572482i
$796$	−11.2758	+	44.6860i	−0.399660	+	1.58385i
$797$			40.1938i			1.42374i	0.702312	+	0.711869i	$0.252151\pi$
$797$			40.1938i			1.42374i	−0.702312	+	0.711869i	$0.747849\pi$
$798$	−0.433538	−	0.556524i	−0.0153471	−	0.0197007i
$799$	15.2593	−	15.2593i	0.539834	−	0.539834i
$800$	−2.81827	−	16.6716i	−0.0996409	−	0.589429i
$801$	2.12078	−	2.12078i	0.0749340	−	0.0749340i
$802$	−5.66834	+	45.6314i	−0.200156	+	1.61130i
$803$	6.11651			0.215847
$804$	2.52902	−	1.50987i	0.0891915	−	0.0532490i
$805$		−	12.6303i		−	0.445159i
$806$	15.2712	−	27.4145i	0.537906	−	0.965635i
$807$			5.61933i			0.197810i
$808$	−10.7470	+	4.73037i	−0.378079	+	0.166414i
$809$	−1.87920			−0.0660693			−0.0330346	−	0.999454i	$-0.510517\pi$
$809$	−1.87920			−0.0660693			−0.0330346	+	0.999454i	$0.510517\pi$
$810$	17.1813	+	2.13426i	0.603690	+	0.0749904i
$811$	21.3023	−	21.3023i	0.748025	−	0.748025i	−0.226083	−	0.974108i	$-0.572592\pi$
$811$	21.3023	−	21.3023i	0.748025	−	0.748025i	0.974108	+	0.226083i	$0.0725922\pi$
$812$	13.2183	−	7.89159i	0.463873	−	0.276941i
$813$	1.84804	−	1.84804i	0.0648135	−	0.0648135i
$814$	−4.10813	+	3.20028i	−0.143990	+	0.112170i
$815$		−	11.1187i		−	0.389471i
$816$	1.78869	+	0.964077i	0.0626165	+	0.0337494i
$817$	9.72725	−	9.72725i	0.340314	−	0.340314i
$818$	−18.9332	−	2.35189i	−0.661985	−	0.0822319i
$819$	−5.45189	−	12.8682i	−0.190504	−	0.449650i
$820$	−6.54272	−	1.65095i	−0.228482	−	0.0576536i
$821$	−1.99619	−	1.99619i	−0.0696676	−	0.0696676i	0.671414	−	0.741082i	$-0.265687\pi$
$821$	−1.99619	−	1.99619i	−0.0696676	−	0.0696676i	−0.741082	+	0.671414i	$0.765687\pi$
$822$	−5.64076	−	0.700696i	−0.196744	−	0.0244396i
$823$	11.7130			0.408290			0.204145	−	0.978941i	$-0.434559\pi$
$823$	11.7130			0.408290			0.204145	+	0.978941i	$0.434559\pi$
$824$	−2.83784	−	6.44736i	−0.0988609	−	0.224604i
$825$	−0.427832	−	0.427832i	−0.0148952	−	0.0148952i
$826$	6.84159	+	8.78240i	0.238049	+	0.305579i
$827$	21.3991	+	21.3991i	0.744119	+	0.744119i	0.973368	−	0.229249i	$-0.0736269\pi$
$827$	21.3991	+	21.3991i	0.744119	+	0.744119i	−0.229249	+	0.973368i	$0.573627\pi$
$828$	9.84482	−	39.0151i	0.342131	−	1.35587i
$829$		−	1.16464i		−	0.0404497i	−0.999795	−	0.0202248i	$-0.993562\pi$
$829$		−	1.16464i		−	0.0404497i	0.999795	−	0.0202248i	$-0.00643821\pi$
$830$	−16.2152	+	12.6318i	−0.562838	+	0.438457i
$831$	3.01505			0.104591
$832$	26.0400	−	12.4065i	0.902773	−	0.430117i
$833$	−13.2604			−0.459447
$834$	−0.415289	+	0.323515i	−0.0143803	+	0.0112024i
$835$			2.39184i			0.0827729i
$836$	−0.920547	+	3.64813i	−0.0318378	+	0.126173i
$837$	−5.24937	−	5.24937i	−0.181445	−	0.181445i
$838$	30.9698	+	39.7553i	1.06983	+	1.37332i
$839$	−12.4254	−	12.4254i	−0.428971	−	0.428971i	0.459307	−	0.888278i	$-0.348098\pi$
$839$	−12.4254	−	12.4254i	−0.428971	−	0.428971i	−0.888278	+	0.459307i	$0.848098\pi$
$840$	−0.428470	−	0.973450i	−0.0147836	−	0.0335872i
$841$	5.53042			0.190704
$842$	8.12313	+	1.00906i	0.279942	+	0.0347744i
$843$	1.94765	+	1.94765i	0.0670806	+	0.0670806i
$844$	−1.04703	−	0.264202i	−0.0360403	−	0.00909419i
$845$	−0.296687	−	18.4331i	−0.0102063	−	0.634116i
$846$	−35.7109	−	4.43601i	−1.22777	−	0.152513i
$847$	−0.926254	+	0.926254i	−0.0318265	+	0.0318265i
$848$	−28.0003	−	15.0918i	−0.961533	−	0.518253i
$849$		−	2.05996i		−	0.0706976i
$850$	8.36821	−	6.51893i	0.287027	−	0.223597i
$851$	17.7036	−	17.7036i	0.606870	−	0.606870i
$852$	−1.85323	+	1.10641i	−0.0634908	+	0.0379051i
$853$	−5.12128	+	5.12128i	−0.175349	+	0.175349i	−0.789325	−	0.613976i	$-0.789569\pi$
$853$	−5.12128	+	5.12128i	−0.175349	+	0.175349i	0.613976	+	0.789325i	$0.289569\pi$
$854$	−12.3701	−	1.53661i	−0.423295	−	0.0525818i
$855$	7.89411			0.269973
$856$	−17.9929	+	7.91965i	−0.614983	+	0.270688i
$857$			23.3428i			0.797375i	0.917087	+	0.398688i	$0.130534\pi$
$857$			23.3428i			0.797375i	−0.917087	+	0.398688i	$0.869466\pi$
$858$	0.502299	−	0.901713i	0.0171482	−	0.0307840i
$859$			32.9101i			1.12288i	0.827518	+	0.561439i	$0.189752\pi$
$859$			32.9101i			1.12288i	−0.827518	+	0.561439i	$0.810248\pi$
$860$	17.8075	−	10.6314i	0.607230	−	0.362527i
$861$	0.630863			0.0214997
$862$	6.29239	−	50.6552i	0.214320	−	1.72532i
$863$	−26.8496	+	26.8496i	−0.913970	+	0.913970i	−0.996582	−	0.0826117i	$-0.973674\pi$
$863$	−26.8496	+	26.8496i	−0.913970	+	0.913970i	0.0826117	+	0.996582i	$0.473674\pi$
$864$	−1.13738	−	6.72821i	−0.0386944	−	0.228898i
$865$	8.38397	−	8.38397i	0.285064	−	0.285064i
$866$	−12.8439	−	16.4874i	−0.436453	−	0.560266i
$867$		−	2.16646i		−	0.0735768i
$868$	3.94481	−	15.6333i	0.133896	−	0.530629i
$869$	7.08387	−	7.08387i	0.240304	−	0.240304i
$870$	0.294077	−	2.36738i	0.00997013	−	0.0802619i
$871$	24.1532	−	10.2331i	0.818402	−	0.346735i
$872$	−18.6541	+	47.9862i	−0.631708	+	1.62502i
$873$	−26.2801	−	26.2801i	−0.889448	−	0.889448i
$874$	2.22989	−	17.9511i	0.0754272	−	0.607207i
$875$	−14.8404			−0.501697
$876$	−2.12619	+	1.26938i	−0.0718373	+	0.0428882i
$877$	−35.5112	−	35.5112i	−1.19913	−	1.19913i	−0.974428	−	0.224698i	$-0.927860\pi$
$877$	−35.5112	−	35.5112i	−1.19913	−	1.19913i	−0.224698	−	0.974428i	$-0.572140\pi$
$878$	26.6261	−	20.7421i	0.898589	−	0.700011i
$879$	1.86112	+	1.86112i	0.0627739	+	0.0627739i
$880$	−2.69134	+	4.99333i	−0.0907249	+	0.168325i
$881$			7.92920i			0.267142i	0.991039	+	0.133571i	$0.0426444\pi$
$881$			7.92920i			0.267142i	−0.991039	+	0.133571i	$0.957356\pi$
$882$	13.5891	+	17.4440i	0.457568	+	0.587370i
$883$	40.0814			1.34885			0.674424	−	0.738344i	$-0.264392\pi$
$883$	40.0814			1.34885			0.674424	+	0.738344i	$0.264392\pi$
$884$	14.6028	+	10.6880i	0.491144	+	0.359476i
$885$	1.72512			0.0579894
$886$	−4.16974	−	5.35261i	−0.140085	−	0.179824i
$887$			36.8307i			1.23665i	0.785921	+	0.618327i	$0.212189\pi$
$887$			36.8307i			1.23665i	−0.785921	+	0.618327i	$0.787811\pi$
$888$	0.763886	−	1.96504i	0.0256343	−	0.0659423i
$889$	−19.0256	−	19.0256i	−0.638098	−	0.638098i
$890$	1.60361	−	1.24923i	0.0537531	−	0.0418742i
$891$	6.10438	+	6.10438i	0.204504	+	0.204504i
$892$	21.6020	+	36.1831i	0.723288	+	1.21150i
$893$	−16.1773			−0.541354
$894$	0.569325	−	4.58319i	0.0190411	−	0.153285i
$895$	5.53866	+	5.53866i	0.185137	+	0.185137i
$896$	11.2805	−	9.61166i	0.376856	−	0.321103i
$897$	−1.86210	+	4.59985i	−0.0621736	+	0.153585i
$898$	−0.215833	+	1.73751i	−0.00720245	+	0.0579813i
$899$	25.5721	−	25.5721i	0.852876	−	0.852876i
$900$	−17.1512	−	4.32783i	−0.571707	−	0.144261i
$901$		−	19.9558i		−	0.664823i
$902$	−2.06772	−	2.65429i	−0.0688476	−	0.0883781i
$903$	−1.37107	+	1.37107i	−0.0456262	+	0.0456262i
$904$	−0.811656	−	1.84402i	−0.0269953	−	0.0613313i
$905$	−22.7485	+	22.7485i	−0.756184	+	0.756184i
$906$	−0.641007	+	5.16026i	−0.0212960	+	0.171438i
$907$	22.4814			0.746483			0.373242	−	0.927734i	$-0.378246\pi$
$907$	22.4814			0.746483			0.373242	+	0.927734i	$0.378246\pi$
$908$	−0.565165	−	0.946646i	−0.0187557	−	0.0314155i
$909$			12.2842i			0.407441i
$910$	−2.59177	−	9.11052i	−0.0859164	−	0.302011i
$911$			17.8084i			0.590019i	0.955494	+	0.295010i	$0.0953228\pi$
$911$			17.8084i			0.590019i	−0.955494	+	0.295010i	$0.904677\pi$
$912$	−0.437111	−	1.45919i	−0.0144742	−	0.0483186i
$913$	−10.2491			−0.339196
$914$	27.7590	+	3.44822i	0.918186	+	0.114057i
$915$	−1.36584	+	1.36584i	−0.0451533	+	0.0451533i
$916$	10.1468	+	16.9958i	0.335259	+	0.561555i
$917$	7.01696	−	7.01696i	0.231720	−	0.231720i
$918$	3.37719	−	2.63087i	0.111464	−	0.0868316i
$919$		−	48.7468i		−	1.60801i	−0.594624	−	0.804004i	$-0.702699\pi$
$919$		−	48.7468i		−	1.60801i	0.594624	−	0.804004i	$-0.297301\pi$
$920$	9.88123	−	25.4187i	0.325775	−	0.838029i
$921$	−2.51103	+	2.51103i	−0.0827412	+	0.0827412i
$922$	−24.3332	−	3.02267i	−0.801371	−	0.0995463i
$923$	−17.6992	+	7.49868i	−0.582577	+	0.246822i
$924$	0.129752	−	0.514208i	0.00426853	−	0.0169162i
$925$	−7.78257	−	7.78257i	−0.255889	−	0.255889i
$926$	19.9222	+	2.47474i	0.654684	+	0.0813249i
$927$	−7.36953			−0.242047
$928$	32.7761	−	5.54069i	1.07593	−	0.181882i
$929$	19.6606	+	19.6606i	0.645043	+	0.645043i	0.951791	−	0.306748i	$-0.0992409\pi$
$929$	19.6606	+	19.6606i	0.645043	+	0.645043i	−0.306748	+	0.951791i	$0.599241\pi$
$930$	−1.53542	−	1.97099i	−0.0503484	−	0.0646312i
$931$	7.02912	+	7.02912i	0.230370	+	0.230370i
$932$	−23.7434	−	5.99125i	−0.777739	−	0.196250i
$933$		−	5.96176i		−	0.195179i
$934$	−3.38156	+	2.63427i	−0.110648	+	0.0861960i
$935$	−3.55874			−0.116383
$936$	−0.904701	−	30.1627i	−0.0295711	−	0.985898i
$937$	−14.8748			−0.485940			−0.242970	−	0.970034i	$-0.578122\pi$
$937$	−14.8748			−0.485940			−0.242970	+	0.970034i	$0.578122\pi$
$938$	10.6322	−	8.28262i	0.347154	−	0.270437i
$939$			0.490043i			0.0159920i
$940$	−23.6482	−	5.96725i	−0.771321	−	0.194630i
$941$	40.7002	+	40.7002i	1.32679	+	1.32679i	0.908155	+	0.418634i	$0.137491\pi$
$941$	40.7002	+	40.7002i	1.32679	+	1.32679i	0.418634	+	0.908155i	$0.362509\pi$
$942$	−1.18867	−	1.52587i	−0.0387289	−	0.0497155i
$943$	11.4384	+	11.4384i	0.372485	+	0.372485i
$944$	6.89797	+	23.0272i	0.224510	+	0.749473i
$945$	−2.24077			−0.0728924
$946$	10.2624	+	1.27480i	0.333661	+	0.0414474i
$947$	−32.8431	−	32.8431i	−1.06726	−	1.06726i	−0.997569	−	0.0696886i	$-0.977799\pi$
$947$	−32.8431	−	32.8431i	−1.06726	−	1.06726i	−0.0696886	−	0.997569i	$-0.522201\pi$
$948$	−0.992327	+	3.93260i	−0.0322293	+	0.127725i
$949$	−20.3061	+	8.60314i	−0.659164	+	0.279270i
$950$	−7.89141	−	0.980272i	−0.256031	−	0.0318042i
$951$	1.64281	−	1.64281i	0.0532718	−	0.0532718i
$952$	8.66596	+	3.36879i	0.280865	+	0.109183i
$953$		−	1.71046i		−	0.0554072i	−0.999616	−	0.0277036i	$-0.991181\pi$
$953$		−	1.71046i		−	0.0554072i	0.999616	−	0.0277036i	$-0.00881946\pi$
$954$	−26.2517	+	20.4503i	−0.849929	+	0.662104i
$955$	8.79684	−	8.79684i	0.284659	−	0.284659i
$956$	−23.4749	−	39.3203i	−0.759233	−	1.27171i
$957$	0.841112	−	0.841112i	0.0271893	−	0.0271893i
$958$	22.5744	+	2.80419i	0.729345	+	0.0905993i
$959$	−26.0091			−0.839878
$960$	−0.100730	−	2.29430i	−0.00325104	−	0.0740482i
$961$		−	6.87558i		−	0.221793i
$962$	9.13717	−	16.4028i	0.294594	−	0.528848i
$963$			20.5664i			0.662742i
$964$	26.4903	+	44.3710i	0.853195	+	1.42909i
$965$	−4.01025			−0.129095
$966$	−0.314306	+	2.53023i	−0.0101126	+	0.0814089i
$967$	35.8427	−	35.8427i	1.15262	−	1.15262i	0.166600	−	0.986025i	$-0.446721\pi$
$967$	35.8427	−	35.8427i	1.15262	−	1.15262i	0.986025	−	0.166600i	$-0.0532787\pi$
$968$	−2.58875	+	1.13945i	−0.0832057	+	0.0366234i
$969$	0.675746	−	0.675746i	0.0217081	−	0.0217081i
$970$	−15.4801	−	19.8715i	−0.497037	−	0.638036i
$971$			2.95844i			0.0949409i	0.998873	+	0.0474705i	$0.0151160\pi$
$971$			2.95844i			0.0949409i	−0.998873	+	0.0474705i	$0.984884\pi$
$972$	−10.4065	−	2.62590i	−0.333787	−	0.0842258i
$973$	−1.70328	+	1.70328i	−0.0546047	+	0.0546047i
$974$	−3.46307	+	27.8785i	−0.110964	+	0.893284i
$975$	2.02212	+	0.818587i	0.0647595	+	0.0262158i
$976$	−23.6928	−	12.7701i	−0.758390	−	0.408761i
$977$	18.2634	+	18.2634i	0.584298	+	0.584298i	0.936082	−	0.351783i	$-0.114425\pi$
$977$	18.2634	+	18.2634i	0.584298	+	0.584298i	−0.351783	+	0.936082i	$0.614425\pi$
$978$	−0.276690	+	2.22742i	−0.00884756	+	0.0712249i
$979$	1.01359			0.0323944
$980$	7.68247	+	12.8681i	0.245407	+	0.411055i
$981$	38.0860	+	38.0860i	1.21599	+	1.21599i
$982$	23.3655	−	18.2020i	0.745624	−	0.580850i
$983$	−15.8459	−	15.8459i	−0.505404	−	0.505404i	0.407708	−	0.913112i	$-0.366328\pi$
$983$	−15.8459	−	15.8459i	−0.505404	−	0.505404i	−0.913112	+	0.407708i	$0.866328\pi$
$984$	1.26962	+	0.493552i	0.0404741	+	0.0157339i
$985$		−	14.1193i		−	0.449877i
$986$	12.8161	+	16.4518i	0.408149	+	0.523932i
$987$	2.28021			0.0725800
$988$	−2.07515	−	13.4062i	−0.0660194	−	0.426507i
$989$	−49.7185			−1.58096
$990$	3.64694	+	4.68150i	0.115907	+	0.148788i
$991$			53.1354i			1.68790i	0.536421	+	0.843951i	$0.319776\pi$
$991$			53.1354i			1.68790i	−0.536421	+	0.843951i	$0.680224\pi$
$992$	20.1696	−	28.3761i	0.640387	−	0.900943i
$993$	4.28213	+	4.28213i	0.135889	+	0.135889i
$994$	−7.79117	+	6.06941i	−0.247121	+	0.192510i
$995$	23.1068	+	23.1068i	0.732536	+	0.732536i
$996$	3.56274	−	2.12702i	0.112890	−	0.0673973i
$997$	40.5857			1.28536			0.642681	−	0.766134i	$-0.277822\pi$
$997$	40.5857			1.28536			0.642681	+	0.766134i	$0.277822\pi$
$998$	−2.32856	+	18.7454i	−0.0737092	+	0.593376i
$999$	−3.14084	−	3.14084i	−0.0993717	−	0.0993717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.j.a.463.15	✓	140
4.3	odd	2	inner	572.2.j.a.463.50	yes	140
13.5	odd	4	inner	572.2.j.a.551.50	yes	140
52.31	even	4	inner	572.2.j.a.551.15	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.j.a.463.15	✓	140	1.1	even	1	trivial
572.2.j.a.463.50	yes	140	4.3	odd	2	inner
572.2.j.a.551.15	yes	140	52.31	even	4	inner
572.2.j.a.551.50	yes	140	13.5	odd	4	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11565 + 0.869100i) q^{2} -0.202427i q^{3} +(0.489330 - 1.93922i) q^{4} +(-1.00276 - 1.00276i) q^{5} +(0.175929 + 0.225836i) q^{6} +(0.926254 + 0.926254i) q^{7} +(1.13945 + 2.58875i) q^{8} +2.95902 q^{9} +O(q^{10})\)	\(q+(-1.11565 + 0.869100i) q^{2} -0.202427i q^{3} +(0.489330 - 1.93922i) q^{4} +(-1.00276 - 1.00276i) q^{5} +(0.175929 + 0.225836i) q^{6} +(0.926254 + 0.926254i) q^{7} +(1.13945 + 2.58875i) q^{8} +2.95902 q^{9} +(1.99022 + 0.247225i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-0.392549 - 0.0990534i) q^{12} +(-3.34209 - 1.35294i) q^{13} +(-1.83838 - 0.228364i) q^{14} +(-0.202985 + 0.202985i) q^{15} +(-3.52111 - 1.89783i) q^{16} -2.50950i q^{17} +(-3.30122 + 2.57169i) q^{18} +(-1.33024 + 1.33024i) q^{19} +(-2.43524 + 1.45388i) q^{20} +(0.187499 - 0.187499i) q^{21} +(-1.40343 - 0.174334i) q^{22} +6.79920 q^{23} +(0.524033 - 0.230656i) q^{24} -2.98896i q^{25} +(4.90442 - 1.39522i) q^{26} -1.20627i q^{27} +(2.24945 - 1.34296i) q^{28} +5.87626 q^{29} +(0.0500449 - 0.402873i) q^{30} +(4.35176 - 4.35176i) q^{31} +(5.57772 - 0.942893i) q^{32} +(0.143137 - 0.143137i) q^{33} +(2.18100 + 2.79971i) q^{34} -1.85761i q^{35} +(1.44794 - 5.73818i) q^{36} +(2.60377 - 2.60377i) q^{37} +(0.327964 - 2.64019i) q^{38} +(-0.273870 + 0.676528i) q^{39} +(1.45329 - 3.73848i) q^{40} +(1.68231 + 1.68231i) q^{41} +(-0.0462269 + 0.372137i) q^{42} -7.31241 q^{43} +(1.71724 - 1.02522i) q^{44} +(-2.96718 - 2.96718i) q^{45} +(-7.58550 + 5.90919i) q^{46} +(6.08062 + 6.08062i) q^{47} +(-0.384172 + 0.712767i) q^{48} -5.28411i q^{49} +(2.59771 + 3.33462i) q^{50} -0.507989 q^{51} +(-4.25902 + 5.81900i) q^{52} +7.95211 q^{53} +(1.04837 + 1.34576i) q^{54} -1.41811i q^{55} +(-1.34242 + 3.45327i) q^{56} +(0.269276 + 0.269276i) q^{57} +(-6.55582 + 5.10706i) q^{58} +(-4.24939 - 4.24939i) q^{59} +(0.294304 + 0.492957i) q^{60} +6.72879 q^{61} +(-1.07291 + 8.63713i) q^{62} +(2.74081 + 2.74081i) q^{63} +(-5.40329 + 5.89953i) q^{64} +(1.99464 + 4.70796i) q^{65} +(-0.0352898 + 0.284091i) q^{66} +(-5.14443 + 5.14443i) q^{67} +(-4.86645 - 1.22797i) q^{68} -1.37634i q^{69} +(1.61445 + 2.07244i) q^{70} +(3.76978 - 3.76978i) q^{71} +(3.37167 + 7.66018i) q^{72} +(4.32502 - 4.32502i) q^{73} +(-0.641947 + 5.16782i) q^{74} -0.605045 q^{75} +(1.92869 + 3.23054i) q^{76} +1.30992i q^{77} +(-0.282429 - 0.992786i) q^{78} -10.0181i q^{79} +(1.62776 + 5.43388i) q^{80} +8.63289 q^{81} +(-3.33896 - 0.414766i) q^{82} +(-7.24721 + 7.24721i) q^{83} +(-0.271851 - 0.455349i) q^{84} +(-2.51641 + 2.51641i) q^{85} +(8.15806 - 6.35522i) q^{86} -1.18951i q^{87} +(-1.02481 + 2.63624i) q^{88} +(0.716716 - 0.716716i) q^{89} +(5.88909 + 0.731544i) q^{90} +(-1.84246 - 4.34879i) q^{91} +(3.32705 - 13.1851i) q^{92} +(-0.880912 - 0.880912i) q^{93} +(-12.0685 - 1.49915i) q^{94} +2.66781 q^{95} +(-0.190867 - 1.12908i) q^{96} +(-8.88136 - 8.88136i) q^{97} +(4.59242 + 5.89519i) q^{98} +(2.09235 + 2.09235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

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