LMFDB - Embedded newform 572.2.j.a.463.17

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			463.17
Character	$\chi$	$=$	572.463
Dual form			572.2.j.a.551.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03582 + 0.962851i) q^{2} +0.112664i q^{3} +(0.145835 - 1.99468i) q^{4} +(2.00381 + 2.00381i) q^{5} +(-0.108479 - 0.116699i) q^{6} +(3.01400 + 3.01400i) q^{7} +(1.76952 + 2.20654i) q^{8} +2.98731 q^{9} +O(q^{10})$	\(q+(-1.03582 + 0.962851i) q^{2} +0.112664i q^{3} +(0.145835 - 1.99468i) q^{4} +(2.00381 + 2.00381i) q^{5} +(-0.108479 - 0.116699i) q^{6} +(3.01400 + 3.01400i) q^{7} +(1.76952 + 2.20654i) q^{8} +2.98731 q^{9} +(-4.00495 - 0.146211i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(0.224728 + 0.0164304i) q^{12} +(2.15056 - 2.89398i) q^{13} +(-6.02399 - 0.219921i) q^{14} +(-0.225757 + 0.225757i) q^{15} +(-3.95746 - 0.581789i) q^{16} -4.16891i q^{17} +(-3.09430 + 2.87633i) q^{18} +(1.57587 - 1.57587i) q^{19} +(4.28918 - 3.70472i) q^{20} +(-0.339570 + 0.339570i) q^{21} +(1.41327 + 0.0515950i) q^{22} -5.31899 q^{23} +(-0.248598 + 0.199361i) q^{24} +3.03050i q^{25} +(0.558885 + 5.06830i) q^{26} +0.674555i q^{27} +(6.45150 - 5.57241i) q^{28} -2.45552 q^{29} +(0.0164727 - 0.451214i) q^{30} +(-1.08997 + 1.08997i) q^{31} +(4.65939 - 3.20782i) q^{32} +(0.0796656 - 0.0796656i) q^{33} +(4.01404 + 4.31823i) q^{34} +12.0790i q^{35} +(0.435655 - 5.95871i) q^{36} +(-0.282237 + 0.282237i) q^{37} +(-0.114985 + 3.14964i) q^{38} +(0.326047 + 0.242291i) q^{39} +(-0.875707 + 7.96726i) q^{40} +(8.51065 + 8.51065i) q^{41} +(0.0247772 - 0.678688i) q^{42} +7.61910 q^{43} +(-1.51357 + 1.30733i) q^{44} +(5.98599 + 5.98599i) q^{45} +(5.50950 - 5.12139i) q^{46} +(-4.57575 - 4.57575i) q^{47} +(0.0655468 - 0.445864i) q^{48} +11.1684i q^{49} +(-2.91792 - 3.13905i) q^{50} +0.469686 q^{51} +(-5.45892 - 4.71171i) q^{52} -10.8179 q^{53} +(-0.649496 - 0.698716i) q^{54} -2.83381i q^{55} +(-1.31718 + 11.9838i) q^{56} +(0.177544 + 0.177544i) q^{57} +(2.54347 - 2.36430i) q^{58} +(-8.02918 - 8.02918i) q^{59} +(0.417390 + 0.483236i) q^{60} -11.4289 q^{61} +(0.0795313 - 2.17849i) q^{62} +(9.00375 + 9.00375i) q^{63} +(-1.73762 + 7.80901i) q^{64} +(10.1083 - 1.48967i) q^{65} +(-0.00581290 + 0.159225i) q^{66} +(5.13815 - 5.13815i) q^{67} +(-8.31562 - 0.607975i) q^{68} -0.599259i q^{69} +(-11.6302 - 12.5116i) q^{70} +(-7.56371 + 7.56371i) q^{71} +(5.28609 + 6.59161i) q^{72} +(1.36657 - 1.36657i) q^{73} +(0.0205938 - 0.564098i) q^{74} -0.341429 q^{75} +(-2.91353 - 3.37317i) q^{76} -4.26244i q^{77} +(-0.571015 + 0.0629663i) q^{78} -3.43419i q^{79} +(-6.76421 - 9.09580i) q^{80} +8.88592 q^{81} +(-17.0100 - 0.620991i) q^{82} +(-3.05733 + 3.05733i) q^{83} +(0.627811 + 0.726853i) q^{84} +(8.35370 - 8.35370i) q^{85} +(-7.89200 + 7.33606i) q^{86} -0.276649i q^{87} +(0.309020 - 2.81150i) q^{88} +(-12.5993 + 12.5993i) q^{89} +(-11.9640 - 0.436776i) q^{90} +(15.2042 - 2.24067i) q^{91} +(-0.775697 + 10.6097i) q^{92} +(-0.122801 - 0.122801i) q^{93} +(9.14541 + 0.333876i) q^{94} +6.31549 q^{95} +(0.361406 + 0.524946i) q^{96} +(-4.13206 - 4.13206i) q^{97} +(-10.7535 - 11.5684i) q^{98} +(-2.11234 - 2.11234i) 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 $

$2$	−1.03582	+	0.962851i	−0.732434	+	0.680839i
$2$	−1.03582	+	0.962851i	−0.732434	+	0.680839i
$3$			0.112664i			0.0650467i	0.999471	+	0.0325233i	$0.0103543\pi$
$3$			0.112664i			0.0650467i	−0.999471	+	0.0325233i	$0.989646\pi$
$4$	0.145835	−	1.99468i	0.0729177	−	0.997338i
$5$	2.00381	+	2.00381i	0.896131	+	0.896131i	0.995091	−	0.0989605i	$-0.0315518\pi$
$5$	2.00381	+	2.00381i	0.896131	+	0.896131i	−0.0989605	+	0.995091i	$0.531552\pi$
$6$	−0.108479	−	0.116699i	−0.0442863	−	0.0476424i
$7$	3.01400	+	3.01400i	1.13919	+	1.13919i	0.988596	+	0.150589i	$0.0481170\pi$
$7$	3.01400	+	3.01400i	1.13919	+	1.13919i	0.150589	+	0.988596i	$0.451883\pi$
$8$	1.76952	+	2.20654i	0.625619	+	0.780129i
$9$	2.98731			0.995769
$10$	−4.00495	−	0.146211i	−1.26648	−	0.0462358i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$12$	0.224728	+	0.0164304i	0.0648735	+	0.00474306i
$13$	2.15056	−	2.89398i	0.596457	−	0.802645i
$13$	2.15056	−	2.89398i	0.596457	−	0.802645i
$14$	−6.02399	−	0.219921i	−1.60998	−	0.0587763i
$15$	−0.225757	+	0.225757i	−0.0582903	+	0.0582903i
$16$	−3.95746	−	0.581789i	−0.989366	−	0.145447i
$17$		−	4.16891i		−	1.01111i	−0.862795	−	0.505554i	$-0.831288\pi$
$17$		−	4.16891i		−	1.01111i	0.862795	−	0.505554i	$-0.168712\pi$
$18$	−3.09430	+	2.87633i	−0.729335	+	0.677958i
$19$	1.57587	−	1.57587i	0.361529	−	0.361529i	−0.502846	−	0.864376i	$-0.667714\pi$
$19$	1.57587	−	1.57587i	0.361529	−	0.361529i	0.864376	+	0.502846i	$0.167714\pi$
$20$	4.28918	−	3.70472i	0.959089	−	0.828401i
$21$	−0.339570	+	0.339570i	−0.0741002	+	0.0741002i
$22$	1.41327	+	0.0515950i	0.301311	+	0.0110001i
$23$	−5.31899			−1.10909			−0.554543	−	0.832155i	$-0.687107\pi$
$23$	−5.31899			−1.10909			−0.554543	+	0.832155i	$0.687107\pi$
$24$	−0.248598	+	0.199361i	−0.0507448	+	0.0406944i
$25$			3.03050i			0.606101i
$26$	0.558885	+	5.06830i	0.109606	+	0.993975i
$27$			0.674555i			0.129818i
$28$	6.45150	−	5.57241i	1.21922	−	1.05309i
$29$	−2.45552			−0.455979			−0.227990	−	0.973664i	$-0.573215\pi$
$29$	−2.45552			−0.455979			−0.227990	+	0.973664i	$0.573215\pi$
$30$	0.0164727	−	0.451214i	0.00300749	−	0.0823801i
$31$	−1.08997	+	1.08997i	−0.195765	+	0.195765i	−0.798182	−	0.602417i	$-0.794205\pi$
$31$	−1.08997	+	1.08997i	−0.195765	+	0.195765i	0.602417	+	0.798182i	$0.294205\pi$
$32$	4.65939	−	3.20782i	0.823671	−	0.567068i
$33$	0.0796656	−	0.0796656i	0.0138680	−	0.0138680i
$34$	4.01404	+	4.31823i	0.688402	+	0.740570i
$35$			12.0790i			2.04172i
$36$	0.435655	−	5.95871i	0.0726092	−	0.993118i
$37$	−0.282237	+	0.282237i	−0.0463995	+	0.0463995i	−0.729926	−	0.683526i	$-0.760445\pi$
$37$	−0.282237	+	0.282237i	−0.0463995	+	0.0463995i	0.683526	+	0.729926i	$0.260445\pi$
$38$	−0.114985	+	3.14964i	−0.0186531	+	0.510939i
$39$	0.326047	+	0.242291i	0.0522094	+	0.0387976i
$40$	−0.875707	+	7.96726i	−0.138461	+	1.25973i
$41$	8.51065	+	8.51065i	1.32914	+	1.32914i	0.906121	+	0.423020i	$0.139030\pi$
$41$	8.51065	+	8.51065i	1.32914	+	1.32914i	0.423020	+	0.906121i	$0.360970\pi$
$42$	0.0247772	−	0.678688i	0.00382320	−	0.104724i
$43$	7.61910			1.16190			0.580951	−	0.813939i	$-0.302681\pi$
$43$	7.61910			1.16190			0.580951	+	0.813939i	$0.302681\pi$
$44$	−1.51357	+	1.30733i	−0.228179	+	0.197087i
$45$	5.98599	+	5.98599i	0.892339	+	0.892339i
$46$	5.50950	−	5.12139i	0.812331	−	0.755108i
$47$	−4.57575	−	4.57575i	−0.667442	−	0.667442i	0.289681	−	0.957123i	$-0.406451\pi$
$47$	−4.57575	−	4.57575i	−0.667442	−	0.667442i	−0.957123	+	0.289681i	$0.906451\pi$
$48$	0.0655468	−	0.445864i	0.00946086	−	0.0643550i
$49$			11.1684i			1.59549i
$50$	−2.91792	−	3.13905i	−0.412657	−	0.443929i
$51$	0.469686			0.0657693
$52$	−5.45892	−	4.71171i	−0.757016	−	0.653396i
$53$	−10.8179			−1.48595			−0.742973	−	0.669321i	$-0.766585\pi$
$53$	−10.8179			−1.48595			−0.742973	+	0.669321i	$0.766585\pi$
$54$	−0.649496	−	0.698716i	−0.0883852	−	0.0950831i
$55$		−	2.83381i		−	0.382111i
$56$	−1.31718	+	11.9838i	−0.176016	+	1.60141i
$57$	0.177544	+	0.177544i	0.0235163	+	0.0235163i
$58$	2.54347	−	2.36430i	0.333975	−	0.310448i
$59$	−8.02918	−	8.02918i	−1.04531	−	1.04531i	−0.998924	−	0.0463866i	$-0.985229\pi$
$59$	−8.02918	−	8.02918i	−1.04531	−	1.04531i	−0.0463866	−	0.998924i	$-0.514771\pi$
$60$	0.417390	+	0.483236i	0.0538848	+	0.0623856i
$61$	−11.4289			−1.46332			−0.731661	−	0.681668i	$-0.761255\pi$
$61$	−11.4289			−1.46332			−0.731661	+	0.681668i	$0.761255\pi$
$62$	0.0795313	−	2.17849i	0.0101005	−	0.276669i
$63$	9.00375	+	9.00375i	1.13437	+	1.13437i
$64$	−1.73762	+	7.80901i	−0.217202	+	0.976127i
$65$	10.1083	−	1.48967i	1.25378	−	0.184771i
$66$	−0.00581290	+	0.159225i	−0.000715519	+	0.0195993i
$67$	5.13815	−	5.13815i	0.627725	−	0.627725i	−0.319770	−	0.947495i	$-0.603606\pi$
$67$	5.13815	−	5.13815i	0.627725	−	0.627725i	0.947495	+	0.319770i	$0.103606\pi$
$68$	−8.31562	−	0.607975i	−1.00842	−	0.0737278i
$69$		−	0.599259i		−	0.0721423i
$70$	−11.6302	−	12.5116i	−1.39008	−	1.49542i
$71$	−7.56371	+	7.56371i	−0.897648	+	0.897648i	−0.995228	−	0.0975801i	$-0.968890\pi$
$71$	−7.56371	+	7.56371i	−0.897648	+	0.897648i	0.0975801	+	0.995228i	$0.468890\pi$
$72$	5.28609	+	6.59161i	0.622972	+	0.776828i
$73$	1.36657	−	1.36657i	0.159945	−	0.159945i	−0.622598	−	0.782542i	$-0.713923\pi$
$73$	1.36657	−	1.36657i	0.159945	−	0.159945i	0.782542	+	0.622598i	$0.213923\pi$
$74$	0.0205938	−	0.564098i	0.00239398	−	0.0655751i
$75$	−0.341429			−0.0394248
$76$	−2.91353	−	3.37317i	−0.334205	−	0.386929i
$77$		−	4.26244i		−	0.485750i
$78$	−0.571015	+	0.0629663i	−0.0646548	+	0.00712953i
$79$		−	3.43419i		−	0.386376i	−0.981162	−	0.193188i	$-0.938117\pi$
$79$		−	3.43419i		−	0.386376i	0.981162	−	0.193188i	$-0.0618828\pi$
$80$	−6.76421	−	9.09580i	−0.756262	−	1.01694i
$81$	8.88592			0.987325
$82$	−17.0100	−	0.620991i	−1.87844	−	0.0685770i
$83$	−3.05733	+	3.05733i	−0.335585	+	0.335585i	−0.854703	−	0.519118i	$-0.826261\pi$
$83$	−3.05733	+	3.05733i	−0.335585	+	0.335585i	0.519118	+	0.854703i	$0.326261\pi$
$84$	0.627811	+	0.726853i	0.0684997	+	0.0793062i
$85$	8.35370	−	8.35370i	0.906086	−	0.906086i
$86$	−7.89200	+	7.33606i	−0.851016	+	0.791067i
$87$		−	0.276649i		−	0.0296599i
$88$	0.309020	−	2.81150i	0.0329417	−	0.299706i
$89$	−12.5993	+	12.5993i	−1.33552	+	1.33552i	−0.435171	+	0.900348i	$0.643312\pi$
$89$	−12.5993	+	12.5993i	−1.33552	+	1.33552i	−0.900348	+	0.435171i	$0.856688\pi$
$90$	−11.9640	−	0.436776i	−1.26112	−	0.0460402i
$91$	15.2042	−	2.24067i	1.59384	−	0.234886i
$92$	−0.775697	+	10.6097i	−0.0808720	+	1.10613i
$93$	−0.122801	−	0.122801i	−0.0127339	−	0.0127339i
$94$	9.14541	+	0.333876i	0.943277	+	0.0344366i
$95$	6.31549			0.647955
$96$	0.361406	+	0.524946i	0.0368859	+	0.0535771i
$97$	−4.13206	−	4.13206i	−0.419547	−	0.419547i	0.465501	−	0.885048i	$-0.345874\pi$
$97$	−4.13206	−	4.13206i	−0.419547	−	0.419547i	−0.885048	+	0.465501i	$0.845874\pi$
$98$	−10.7535	−	11.5684i	−1.08627	−	1.16859i
$99$	−2.11234	−	2.11234i	−0.212299	−	0.212299i
$100$	6.04487	+	0.441955i	0.604487	+	0.0441955i
$101$			5.16773i			0.514209i	0.966384	+	0.257104i	$0.0827684\pi$
$101$			5.16773i			0.514209i	−0.966384	+	0.257104i	$0.917232\pi$
$102$	−0.486509	+	0.452238i	−0.0481716	+	0.0447782i
$103$	−9.32713			−0.919030			−0.459515	−	0.888170i	$-0.651977\pi$
$103$	−9.32713			−0.919030			−0.459515	+	0.888170i	$0.651977\pi$
$104$	10.1911	−	0.375657i	0.999321	−	0.0368362i
$105$	−1.36087			−0.132807
$106$	11.2053	−	10.4160i	1.08836	−	1.01169i
$107$		−	17.7893i		−	1.71976i	−0.510498	−	0.859879i	$-0.670539\pi$
$107$		−	17.7893i		−	1.71976i	0.510498	−	0.859879i	$-0.329461\pi$
$108$	1.34552	+	0.0983740i	0.129473	+	0.00946604i
$109$	7.05062	+	7.05062i	0.675326	+	0.675326i	0.958939	−	0.283612i	$-0.0915329\pi$
$109$	7.05062	+	7.05062i	0.675326	+	0.675326i	−0.283612	+	0.958939i	$0.591533\pi$
$110$	2.72854	+	2.93531i	0.260156	+	0.279871i
$111$	−0.0317980	−	0.0317980i	−0.00301813	−	0.00301813i
$112$	−10.1743	−	13.6813i	−0.961380	−	1.29276i
$113$	10.6578			1.00260			0.501302	−	0.865273i	$-0.332855\pi$
$113$	10.6578			1.00260			0.501302	+	0.865273i	$0.332855\pi$
$114$	−0.354852	−	0.0129547i	−0.0332349	−	0.00121332i
$115$	−10.6582	−	10.6582i	−0.993885	−	0.993885i
$116$	−0.358103	+	4.89797i	−0.0332490	+	0.454766i
$117$	6.42437	−	8.64520i	0.593934	−	0.799249i
$118$	16.0477	+	0.585860i	1.47731	+	0.0539328i
$119$	12.5651	−	12.5651i	1.15184	−	1.15184i
$120$	−0.897624	−	0.0986607i	−0.0819415	−	0.00900645i
$121$			1.00000i			0.0909091i
$122$	11.8383	−	11.0043i	1.07179	−	0.996287i
$123$	−0.958845	+	0.958845i	−0.0864561	+	0.0864561i
$124$	2.01519	+	2.33310i	0.180969	+	0.209518i
$125$	3.94649	−	3.94649i	0.352985	−	0.352985i
$126$	−17.9955	−	0.656970i	−1.60317	−	0.0585276i
$127$	−5.58139			−0.495268			−0.247634	−	0.968854i	$-0.579653\pi$
$127$	−5.58139			−0.495268			−0.247634	+	0.968854i	$0.579653\pi$
$128$	−5.71906	−	9.76178i	−0.505498	−	0.862828i
$129$			0.858399i			0.0755778i
$130$	−9.03600	+	11.2758i	−0.792510	+	0.988953i
$131$			21.7793i			1.90286i	0.307860	+	0.951432i	$0.400387\pi$
$131$			21.7793i			1.90286i	−0.307860	+	0.951432i	$0.599613\pi$
$132$	−0.147289	−	0.170525i	−0.0128199	−	0.0148423i
$133$	9.49935			0.823698
$134$	−0.374912	+	10.2695i	−0.0323874	+	0.887146i
$135$	−1.35168	+	1.35168i	−0.116334	+	0.116334i
$136$	9.19885	−	7.37695i	0.788795	−	0.632569i
$137$	−2.77197	+	2.77197i	−0.236825	+	0.236825i	−0.815534	−	0.578709i	$-0.803557\pi$
$137$	−2.77197	+	2.77197i	−0.236825	+	0.236825i	0.578709	+	0.815534i	$0.303557\pi$
$138$	0.576997	+	0.620723i	0.0491173	+	0.0528394i
$139$		−	11.2679i		−	0.955728i	−0.878434	−	0.477864i	$-0.841411\pi$
$139$		−	11.2679i		−	0.955728i	0.878434	−	0.477864i	$-0.158589\pi$
$140$	24.0936	+	1.76154i	2.03628	+	0.148877i
$141$	0.515523	−	0.515523i	0.0434149	−	0.0434149i
$142$	0.551896	−	15.1174i	0.0463141	−	1.26862i
$143$	−3.56702	+	0.525678i	−0.298290	+	0.0439594i
$144$	−11.8222	−	1.73798i	−0.985180	−	0.144832i
$145$	−4.92040	−	4.92040i	−0.408617	−	0.408617i
$146$	−0.0997133	+	2.73131i	−0.00825233	+	0.226045i
$147$	−1.25828			−0.103781
$148$	0.521811	+	0.604132i	0.0428926	+	0.0496593i
$149$	2.43811	+	2.43811i	0.199737	+	0.199737i	0.799887	−	0.600150i	$-0.204892\pi$
$149$	2.43811	+	2.43811i	0.199737	+	0.199737i	−0.600150	+	0.799887i	$0.704892\pi$
$150$	0.353658	−	0.328745i	0.0288761	−	0.0268420i
$151$	−10.2656	−	10.2656i	−0.835400	−	0.835400i	0.152850	−	0.988249i	$-0.451155\pi$
$151$	−10.2656	−	10.2656i	−0.835400	−	0.835400i	−0.988249	+	0.152850i	$0.951155\pi$
$152$	6.26575	+	0.688688i	0.508219	+	0.0558600i
$153$		−	12.4538i		−	1.00683i
$154$	4.10410	+	4.41511i	0.330718	+	0.355780i
$155$	−4.36819			−0.350862
$156$	0.530841	−	0.615024i	0.0425013	−	0.0492414i
$157$	−7.53990			−0.601750			−0.300875	−	0.953664i	$-0.597279\pi$
$157$	−7.53990			−0.601750			−0.300875	+	0.953664i	$0.597279\pi$
$158$	3.30661	+	3.55719i	0.263060	+	0.282995i
$159$		−	1.21878i		−	0.0966559i
$160$	15.7644	+	2.90866i	1.24628	+	0.229950i
$161$	−16.0314	−	16.0314i	−1.26345	−	1.26345i
$162$	−9.20419	+	8.55582i	−0.723150	+	0.672209i
$163$	−0.0393208	−	0.0393208i	−0.00307984	−	0.00307984i	0.705565	−	0.708645i	$-0.250693\pi$
$163$	−0.0393208	−	0.0393208i	−0.00307984	−	0.00307984i	−0.708645	+	0.705565i	$0.750693\pi$
$164$	18.2171	−	15.7348i	1.42252	−	1.22868i
$165$	0.319269			0.0248551
$166$	0.223082	−	6.11058i	0.0173145	−	0.474273i
$167$	5.93514	+	5.93514i	0.459275	+	0.459275i	0.898417	−	0.439142i	$-0.144718\pi$
$167$	5.93514	+	5.93514i	0.459275	+	0.459275i	−0.439142	+	0.898417i	$0.644718\pi$
$168$	−1.35015	−	0.148399i	−0.104166	−	0.0114492i
$169$	−3.75021	−	12.4473i	−0.288478	−	0.957487i
$170$	−0.609538	+	16.6963i	−0.0467495	+	1.28055i
$171$	4.70761	−	4.70761i	0.360000	−	0.360000i
$172$	1.11113	−	15.1976i	0.0847232	−	1.15881i
$173$		−	4.38482i		−	0.333371i	−0.986010	−	0.166686i	$-0.946693\pi$
$173$		−	4.38482i		−	0.333371i	0.986010	−	0.166686i	$-0.0533065\pi$
$174$	0.266372	+	0.286558i	0.0201936	+	0.0217239i
$175$	−9.13394	+	9.13394i	−0.690461	+	0.690461i
$176$	2.38696	+	3.20974i	0.179924	+	0.241943i
$177$	0.904601	−	0.904601i	0.0679939	−	0.0679939i
$178$	0.919321	−	25.1817i	0.0689061	−	1.88745i
$179$	11.6330			0.869491			0.434745	−	0.900553i	$-0.356838\pi$
$179$	11.6330			0.869491			0.434745	+	0.900553i	$0.356838\pi$
$180$	12.8131	−	11.0671i	0.955031	−	0.824896i
$181$		−	2.55105i		−	0.189618i	−0.995495	−	0.0948090i	$-0.969776\pi$
$181$		−	2.55105i		−	0.189618i	0.995495	−	0.0948090i	$-0.0302240\pi$
$182$	−13.5914	+	16.9603i	−1.00746	+	1.25718i
$183$		−	1.28763i		−	0.0951843i
$184$	−9.41204	−	11.7365i	−0.693864	−	0.865229i
$185$	−1.13110			−0.0831600
$186$	0.245438	+	0.00896032i	0.0179964	+	0.000657003i
$187$	−2.94786	+	2.94786i	−0.215569	+	0.215569i
$188$	−9.79445	+	8.45983i	−0.714333	+	0.616997i
$189$	−2.03311	+	2.03311i	−0.147887	+	0.147887i
$190$	−6.54169	+	6.08087i	−0.474584	+	0.441153i
$191$			14.0238i			1.01473i	0.861732	+	0.507364i	$0.169380\pi$
$191$			14.0238i			1.01473i	−0.861732	+	0.507364i	$0.830620\pi$
$192$	−0.879796	−	0.195767i	−0.0634938	−	0.0141283i
$193$	−7.64104	+	7.64104i	−0.550014	+	0.550014i	−0.926445	−	0.376431i	$-0.877151\pi$
$193$	−7.64104	+	7.64104i	−0.550014	+	0.550014i	0.376431	+	0.926445i	$0.377151\pi$
$194$	8.25862	+	0.301501i	0.592934	+	0.0216465i
$195$	0.167833	+	1.13884i	0.0120188	+	0.0815541i
$196$	22.2774	+	1.62875i	1.59124	+	0.116339i
$197$	−16.4011	−	16.4011i	−1.16853	−	1.16853i	−0.982554	−	0.185979i	$-0.940454\pi$
$197$	−16.4011	−	16.4011i	−1.16853	−	1.16853i	−0.185979	−	0.982554i	$-0.559546\pi$
$198$	4.22188	+	0.154130i	0.300036	+	0.0109535i
$199$	14.7182			1.04335			0.521674	−	0.853145i	$-0.325308\pi$
$199$	14.7182			1.04335			0.521674	+	0.853145i	$0.325308\pi$
$200$	−6.68692	+	5.36253i	−0.472837	+	0.379188i
$201$	0.578885	+	0.578885i	0.0408314	+	0.0408314i
$202$	−4.97576	−	5.35283i	−0.350093	−	0.376624i
$203$	−7.40095	−	7.40095i	−0.519445	−	0.519445i
$204$	0.0684969	−	0.936872i	0.00479575	−	0.0655942i
$205$			34.1074i			2.38217i
$206$	9.66120	−	8.98064i	0.673128	−	0.625711i
$207$	−15.8894			−1.10439
$208$	−10.1944	+	10.2016i	−0.706857	+	0.707357i
$209$	−2.22862			−0.154157
$210$	1.40961	−	1.31031i	0.0972723	−	0.0904201i
$211$		−	3.14095i		−	0.216232i	−0.994138	−	0.108116i	$-0.965518\pi$
$211$		−	3.14095i		−	0.216232i	0.994138	−	0.108116i	$-0.0344818\pi$
$212$	−1.57763	+	21.5781i	−0.108352	+	1.48199i
$213$	−0.852159	−	0.852159i	−0.0583890	−	0.0583890i
$214$	17.1285	+	18.4265i	1.17088	+	1.25961i
$215$	15.2672	+	15.2672i	1.04122	+	1.04122i
$216$	−1.48843	+	1.19364i	−0.101275	+	0.0812167i
$217$	−6.57036			−0.446025
$218$	−14.0918	−	0.514457i	−0.954420	−	0.0348435i
$219$	0.153963	+	0.153963i	0.0104039	+	0.0104039i
$220$	−5.65254	−	0.413271i	−0.381094	−	0.0278627i
$221$	−12.0647	−	8.96547i	−0.811561	−	0.603083i
$222$	0.0635537	+	0.00232018i	0.00426544	+	0.000155720i
$223$	−13.9355	+	13.9355i	−0.933192	+	0.933192i	−0.997904	−	0.0647117i	$-0.979387\pi$
$223$	−13.9355	+	13.9355i	−0.933192	+	0.933192i	0.0647117	+	0.997904i	$0.479387\pi$
$224$	23.7118	+	4.37502i	1.58431	+	0.292318i
$225$			9.05305i			0.603536i
$226$	−11.0396	+	10.2619i	−0.734340	+	0.682611i
$227$	4.05369	−	4.05369i	0.269053	−	0.269053i	−0.559666	−	0.828718i	$-0.689070\pi$
$227$	4.05369	−	4.05369i	0.269053	−	0.269053i	0.828718	+	0.559666i	$0.189070\pi$
$228$	0.380035	−	0.328251i	0.0251684	−	0.0217389i
$229$	9.84351	−	9.84351i	0.650477	−	0.650477i	−0.302631	−	0.953108i	$-0.597865\pi$
$229$	9.84351	−	9.84351i	0.650477	−	0.650477i	0.953108	+	0.302631i	$0.0978649\pi$
$230$	21.3023	+	0.777692i	1.40463	+	0.0512795i
$231$	0.480224			0.0315964
$232$	−4.34509	−	5.41821i	−0.285269	−	0.355723i
$233$			16.0934i			1.05431i	0.849769	+	0.527156i	$0.176742\pi$
$233$			16.0934i			1.05431i	−0.849769	+	0.527156i	$0.823258\pi$
$234$	1.66956	+	15.1406i	0.109143	+	0.989769i
$235$		−	18.3379i		−	1.19623i
$236$	−17.1866	+	14.8447i	−1.11875	+	0.966306i
$237$	0.386910			0.0251325
$238$	−0.916829	+	25.1135i	−0.0594292	+	1.62786i
$239$	13.6270	−	13.6270i	0.881459	−	0.881459i	−0.112224	−	0.993683i	$-0.535797\pi$
$239$	13.6270	−	13.6270i	0.881459	−	0.881459i	0.993683	+	0.112224i	$0.0357974\pi$
$240$	1.02477	−	0.762084i	0.0661486	−	0.0491923i
$241$	11.6015	−	11.6015i	0.747321	−	0.747321i	−0.226655	−	0.973975i	$-0.572779\pi$
$241$	11.6015	−	11.6015i	0.747321	−	0.747321i	0.973975	+	0.226655i	$0.0727789\pi$
$242$	−0.962851	−	1.03582i	−0.0618944	−	0.0665849i
$243$			3.02479i			0.194040i
$244$	−1.66674	+	22.7970i	−0.106702	+	1.45943i
$245$	−22.3794	+	22.3794i	−1.42977	+	1.42977i
$246$	0.0699634	−	1.91641i	0.00446070	−	0.122186i
$247$	−1.17153	−	7.94953i	−0.0745429	−	0.505817i
$248$	−4.33379	−	0.476341i	−0.275196	−	0.0302477i
$249$	−0.344451	−	0.344451i	−0.0218287	−	0.0218287i
$250$	−0.287961	+	7.88773i	−0.0182123	+	0.498864i
$251$	4.07486			0.257203			0.128601	−	0.991696i	$-0.458951\pi$
$251$	4.07486			0.257203			0.128601	+	0.991696i	$0.458951\pi$
$252$	19.2726	−	16.6465i	1.21406	−	1.04863i
$253$	3.76109	+	3.76109i	0.236458	+	0.236458i
$254$	5.78130	−	5.37405i	0.362751	−	0.337198i
$255$	0.941162	+	0.941162i	0.0589379	+	0.0589379i
$256$	15.3230	+	4.60482i	0.957690	+	0.287801i
$257$		−	22.6333i		−	1.41183i	−0.708298	−	0.705913i	$-0.750537\pi$
$257$		−	22.6333i		−	1.41183i	0.708298	−	0.705913i	$-0.249463\pi$
$258$	−0.826511	−	0.889145i	−0.0514563	−	0.0553557i
$259$	−1.70133			−0.105715
$260$	−1.49727	−	20.3800i	−0.0928566	−	1.26391i
$261$	−7.33540			−0.454050
$262$	−20.9702	−	22.5593i	−1.29554	−	1.39372i
$263$			13.7525i			0.848016i	0.905659	+	0.424008i	$0.139377\pi$
$263$			13.7525i			0.848016i	−0.905659	+	0.424008i	$0.860623\pi$
$264$	0.316755	+	0.0348155i	0.0194949	+	0.00214275i
$265$	−21.6769	−	21.6769i	−1.33160	−	1.33160i
$266$	−9.83959	+	9.14646i	−0.603304	+	0.560805i
$267$	−1.41948	−	1.41948i	−0.0868710	−	0.0868710i
$268$	−9.49962	−	10.9983i	−0.580281	−	0.671826i
$269$	−20.5315			−1.25183			−0.625915	−	0.779892i	$-0.715274\pi$
$269$	−20.5315			−1.25183			−0.625915	+	0.779892i	$0.715274\pi$
$270$	0.0986270	−	2.70156i	0.00600225	−	0.164412i
$271$	0.0640989	+	0.0640989i	0.00389373	+	0.00389373i	0.709051	−	0.705157i	$-0.249124\pi$
$271$	0.0640989	+	0.0640989i	0.00389373	+	0.00389373i	−0.705157	+	0.709051i	$0.749124\pi$
$272$	−2.42542	+	16.4983i	−0.147063	+	1.00036i
$273$	0.252443	+	1.71297i	0.0152786	+	0.103674i
$274$	0.202260	−	5.54025i	0.0122190	−	0.334699i
$275$	2.14289	−	2.14289i	0.129221	−	0.129221i
$276$	−1.19533	−	0.0873932i	−0.0719503	−	0.00526045i
$277$		−	5.97720i		−	0.359135i	−0.983746	−	0.179568i	$-0.942530\pi$
$277$		−	5.97720i		−	0.359135i	0.983746	−	0.179568i	$-0.0574698\pi$
$278$	10.8493	+	11.6715i	0.650696	+	0.700007i
$279$	−3.25608	+	3.25608i	−0.194937	+	0.194937i
$280$	−26.6527	+	21.3739i	−1.59280	+	1.27734i
$281$	−14.9757	+	14.9757i	−0.893372	+	0.893372i	−0.994839	−	0.101467i	$-0.967647\pi$
$281$	−14.9757	+	14.9757i	−0.893372	+	0.893372i	0.101467	+	0.994839i	$0.467647\pi$
$282$	−0.0376158	+	1.03036i	−0.00223999	+	0.0613570i
$283$	12.8692			0.764992			0.382496	−	0.923957i	$-0.375065\pi$
$283$	12.8692			0.764992			0.382496	+	0.923957i	$0.375065\pi$
$284$	13.9841	+	16.1902i	0.829804	+	0.960712i
$285$			0.711529i			0.0421473i
$286$	3.18864	−	3.97902i	0.188548	−	0.235284i
$287$			51.3022i			3.02827i
$288$	13.9190	−	9.58275i	0.820186	−	0.564669i
$289$	−0.379794			−0.0223408
$290$	9.83425	+	0.359024i	0.577487	+	0.0210826i
$291$	0.465535	−	0.465535i	0.0272901	−	0.0272901i
$292$	−2.52656	−	2.92515i	−0.147856	−	0.171182i
$293$	17.1209	−	17.1209i	1.00021	−	1.00021i	0.000214375	−	1.00000i	$-0.499932\pi$
$293$	17.1209	−	17.1209i	1.00021	−	1.00021i	1.00000		0.000214375i	$-6.82378e-5\pi$
$294$	1.30335	−	1.21154i	0.0760128	−	0.0706582i
$295$		−	32.1779i		−	1.87347i
$296$	−1.12219	−	0.123344i	−0.0652260	−	0.00716920i
$297$	0.476982	−	0.476982i	0.0276773	−	0.0276773i
$298$	−4.87296	−	0.177900i	−0.282283	−	0.0103054i
$299$	−11.4388	+	15.3930i	−0.661522	+	0.890202i
$300$	−0.0497925	+	0.681041i	−0.00287477	+	0.0393199i
$301$	22.9640	+	22.9640i	1.32362	+	1.32362i
$302$	20.5175	+	0.749040i	1.18065	+	0.0431024i
$303$	−0.582218			−0.0334476
$304$	−7.15327	+	5.31963i	−0.410268	+	0.305101i
$305$	−22.9014	−	22.9014i	−1.31133	−	1.31133i
$306$	11.9912	+	12.8999i	0.685489	+	0.737437i
$307$	2.70798	+	2.70798i	0.154553	+	0.154553i	0.780148	−	0.625595i	$-0.215144\pi$
$307$	2.70798	+	2.70798i	0.154553	+	0.154553i	−0.625595	+	0.780148i	$0.715144\pi$
$308$	−8.50219	−	0.621615i	−0.484457	−	0.0354198i
$309$		−	1.05083i		−	0.0597798i
$310$	4.52465	−	4.20592i	0.256983	−	0.238880i
$311$	31.5003			1.78622			0.893108	−	0.449842i	$-0.148520\pi$
$311$	31.5003			1.78622			0.893108	+	0.449842i	$0.148520\pi$
$312$	0.0423230	+	1.14817i	0.00239607	+	0.0650025i
$313$	−15.3877			−0.869766			−0.434883	−	0.900487i	$-0.643210\pi$
$313$	−15.3877			−0.869766			−0.434883	+	0.900487i	$0.643210\pi$
$314$	7.80996	−	7.25981i	0.440742	−	0.409695i
$315$			36.0836i			2.03308i
$316$	−6.85009	−	0.500826i	−0.385348	−	0.0281737i
$317$	0.701153	+	0.701153i	0.0393807	+	0.0393807i	0.726523	−	0.687142i	$-0.241135\pi$
$317$	0.701153	+	0.701153i	0.0393807	+	0.0393807i	−0.687142	+	0.726523i	$0.741135\pi$
$318$	1.17351	+	1.26244i	0.0658070	+	0.0707940i
$319$	1.73632	+	1.73632i	0.0972151	+	0.0972151i
$320$	−19.1296	+	12.1659i	−1.06938	+	0.680095i
$321$	2.00422			0.111864
$322$	32.0415	+	1.16975i	1.78560	+	0.0651879i
$323$	−6.56966	−	6.56966i	−0.365546	−	0.365546i
$324$	1.29588	−	17.7245i	0.0719935	−	0.984696i
$325$	8.77021	+	6.51727i	0.486484	+	0.361513i
$326$	0.0785892	+	0.00286909i	0.00435265	+	0.000158904i
$327$	−0.794352	+	0.794352i	−0.0439277	+	0.0439277i
$328$	−3.71933	+	33.8388i	−0.205366	+	1.86844i
$329$		−	27.5826i		−	1.52068i
$330$	−0.330705	+	0.307409i	−0.0182047	+	0.0169223i
$331$	−12.4898	+	12.4898i	−0.686504	+	0.686504i	−0.961457	−	0.274954i	$-0.911337\pi$
$331$	−12.4898	+	12.4898i	−0.686504	+	0.686504i	0.274954	+	0.961457i	$0.411337\pi$
$332$	5.65251	+	6.54424i	0.310222	+	0.359162i
$333$	−0.843129	+	0.843129i	−0.0462032	+	0.0462032i
$334$	−11.8624	−	0.433065i	−0.649081	−	0.0236963i
$335$	20.5917			1.12505
$336$	1.54139	−	1.14628i	0.0840899	−	0.0625346i
$337$			2.75800i			0.150238i	0.997175	+	0.0751190i	$0.0239337\pi$
$337$			2.75800i			0.150238i	−0.997175	+	0.0751190i	$0.976066\pi$
$338$	15.8695	+	9.28226i	0.863185	+	0.504889i
$339$			1.20075i			0.0652160i
$340$	−15.4447	−	17.8812i	−0.837604	−	0.969743i
$341$	1.54145			0.0834744
$342$	−0.343497	+	9.40895i	−0.0185742	+	0.508778i
$343$	−12.5636	+	12.5636i	−0.678371	+	0.678371i
$344$	13.4821	+	16.8118i	0.726907	+	0.906433i
$345$	1.20080	−	1.20080i	0.0646489	−	0.0646489i
$346$	4.22193	+	4.54187i	0.226972	+	0.244172i
$347$		−	28.7580i		−	1.54381i	−0.635738	−	0.771905i	$-0.719304\pi$
$347$		−	28.7580i		−	1.54381i	0.635738	−	0.771905i	$-0.280696\pi$
$348$	−0.551826	−	0.0403453i	−0.0295810	−	0.00216274i
$349$	14.7918	−	14.7918i	0.791787	−	0.791787i	−0.189997	−	0.981785i	$-0.560848\pi$
$349$	14.7918	−	14.7918i	0.791787	−	0.791787i	0.981785	+	0.189997i	$0.0608479\pi$
$350$	0.666470	−	18.2557i	0.0356243	−	0.975810i
$351$	1.95215	+	1.45067i	0.104198	+	0.0774310i
$352$	−5.56296	−	1.02641i	−0.296507	−	0.0547079i
$353$	5.37051	+	5.37051i	0.285843	+	0.285843i	0.835434	−	0.549591i	$-0.185216\pi$
$353$	5.37051	+	5.37051i	0.285843	+	0.285843i	−0.549591	+	0.835434i	$0.685216\pi$
$354$	−0.0660054	+	1.80800i	−0.00350815	+	0.0960939i
$355$	−30.3125			−1.60882
$356$	23.2940	+	26.9689i	1.23458	+	1.42935i
$357$	1.41564	+	1.41564i	0.0749234	+	0.0749234i
$358$	−12.0497	+	11.2008i	−0.636844	+	0.591983i
$359$	−2.92874	−	2.92874i	−0.154573	−	0.154573i	0.625584	−	0.780157i	$-0.284861\pi$
$359$	−2.92874	−	2.92874i	−0.154573	−	0.154573i	−0.780157	+	0.625584i	$0.784861\pi$
$360$	−2.61600	+	23.8006i	−0.137876	+	1.25440i
$361$			14.0333i			0.738593i
$362$	2.45628	+	2.64242i	0.129099	+	0.138883i
$363$	−0.112664			−0.00591333
$364$	−2.25209	−	30.6543i	−0.118042	−	1.60672i
$365$	5.47668			0.286662
$366$	1.23980	+	1.33375i	0.0648051	+	0.0697162i
$367$			32.0427i			1.67262i	0.548260	+	0.836308i	$0.315290\pi$
$367$			32.0427i			1.67262i	−0.548260	+	0.836308i	$0.684710\pi$
$368$	21.0497	+	3.09453i	1.09729	+	0.161313i
$369$	25.4239	+	25.4239i	1.32352	+	1.32352i
$370$	1.17161	−	1.08908i	0.0609092	−	0.0566186i
$371$	−32.6050	−	32.6050i	−1.69277	−	1.69277i
$372$	−0.262857	+	0.227039i	−0.0136285	+	0.0117714i
$373$	24.7678			1.28243			0.641215	−	0.767361i	$-0.278431\pi$
$373$	24.7678			1.28243			0.641215	+	0.767361i	$0.278431\pi$
$374$	0.215095	−	5.89180i	0.0111223	−	0.304658i
$375$	0.444628	+	0.444628i	0.0229605	+	0.0229605i
$376$	1.99970	−	18.1934i	0.103127	−	0.938255i
$377$	−5.28074	+	7.10623i	−0.271972	+	0.365990i
$378$	0.148348	−	4.06351i	0.00763022	−	0.209004i
$379$	9.17659	−	9.17659i	0.471370	−	0.471370i	−0.430988	−	0.902358i	$-0.641835\pi$
$379$	9.17659	−	9.17659i	0.471370	−	0.471370i	0.902358	+	0.430988i	$0.141835\pi$
$380$	0.921022	−	12.5973i	0.0472474	−	0.646230i
$381$		−	0.628822i		−	0.0322155i
$382$	−13.5028	−	14.5261i	−0.690866	−	0.743220i
$383$	5.57637	−	5.57637i	0.284939	−	0.284939i	−0.550136	−	0.835075i	$-0.685424\pi$
$383$	5.57637	−	5.57637i	0.284939	−	0.284939i	0.835075	+	0.550136i	$0.185424\pi$
$384$	1.09980	−	0.644333i	0.0561241	−	0.0328810i
$385$	8.54112	−	8.54112i	0.435296	−	0.435296i
$386$	0.557538	−	15.2719i	0.0283779	−	0.777319i
$387$	22.7606			1.15699
$388$	−8.84472	+	7.63952i	−0.449023	+	0.387838i
$389$			0.208383i			0.0105654i	0.999986	+	0.00528272i	$0.00168155\pi$
$389$			0.208383i			0.0105654i	−0.999986	+	0.00528272i	$0.998318\pi$
$390$	−1.27038	−	1.01803i	−0.0643281	−	0.0515501i
$391$			22.1744i			1.12141i
$392$	−24.6435	+	19.7627i	−1.24469	+	0.998167i
$393$	−2.45374			−0.123775
$394$	32.7804	+	1.19673i	1.65145	+	0.0602904i
$395$	6.88145	−	6.88145i	0.346244	−	0.346244i
$396$	−4.52150	+	3.90539i	−0.227214	+	0.196253i
$397$	−6.48651	+	6.48651i	−0.325549	+	0.325549i	−0.850891	−	0.525342i	$-0.823937\pi$
$397$	−6.48651	+	6.48651i	−0.325549	+	0.325549i	0.525342	+	0.850891i	$0.323937\pi$
$398$	−15.2454	+	14.1715i	−0.764184	+	0.710352i
$399$			1.07024i			0.0535788i
$400$	1.76311	−	11.9931i	0.0881557	−	0.599656i
$401$	2.84261	−	2.84261i	0.141953	−	0.141953i	−0.632559	−	0.774512i	$-0.717995\pi$
$401$	2.84261	−	2.84261i	0.141953	−	0.141953i	0.774512	+	0.632559i	$0.217995\pi$
$402$	−1.15700	−	0.0422391i	−0.0577059	−	0.00210670i
$403$	0.810308	+	5.49840i	0.0403643	+	0.273895i
$404$	10.3080	+	0.753639i	0.512840	+	0.0374949i
$405$	17.8057	+	17.8057i	0.884772	+	0.884772i
$406$	14.7921	+	0.540020i	0.734117	+	0.0268008i
$407$	0.399144			0.0197848
$408$	0.831118	+	1.03638i	0.0411465	+	0.0513085i
$409$	5.15000	+	5.15000i	0.254651	+	0.254651i	0.822874	−	0.568223i	$-0.192369\pi$
$409$	5.15000	+	5.15000i	0.254651	+	0.254651i	−0.568223	+	0.822874i	$0.692369\pi$
$410$	−32.8404	−	35.3291i	−1.62187	−	1.74478i
$411$	−0.312302	−	0.312302i	−0.0154047	−	0.0154047i
$412$	−1.36023	+	18.6046i	−0.0670136	+	0.916583i
$413$		−	48.3999i		−	2.38160i
$414$	16.4586	−	15.2992i	0.808894	−	0.751913i
$415$	−12.2526			−0.601456
$416$	0.736913	−	20.3828i	0.0361301	−	0.999347i
$417$	1.26948			0.0621669
$418$	2.30844	−	2.14583i	0.112910	−	0.104956i
$419$		−	11.0946i		−	0.542005i	−0.962579	−	0.271003i	$-0.912645\pi$
$419$		−	11.0946i		−	0.542005i	0.962579	−	0.271003i	$-0.0873552\pi$
$420$	−0.198463	+	2.71449i	−0.00968399	+	0.132453i
$421$	−16.0079	−	16.0079i	−0.780177	−	0.780177i	0.199684	−	0.979860i	$-0.436009\pi$
$421$	−16.0079	−	16.0079i	−0.780177	−	0.780177i	−0.979860	+	0.199684i	$0.936009\pi$
$422$	3.02427	+	3.25345i	0.147219	+	0.158375i
$423$	−13.6692	−	13.6692i	−0.664618	−	0.664618i
$424$	−19.1424	−	23.8700i	−0.929636	−	1.15923i
$425$	12.6339			0.612834
$426$	1.70318	+	0.0621789i	0.0825195	+	0.00301258i
$427$	−34.4468	−	34.4468i	−1.66700	−	1.66700i
$428$	−35.4839	−	2.59431i	−1.71518	−	0.125401i
$429$	−0.0592250	−	0.401876i	−0.00285941	−	0.0194027i
$430$	−30.5141	−	1.11399i	−1.47152	−	0.0537215i
$431$	−13.3406	+	13.3406i	−0.642595	+	0.642595i	−0.951193	−	0.308598i	$-0.900140\pi$
$431$	−13.3406	+	13.3406i	−0.642595	+	0.642595i	0.308598	+	0.951193i	$0.400140\pi$
$432$	0.392449	−	2.66953i	0.0188817	−	0.128438i
$433$		−	25.2309i		−	1.21252i	−0.795267	−	0.606260i	$-0.792669\pi$
$433$		−	25.2309i		−	1.21252i	0.795267	−	0.606260i	$-0.207331\pi$
$434$	6.80569	−	6.32628i	0.326684	−	0.303671i
$435$	0.554353	−	0.554353i	0.0265792	−	0.0265792i
$436$	15.0919	−	13.0355i	0.722772	−	0.624285i
$437$	−8.38203	+	8.38203i	−0.400967	+	0.400967i
$438$	−0.307721	−	0.0112341i	−0.0147035	−	0.000536787i
$439$	6.01826			0.287236			0.143618	−	0.989633i	$-0.454126\pi$
$439$	6.01826			0.287236			0.143618	+	0.989633i	$0.454126\pi$
$440$	6.25292	−	5.01448i	0.298096	−	0.239056i
$441$			33.3635i			1.58874i
$442$	21.1293	−	2.32994i	1.00502	−	0.110824i
$443$		−	15.4206i		−	0.732654i	−0.930486	−	0.366327i	$-0.880615\pi$
$443$		−	15.4206i		−	0.732654i	0.930486	−	0.366327i	$-0.119385\pi$
$444$	−0.0680640	+	0.0587894i	−0.00323017	+	0.00279002i
$445$	−50.4930			−2.39360
$446$	1.01682	−	27.8525i	0.0481480	−	1.31885i
$447$	−0.274687	+	0.274687i	−0.0129923	+	0.0129923i
$448$	−28.7736	+	18.2992i	−1.35942	+	0.864555i
$449$	11.1606	−	11.1606i	0.526699	−	0.526699i	−0.392888	−	0.919587i	$-0.628524\pi$
$449$	11.1606	−	11.1606i	0.526699	−	0.526699i	0.919587	+	0.392888i	$0.128524\pi$
$450$	−8.71674	−	9.37730i	−0.410911	−	0.442050i
$451$		−	12.0359i		−	0.566747i
$452$	1.55429	−	21.2589i	0.0731076	−	0.999934i
$453$	1.15656	−	1.15656i	0.0543400	−	0.0543400i
$454$	−0.295783	+	8.10198i	−0.0138818	+	0.380245i
$455$	34.9563	+	25.9765i	1.63877	+	1.21780i
$456$	−0.0775905	+	0.705925i	−0.00363351	+	0.0330580i
$457$	28.2610	+	28.2610i	1.32200	+	1.32200i	0.912158	+	0.409838i	$0.134415\pi$
$457$	28.2610	+	28.2610i	1.32200	+	1.32200i	0.409838	+	0.912158i	$0.365585\pi$
$458$	−0.718244	+	19.6739i	−0.0335614	+	0.919301i
$459$	2.81216			0.131260
$460$	−22.8141	+	19.7054i	−1.06371	+	0.918768i
$461$	7.21486	+	7.21486i	0.336030	+	0.336030i	0.854871	−	0.518841i	$-0.173636\pi$
$461$	7.21486	+	7.21486i	0.336030	+	0.336030i	−0.518841	+	0.854871i	$0.673636\pi$
$462$	−0.497425	+	0.462385i	−0.0231423	+	0.0215121i
$463$	3.67039	+	3.67039i	0.170577	+	0.170577i	0.787233	−	0.616656i	$-0.211513\pi$
$463$	3.67039	+	3.67039i	0.170577	+	0.170577i	−0.616656	+	0.787233i	$0.711513\pi$
$464$	9.71765	+	1.42860i	0.451130	+	0.0663209i
$465$		−	0.492139i		−	0.0228224i
$466$	−15.4955	−	16.6698i	−0.717816	−	0.772213i
$467$	3.32406			0.153819			0.0769096	−	0.997038i	$-0.475495\pi$
$467$	3.32406			0.153819			0.0769096	+	0.997038i	$0.475495\pi$
$468$	−16.3075	−	14.0753i	−0.753813	−	0.650632i
$469$	30.9728			1.43019
$470$	17.6566	+	18.9947i	0.814440	+	0.876159i
$471$		−	0.849477i		−	0.0391418i
$472$	3.50892	−	31.9245i	0.161511	−	1.46944i
$473$	−5.38752	−	5.38752i	−0.247718	−	0.247718i
$474$	−0.400768	+	0.372536i	−0.0184079	+	0.0171112i
$475$	4.77568	+	4.77568i	0.219123	+	0.219123i
$476$	−23.2309	−	26.8957i	−1.06478	−	1.23276i
$477$	−32.3162			−1.47966
$478$	−0.994314	+	27.2359i	−0.0454788	+	1.24574i
$479$	13.9689	+	13.9689i	0.638255	+	0.638255i	0.950125	−	0.311869i	$-0.100955\pi$
$479$	13.9689	+	13.9689i	0.638255	+	0.638255i	−0.311869	+	0.950125i	$0.600955\pi$
$480$	−0.327702	+	1.77608i	−0.0149575	+	0.0810666i
$481$	0.209821	+	1.42375i	0.00956701	+	0.0649176i
$482$	−0.846521	+	23.1876i	−0.0385580	+	1.05617i
$483$	1.80617	−	1.80617i	0.0821835	−	0.0821835i
$484$	1.99468	+	0.145835i	0.0906671	+	0.00662889i
$485$		−	16.5597i		−	0.751938i
$486$	−2.91242	−	3.13313i	−0.132110	−	0.142122i
$487$	−0.360622	+	0.360622i	−0.0163414	+	0.0163414i	−0.715230	−	0.698889i	$-0.753678\pi$
$487$	−0.360622	+	0.360622i	−0.0163414	+	0.0163414i	0.698889	+	0.715230i	$0.253678\pi$
$488$	−20.2237	−	25.2183i	−0.915482	−	1.14158i
$489$	0.00443004	−	0.00443004i	0.000200333	−	0.000200333i
$490$	1.63294	−	44.7289i	0.0737687	−	2.02065i
$491$	−24.0149			−1.08378			−0.541888	−	0.840451i	$-0.682290\pi$
$491$	−24.0149			−1.08378			−0.541888	+	0.840451i	$0.682290\pi$
$492$	1.77275	+	2.05242i	0.0799218	+	0.0925302i
$493$			10.2369i			0.461045i
$494$	8.86771	+	7.10625i	0.398977	+	0.319725i
$495$		−	8.46547i		−	0.380495i
$496$	4.94766	−	3.67939i	0.222157	−	0.165210i
$497$	−45.5941			−2.04517
$498$	0.688443	+	0.0251333i	0.0308499	+	0.00112625i
$499$	26.1614	−	26.1614i	1.17114	−	1.17114i	0.189207	−	0.981937i	$-0.439408\pi$
$499$	26.1614	−	26.1614i	1.17114	−	1.17114i	0.981937	−	0.189207i	$-0.0605917\pi$
$500$	−7.29644	−	8.44752i	−0.326307	−	0.377784i
$501$	−0.668678	+	0.668678i	−0.0298743	+	0.0298743i
$502$	−4.22081	+	3.92348i	−0.188384	+	0.175113i
$503$		−	1.03191i		−	0.0460107i	−0.999735	−	0.0230053i	$-0.992677\pi$
$503$		−	1.03191i		−	0.0460107i	0.999735	−	0.0230053i	$-0.00732348\pi$
$504$	−3.93483	+	35.7994i	−0.175271	+	1.59463i
$505$	−10.3552	+	10.3552i	−0.460798	+	0.460798i
$506$	−7.51717	−	0.274433i	−0.334179	−	0.0122000i
$507$	1.40237	−	0.422514i	0.0622813	−	0.0187645i
$508$	−0.813964	+	11.1331i	−0.0361138	+	0.493950i
$509$	4.85218	+	4.85218i	0.215069	+	0.215069i	0.806417	−	0.591348i	$-0.201404\pi$
$509$	4.85218	+	4.85218i	0.215069	+	0.215069i	−0.591348	+	0.806417i	$0.701404\pi$
$510$	−1.88107	−	0.0686731i	−0.0832952	−	0.00304090i
$511$	8.23767			0.364413
$512$	−20.3056	+	9.98406i	−0.897391	+	0.441237i
$513$	1.06301	+	1.06301i	0.0469331	+	0.0469331i
$514$	21.7925	+	23.4440i	0.961226	+	1.03407i
$515$	−18.6898	−	18.6898i	−0.823571	−	0.823571i
$516$	1.71223	+	0.125185i	0.0753766	+	0.00551097i
$517$			6.47109i			0.284598i
$518$	1.76226	−	1.63812i	0.0774294	−	0.0719750i
$519$	0.494012			0.0216847
$520$	21.1738	+	19.6683i	0.928533	+	0.862513i
$521$	−8.14660			−0.356909			−0.178454	−	0.983948i	$-0.557110\pi$
$521$	−8.14660			−0.356909			−0.178454	+	0.983948i	$0.557110\pi$
$522$	7.59814	−	7.06290i	0.332562	−	0.309135i
$523$			17.9615i			0.785401i	0.919666	+	0.392701i	$0.128459\pi$
$523$			17.9615i			0.785401i	−0.919666	+	0.392701i	$0.871541\pi$
$524$	43.4426	+	3.17619i	1.89780	+	0.138753i
$525$	−1.02907	−	1.02907i	−0.0449122	−	0.0449122i
$526$	−13.2416	−	14.2451i	−0.577362	−	0.621115i
$527$	4.54400	+	4.54400i	0.197940	+	0.197940i
$528$	−0.361622	+	0.268925i	−0.0157376	+	0.0117035i
$529$	5.29161			0.230070
$530$	43.3250	+	1.58168i	1.88192	+	0.0687040i
$531$	−23.9856	−	23.9856i	−1.04089	−	1.04089i
$532$	1.38534	−	18.9481i	0.0600622	−	0.821505i
$533$	42.9323	−	6.32699i	1.85960	−	0.274052i
$534$	2.83708	+	0.103575i	0.122772	+	0.00448211i
$535$	35.6464	−	35.6464i	1.54113	−	1.54113i
$536$	20.4296	+	2.24548i	0.882423	+	0.0969899i
$537$			1.31062i			0.0565575i
$538$	21.2669	−	19.7688i	0.916882	−	0.852294i
$539$	7.89726	−	7.89726i	0.340159	−	0.340159i
$540$	2.49904	+	2.89328i	0.107542	+	0.124507i
$541$	10.4403	−	10.4403i	0.448862	−	0.448862i	−0.446114	−	0.894976i	$-0.647193\pi$
$541$	10.4403	−	10.4403i	0.448862	−	0.448862i	0.894976	+	0.446114i	$0.147193\pi$
$542$	−0.128112	−	0.00467706i	−0.00550290	−	0.000200897i
$543$	0.287412			0.0123340
$544$	−13.3731	−	19.4246i	−0.573367	−	0.832821i
$545$			28.2562i			1.21036i
$546$	−1.91082	−	1.53126i	−0.0817756	−	0.0655319i
$547$			2.68012i			0.114594i	0.998357	+	0.0572969i	$0.0182482\pi$
$547$			2.68012i			0.114594i	−0.998357	+	0.0572969i	$0.981752\pi$
$548$	5.12493	+	5.93343i	0.218926	+	0.253464i
$549$	−34.1417			−1.45713
$550$	−0.156359	+	4.28293i	−0.00666716	+	0.182625i
$551$	−3.86959	+	3.86959i	−0.164850	+	0.164850i
$552$	1.32229	−	1.06040i	0.0562803	−	0.0451336i
$553$	10.3506	−	10.3506i	0.440154	−	0.440154i
$554$	5.75515	+	6.19129i	0.244513	+	0.263043i
$555$		−	0.127434i		−	0.00540928i
$556$	−22.4757	−	1.64325i	−0.953184	−	0.0696895i
$557$	−16.6599	+	16.6599i	−0.705901	+	0.705901i	−0.965671	−	0.259770i	$-0.916353\pi$
$557$	−16.6599	+	16.6599i	−0.705901	+	0.705901i	0.259770	+	0.965671i	$0.416353\pi$
$558$	0.237584	−	6.50783i	0.0100577	−	0.275498i
$559$	16.3853	−	22.0495i	0.693025	−	0.932594i
$560$	7.02741	−	47.8021i	0.296962	−	2.02001i
$561$	−0.332118	−	0.332118i	−0.0140221	−	0.0140221i
$562$	1.09272	−	29.9314i	0.0460935	−	1.26258i
$563$	−16.3002			−0.686973			−0.343487	−	0.939158i	$-0.611608\pi$
$563$	−16.3002			−0.686973			−0.343487	+	0.939158i	$0.611608\pi$
$564$	−0.953120	−	1.10348i	−0.0401336	−	0.0464650i
$565$	21.3562	+	21.3562i	0.898464	+	0.898464i
$566$	−13.3301	+	12.3911i	−0.560306	+	0.520836i
$567$	26.7822	+	26.7822i	1.12475	+	1.12475i
$568$	−30.0737	−	3.30550i	−1.26187	−	0.138696i
$569$		−	27.4723i		−	1.15170i	−0.817556	−	0.575849i	$-0.804672\pi$
$569$		−	27.4723i		−	1.15170i	0.817556	−	0.575849i	$-0.195328\pi$
$570$	−0.685096	−	0.737014i	−0.0286955	−	0.0308701i
$571$	−30.4448			−1.27407			−0.637037	−	0.770833i	$-0.719840\pi$
$571$	−30.4448			−1.27407			−0.637037	+	0.770833i	$0.719840\pi$
$572$	0.528358	+	7.19172i	0.0220918	+	0.300701i
$573$	−1.57998			−0.0660046
$574$	−49.3964	−	53.1397i	−2.06177	−	2.21801i
$575$		−	16.1192i		−	0.672217i
$576$	−5.19080	+	23.3279i	−0.216283	+	0.971997i
$577$	18.8742	+	18.8742i	0.785744	+	0.785744i	0.980793	−	0.195050i	$-0.0624868\pi$
$577$	18.8742	+	18.8742i	0.785744	+	0.785744i	−0.195050	+	0.980793i	$0.562487\pi$
$578$	0.393397	−	0.365685i	0.0163632	−	0.0152105i
$579$	−0.860871	−	0.860871i	−0.0357766	−	0.0357766i
$580$	−10.5322	+	9.09704i	−0.437325	+	0.377734i
$581$	−18.4296			−0.764588
$582$	−0.0339684	+	0.930450i	−0.00140803	+	0.0385684i
$583$	7.64938	+	7.64938i	0.316805	+	0.316805i
$584$	5.43354	+	0.597218i	0.224842	+	0.0247131i
$585$	30.1965	−	4.45011i	1.24847	−	0.183989i
$586$	−1.24925	+	34.2190i	−0.0516060	+	1.41358i
$587$	16.8766	−	16.8766i	0.696571	−	0.696571i	−0.267098	−	0.963669i	$-0.586065\pi$
$587$	16.8766	−	16.8766i	0.696571	−	0.696571i	0.963669	+	0.267098i	$0.0860648\pi$
$588$	−0.183502	+	2.50986i	−0.00756749	+	0.103505i
$589$			3.43531i			0.141550i
$590$	30.9825	+	33.3304i	1.27553	+	1.37219i
$591$	1.84782	−	1.84782i	0.0760091	−	0.0760091i
$592$	1.28115	−	0.952741i	0.0526548	−	0.0391574i
$593$	5.91428	−	5.91428i	0.242870	−	0.242870i	−0.575166	−	0.818037i	$-0.695063\pi$
$593$	5.91428	−	5.91428i	0.242870	−	0.242870i	0.818037	+	0.575166i	$0.195063\pi$
$594$	−0.0348036	+	0.953329i	−0.00142801	+	0.0391156i
$595$	50.3561			2.06440
$596$	5.21879	−	4.50767i	0.213770	−	0.184641i
$597$			1.65822i			0.0678664i
$598$	−2.97270	−	26.9582i	−0.121563	−	1.10240i
$599$			39.4426i			1.61158i	0.592200	+	0.805791i	$0.298260\pi$
$599$			39.4426i			1.61158i	−0.592200	+	0.805791i	$0.701740\pi$
$600$	−0.604165	−	0.753376i	−0.0246649	−	0.0307565i
$601$	−1.59397			−0.0650193			−0.0325096	−	0.999471i	$-0.510350\pi$
$601$	−1.59397			−0.0650193			−0.0325096	+	0.999471i	$0.510350\pi$
$602$	−45.8974	−	1.67560i	−1.87064	−	0.0682922i
$603$	15.3492	−	15.3492i	0.625069	−	0.625069i
$604$	−21.9736	+	18.9794i	−0.894091	+	0.772260i
$605$	−2.00381	+	2.00381i	−0.0814664	+	0.0814664i
$606$	0.603072	−	0.560589i	0.0244981	−	0.0227724i
$607$		−	21.9235i		−	0.889846i	−0.895569	−	0.444923i	$-0.853231\pi$
$607$		−	21.9235i		−	0.889846i	0.895569	−	0.444923i	$-0.146769\pi$
$608$	2.28748	−	12.3977i	0.0927695	−	0.502793i
$609$	0.833822	−	0.833822i	0.0337882	−	0.0337882i
$610$	45.7723	+	1.67103i	1.85326	+	0.0676580i
$611$	−23.0825	+	3.40171i	−0.933819	+	0.137618i
$612$	−24.8413	−	1.81621i	−1.00415	−	0.0734158i
$613$	22.3658	+	22.3658i	0.903345	+	0.903345i	0.995724	−	0.0923790i	$-0.0294471\pi$
$613$	22.3658	+	22.3658i	0.903345	+	0.903345i	−0.0923790	+	0.995724i	$0.529447\pi$
$614$	−5.41236	−	0.197591i	−0.218425	−	0.00797414i
$615$	−3.84269			−0.154952
$616$	9.40524	−	7.54246i	0.378948	−	0.303895i
$617$	28.6061	+	28.6061i	1.15164	+	1.15164i	0.986224	+	0.165414i	$0.0528960\pi$
$617$	28.6061	+	28.6061i	1.15164	+	1.15164i	0.165414	+	0.986224i	$0.447104\pi$
$618$	1.01180	+	1.08847i	0.0407004	+	0.0437847i
$619$	1.75532	+	1.75532i	0.0705522	+	0.0705522i	0.741502	−	0.670950i	$-0.234114\pi$
$619$	1.75532	+	1.75532i	0.0705522	+	0.0705522i	−0.670950	+	0.741502i	$0.734114\pi$
$620$	−0.637038	+	8.71313i	−0.0255841	+	0.349928i
$621$		−	3.58795i		−	0.143979i
$622$	−32.6285	+	30.3301i	−1.30828	+	1.21612i
$623$	−75.9484			−3.04281
$624$	−1.14936	−	1.14855i	−0.0460112	−	0.0459787i
$625$	30.9686			1.23874
$626$	15.9389	−	14.8161i	0.637045	−	0.592170i
$627$		−	0.251085i		−	0.0100274i
$628$	−1.09959	+	15.0397i	−0.0438782	+	0.600148i
$629$	1.17662	+	1.17662i	0.0469149	+	0.0469149i
$630$	−34.7431	−	37.3760i	−1.38420	−	1.48910i
$631$	17.8351	+	17.8351i	0.710005	+	0.710005i	0.966536	−	0.256531i	$-0.0825795\pi$
$631$	17.8351	+	17.8351i	0.710005	+	0.710005i	−0.256531	+	0.966536i	$0.582580\pi$
$632$	7.57766	−	6.07685i	0.301423	−	0.241724i
$633$	0.353872			0.0140652
$634$	−1.40137	−	0.0511606i	−0.0556556	−	0.00203185i
$635$	−11.1840	−	11.1840i	−0.443825	−	0.443825i
$636$	−2.43108	−	0.177742i	−0.0963986	−	0.00704793i
$637$	32.3211	+	24.0183i	1.28061	+	0.951640i
$638$	−3.47032	−	0.126693i	−0.137391	−	0.00501581i
$639$	−22.5951	+	22.5951i	−0.893850	+	0.893850i
$640$	8.10084	−	31.0207i	0.320214	−	1.22620i
$641$		−	14.5574i		−	0.574983i	−0.957783	−	0.287492i	$-0.907179\pi$
$641$		−	14.5574i		−	0.574983i	0.957783	−	0.287492i	$-0.0928213\pi$
$642$	−2.07600	+	1.92976i	−0.0819333	+	0.0761617i
$643$	12.6200	−	12.6200i	0.497682	−	0.497682i	−0.413034	−	0.910716i	$-0.635531\pi$
$643$	12.6200	−	12.6200i	0.497682	−	0.497682i	0.910716	+	0.413034i	$0.135531\pi$
$644$	−34.3155	+	29.6396i	−1.35222	+	1.16796i
$645$	−1.72007	+	1.72007i	−0.0677276	+	0.0677276i
$646$	13.1306	+	0.479364i	0.516615	+	0.0188603i
$647$	−28.6053			−1.12459			−0.562296	−	0.826936i	$-0.690082\pi$
$647$	−28.6053			−1.12459			−0.562296	+	0.826936i	$0.690082\pi$
$648$	15.7238	+	19.6071i	0.617689	+	0.770241i
$649$			11.3550i			0.445722i
$650$	−15.3595	+	1.69370i	−0.602449	+	0.0664325i
$651$		−	0.740244i		−	0.0290124i
$652$	−0.0841665	+	0.0726978i	−0.00329622	+	0.00284707i
$653$	15.8775			0.621336			0.310668	−	0.950519i	$-0.399447\pi$
$653$	15.8775			0.621336			0.310668	+	0.950519i	$0.399447\pi$
$654$	0.0579609	−	1.58765i	0.00226645	−	0.0620818i
$655$	−43.6415	+	43.6415i	−1.70521	+	1.70521i
$656$	−28.7292	−	38.6320i	−1.12169	−	1.50833i
$657$	4.08235	−	4.08235i	0.159268	−	0.159268i
$658$	26.5580	+	28.5706i	1.03534	+	1.11380i
$659$			32.5686i			1.26869i	0.773049	+	0.634346i	$0.218730\pi$
$659$			32.5686i			1.26869i	−0.773049	+	0.634346i	$0.781270\pi$
$660$	0.0465608	−	0.636839i	0.00181238	−	0.0247889i
$661$	−21.4184	+	21.4184i	−0.833078	+	0.833078i	−0.987937	−	0.154858i	$-0.950508\pi$
$661$	−21.4184	+	21.4184i	−0.833078	+	0.833078i	0.154858	+	0.987937i	$0.450508\pi$
$662$	0.911338	−	24.9631i	0.0354201	−	0.970217i
$663$	1.01009	−	1.35926i	0.0392285	−	0.0527894i
$664$	−12.1561	−	1.33612i	−0.471748	−	0.0518513i
$665$	19.0349	+	19.0349i	0.738141	+	0.738141i
$666$	0.0615200	−	1.68513i	0.00238385	−	0.0652977i
$667$	13.0609			0.505720
$668$	12.7042	−	10.9731i	0.491542	−	0.424563i
$669$	−1.57003	−	1.57003i	−0.0607011	−	0.0607011i
$670$	−21.3293	+	19.8268i	−0.824022	+	0.765975i
$671$	8.08147	+	8.08147i	0.311982	+	0.311982i
$672$	−0.492908	+	2.67147i	−0.0190143	+	0.103054i
$673$			26.1554i			1.00822i	0.863640	+	0.504109i	$0.168179\pi$
$673$			26.1554i			1.00822i	−0.863640	+	0.504109i	$0.831821\pi$
$674$	−2.65555	−	2.85679i	−0.102288	−	0.110039i
$675$	−2.04424			−0.0786829
$676$	−25.3753	+	5.66519i	−0.975973	+	0.217892i
$677$	−35.8314			−1.37711			−0.688557	−	0.725182i	$-0.741755\pi$
$677$	−35.8314			−1.37711			−0.688557	+	0.725182i	$0.741755\pi$
$678$	−1.15615	−	1.24376i	−0.0444016	−	0.0477664i
$679$		−	24.9081i		−	0.955884i
$680$	33.2148	+	3.65074i	1.27373	+	0.140000i
$681$	0.456705	+	0.456705i	0.0175010	+	0.0175010i
$682$	−1.59666	+	1.48419i	−0.0611395	+	0.0568326i
$683$	−26.6425	−	26.6425i	−1.01945	−	1.01945i	−0.999807	−	0.0196395i	$-0.993748\pi$
$683$	−26.6425	−	26.6425i	−1.01945	−	1.01945i	−0.0196395	−	0.999807i	$-0.506252\pi$
$684$	−8.70362	−	10.0767i	−0.332791	−	0.385292i
$685$	−11.1090			−0.424453
$686$	0.916720	−	25.1105i	0.0350005	−	0.958722i
$687$	1.10901	+	1.10901i	0.0423114	+	0.0423114i
$688$	−30.1523	−	4.43271i	−1.14955	−	0.168995i
$689$	−23.2644	+	31.3066i	−0.886303	+	1.19269i
$690$	−0.0876180	+	2.40000i	−0.00333556	+	0.0913665i
$691$	14.4916	−	14.4916i	0.551288	−	0.551288i	−0.375525	−	0.926812i	$-0.622537\pi$
$691$	14.4916	−	14.4916i	0.551288	−	0.551288i	0.926812	+	0.375525i	$0.122537\pi$
$692$	−8.74629	−	0.639462i	−0.332484	−	0.0243087i
$693$		−	12.7332i		−	0.483695i
$694$	27.6897	+	29.7880i	1.05109	+	1.13074i
$695$	22.5787	−	22.5787i	0.856457	−	0.856457i
$696$	0.610438	−	0.489536i	0.0231386	−	0.0185558i
$697$	35.4801	−	35.4801i	1.34391	−	1.34391i
$698$	−1.07930	+	29.5639i	−0.0408523	+	1.11901i
$699$	−1.81315			−0.0685795
$700$	16.8872	+	19.5513i	0.638276	+	0.738970i
$701$			40.0984i			1.51450i	0.653128	+	0.757248i	$0.273456\pi$
$701$			40.0984i			1.51450i	−0.653128	+	0.757248i	$0.726544\pi$
$702$	−3.41884	+	0.376999i	−0.129036	+	0.0142289i
$703$			0.889538i			0.0335496i
$704$	6.75049	−	4.29312i	0.254419	−	0.161803i
$705$	2.06602			0.0778108
$706$	−10.7339	−	0.391866i	−0.403974	−	0.0147481i
$707$	−15.5756	+	15.5756i	−0.585779	+	0.585779i
$708$	−1.67246	−	1.93631i	−0.0628550	−	0.0727709i
$709$	−8.10511	+	8.10511i	−0.304394	+	0.304394i	−0.842730	−	0.538336i	$-0.819053\pi$
$709$	−8.10511	+	8.10511i	−0.304394	+	0.304394i	0.538336	+	0.842730i	$0.319053\pi$
$710$	31.3982	−	29.1864i	1.17835	−	1.09535i
$711$		−	10.2590i		−	0.384741i
$712$	−50.0953	−	5.50614i	−1.87740	−	0.206351i
$713$	5.79755	−	5.79755i	0.217120	−	0.217120i
$714$	−2.82939	−	0.103294i	−0.105887	−	0.00386567i
$715$	−8.20099	−	6.09428i	−0.306700	−	0.227913i
$716$	1.69650	−	23.2040i	0.0634013	−	0.867176i
$717$	1.53528	+	1.53528i	0.0573360	+	0.0573360i
$718$	5.85358	+	0.213699i	0.218454	+	0.00797519i
$719$	−20.5480			−0.766312			−0.383156	−	0.923684i	$-0.625163\pi$
$719$	−20.5480			−0.766312			−0.383156	+	0.923684i	$0.625163\pi$
$720$	−20.2068	−	27.1719i	−0.753062	−	1.01264i
$721$	−28.1120	−	28.1120i	−1.04695	−	1.04695i
$722$	−13.5119	−	14.5359i	−0.502863	−	0.540970i
$723$	1.30708	+	1.30708i	0.0486107	+	0.0486107i
$724$	−5.08852	−	0.372034i	−0.189113	−	0.0138265i
$725$		−	7.44148i		−	0.276369i
$726$	0.116699	−	0.108479i	0.00433112	−	0.00402603i
$727$	31.6216			1.17278			0.586389	−	0.810029i	$-0.300549\pi$
$727$	31.6216			1.17278			0.586389	+	0.810029i	$0.300549\pi$
$728$	31.8483	+	29.5838i	1.18038	+	1.09645i
$729$	26.3170			0.974703
$730$	−5.67284	+	5.27323i	−0.209961	+	0.195171i
$731$		−	31.7633i		−	1.17481i
$732$	−2.56840	−	0.187782i	−0.0949309	−	0.00694062i
$733$	−20.9212	−	20.9212i	−0.772741	−	0.772741i	0.205844	−	0.978585i	$-0.434006\pi$
$733$	−20.9212	−	20.9212i	−0.772741	−	0.772741i	−0.978585	+	0.205844i	$0.934006\pi$
$734$	−30.8524	−	33.1904i	−1.13878	−	1.22508i
$735$	−2.52135	−	2.52135i	−0.0930015	−	0.0930015i
$736$	−24.7832	+	17.0624i	−0.913521	+	0.628927i
$737$	−7.26644			−0.267663
$738$	−50.8140	−	1.85509i	−1.87049	−	0.0682868i
$739$	28.4737	+	28.4737i	1.04742	+	1.04742i	0.998818	+	0.0486049i	$0.0154775\pi$
$739$	28.4737	+	28.4737i	1.04742	+	1.04742i	0.0486049	+	0.998818i	$0.484522\pi$
$740$	−0.164954	+	2.25618i	−0.00606384	+	0.0829387i
$741$	0.895627	−	0.131990i	0.0329017	−	0.00484877i
$742$	65.1666	+	2.37907i	2.39234	+	0.0873384i
$743$	3.56265	−	3.56265i	0.130701	−	0.130701i	−0.638730	−	0.769431i	$-0.720540\pi$
$743$	3.56265	−	3.56265i	0.130701	−	0.130701i	0.769431	+	0.638730i	$0.220540\pi$
$744$	0.0536665	−	0.488263i	0.00196751	−	0.0179006i
$745$			9.77100i			0.357982i
$746$	−25.6549	+	23.8477i	−0.939294	+	0.873127i
$747$	−9.13317	+	9.13317i	−0.334165	+	0.334165i
$748$	5.45013	+	6.30993i	0.199276	+	0.230714i
$749$	53.6170	−	53.6170i	1.95912	−	1.95912i
$750$	−0.888665	−	0.0324429i	−0.0324494	−	0.00118465i
$751$	−29.4022			−1.07290			−0.536451	−	0.843932i	$-0.680235\pi$
$751$	−29.4022			−1.07290			−0.536451	+	0.843932i	$0.680235\pi$
$752$	15.4462	+	20.7705i	0.563267	+	0.757422i
$753$			0.459090i			0.0167302i
$754$	−1.37236	−	12.4453i	−0.0499782	−	0.453232i
$755$		−	41.1405i		−	1.49725i
$756$	3.75889	+	4.35189i	0.136710	+	0.158277i
$757$	−41.5411			−1.50984			−0.754918	−	0.655819i	$-0.772323\pi$
$757$	−41.5411			−1.50984			−0.754918	+	0.655819i	$0.772323\pi$
$758$	−0.669582	+	18.3410i	−0.0243203	+	0.666174i
$759$	−0.423740	+	0.423740i	−0.0153808	+	0.0153808i
$760$	11.1754	+	13.9354i	0.405373	+	0.505489i
$761$	17.7038	−	17.7038i	0.641763	−	0.641763i	−0.309226	−	0.950989i	$-0.600070\pi$
$761$	17.7038	−	17.7038i	0.641763	−	0.641763i	0.950989	+	0.309226i	$0.100070\pi$
$762$	0.605462	+	0.651345i	0.0219336	+	0.0235957i
$763$			42.5011i			1.53864i
$764$	27.9730	+	2.04517i	1.01203	+	0.0739916i
$765$	24.9551	−	24.9551i	0.902252	−	0.902252i
$766$	−0.406888	+	11.1453i	−0.0147014	+	0.402697i
$767$	−40.5035	+	5.96906i	−1.46250	+	0.215530i
$768$	−0.518798	+	1.72636i	−0.0187205	+	0.0622946i
$769$	25.9738	+	25.9738i	0.936640	+	0.936640i	0.998109	−	0.0614694i	$-0.0195786\pi$
$769$	25.9738	+	25.9738i	0.936640	+	0.936640i	−0.0614694	+	0.998109i	$0.519579\pi$
$770$	−0.623214	+	17.0709i	−0.0224591	+	0.615191i
$771$	2.54996			0.0918346
$772$	14.1271	+	16.3557i	0.508444	+	0.588655i
$773$	5.15357	+	5.15357i	0.185361	+	0.185361i	0.793687	−	0.608326i	$-0.208159\pi$
$773$	5.15357	+	5.15357i	0.185361	+	0.185361i	−0.608326	+	0.793687i	$0.708159\pi$
$774$	−23.5758	+	21.9151i	−0.847415	+	0.787720i
$775$	−3.30317	−	3.30317i	−0.118653	−	0.118653i
$776$	1.80580	−	16.4293i	0.0648243	−	0.589777i
$777$		−	0.191678i		−	0.00687643i
$778$	−0.200642	−	0.215847i	−0.00719336	−	0.00773848i
$779$	26.8234			0.961046
$780$	2.29610	−	0.168688i	0.0822134	−	0.00604001i
$781$	10.6967			0.382758
$782$	−21.3506	−	22.9686i	−0.763496	−	0.821355i
$783$		−	1.65639i		−	0.0591944i
$784$	6.49766	−	44.1986i	0.232059	−	1.57852i
$785$	−15.1085	−	15.1085i	−0.539247	−	0.539247i
$786$	2.54163	−	2.36259i	0.0906569	−	0.0842708i
$787$	33.2639	+	33.2639i	1.18573	+	1.18573i	0.978236	+	0.207495i	$0.0665309\pi$
$787$	33.2639	+	33.2639i	1.18573	+	1.18573i	0.207495	+	0.978236i	$0.433469\pi$
$788$	−35.1068	+	30.3231i	−1.25063	+	1.08022i
$789$	−1.54941			−0.0551606
$790$	−0.502114	+	13.7537i	−0.0178644	+	0.489336i
$791$	32.1227	+	32.1227i	1.14215	+	1.14215i
$792$	0.923139	−	8.39880i	0.0328023	−	0.298438i
$793$	−24.5785	+	33.0750i	−0.872809	+	1.17453i
$794$	0.473297	−	12.9644i	0.0167967	−	0.460089i
$795$	2.44221	−	2.44221i	0.0866163	−	0.0866163i
$796$	2.14644	−	29.3581i	0.0760786	−	1.04057i
$797$		−	18.4499i		−	0.653529i	−0.945106	−	0.326765i	$-0.894042\pi$
$797$		−	18.4499i		−	0.653529i	0.945106	−	0.326765i	$-0.105958\pi$
$798$	−1.03048	−	1.10857i	−0.0364785	−	0.0392429i
$799$	−19.0759	+	19.0759i	−0.674856	+	0.674856i
$800$	9.72132	+	14.1203i	0.343700	+	0.499228i
$801$	−37.6378	+	37.6378i	−1.32987	+	1.32987i
$802$	−0.207415	+	5.68143i	−0.00732407	+	0.200618i
$803$	−1.93262			−0.0682006
$804$	1.23911	−	1.07027i	0.0437000	−	0.0377454i
$805$		−	64.2479i		−	2.26444i
$806$	−6.13348	−	4.91514i	−0.216042	−	0.173128i
$807$		−	2.31317i		−	0.0814273i
$808$	−11.4028	+	9.14439i	−0.401149	+	0.321699i
$809$	−30.4521			−1.07064			−0.535319	−	0.844650i	$-0.679809\pi$
$809$	−30.4521			−1.07064			−0.535319	+	0.844650i	$0.679809\pi$
$810$	−35.5877	−	1.29922i	−1.25042	−	0.0456498i
$811$	−0.00632149	+	0.00632149i	−0.000221978	+	0.000221978i	−0.707218	−	0.706996i	$-0.750050\pi$
$811$	−0.00632149	+	0.00632149i	−0.000221978	+	0.000221978i	0.706996	+	0.707218i	$0.250050\pi$
$812$	−15.8418	+	13.6832i	−0.555939	+	0.480186i
$813$	−0.00722165	+	0.00722165i	−0.000253274	+	0.000253274i
$814$	−0.413440	+	0.384316i	−0.0144911	+	0.0134703i
$815$		−	0.157583i		−	0.00551988i
$816$	−1.85877	−	0.273258i	−0.0650699	−	0.00956596i
$817$	12.0067	−	12.0067i	0.420062	−	0.420062i
$818$	−10.2931	−	0.375777i	−0.359891	−	0.0131387i
$819$	45.4197	−	6.69357i	1.58709	−	0.233892i
$820$	68.0333	+	4.97407i	2.37583	+	0.173702i
$821$	−20.2300	−	20.2300i	−0.706033	−	0.706033i	0.259666	−	0.965699i	$-0.416388\pi$
$821$	−20.2300	−	20.2300i	−0.706033	−	0.706033i	−0.965699	+	0.259666i	$0.916388\pi$
$822$	0.624187	+	0.0227875i	0.0217710	+	0.000794805i
$823$	−7.40896			−0.258260			−0.129130	−	0.991628i	$-0.541218\pi$
$823$	−7.40896			−0.258260			−0.129130	+	0.991628i	$0.541218\pi$
$824$	−16.5045	−	20.5807i	−0.574962	−	0.716962i
$825$	0.241427	+	0.241427i	0.00840540	+	0.00840540i
$826$	46.6019	+	50.1335i	1.62149	+	1.74437i
$827$	14.5308	+	14.5308i	0.505285	+	0.505285i	0.913075	−	0.407791i	$-0.133701\pi$
$827$	14.5308	+	14.5308i	0.505285	+	0.505285i	−0.407791	+	0.913075i	$0.633701\pi$
$828$	−2.31724	+	31.6943i	−0.0805298	+	1.10145i
$829$			12.4006i			0.430690i	0.976538	+	0.215345i	$0.0690876\pi$
$829$			12.4006i			0.430690i	−0.976538	+	0.215345i	$0.930912\pi$
$830$	12.6915	−	11.7974i	0.440527	−	0.409495i
$831$	0.673416			0.0233605
$832$	18.8623	+	21.8224i	0.653931	+	0.756554i
$833$	46.5601			1.61321
$834$	−1.31495	+	1.22232i	−0.0455331	+	0.0423256i
$835$			23.7858i			0.823141i
$836$	−0.325011	+	4.44537i	−0.0112408	+	0.153746i
$837$	−0.735246	−	0.735246i	−0.0254138	−	0.0254138i
$838$	10.6824	+	11.4919i	0.369018	+	0.396983i
$839$	30.7228	+	30.7228i	1.06067	+	1.06067i	0.998037	+	0.0626315i	$0.0199493\pi$
$839$	30.7228	+	30.7228i	1.06067	+	1.06067i	0.0626315	+	0.998037i	$0.480051\pi$
$840$	−2.40808	−	3.00280i	−0.0830865	−	0.103607i
$841$	−22.9704			−0.792083
$842$	31.9945	+	1.16804i	1.10260	+	0.0402532i
$843$	−1.68722	−	1.68722i	−0.0581109	−	0.0581109i
$844$	−6.26517	−	0.458062i	−0.215656	−	0.0157671i
$845$	17.4274	−	32.4568i	0.599520	−	1.11655i
$846$	27.3201	+	0.997389i	0.939286	+	0.0342909i
$847$	−3.01400	+	3.01400i	−0.103562	+	0.103562i
$848$	42.8113	+	6.29371i	1.47014	+	0.216127i
$849$			1.44989i			0.0497602i
$850$	−13.0864	+	12.1646i	−0.448860	+	0.417241i
$851$	1.50122	−	1.50122i	0.0514610	−	0.0514610i
$852$	−1.82406	+	1.57551i	−0.0624911	+	0.0539760i
$853$	11.5366	−	11.5366i	0.395005	−	0.395005i	−0.481462	−	0.876467i	$-0.659894\pi$
$853$	11.5366	−	11.5366i	0.395005	−	0.395005i	0.876467	+	0.481462i	$0.159894\pi$
$854$	68.8477	+	2.51345i	2.35592	+	0.0860086i
$855$	18.8663			0.645214
$856$	39.2528	−	31.4785i	1.34163	−	1.07591i
$857$		−	27.2335i		−	0.930280i	−0.885237	−	0.465140i	$-0.846004\pi$
$857$		−	27.2335i		−	0.930280i	0.885237	−	0.465140i	$-0.153996\pi$
$858$	0.448293	+	0.359245i	0.0153045	+	0.0122644i
$859$			49.4080i			1.68578i	0.538086	+	0.842890i	$0.319147\pi$
$859$			49.4080i			1.68578i	−0.538086	+	0.842890i	$0.680853\pi$
$860$	32.6797	−	28.2267i	1.11437	−	0.962521i
$861$	−5.77992			−0.196979
$862$	0.973416	−	26.6635i	0.0331547	−	0.908162i
$863$	20.5538	−	20.5538i	0.699661	−	0.699661i	−0.264677	−	0.964337i	$-0.585265\pi$
$863$	20.5538	−	20.5538i	0.699661	−	0.699661i	0.964337	+	0.264677i	$0.0852652\pi$
$864$	2.16385	+	3.14301i	0.0736157	+	0.106927i
$865$	8.78634	−	8.78634i	0.298744	−	0.298744i
$866$	24.2936	+	26.1346i	0.825530	+	0.888090i
$867$		−	0.0427891i		−	0.00145320i
$868$	−0.958191	+	13.1057i	−0.0325231	+	0.444838i
$869$	−2.42834	+	2.42834i	−0.0823757	+	0.0823757i
$870$	−0.0404491	+	1.10797i	−0.00137135	+	0.0375636i
$871$	−3.81980	−	25.9196i	−0.129429	−	0.878251i
$872$	−3.08127	+	28.0336i	−0.104345	+	0.949339i
$873$	−12.3437	−	12.3437i	−0.417772	−	0.417772i
$874$	0.611606	−	16.7529i	0.0206879	−	0.566675i
$875$	23.7895			0.804231
$876$	0.329560	−	0.284653i	0.0111348	−	0.00961754i
$877$	11.9172	+	11.9172i	0.402415	+	0.402415i	0.879083	−	0.476669i	$-0.158156\pi$
$877$	11.9172	+	11.9172i	0.402415	+	0.402415i	−0.476669	+	0.879083i	$0.658156\pi$
$878$	−6.23382	+	5.79469i	−0.210381	+	0.195561i
$879$	1.92891	+	1.92891i	0.0650606	+	0.0650606i
$880$	−1.64868	+	11.2147i	−0.0555771	+	0.378048i
$881$			31.1325i			1.04888i	0.851448	+	0.524440i	$0.175725\pi$
$881$			31.1325i			1.04888i	−0.851448	+	0.524440i	$0.824275\pi$
$882$	−32.1241	−	34.5585i	−1.08167	−	1.16364i
$883$	28.6629			0.964582			0.482291	−	0.876011i	$-0.339805\pi$
$883$	28.6629			0.964582			0.482291	+	0.876011i	$0.339805\pi$
$884$	−19.6427	+	22.7577i	−0.660655	+	0.765425i
$885$	3.62529			0.121863
$886$	14.8477	+	15.9729i	0.498819	+	0.536621i
$887$		−	22.9019i		−	0.768971i	−0.923131	−	0.384485i	$-0.874379\pi$
$887$		−	22.9019i		−	0.768971i	0.923131	−	0.384485i	$-0.125621\pi$
$888$	0.0138964	−	0.126431i	0.000466332	−	0.00424273i
$889$	−16.8223	−	16.8223i	−0.564202	−	0.564202i
$890$	52.3016	−	48.6173i	1.75315	−	1.62965i
$891$	−6.28330	−	6.28330i	−0.210498	−	0.210498i
$892$	25.7646	+	29.8292i	0.862662	+	0.998754i
$893$	−14.4216			−0.482600
$894$	0.0200429	−	0.549008i	0.000670335	−	0.0183616i
$895$	23.3103	+	23.3103i	0.779177	+	0.779177i
$896$	12.1848	−	46.6593i	0.407064	−	1.55878i
$897$	−1.73424	−	1.28874i	−0.0579046	−	0.0430298i
$898$	−0.814344	+	22.3062i	−0.0271750	+	0.744369i
$899$	2.67645	−	2.67645i	0.0892647	−	0.0892647i
$900$	18.0579	+	1.32026i	0.601930	+	0.0440085i
$901$			45.0986i			1.50245i
$902$	11.5888	+	12.4670i	0.385863	+	0.415105i
$903$	−2.58722	+	2.58722i	−0.0860972	+	0.0860972i
$904$	18.8592	+	23.5169i	0.627247	+	0.782160i
$905$	5.11182	−	5.11182i	0.169923	−	0.169923i
$906$	−0.0843900	+	2.31158i	−0.00280367	+	0.0767971i
$907$	−43.3441			−1.43922			−0.719608	−	0.694381i	$-0.755678\pi$
$907$	−43.3441			−1.43922			−0.719608	+	0.694381i	$0.755678\pi$
$908$	−7.49462	−	8.67696i	−0.248718	−	0.287955i
$909$			15.4376i			0.512033i
$910$	−61.2198	+	6.75076i	−2.02942	+	0.223785i
$911$		−	24.7992i		−	0.821635i	−0.911718	−	0.410817i	$-0.865243\pi$
$911$		−	24.7992i		−	0.821635i	0.911718	−	0.410817i	$-0.134757\pi$
$912$	−0.599331	−	0.805917i	−0.0198458	−	0.0266866i
$913$	4.32371			0.143094
$914$	−56.4845	−	2.06210i	−1.86834	−	0.0682084i
$915$	2.58016	−	2.58016i	0.0852976	−	0.0852976i
$916$	−18.1991	−	21.0701i	−0.601314	−	0.696177i
$917$	−65.6428	+	65.6428i	−2.16771	+	2.16771i
$918$	−2.91288	+	2.70769i	−0.0961394	+	0.0893670i
$919$			11.5814i			0.382034i	0.981587	+	0.191017i	$0.0611786\pi$
$919$			11.5814i			0.382034i	−0.981587	+	0.191017i	$0.938821\pi$
$920$	4.65787	−	42.3777i	0.153565	−	1.39715i
$921$	−0.305092	+	0.305092i	−0.0100531	+	0.0100531i
$922$	−14.4201	−	0.526442i	−0.474901	−	0.0173374i
$923$	5.62302	+	38.1554i	0.185084	+	1.25590i
$924$	0.0700337	−	0.957892i	0.00230394	−	0.0315123i
$925$	−0.855321	−	0.855321i	−0.0281228	−	0.0281228i
$926$	−7.33589	−	0.267815i	−0.241072	−	0.00880094i
$927$	−27.8630			−0.915141
$928$	−11.4412	+	7.87688i	−0.375577	+	0.258571i
$929$	10.6558	+	10.6558i	0.349607	+	0.349607i	0.859963	−	0.510356i	$-0.170486\pi$
$929$	10.6558	+	10.6558i	0.349607	+	0.349607i	−0.510356	+	0.859963i	$0.670486\pi$
$930$	0.473856	+	0.509766i	0.0155384	+	0.0167159i
$931$	17.6000	+	17.6000i	0.576816	+	0.576816i
$932$	32.1011	+	2.34698i	1.05151	+	0.0768780i
$933$			3.54895i			0.116187i
$934$	−3.44312	+	3.20058i	−0.112662	+	0.104726i
$935$	−11.8139			−0.386356
$936$	30.4440	−	1.12220i	0.995093	−	0.0366803i
$937$	−28.6839			−0.937062			−0.468531	−	0.883447i	$-0.655217\pi$
$937$	−28.6839			−0.937062			−0.468531	+	0.883447i	$0.655217\pi$
$938$	−32.0821	+	29.8222i	−1.04752	+	0.973728i
$939$		−	1.73364i		−	0.0565754i
$940$	−36.5781	−	2.67431i	−1.19305	−	0.0872264i
$941$	−0.952351	−	0.952351i	−0.0310458	−	0.0310458i	0.691413	−	0.722459i	$-0.256988\pi$
$941$	−0.952351	−	0.952351i	−0.0310458	−	0.0310458i	−0.722459	+	0.691413i	$0.756988\pi$
$942$	0.817920	+	0.879903i	0.0266493	+	0.0286688i
$943$	−45.2680	−	45.2680i	−1.47413	−	1.47413i
$944$	27.1039	+	36.4465i	0.882157	+	1.18623i
$945$	−8.14793			−0.265052
$946$	10.7679	+	0.393107i	0.350093	+	0.0127810i
$947$	1.96659	+	1.96659i	0.0639057	+	0.0639057i	0.738337	−	0.674432i	$-0.235611\pi$
$947$	1.96659	+	1.96659i	0.0639057	+	0.0639057i	−0.674432	+	0.738337i	$0.735611\pi$
$948$	0.0564252	−	0.771759i	0.00183260	−	0.0250656i
$949$	−1.01593	−	6.89369i	−0.0329786	−	0.223779i
$950$	−9.54500	−	0.348464i	−0.309681	−	0.0113057i
$951$	−0.0789949	+	0.0789949i	−0.00256158	+	0.00256158i
$952$	49.9595	+	5.49121i	1.61920	+	0.177971i
$953$		−	48.3932i		−	1.56761i	−0.621008	−	0.783804i	$-0.713276\pi$
$953$		−	48.3932i		−	1.56761i	0.621008	−	0.783804i	$-0.286724\pi$
$954$	33.4737	−	31.1157i	1.08375	−	1.00741i
$955$	−28.1010	+	28.1010i	−0.909329	+	0.909329i
$956$	−25.1942	−	29.1688i	−0.814838	−	0.943386i
$957$	−0.195621	+	0.195621i	−0.00632352	+	0.00632352i
$958$	−27.9192	−	1.01926i	−0.902029	−	0.0329308i
$959$	−16.7094			−0.539576
$960$	−1.37066	−	2.15522i	−0.0442379	−	0.0695595i
$961$			28.6239i			0.923352i
$962$	−1.58820	−	1.27272i	−0.0512056	−	0.0410343i
$963$		−	53.1421i		−	1.71248i
$964$	−21.4494	−	24.8332i	−0.690838	−	0.799824i
$965$	−30.6224			−0.985769
$966$	−0.131789	+	3.60993i	−0.00424025	+	0.116148i
$967$	−12.6657	+	12.6657i	−0.407302	+	0.407302i	−0.880797	−	0.473495i	$-0.842992\pi$
$967$	−12.6657	+	12.6657i	−0.407302	+	0.407302i	0.473495	+	0.880797i	$0.342992\pi$
$968$	−2.20654	+	1.76952i	−0.0709208	+	0.0568744i
$969$	0.740165	−	0.740165i	0.0237775	−	0.0237775i
$970$	15.9445	+	17.1528i	0.511948	+	0.550745i
$971$			46.0879i			1.47903i	0.673139	+	0.739516i	$0.264946\pi$
$971$			46.0879i			1.47903i	−0.673139	+	0.739516i	$0.735054\pi$
$972$	6.03347	+	0.441122i	0.193524	+	0.0141490i
$973$	33.9614	−	33.9614i	1.08875	−	1.08875i
$974$	0.0263133	−	0.720764i	0.000843132	−	0.0230948i
$975$	−0.734263	+	0.988088i	−0.0235152	+	0.0316441i
$976$	45.2295	+	6.64922i	1.44776	+	0.212836i
$977$	−18.1628	−	18.1628i	−0.581079	−	0.581079i	0.354121	−	0.935200i	$-0.384780\pi$
$977$	−18.1628	−	18.1628i	−0.581079	−	0.581079i	−0.935200	+	0.354121i	$0.884780\pi$
$978$	−0.000323244		0.00885418i	−1.03362e−5		0.000283126i
$979$	17.8180			0.569467
$980$	41.3759	+	47.9033i	1.32170	+	1.53021i
$981$	21.0624	+	21.0624i	0.672469	+	0.672469i
$982$	24.8750	−	23.1227i	0.793794	−	0.737877i
$983$	−36.8960	−	36.8960i	−1.17680	−	1.17680i	−0.980555	−	0.196244i	$-0.937126\pi$
$983$	−36.8960	−	36.8960i	−1.17680	−	1.17680i	−0.196244	−	0.980555i	$-0.562874\pi$
$984$	−3.81242	−	0.419035i	−0.121536	−	0.0133584i
$985$		−	65.7295i		−	2.09432i
$986$	−9.85657	−	10.6035i	−0.313897	−	0.337685i
$987$	3.10757			0.0989152
$988$	−16.0276	+	1.17751i	−0.509906	+	0.0374615i
$989$	−40.5259			−1.28865
$990$	8.15099	+	8.76868i	0.259055	+	0.278687i
$991$		−	23.6922i		−	0.752607i	−0.926496	−	0.376303i	$-0.877195\pi$
$991$		−	23.6922i		−	0.752607i	0.926496	−	0.376303i	$-0.122805\pi$
$992$	−1.58217	+	8.57504i	−0.0502338	+	0.272258i
$993$	−1.40716	−	1.40716i	−0.0446548	−	0.0446548i
$994$	47.2271	−	43.9003i	1.49795	−	1.39243i
$995$	29.4926	+	29.4926i	0.934977	+	0.934977i
$996$	−0.737301	+	0.636835i	−0.0233623	+	0.0201789i
$997$	18.4238			0.583487			0.291743	−	0.956497i	$-0.405765\pi$
$997$	18.4238			0.583487			0.291743	+	0.956497i	$0.405765\pi$
$998$	−1.90890	+	52.2879i	−0.0604252	+	1.65515i
$999$	−0.190384	−	0.190384i	−0.00602350	−	0.00602350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.j.a.463.17	✓	140
4.3	odd	2	inner	572.2.j.a.463.53	yes	140
13.5	odd	4	inner	572.2.j.a.551.53	yes	140
52.31	even	4	inner	572.2.j.a.551.17	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.j.a.463.17	✓	140	1.1	even	1	trivial
572.2.j.a.463.53	yes	140	4.3	odd	2	inner
572.2.j.a.551.17	yes	140	52.31	even	4	inner
572.2.j.a.551.53	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)

\(f(q)\)	\(=\)	\(q+(-1.03582 + 0.962851i) q^{2} +0.112664i q^{3} +(0.145835 - 1.99468i) q^{4} +(2.00381 + 2.00381i) q^{5} +(-0.108479 - 0.116699i) q^{6} +(3.01400 + 3.01400i) q^{7} +(1.76952 + 2.20654i) q^{8} +2.98731 q^{9} +O(q^{10})\)	\(q+(-1.03582 + 0.962851i) q^{2} +0.112664i q^{3} +(0.145835 - 1.99468i) q^{4} +(2.00381 + 2.00381i) q^{5} +(-0.108479 - 0.116699i) q^{6} +(3.01400 + 3.01400i) q^{7} +(1.76952 + 2.20654i) q^{8} +2.98731 q^{9} +(-4.00495 - 0.146211i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(0.224728 + 0.0164304i) q^{12} +(2.15056 - 2.89398i) q^{13} +(-6.02399 - 0.219921i) q^{14} +(-0.225757 + 0.225757i) q^{15} +(-3.95746 - 0.581789i) q^{16} -4.16891i q^{17} +(-3.09430 + 2.87633i) q^{18} +(1.57587 - 1.57587i) q^{19} +(4.28918 - 3.70472i) q^{20} +(-0.339570 + 0.339570i) q^{21} +(1.41327 + 0.0515950i) q^{22} -5.31899 q^{23} +(-0.248598 + 0.199361i) q^{24} +3.03050i q^{25} +(0.558885 + 5.06830i) q^{26} +0.674555i q^{27} +(6.45150 - 5.57241i) q^{28} -2.45552 q^{29} +(0.0164727 - 0.451214i) q^{30} +(-1.08997 + 1.08997i) q^{31} +(4.65939 - 3.20782i) q^{32} +(0.0796656 - 0.0796656i) q^{33} +(4.01404 + 4.31823i) q^{34} +12.0790i q^{35} +(0.435655 - 5.95871i) q^{36} +(-0.282237 + 0.282237i) q^{37} +(-0.114985 + 3.14964i) q^{38} +(0.326047 + 0.242291i) q^{39} +(-0.875707 + 7.96726i) q^{40} +(8.51065 + 8.51065i) q^{41} +(0.0247772 - 0.678688i) q^{42} +7.61910 q^{43} +(-1.51357 + 1.30733i) q^{44} +(5.98599 + 5.98599i) q^{45} +(5.50950 - 5.12139i) q^{46} +(-4.57575 - 4.57575i) q^{47} +(0.0655468 - 0.445864i) q^{48} +11.1684i q^{49} +(-2.91792 - 3.13905i) q^{50} +0.469686 q^{51} +(-5.45892 - 4.71171i) q^{52} -10.8179 q^{53} +(-0.649496 - 0.698716i) q^{54} -2.83381i q^{55} +(-1.31718 + 11.9838i) q^{56} +(0.177544 + 0.177544i) q^{57} +(2.54347 - 2.36430i) q^{58} +(-8.02918 - 8.02918i) q^{59} +(0.417390 + 0.483236i) q^{60} -11.4289 q^{61} +(0.0795313 - 2.17849i) q^{62} +(9.00375 + 9.00375i) q^{63} +(-1.73762 + 7.80901i) q^{64} +(10.1083 - 1.48967i) q^{65} +(-0.00581290 + 0.159225i) q^{66} +(5.13815 - 5.13815i) q^{67} +(-8.31562 - 0.607975i) q^{68} -0.599259i q^{69} +(-11.6302 - 12.5116i) q^{70} +(-7.56371 + 7.56371i) q^{71} +(5.28609 + 6.59161i) q^{72} +(1.36657 - 1.36657i) q^{73} +(0.0205938 - 0.564098i) q^{74} -0.341429 q^{75} +(-2.91353 - 3.37317i) q^{76} -4.26244i q^{77} +(-0.571015 + 0.0629663i) q^{78} -3.43419i q^{79} +(-6.76421 - 9.09580i) q^{80} +8.88592 q^{81} +(-17.0100 - 0.620991i) q^{82} +(-3.05733 + 3.05733i) q^{83} +(0.627811 + 0.726853i) q^{84} +(8.35370 - 8.35370i) q^{85} +(-7.89200 + 7.33606i) q^{86} -0.276649i q^{87} +(0.309020 - 2.81150i) q^{88} +(-12.5993 + 12.5993i) q^{89} +(-11.9640 - 0.436776i) q^{90} +(15.2042 - 2.24067i) q^{91} +(-0.775697 + 10.6097i) q^{92} +(-0.122801 - 0.122801i) q^{93} +(9.14541 + 0.333876i) q^{94} +6.31549 q^{95} +(0.361406 + 0.524946i) q^{96} +(-4.13206 - 4.13206i) q^{97} +(-10.7535 - 11.5684i) q^{98} +(-2.11234 - 2.11234i) 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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