LMFDB - Embedded newform 968.2.o.c.493.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

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

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

chi := DirichletCharacter("968.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, not 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			493.5
Character	$\chi$	$=$	968.493
Dual form			968.2.o.c.269.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0567584 - 1.41307i) q^{2} +(-0.866175 - 1.19219i) q^{3} +(-1.99356 - 0.160408i) q^{4} +(-3.38352 + 1.09937i) q^{5} +(-1.73381 + 1.15630i) q^{6} +(-3.11534 - 2.26343i) q^{7} +(-0.339819 + 2.80794i) q^{8} +(0.255998 - 0.787881i) q^{9} +(1.36145 + 4.84357i) q^{10} +(1.53553 + 2.51564i) q^{12} +(-4.54406 - 1.47646i) q^{13} +(-3.37521 + 4.27374i) q^{14} +(4.24139 + 3.08155i) q^{15} +(3.94854 + 0.639564i) q^{16} +(-0.492895 - 1.51697i) q^{17} +(-1.09880 - 0.406463i) q^{18} +(2.43570 + 3.35245i) q^{19} +(6.92160 - 1.64892i) q^{20} +5.67459i q^{21} -3.24264 q^{23} +(3.64194 - 2.02704i) q^{24} +(6.19453 - 4.50059i) q^{25} +(-2.34425 + 6.33730i) q^{26} +(-5.36555 + 1.74337i) q^{27} +(5.84753 + 5.01199i) q^{28} +(4.34434 - 5.97947i) q^{29} +(4.59519 - 5.81849i) q^{30} +(-1.10807 + 3.41029i) q^{31} +(1.12786 - 5.54328i) q^{32} +(-2.17157 + 0.610396i) q^{34} +(13.0292 + 4.23343i) q^{35} +(-0.636729 + 1.52962i) q^{36} +(-0.358782 + 0.493821i) q^{37} +(4.87551 - 3.25154i) q^{38} +(2.17574 + 6.69625i) q^{39} +(-1.93719 - 9.87432i) q^{40} +(7.52109 - 5.46439i) q^{41} +(8.01862 + 0.322081i) q^{42} -3.06147i q^{43} +2.94725i q^{45} +(-0.184047 + 4.58209i) q^{46} +(3.90628 - 2.83808i) q^{47} +(-2.65765 - 5.26138i) q^{48} +(2.41912 + 7.44528i) q^{49} +(-6.00807 - 9.00877i) q^{50} +(-1.38159 + 1.90159i) q^{51} +(8.82201 + 3.67230i) q^{52} +(-3.96404 - 1.28800i) q^{53} +(2.15897 + 7.68087i) q^{54} +(7.41421 - 7.97852i) q^{56} +(1.88701 - 5.80763i) q^{57} +(-8.20286 - 6.47826i) q^{58} +(-3.31609 + 4.56421i) q^{59} +(-7.96114 - 6.82359i) q^{60} +(2.05883 - 0.668955i) q^{61} +(4.75609 + 1.75935i) q^{62} +(-2.58083 + 1.87508i) q^{63} +(-7.76905 - 1.90838i) q^{64} +16.9981 q^{65} +1.47363i q^{67} +(0.739279 + 3.10324i) q^{68} +(2.80870 + 3.86584i) q^{69} +(6.72167 - 18.1709i) q^{70} +(3.21817 + 9.90451i) q^{71} +(2.12533 + 0.986564i) q^{72} +(7.52109 + 5.46439i) q^{73} +(0.677441 + 0.535014i) q^{74} +(-10.7311 - 3.48674i) q^{75} +(-4.31795 - 7.07401i) q^{76} +(9.58579 - 2.69442i) q^{78} +(0.985790 - 3.03395i) q^{79} +(-14.0631 + 2.17694i) q^{80} +(4.71530 + 3.42586i) q^{81} +(-7.29471 - 10.9380i) q^{82} +(-11.9998 + 3.89896i) q^{83} +(0.910249 - 11.3126i) q^{84} +(3.33544 + 4.59084i) q^{85} +(-4.32608 - 0.173764i) q^{86} -10.8916 q^{87} -10.6569 q^{89} +(4.16468 + 0.167281i) q^{90} +(10.8144 + 14.8848i) q^{91} +(6.46439 + 0.520145i) q^{92} +(5.02548 - 1.63288i) q^{93} +(-3.78870 - 5.68095i) q^{94} +(-11.9268 - 8.66536i) q^{95} +(-7.58556 + 3.45682i) q^{96} +(-5.29721 + 16.3031i) q^{97} +(10.6580 - 2.99581i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{4} + 16 q^{9} - 64 q^{12} - 8 q^{14} + 8 q^{15} + 8 q^{16} - 24 q^{20} + 32 q^{23} + 16 q^{25} - 8 q^{26} + 40 q^{31} - 160 q^{34} + 24 q^{38} - 40 q^{42} + 16 q^{47} - 8 q^{48} - 40 q^{49}+ \cdots + 24 q^{97}+O(q^{100}) $ 32 * q - 8 * q^4 + 16 * q^9 - 64 * q^12 - 8 * q^14 + 8 * q^15 + 8 * q^16 - 24 * q^20 + 32 * q^23 + 16 * q^25 - 8 * q^26 + 40 * q^31 - 160 * q^34 + 24 * q^38 - 40 * q^42 + 16 * q^47 - 8 * q^48 - 40 * q^49 + 192 * q^56 + 32 * q^60 + 16 * q^64 - 8 * q^70 - 72 * q^71 + 352 * q^78 - 56 * q^80 + 24 * q^81 + 56 * q^82 + 32 * q^86 - 160 * q^89 + 16 * q^92 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0567584	−	1.41307i	0.0401343	−	0.999194i
$2$	0.0567584	−	1.41307i	0.0401343	−	0.999194i
$3$	−0.866175	−	1.19219i	−0.500087	−	0.688310i	0.482122	−	0.876104i	$-0.339866\pi$
$3$	−0.866175	−	1.19219i	−0.500087	−	0.688310i	−0.982208	+	0.187794i	$0.939866\pi$
$4$	−1.99356	−	0.160408i	−0.996778	−	0.0802039i
$5$	−3.38352	+	1.09937i	−1.51316	+	0.491655i	−0.943823	−	0.330451i	$-0.892799\pi$
$5$	−3.38352	+	1.09937i	−1.51316	+	0.491655i	−0.569335	+	0.822106i	$0.692799\pi$
$6$	−1.73381	+	1.15630i	−0.707826	+	0.472059i
$7$	−3.11534	−	2.26343i	−1.17749	−	0.855494i	−0.185601	−	0.982625i	$-0.559423\pi$
$7$	−3.11534	−	2.26343i	−1.17749	−	0.855494i	−0.991886	+	0.127131i	$0.959423\pi$
$8$	−0.339819	+	2.80794i	−0.120144	+	0.992756i
$9$	0.255998	−	0.787881i	0.0853327	−	0.262627i
$10$	1.36145	+	4.84357i	0.430529	+	1.53167i
$11$		0			0
$11$		0			0
$12$	1.53553	+	2.51564i	0.443270	+	0.726202i
$13$	−4.54406	−	1.47646i	−1.26030	−	0.409495i	−0.398696	−	0.917083i	$-0.630537\pi$
$13$	−4.54406	−	1.47646i	−1.26030	−	0.409495i	−0.861600	+	0.507588i	$0.830537\pi$
$14$	−3.37521	+	4.27374i	−0.902063	+	1.14220i
$15$	4.24139	+	3.08155i	1.09512	+	0.795652i
$16$	3.94854	+	0.639564i	0.987135	+	0.159891i
$17$	−0.492895	−	1.51697i	−0.119545	−	0.367920i	0.873323	−	0.487141i	$-0.161960\pi$
$17$	−0.492895	−	1.51697i	−0.119545	−	0.367920i	−0.992868	+	0.119221i	$0.961960\pi$
$18$	−1.09880	−	0.406463i	−0.258991	−	0.0958043i
$19$	2.43570	+	3.35245i	0.558788	+	0.769105i	0.991172	−	0.132584i	$-0.0423275\pi$
$19$	2.43570	+	3.35245i	0.558788	+	0.769105i	−0.432384	+	0.901690i	$0.642327\pi$
$20$	6.92160	−	1.64892i	1.54772	−	0.368710i
$21$			5.67459i			1.23830i
$22$		0			0
$23$	−3.24264			−0.676137			−0.338069	−	0.941121i	$-0.609774\pi$
$23$	−3.24264			−0.676137			−0.338069	+	0.941121i	$0.609774\pi$
$24$	3.64194	−	2.02704i	0.743407	−	0.413768i
$25$	6.19453	−	4.50059i	1.23891	−	0.900117i
$26$	−2.34425	+	6.33730i	−0.459746	+	1.24285i
$27$	−5.36555	+	1.74337i	−1.03260	+	0.335512i
$28$	5.84753	+	5.01199i	1.10508	+	0.947178i
$29$	4.34434	−	5.97947i	0.806724	−	1.11036i	−0.185096	−	0.982720i	$-0.559260\pi$
$29$	4.34434	−	5.97947i	0.806724	−	1.11036i	0.991821	−	0.127640i	$-0.0407402\pi$
$30$	4.59519	−	5.81849i	0.838963	−	1.06231i
$31$	−1.10807	+	3.41029i	−0.199015	+	0.612505i	0.800891	+	0.598810i	$0.204360\pi$
$31$	−1.10807	+	3.41029i	−0.199015	+	0.612505i	−0.999906	+	0.0136954i	$0.995640\pi$
$32$	1.12786	−	5.54328i	0.199380	−	0.979922i
$33$		0			0
$34$	−2.17157	+	0.610396i	−0.372422	+	0.104682i
$35$	13.0292	+	4.23343i	2.20233	+	0.715581i
$36$	−0.636729	+	1.52962i	−0.106121	+	0.254937i
$37$	−0.358782	+	0.493821i	−0.0589833	+	0.0811836i	−0.837490	−	0.546453i	$-0.815978\pi$
$37$	−0.358782	+	0.493821i	−0.0589833	+	0.0811836i	0.778506	+	0.627637i	$0.215978\pi$
$38$	4.87551	−	3.25154i	0.790912	−	0.527470i
$39$	2.17574	+	6.69625i	0.348398	+	1.07226i
$40$	−1.93719	−	9.87432i	−0.306296	−	1.56127i
$41$	7.52109	−	5.46439i	1.17460	−	0.853395i	0.183045	−	0.983105i	$-0.441405\pi$
$41$	7.52109	−	5.46439i	1.17460	−	0.853395i	0.991552	+	0.129710i	$0.0414045\pi$
$42$	8.01862	+	0.322081i	1.23730	+	0.0496982i
$43$		−	3.06147i		−	0.466869i	−0.972372	−	0.233435i	$-0.925003\pi$
$43$		−	3.06147i		−	0.466869i	0.972372	−	0.233435i	$-0.0749965\pi$
$44$		0			0
$45$			2.94725i			0.439350i
$46$	−0.184047	+	4.58209i	−0.0271363	+	0.675593i
$47$	3.90628	−	2.83808i	0.569789	−	0.413976i	−0.265239	−	0.964183i	$-0.585451\pi$
$47$	3.90628	−	2.83808i	0.569789	−	0.413976i	0.835029	+	0.550206i	$0.185451\pi$
$48$	−2.65765	−	5.26138i	−0.383598	−	0.759414i
$49$	2.41912	+	7.44528i	0.345588	+	1.06361i
$50$	−6.00807	−	9.00877i	−0.849669	−	1.27403i
$51$	−1.38159	+	1.90159i	−0.193461	+	0.266276i
$52$	8.82201	+	3.67230i	1.22339	+	0.509257i
$53$	−3.96404	−	1.28800i	−0.544503	−	0.176920i	0.0238333	−	0.999716i	$-0.492413\pi$
$53$	−3.96404	−	1.28800i	−0.544503	−	0.176920i	−0.568337	+	0.822796i	$0.692413\pi$
$54$	2.15897	+	7.68087i	0.293799	+	1.04523i
$55$		0			0
$56$	7.41421	−	7.97852i	0.990766	−	1.06618i
$57$	1.88701	−	5.80763i	0.249941	−	0.769239i
$58$	−8.20286	−	6.47826i	−1.07709	−	0.850638i
$59$	−3.31609	+	4.56421i	−0.431718	+	0.594209i	−0.968347	−	0.249610i	$-0.919698\pi$
$59$	−3.31609	+	4.56421i	−0.431718	+	0.594209i	0.536628	+	0.843819i	$0.319698\pi$
$60$	−7.96114	−	6.82359i	−1.02778	−	0.880922i
$61$	2.05883	−	0.668955i	0.263606	−	0.0856509i	−0.174232	−	0.984705i	$-0.555744\pi$
$61$	2.05883	−	0.668955i	0.263606	−	0.0856509i	0.437838	+	0.899054i	$0.355744\pi$
$62$	4.75609	+	1.75935i	0.604025	+	0.223437i
$63$	−2.58083	+	1.87508i	−0.325154	+	0.236238i
$64$	−7.76905	−	1.90838i	−0.971131	−	0.238548i
$65$	16.9981			2.10836
$66$		0			0
$67$			1.47363i			0.180032i	0.995940	+	0.0900160i	$0.0286918\pi$
$67$			1.47363i			0.180032i	−0.995940	+	0.0900160i	$0.971308\pi$
$68$	0.739279	+	3.10324i	0.0896508	+	0.376323i
$69$	2.80870	+	3.86584i	0.338127	+	0.465392i
$70$	6.72167	−	18.1709i	0.803393	−	2.17184i
$71$	3.21817	+	9.90451i	0.381926	+	1.17545i	0.938686	+	0.344775i	$0.112045\pi$
$71$	3.21817	+	9.90451i	0.381926	+	1.17545i	−0.556759	+	0.830674i	$0.687955\pi$
$72$	2.12533	+	0.986564i	0.250472	+	0.116268i
$73$	7.52109	+	5.46439i	0.880277	+	0.639559i	0.933325	−	0.359033i	$-0.116894\pi$
$73$	7.52109	+	5.46439i	0.880277	+	0.639559i	−0.0530476	+	0.998592i	$0.516894\pi$
$74$	0.677441	+	0.535014i	0.0787509	+	0.0621941i
$75$	−10.7311	−	3.48674i	−1.23912	−	0.402614i
$76$	−4.31795	−	7.07401i	−0.495302	−	0.811445i
$77$		0			0
$78$	9.58579	−	2.69442i	1.08538	−	0.305083i
$79$	0.985790	−	3.03395i	0.110910	−	0.341346i	−0.880162	−	0.474673i	$-0.842566\pi$
$79$	0.985790	−	3.03395i	0.110910	−	0.341346i	0.991072	+	0.133327i	$0.0425662\pi$
$80$	−14.0631	+	2.17694i	−1.57230	+	0.243389i
$81$	4.71530	+	3.42586i	0.523922	+	0.380652i
$82$	−7.29471	−	10.9380i	−0.805566	−	1.20790i
$83$	−11.9998	+	3.89896i	−1.31714	+	0.427966i	−0.881513	−	0.472159i	$-0.843475\pi$
$83$	−11.9998	+	3.89896i	−1.31714	+	0.427966i	−0.435631	+	0.900125i	$0.643475\pi$
$84$	0.910249	−	11.3126i	0.0993163	−	1.23431i
$85$	3.33544	+	4.59084i	0.361780	+	0.497947i
$86$	−4.32608	−	0.173764i	−0.466493	−	0.0187375i
$87$	−10.8916			−1.16770
$88$		0			0
$89$	−10.6569			−1.12962			−0.564812	−	0.825220i	$-0.691051\pi$
$89$	−10.6569			−1.12962			−0.564812	+	0.825220i	$0.691051\pi$
$90$	4.16468	+	0.167281i	0.438996	+	0.0176330i
$91$	10.8144	+	14.8848i	1.13366	+	1.56035i
$92$	6.46439	+	0.520145i	0.673959	+	0.0542288i
$93$	5.02548	−	1.63288i	0.521118	−	0.169322i
$94$	−3.78870	−	5.68095i	−0.390775	−	0.585945i
$95$	−11.9268	−	8.66536i	−1.22367	−	0.889047i
$96$	−7.58556	+	3.45682i	−0.774198	+	0.352811i
$97$	−5.29721	+	16.3031i	−0.537850	+	1.65533i	0.199558	+	0.979886i	$0.436049\pi$
$97$	−5.29721	+	16.3031i	−0.537850	+	1.65533i	−0.737408	+	0.675447i	$0.763951\pi$
$98$	10.6580	−	2.99581i	1.07662	−	0.302622i
$99$		0			0
$100$	−13.0711	+	7.97852i	−1.30711	+	0.797852i
$101$	−4.54406	−	1.47646i	−0.452151	−	0.146913i	0.0740838	−	0.997252i	$-0.476397\pi$
$101$	−4.54406	−	1.47646i	−0.452151	−	0.146913i	−0.526235	+	0.850339i	$0.676397\pi$
$102$	2.60867	+	2.06021i	0.258297	+	0.203992i
$103$	−7.53495	−	5.47446i	−0.742441	−	0.539415i	0.151034	−	0.988529i	$-0.451740\pi$
$103$	−7.53495	−	5.47446i	−0.742441	−	0.539415i	−0.893474	+	0.449114i	$0.851740\pi$
$104$	5.68996	−	12.2577i	0.557946	−	1.20197i
$105$	−6.23850	−	19.2001i	−0.608815	−	1.87374i
$106$	−2.04503	+	5.52838i	−0.198631	+	0.536964i
$107$	−4.23519	−	5.82923i	−0.409431	−	0.563533i	0.553649	−	0.832750i	$-0.313235\pi$
$107$	−4.23519	−	5.82923i	−0.409431	−	0.563533i	−0.963079	+	0.269217i	$0.913235\pi$
$108$	10.9762	−	2.61484i	1.05618	−	0.251613i
$109$		−	4.32957i		−	0.414697i	−0.978267	−	0.207349i	$-0.933517\pi$
$109$		−	4.32957i		−	0.414697i	0.978267	−	0.207349i	$-0.0664835\pi$
$110$		0			0
$111$	0.899495			0.0853763
$112$	−10.8534	−	10.9297i	−1.02555	−	1.03276i
$113$	−2.81965	+	2.04860i	−0.265251	+	0.192716i	−0.712459	−	0.701714i	$-0.752418\pi$
$113$	−2.81965	+	2.04860i	−0.265251	+	0.192716i	0.447208	+	0.894430i	$0.352418\pi$
$114$	−8.09950	−	2.99612i	−0.758588	−	0.280612i
$115$	10.9716	−	3.56487i	1.02310	−	0.332426i
$116$	−9.61985	+	11.2236i	−0.893180	+	1.04208i
$117$	−2.32654	+	3.20221i	−0.215089	+	0.296045i
$118$	6.26135	+	4.94494i	0.576404	+	0.455218i
$119$	−1.89802	+	5.84152i	−0.173992	+	0.535491i
$120$	−10.0941	+	10.8624i	−0.921461	+	0.991595i
$121$		0			0
$122$	−0.828427	−	2.94725i	−0.0750023	−	0.266832i
$123$	−13.0292	−	4.23343i	−1.17480	−	0.381716i
$124$	2.75603	−	6.62086i	0.247499	−	0.594570i
$125$	−5.55583	+	7.64695i	−0.496929	+	0.683964i
$126$	2.50315	+	3.75333i	0.222998	+	0.334373i
$127$	4.55565	+	14.0208i	0.404249	+	1.24415i	0.921521	+	0.388328i	$0.126947\pi$
$127$	4.55565	+	14.0208i	0.404249	+	1.24415i	−0.517273	+	0.855821i	$0.673053\pi$
$128$	−3.13765	+	10.8699i	−0.277331	+	0.960774i
$129$	−3.64985	+	2.65177i	−0.321351	+	0.233475i
$130$	0.964787	−	24.0196i	0.0846174	−	2.10666i
$131$			10.6382i			0.929465i	0.885451	+	0.464732i	$0.153850\pi$
$131$			10.6382i			0.929465i	−0.885451	+	0.464732i	$0.846150\pi$
$132$		0			0
$133$		−	15.9570i		−	1.38365i
$134$	2.08234	+	0.0836407i	0.179887	+	0.00722546i
$135$	16.2378	−	11.7975i	1.39753	−	1.01537i
$136$	4.42707	−	0.868522i	0.379618	−	0.0744751i
$137$	0.927051	+	2.85317i	0.0792033	+	0.243763i	0.982816	−	0.184588i	$-0.0590949\pi$
$137$	0.927051	+	2.85317i	0.0792033	+	0.243763i	−0.903613	+	0.428350i	$0.859095\pi$
$138$	5.62213	−	3.74948i	0.478588	−	0.319177i
$139$	4.98056	−	6.85515i	0.422445	−	0.581446i	−0.543753	−	0.839245i	$-0.682997\pi$
$139$	4.98056	−	6.85515i	0.422445	−	0.581446i	0.966199	+	0.257799i	$0.0829973\pi$
$140$	−25.2953	−	10.5296i	−2.13784	−	0.889911i
$141$	−6.76705	−	2.19875i	−0.569888	−	0.185168i
$142$	14.1785	−	3.98535i	1.18983	−	0.334443i
$143$		0			0
$144$	1.51472	−	2.94725i	0.126227	−	0.245604i
$145$	−8.12551	+	25.0077i	−0.674787	+	2.07678i
$146$	8.14848	−	10.3177i	0.674373	−	0.853900i
$147$	6.78079	−	9.33296i	0.559270	−	0.769769i
$148$	0.794464	−	0.926908i	0.0653046	−	0.0761914i
$149$	18.2494	−	5.92959i	1.49505	−	0.485771i	0.556480	−	0.830861i	$-0.312152\pi$
$149$	18.2494	−	5.92959i	1.49505	−	0.485771i	0.938570	+	0.345090i	$0.112152\pi$
$150$	−5.53611	+	14.9659i	−0.452021	+	1.22196i
$151$	−6.23068	+	4.52685i	−0.507045	+	0.368390i	−0.811702	−	0.584072i	$-0.801458\pi$
$151$	−6.23068	+	4.52685i	−0.507045	+	0.368390i	0.304656	+	0.952462i	$0.401458\pi$
$152$	−10.2412	+	5.70007i	−0.830670	+	0.462337i
$153$	−1.32138			−0.106827
$154$		0			0
$155$		−	12.7570i		−	1.02466i
$156$	−3.26334	−	13.6984i	−0.261276	−	1.09675i
$157$	8.00575	+	11.0190i	0.638928	+	0.879409i	0.998558	−	0.0536858i	$-0.0170969\pi$
$157$	8.00575	+	11.0190i	0.638928	+	0.879409i	−0.359630	+	0.933095i	$0.617097\pi$
$158$	−4.23124	−	1.56520i	−0.336620	−	0.124520i
$159$	1.89802	+	5.84152i	0.150523	+	0.463263i
$160$	2.27798	+	19.9958i	0.180090	+	1.58080i
$161$	10.1019	+	7.33948i	0.796143	+	0.578432i
$162$	5.10863	−	6.46862i	0.401372	−	0.508223i
$163$	19.1401	+	6.21900i	1.49917	+	0.487109i	0.939775	−	0.341793i	$-0.111034\pi$
$163$	19.1401	+	6.21900i	1.49917	+	0.487109i	0.559393	+	0.828902i	$0.311034\pi$
$164$	−15.8703	+	9.68714i	−1.23926	+	0.756438i
$165$		0			0
$166$	4.82843	+	17.1778i	0.374759	+	1.33326i
$167$	1.18995	−	3.66230i	0.0920813	−	0.283397i	−0.894401	−	0.447267i	$-0.852398\pi$
$167$	1.18995	−	3.66230i	0.0920813	−	0.283397i	0.986482	+	0.163869i	$0.0523975\pi$
$168$	−15.9339	−	1.92834i	−1.22933	−	0.148774i
$169$	7.95136	+	5.77700i	0.611643	+	0.444385i
$170$	6.67652	−	4.45266i	0.512065	−	0.341503i
$171$	3.26487	−	1.06082i	0.249671	−	0.0811229i
$172$	−0.491083	+	6.10321i	−0.0374447	+	0.465365i
$173$	3.07191	+	4.22813i	0.233553	+	0.321459i	0.909667	−	0.415339i	$-0.136337\pi$
$173$	3.07191	+	4.22813i	0.233553	+	0.321459i	−0.676113	+	0.736798i	$0.736337\pi$
$174$	−0.618191	+	15.3907i	−0.0468650	+	1.16676i
$175$	−29.4848			−2.22884
$176$		0			0
$177$	8.31371			0.624897
$178$	−0.604866	+	15.0589i	−0.0453367	+	1.12871i
$179$	−11.6806	−	16.0770i	−0.873051	−	1.20165i	−0.978298	−	0.207205i	$-0.933563\pi$
$179$	−11.6806	−	16.0770i	−0.873051	−	1.20165i	0.105247	−	0.994446i	$-0.466437\pi$
$180$	0.472762	−	5.87551i	0.0352376	−	0.437935i
$181$	−14.5955	+	4.74238i	−1.08488	+	0.352498i	−0.796265	−	0.604948i	$-0.793194\pi$
$181$	−14.5955	+	4.74238i	−1.08488	+	0.352498i	−0.288612	+	0.957446i	$0.593194\pi$
$182$	21.6471	−	14.4368i	1.60459	−	1.07012i
$183$	−2.58083	−	1.87508i	−0.190780	−	0.138610i
$184$	1.10191	−	9.10514i	0.0812340	−	0.671240i
$185$	0.671053	−	2.06529i	0.0493368	−	0.151843i
$186$	−2.02214	−	7.19406i	−0.148271	−	0.527494i
$187$		0			0
$188$	−8.24264	+	5.03127i	−0.601156	+	0.366943i
$189$	20.6615	+	6.71332i	1.50290	+	0.488322i
$190$	−12.9217	+	16.3617i	−0.937442	+	1.18700i
$191$	9.76570	+	7.09520i	0.706621	+	0.513390i	0.882082	−	0.471096i	$-0.156141\pi$
$191$	9.76570	+	7.09520i	0.706621	+	0.513390i	−0.175461	+	0.984486i	$0.556141\pi$
$192$	4.45420	+	10.9152i	0.321455	+	0.787734i
$193$	−0.985790	−	3.03395i	−0.0709587	−	0.218388i	0.909288	−	0.416168i	$-0.136627\pi$
$193$	−0.985790	−	3.03395i	−0.0709587	−	0.218388i	−0.980247	+	0.197779i	$0.936627\pi$
$194$	22.7369	+	8.41069i	1.63241	+	0.603853i
$195$	−14.7234	−	20.2650i	−1.05436	−	1.45120i
$196$	−3.62837	−	15.2306i	−0.259169	−	1.08790i
$197$		−	15.6788i		−	1.11707i	−0.829483	−	0.558533i	$-0.811365\pi$
$197$		−	15.6788i		−	1.11707i	0.829483	−	0.558533i	$-0.188635\pi$
$198$		0			0
$199$	16.8284			1.19294			0.596468	−	0.802637i	$-0.296570\pi$
$199$	16.8284			1.19294			0.596468	+	0.802637i	$0.296570\pi$
$200$	10.5324	+	18.9232i	0.744750	+	1.33807i
$201$	1.75684	−	1.27642i	0.123918	−	0.0900316i
$202$	−2.34425	+	6.33730i	−0.164941	+	0.445891i
$203$	−27.0682	+	8.79499i	−1.89981	+	0.617287i
$204$	3.05930	−	3.56931i	0.214194	−	0.249902i
$205$	−19.4404	+	26.7574i	−1.35778	+	1.86882i
$206$	−8.16349	+	10.3367i	−0.568777	+	0.720193i
$207$	−0.830110	+	2.55482i	−0.0576966	+	0.177572i
$208$	−16.9981	−	8.73606i	−1.17861	−	0.605737i
$209$		0			0
$210$	−27.4853	+	7.72569i	−1.89666	+	0.533123i
$211$	−21.9407	−	7.12896i	−1.51046	−	0.490778i	−0.567411	−	0.823435i	$-0.692055\pi$
$211$	−21.9407	−	7.12896i	−1.51046	−	0.490778i	−0.943048	+	0.332657i	$0.892055\pi$
$212$	7.69594	+	3.20356i	0.528560	+	0.220021i
$213$	9.02054	−	12.4157i	0.618077	−	0.850710i
$214$	−8.47752	+	5.65377i	−0.579511	+	0.386484i
$215$	3.36570	+	10.3585i	0.229539	+	0.706447i
$216$	−3.07197	−	15.6586i	−0.209021	−	1.06543i
$217$	11.1709	−	8.11616i	0.758333	−	0.550961i
$218$	−6.11800	−	0.245740i	−0.414363	−	0.0166436i
$219$		−	13.6997i		−	0.925739i
$220$		0			0
$221$			7.62096i			0.512641i
$222$	0.0510539	−	1.27105i	0.00342652	−	0.0853075i
$223$	−20.8143	+	15.1225i	−1.39383	+	1.01268i	−0.398398	+	0.917213i	$0.630434\pi$
$223$	−20.8143	+	15.1225i	−1.39383	+	1.01268i	−0.995433	+	0.0954642i	$0.969566\pi$
$224$	−16.0605	+	14.7163i	−1.07309	+	0.983277i
$225$	−1.96014	−	6.03269i	−0.130676	−	0.402179i
$226$	2.73478	+	4.10065i	0.181915	+	0.272771i
$227$	−1.69033	+	2.32654i	−0.112191	+	0.154418i	−0.861420	−	0.507894i	$-0.830424\pi$
$227$	−1.69033	+	2.32654i	−0.112191	+	0.154418i	0.749229	+	0.662311i	$0.230424\pi$
$228$	−4.69345	+	11.2751i	−0.310832	+	0.746714i
$229$	19.7206	+	6.40762i	1.30318	+	0.423427i	0.876685	−	0.481065i	$-0.159750\pi$
$229$	19.7206	+	6.40762i	1.30318	+	0.423427i	0.426490	+	0.904492i	$0.359750\pi$
$230$	−4.41470	−	15.7060i	−0.291097	−	1.03562i
$231$		0			0
$232$	15.3137	+	14.2306i	1.00539	+	0.934284i
$233$	3.36570	−	10.3585i	0.220494	−	0.678611i	−0.778224	−	0.627987i	$-0.783879\pi$
$233$	3.36570	−	10.3585i	0.220494	−	0.678611i	0.998718	−	0.0506239i	$-0.0161210\pi$
$234$	4.39291	+	3.46933i	0.287174	+	0.226797i
$235$	−10.0969	+	13.8972i	−0.658648	+	0.906551i
$236$	7.34295	−	8.56708i	0.477985	−	0.557669i
$237$	−4.47090	+	1.45268i	−0.290416	+	0.0943620i
$238$	8.14677	+	3.01360i	0.528077	+	0.195343i
$239$	−18.6920	+	13.5806i	−1.20909	+	0.878453i	−0.995148	−	0.0983940i	$-0.968629\pi$
$239$	−18.6920	+	13.5806i	−1.20909	+	0.878453i	−0.213939	+	0.976847i	$0.568629\pi$
$240$	14.7764	+	14.8802i	0.953814	+	0.960516i
$241$	29.4848			1.89928			0.949641	−	0.313340i	$-0.101448\pi$
$241$	29.4848			1.89928			0.949641	+	0.313340i	$0.101448\pi$
$242$		0			0
$243$			8.33609i			0.534760i
$244$	−4.21171	+	1.00335i	−0.269627	+	0.0642327i
$245$	−16.3703	−	22.5318i	−1.04586	−	1.43950i
$246$	−6.72167	+	18.1709i	−0.428558	+	1.15853i
$247$	−6.11822	−	18.8300i	−0.389293	−	1.19812i
$248$	−9.19933	−	4.27027i	−0.584158	−	0.271162i
$249$	15.0422	+	10.9288i	0.953260	+	0.692584i
$250$	10.4904	+	8.28484i	0.663469	+	0.523979i
$251$	−13.7746	−	4.47562i	−0.869442	−	0.282499i	−0.159875	−	0.987137i	$-0.551109\pi$
$251$	−13.7746	−	4.47562i	−0.869442	−	0.282499i	−0.709567	+	0.704638i	$0.751109\pi$
$252$	5.44581	−	3.32410i	0.343054	−	0.209399i
$253$		0			0
$254$	20.0711	−	5.64167i	1.25937	−	0.353990i
$255$	2.58407	−	7.95295i	0.161821	−	0.498033i
$256$	15.1819	+	5.05069i	0.948870	+	0.315668i
$257$	−14.9549	−	10.8654i	−0.932861	−	0.677764i	0.0138303	−	0.999904i	$-0.495598\pi$
$257$	−14.9549	−	10.8654i	−0.932861	−	0.677764i	−0.946692	+	0.322141i	$0.895598\pi$
$258$	3.53999	+	5.30801i	0.220390	+	0.330462i
$259$	2.23545	−	0.726342i	0.138904	−	0.0451327i
$260$	−33.8867	−	2.72663i	−2.10157	−	0.169098i
$261$	−3.59897	−	4.95356i	−0.222771	−	0.306618i
$262$	15.0326	+	0.603808i	0.928716	+	0.0373034i
$263$	−7.04085			−0.434158			−0.217079	−	0.976154i	$-0.569653\pi$
$263$	−7.04085			−0.434158			−0.217079	+	0.976154i	$0.569653\pi$
$264$		0			0
$265$	14.8284			0.910903
$266$	−22.5485	−	0.905697i	−1.38254	−	0.0555319i
$267$	9.23071	+	12.7050i	0.564910	+	0.777532i
$268$	0.236381	−	2.93776i	0.0144393	−	0.179452i
$269$	7.24797	−	2.35501i	0.441916	−	0.143587i	−0.0796033	−	0.996827i	$-0.525365\pi$
$269$	7.24797	−	2.35501i	0.441916	−	0.143587i	0.521520	+	0.853239i	$0.325365\pi$
$270$	−15.7491	−	23.6149i	−0.958458	−	1.43716i
$271$	12.9959	+	9.44204i	0.789442	+	0.573563i	0.907798	−	0.419408i	$-0.137762\pi$
$271$	12.9959	+	9.44204i	0.789442	+	0.573563i	−0.118356	+	0.992971i	$0.537762\pi$
$272$	−0.976012	−	6.30507i	−0.0591794	−	0.382301i
$273$	8.37828	−	25.7857i	0.507077	−	1.56062i
$274$	4.08436	−	1.14805i	0.246745	−	0.0693563i
$275$		0			0
$276$	−4.97918	−	8.15731i	−0.299712	−	0.491012i
$277$	5.32370	+	1.72978i	0.319870	+	0.103932i	0.464551	−	0.885546i	$-0.346216\pi$
$277$	5.32370	+	1.72978i	0.319870	+	0.103932i	−0.144681	+	0.989478i	$0.546216\pi$
$278$	−9.40414	−	7.42698i	−0.564023	−	0.445441i
$279$	2.40324	+	1.74605i	0.143878	+	0.104533i
$280$	−16.3148	+	35.1465i	−0.974995	+	2.10041i
$281$	−7.13972	−	21.9738i	−0.425920	−	1.31085i	−0.902111	−	0.431505i	$-0.857983\pi$
$281$	−7.13972	−	21.9738i	−0.425920	−	1.31085i	0.476191	−	0.879342i	$-0.342017\pi$
$282$	−3.49108	+	9.43754i	−0.207891	+	0.561997i
$283$	10.4882	+	14.4357i	0.623457	+	0.858115i	0.997599	−	0.0692566i	$-0.0220627\pi$
$283$	10.4882	+	14.4357i	0.623457	+	0.858115i	−0.374142	+	0.927371i	$0.622063\pi$
$284$	−4.82684	−	20.2614i	−0.286420	−	1.20229i
$285$			21.7248i			1.28686i
$286$		0			0
$287$	−35.7990			−2.11315
$288$	−4.07871	−	2.30769i	−0.240340	−	0.135982i
$289$	11.6950	−	8.49693i	0.687943	−	0.499820i
$290$	34.8766	+	12.9013i	2.04802	+	0.757593i
$291$	24.0247	−	7.80611i	1.40835	−	0.457602i
$292$	−14.1172	−	12.1000i	−0.826146	−	0.708100i
$293$	−1.75427	+	2.41455i	−0.102486	+	0.141059i	−0.857180	−	0.515018i	$-0.827785\pi$
$293$	−1.75427	+	2.41455i	−0.102486	+	0.141059i	0.754694	+	0.656077i	$0.227785\pi$
$294$	−12.8033	−	10.1115i	−0.746703	−	0.589714i
$295$	6.20230	−	19.0887i	0.361112	−	1.11139i
$296$	−1.26470	−	1.17525i	−0.0735090	−	0.0683098i
$297$		0			0
$298$	−7.34315	−	26.1243i	−0.425377	−	1.51334i
$299$	14.7348	+	4.78761i	0.852133	+	0.276875i
$300$	20.8337	+	8.67237i	1.20284	+	0.500700i
$301$	−6.92940	+	9.53751i	−0.399404	+	0.549733i
$302$	6.04313	+	9.06134i	0.347743	+	0.521422i
$303$	2.17574	+	6.69625i	0.124993	+	0.384689i
$304$	7.47335	+	14.7951i	0.428626	+	0.848556i
$305$	−6.23068	+	4.52685i	−0.356767	+	0.259207i
$306$	−0.0749992	+	1.86720i	−0.00428742	+	0.106741i
$307$		−	28.1103i		−	1.60434i	−0.597095	−	0.802171i	$-0.703678\pi$
$307$		−	28.1103i		−	1.60434i	0.597095	−	0.802171i	$-0.296322\pi$
$308$		0			0
$309$			13.7249i			0.780783i
$310$	−18.0265	−	0.724065i	−1.02384	−	0.0411241i
$311$	−8.48277	+	6.16309i	−0.481014	+	0.349477i	−0.801718	−	0.597702i	$-0.796080\pi$
$311$	−8.48277	+	6.16309i	−0.481014	+	0.349477i	0.320704	+	0.947179i	$0.396080\pi$
$312$	−19.5420	+	3.83384i	−1.10635	+	0.217048i
$313$	−0.565015	−	1.73894i	−0.0319365	−	0.0982906i	0.933818	−	0.357749i	$-0.116456\pi$
$313$	−0.565015	−	1.73894i	−0.0319365	−	0.0982906i	−0.965754	+	0.259459i	$0.916456\pi$
$314$	16.0250	−	10.6873i	0.904344	−	0.603119i
$315$	6.67088	−	9.18168i	0.375862	−	0.517329i
$316$	−2.45190	+	5.89022i	−0.137930	+	0.331351i
$317$	1.74156	+	0.565868i	0.0978159	+	0.0317823i	0.357516	−	0.933907i	$-0.383624\pi$
$317$	1.74156	+	0.565868i	0.0978159	+	0.0317823i	−0.259700	+	0.965689i	$0.583624\pi$
$318$	8.36223	−	2.35049i	0.468930	−	0.131809i
$319$		0			0
$320$	28.3848	−	2.08402i	1.58676	−	0.116500i
$321$	−3.28113	+	10.0983i	−0.183135	+	0.563631i
$322$	10.9446	−	13.8582i	0.609918	−	0.772287i
$323$	3.88504	−	5.34730i	0.216169	−	0.297532i
$324$	−8.85068	−	7.58602i	−0.491704	−	0.421446i
$325$	−34.7932	+	11.3050i	−1.92998	+	0.627089i
$326$	9.87426	−	26.6934i	0.546885	−	1.47841i
$327$	−5.16166	+	3.75017i	−0.285441	+	0.207385i
$328$	12.7879	+	22.9757i	0.706092	+	1.26862i
$329$	−18.5932			−1.02507
$330$		0			0
$331$			12.7570i			0.701186i	0.936528	+	0.350593i	$0.114020\pi$
$331$			12.7570i			0.701186i	−0.936528	+	0.350593i	$0.885980\pi$
$332$	24.5476	−	5.84794i	1.34723	−	0.320947i
$333$	0.297224	+	0.409094i	0.0162878	+	0.0224182i
$334$	−5.10756	−	1.88936i	−0.279473	−	0.103381i
$335$	−1.62007	−	4.98605i	−0.0885136	−	0.272417i
$336$	−3.62927	+	22.4064i	−0.197993	+	1.22237i
$337$	−4.94026	−	3.58931i	−0.269113	−	0.195522i	0.445042	−	0.895510i	$-0.353189\pi$
$337$	−4.94026	−	3.58931i	−0.269113	−	0.195522i	−0.714155	+	0.699988i	$0.753189\pi$
$338$	8.61464	−	10.9080i	0.468575	−	0.593316i
$339$	4.88463	+	1.58711i	0.265297	+	0.0862001i
$340$	−5.91299	−	9.68714i	−0.320677	−	0.525359i
$341$		0			0
$342$	−1.31371	−	4.67371i	−0.0710372	−	0.252725i
$343$	0.985790	−	3.03395i	0.0532276	−	0.163818i
$344$	8.59641	+	1.04035i	0.463488	+	0.0560917i
$345$	−13.7533	−	9.99235i	−0.740452	−	0.537970i
$346$	6.14901	−	4.10086i	0.330573	−	0.220464i
$347$	1.02942	−	0.334478i	0.0552620	−	0.0179557i	−0.281256	−	0.959633i	$-0.590751\pi$
$347$	1.02942	−	0.334478i	0.0552620	−	0.0179557i	0.336518	+	0.941677i	$0.390751\pi$
$348$	21.7131	+	1.74710i	1.16394	+	0.0936544i
$349$	−10.9700	−	15.0989i	−0.587211	−	0.808227i	0.407252	−	0.913316i	$-0.366487\pi$
$349$	−10.9700	−	15.0989i	−0.587211	−	0.808227i	−0.994463	+	0.105089i	$0.966487\pi$
$350$	−1.67351	+	41.6642i	−0.0894529	+	2.22704i
$351$	26.9554			1.43877
$352$		0			0
$353$	−16.7990			−0.894120			−0.447060	−	0.894504i	$-0.647529\pi$
$353$	−16.7990			−0.894120			−0.447060	+	0.894504i	$0.647529\pi$
$354$	0.471873	−	11.7479i	0.0250798	−	0.624393i
$355$	−21.7775	−	29.9742i	−1.15583	−	1.59086i
$356$	21.2450	+	1.70944i	1.12599	+	0.0906003i
$357$	8.60821	−	2.79698i	0.455595	−	0.148032i
$358$	−23.3810	+	15.5931i	−1.23572	+	0.824120i
$359$	−14.5077	−	10.5404i	−0.765686	−	0.556303i	0.134963	−	0.990851i	$-0.456908\pi$
$359$	−14.5077	−	10.5404i	−0.765686	−	0.556303i	−0.900649	+	0.434547i	$0.856908\pi$
$360$	−8.27570	−	1.00153i	−0.436168	−	0.0527854i
$361$	0.565015	−	1.73894i	0.0297376	−	0.0915230i
$362$	5.87291	+	20.8937i	0.308673	+	1.09815i
$363$		0			0
$364$	−19.1716	−	31.4084i	−1.00486	−	1.64625i
$365$	−31.4552	−	10.2204i	−1.64644	−	0.534961i
$366$	−2.79612	+	3.54048i	−0.146155	+	0.185064i
$367$	4.79661	+	3.48494i	0.250381	+	0.181912i	0.705896	−	0.708316i	$-0.250545\pi$
$367$	4.79661	+	3.48494i	0.250381	+	0.181912i	−0.455515	+	0.890228i	$0.650545\pi$
$368$	−12.8037	−	2.07388i	−0.667439	−	0.108108i
$369$	−2.37991	−	7.32460i	−0.123893	−	0.381303i
$370$	−2.88032	−	1.06547i	−0.149741	−	0.0553912i
$371$	9.43406	+	12.9849i	0.489792	+	0.674141i
$372$	−10.2805	+	2.44911i	−0.533020	+	0.126980i
$373$			28.7444i			1.48833i	0.667997	+	0.744164i	$0.267152\pi$
$373$			28.7444i			1.48833i	−0.667997	+	0.744164i	$0.732848\pi$
$374$		0			0
$375$	13.9289			0.719287
$376$	6.64172	+	11.9330i	0.342521	+	0.615399i
$377$	−28.5694	+	20.7569i	−1.47140	+	1.06903i
$378$	10.6591	−	28.8152i	0.548247	−	1.48209i
$379$	2.56254	−	0.832621i	0.131629	−	0.0427689i	−0.242462	−	0.970161i	$-0.577955\pi$
$379$	2.56254	−	0.832621i	0.131629	−	0.0427689i	0.374091	+	0.927392i	$0.377955\pi$
$380$	22.3869	+	19.1880i	1.14842	+	0.984326i
$381$	12.7695	−	17.5757i	0.654201	−	0.900431i
$382$	10.5803	−	13.3969i	0.541336	−	0.685447i
$383$	0.383997	−	1.18182i	0.0196213	−	0.0603883i	−0.940766	−	0.339055i	$-0.889893\pi$
$383$	0.383997	−	1.18182i	0.0196213	−	0.0603883i	0.960388	+	0.278667i	$0.0898926\pi$
$384$	15.6767	−	5.67459i	0.800001	−	0.289580i
$385$		0			0
$386$	−4.34315	+	1.22079i	−0.221060	+	0.0621367i
$387$	−2.41207	−	0.783730i	−0.122613	−	0.0398392i
$388$	13.1754	−	31.6515i	0.668882	−	1.60686i
$389$	9.73810	−	13.4033i	0.493741	−	0.679577i	−0.487331	−	0.873217i	$-0.662030\pi$
$389$	9.73810	−	13.4033i	0.493741	−	0.679577i	0.981073	+	0.193641i	$0.0620296\pi$
$390$	−29.4716	+	19.6550i	−1.49235	+	0.995269i
$391$	1.59828	+	4.91900i	0.0808285	+	0.248765i
$392$	−21.7279	+	4.26269i	−1.09743	+	0.215298i
$393$	12.6828	−	9.21456i	0.639760	−	0.464813i
$394$	−22.1552	−	0.889902i	−1.11617	−	0.0448326i
$395$			11.3492i			0.571040i
$396$		0			0
$397$			36.0821i			1.81091i	0.424441	+	0.905455i	$0.360470\pi$
$397$			36.0821i			1.81091i	−0.424441	+	0.905455i	$0.639530\pi$
$398$	0.955155	−	23.7798i	0.0478776	−	1.19197i
$399$	−19.0238	+	13.8216i	−0.952382	+	0.691946i
$400$	27.3377	−	13.8089i	1.36689	−	0.690447i
$401$	−3.54005	−	10.8952i	−0.176782	−	0.544078i	0.822929	−	0.568145i	$-0.192339\pi$
$401$	−3.54005	−	10.8952i	−0.176782	−	0.544078i	−0.999710	+	0.0240666i	$0.992339\pi$
$402$	−1.70396	−	2.55499i	−0.0849857	−	0.127431i
$403$	10.0703	−	13.8605i	0.501636	−	0.690443i
$404$	8.82201	+	3.67230i	0.438912	+	0.182704i
$405$	−19.7206	−	6.40762i	−0.979926	−	0.318397i
$406$	10.8916	+	38.7485i	0.540542	+	1.92306i
$407$		0			0
$408$	−4.87006	−	4.52560i	−0.241104	−	0.224051i
$409$	−1.97158	+	6.06790i	−0.0974883	+	0.300038i	−0.987894	−	0.155129i	$-0.950421\pi$
$409$	−1.97158	+	6.06790i	−0.0974883	+	0.300038i	0.890406	+	0.455167i	$0.150421\pi$
$410$	36.7068	+	28.9894i	1.81282	+	1.43168i
$411$	2.59853	−	3.57656i	0.128176	−	0.176419i
$412$	14.1432	+	12.1223i	0.696786	+	0.597224i
$413$	20.6615	−	6.71332i	1.01669	−	0.330341i
$414$	3.56303	+	1.31801i	0.175113	+	0.0647768i
$415$	36.3150	−	26.3844i	1.78264	−	1.29516i
$416$	−13.3095	+	23.5238i	−0.652551	+	1.15335i
$417$	−12.4867			−0.611474
$418$		0			0
$419$			11.7890i			0.575931i	0.957641	+	0.287965i	$0.0929788\pi$
$419$			11.7890i			0.575931i	−0.957641	+	0.287965i	$0.907021\pi$
$420$	9.35695	+	39.2772i	0.456572	+	1.91653i
$421$	2.44991	+	3.37202i	0.119402	+	0.164342i	0.864534	−	0.502574i	$-0.167614\pi$
$421$	2.44991	+	3.37202i	0.119402	+	0.164342i	−0.745132	+	0.666917i	$0.767614\pi$
$422$	−11.3191	+	30.5992i	−0.551003	+	1.48954i
$423$	−1.23607	−	3.80423i	−0.0600997	−	0.184968i
$424$	4.96367	−	10.6931i	0.241057	−	0.519303i
$425$	−9.88052	−	7.17862i	−0.479276	−	0.348214i
$426$	−17.0323	−	13.4514i	−0.825218	−	0.651722i
$427$	−7.92809	−	2.57599i	−0.383667	−	0.124661i
$428$	7.50803	+	12.3003i	0.362914	+	0.594556i
$429$		0			0
$430$	14.8284	−	4.16804i	0.715090	−	0.201001i
$431$	−7.92135	+	24.3794i	−0.381558	+	1.17431i	0.557389	+	0.830252i	$0.311803\pi$
$431$	−7.92135	+	24.3794i	−0.381558	+	1.17431i	−0.938947	+	0.344063i	$0.888197\pi$
$432$	−22.3011	+	3.45216i	−1.07296	+	0.166092i
$433$	2.70466	+	1.96505i	0.129978	+	0.0944344i	0.650875	−	0.759185i	$-0.274402\pi$
$433$	2.70466	+	1.96505i	0.129978	+	0.0944344i	−0.520897	+	0.853620i	$0.674402\pi$
$434$	−10.8347	−	16.2460i	−0.520082	−	0.779834i
$435$	36.8521	−	11.9740i	1.76692	−	0.574107i
$436$	−0.694496	+	8.63124i	−0.0332603	+	0.413362i
$437$	−7.89810	−	10.8708i	−0.377817	−	0.520021i
$438$	−19.3587	−	0.777573i	−0.924993	−	0.0371539i
$439$	−4.51146			−0.215320			−0.107660	−	0.994188i	$-0.534336\pi$
$439$	−4.51146			−0.215320			−0.107660	+	0.994188i	$0.534336\pi$
$440$		0			0
$441$	6.48528			0.308823
$442$	10.7690	+	0.432554i	0.512228	+	0.0205745i
$443$	3.61331	+	4.97330i	0.171674	+	0.236289i	0.886181	−	0.463340i	$-0.153349\pi$
$443$	3.61331	+	4.97330i	0.171674	+	0.236289i	−0.714507	+	0.699628i	$0.753349\pi$
$444$	−1.79319	−	0.144286i	−0.0851012	−	0.00684751i
$445$	36.0577	−	11.7159i	1.70930	−	0.555385i
$446$	20.1878	+	30.2705i	0.955921	+	1.43335i
$447$	−22.8764	−	16.6207i	−1.08202	−	0.786130i
$448$	19.8837	+	23.5299i	0.939417	+	1.11168i
$449$	5.35933	−	16.4943i	0.252922	−	0.778415i	−0.741310	−	0.671163i	$-0.765795\pi$
$449$	5.35933	−	16.4943i	0.252922	−	0.778415i	0.994232	−	0.107252i	$-0.0342050\pi$
$450$	−8.63589	+	2.42742i	−0.407100	+	0.114430i
$451$		0			0
$452$	5.94975	−	3.63170i	0.279853	−	0.170821i
$453$	10.7937	+	3.50709i	0.507133	+	0.164778i
$454$	3.19163	+	2.52061i	0.149791	+	0.118298i
$455$	−52.9549	−	38.4740i	−2.48256	−	1.80369i
$456$	15.6662	+	7.27216i	0.733638	+	0.340550i
$457$	8.12551	+	25.0077i	0.380095	+	1.16981i	0.939976	+	0.341240i	$0.110847\pi$
$457$	8.12551	+	25.0077i	0.380095	+	1.16981i	−0.559881	+	0.828573i	$0.689153\pi$
$458$	10.1738	−	27.5030i	0.475388	−	1.28513i
$459$	5.28930	+	7.28010i	0.246883	+	0.339806i
$460$	−22.4442	+	5.34686i	−1.04647	+	0.249298i
$461$			4.85483i			0.226112i	0.993589	+	0.113056i	$0.0360640\pi$
$461$			4.85483i			0.226112i	−0.993589	+	0.113056i	$0.963936\pi$
$462$		0			0
$463$	7.72792			0.359147			0.179573	−	0.983745i	$-0.442528\pi$
$463$	7.72792			0.359147			0.179573	+	0.983745i	$0.442528\pi$
$464$	20.9781	−	20.8317i	0.973882	−	0.967087i
$465$	−15.2087	+	11.0498i	−0.705287	+	0.512421i
$466$	−14.4464	−	5.34391i	−0.669215	−	0.247552i
$467$	27.3086	−	8.87312i	1.26369	−	0.410599i	0.400884	−	0.916129i	$-0.368703\pi$
$467$	27.3086	−	8.87312i	1.26369	−	0.410599i	0.862809	+	0.505530i	$0.168703\pi$
$468$	5.15175	−	6.01059i	0.238140	−	0.277840i
$469$	3.33544	−	4.59084i	0.154016	−	0.211985i
$470$	19.0646	+	15.0564i	0.879386	+	0.694501i
$471$	6.20230	−	19.0887i	0.285787	−	0.879562i
$472$	−11.6891	−	10.8624i	−0.538036	−	0.499982i
$473$		0			0
$474$	1.79899	+	6.40017i	0.0826303	+	0.293970i
$475$	30.1760	+	9.80478i	1.38457	+	0.449874i
$476$	4.72084	−	11.3409i	0.216380	−	0.519811i
$477$	−2.02958	+	2.79347i	−0.0929279	+	0.127904i
$478$	18.1294	+	27.1840i	0.829219	+	1.24337i
$479$	−1.18995	−	3.66230i	−0.0543704	−	0.167335i	0.920184	−	0.391486i	$-0.128039\pi$
$479$	−1.18995	−	3.66230i	−0.0543704	−	0.167335i	−0.974554	+	0.224152i	$0.928039\pi$
$480$	21.8656	−	20.0356i	0.998022	−	0.914496i
$481$	2.35943	−	1.71423i	0.107581	−	0.0781620i
$482$	1.67351	−	41.6642i	0.0762263	−	1.89775i
$483$		−	18.4007i		−	0.837259i
$484$		0			0
$485$		−	60.9857i		−	2.76922i
$486$	11.7795	+	0.473143i	0.534329	+	0.0214622i
$487$	28.2343	−	20.5134i	1.27942	−	0.929551i	0.279882	−	0.960034i	$-0.409705\pi$
$487$	28.2343	−	20.5134i	1.27942	−	0.929551i	0.999535	+	0.0304831i	$0.00970456\pi$
$488$	1.17875	+	6.00840i	0.0533597	+	0.271987i
$489$	−9.16447	−	28.2053i	−0.414432	−	1.27549i
$490$	−32.7682	+	21.8536i	−1.48032	+	0.987243i
$491$	−13.7784	+	18.9643i	−0.621810	+	0.855849i	−0.997483	−	0.0709038i	$-0.977412\pi$
$491$	−13.7784	+	18.9643i	−0.621810	+	0.855849i	0.375673	+	0.926752i	$0.377412\pi$
$492$	25.2953	+	10.5296i	1.14040	+	0.474710i
$493$	−11.2120	−	3.64300i	−0.504964	−	0.164073i
$494$	−26.9554	+	7.57675i	−1.21278	+	0.340894i
$495$		0			0
$496$	−6.55635	+	12.7570i	−0.294389	+	0.572805i
$497$	12.3924	−	38.1400i	0.555876	−	1.71081i
$498$	16.2970	−	20.6354i	0.730284	−	0.924695i
$499$	18.7586	−	25.8190i	0.839752	−	1.15582i	−0.146277	−	0.989244i	$-0.546729\pi$
$499$	18.7586	−	25.8190i	0.839752	−	1.15582i	0.986029	−	0.166576i	$-0.0532710\pi$
$500$	12.3025	−	14.3534i	0.550185	−	0.641905i
$501$	−5.39686	+	1.75355i	−0.241114	+	0.0783426i
$502$	−7.10621	+	19.2104i	−0.317166	+	0.857404i
$503$	−8.81151	+	6.40193i	−0.392886	+	0.285448i	−0.766637	−	0.642081i	$-0.778071\pi$
$503$	−8.81151	+	6.40193i	−0.392886	+	0.285448i	0.373751	+	0.927529i	$0.378071\pi$
$504$	−4.38810	−	7.88400i	−0.195462	−	0.351181i
$505$	16.9981			0.756406
$506$		0			0
$507$		−	14.4834i		−	0.643231i
$508$	−6.83289	−	28.6821i	−0.303161	−	1.27256i
$509$	−1.79391	−	2.46910i	−0.0795136	−	0.109441i	0.767407	−	0.641160i	$-0.221546\pi$
$509$	−1.79391	−	2.46910i	−0.0795136	−	0.109441i	−0.846921	+	0.531719i	$0.821546\pi$
$510$	−11.0914	−	4.10288i	−0.491137	−	0.181679i
$511$	−11.0625	−	34.0469i	−0.489376	−	1.50614i
$512$	7.99870	−	21.1665i	0.353496	−	0.935436i
$513$	−18.9134	−	13.7414i	−0.835048	−	0.606698i
$514$	−16.2024	+	20.5157i	−0.714657	+	0.904908i
$515$	31.5132	+	10.2392i	1.38864	+	0.451195i
$516$	7.70154	−	4.70099i	0.339041	−	0.206949i
$517$		0			0
$518$	−0.899495	−	3.20009i	−0.0395215	−	0.140604i
$519$	2.37991	−	7.32460i	0.104466	−	0.321514i
$520$	−5.77629	+	47.7297i	−0.253307	+	2.09309i
$521$	−1.20162	−	0.873026i	−0.0526438	−	0.0382480i	0.561152	−	0.827713i	$-0.310358\pi$
$521$	−1.20162	−	0.873026i	−0.0526438	−	0.0382480i	−0.613796	+	0.789465i	$0.710358\pi$
$522$	−7.20402	+	4.80446i	−0.315311	+	0.210285i
$523$	−27.4410	+	8.91612i	−1.19991	+	0.389875i	−0.839728	−	0.543007i	$-0.817286\pi$
$523$	−27.4410	+	8.91612i	−1.19991	+	0.389875i	−0.360183	+	0.932882i	$0.617286\pi$
$524$	1.70645	−	21.2079i	0.0745467	−	0.926471i
$525$	25.5390	+	35.1514i	1.11461	+	1.53413i
$526$	−0.399628	+	9.94925i	−0.0174246	+	0.433808i
$527$	5.71948			0.249144
$528$		0			0
$529$	−12.4853			−0.542838
$530$	0.841638	−	20.9537i	0.0365584	−	0.910169i
$531$	2.74714	+	3.78111i	0.119216	+	0.164086i
$532$	−2.55963	+	31.8113i	−0.110974	+	1.37919i
$533$	−42.2442	+	13.7260i	−1.82980	+	0.594539i
$534$	18.4770	−	12.3226i	0.799578	−	0.533249i
$535$	20.7384	+	15.0673i	0.896597	+	0.651416i
$536$	−4.13785	−	0.500766i	−0.178728	−	0.0216298i
$537$	−9.04934	+	27.8510i	−0.390508	+	1.20186i
$538$	−2.91642	−	10.3756i	−0.125736	−	0.447323i
$539$		0			0
$540$	−34.2635	+	20.9143i	−1.47446	+	0.900007i
$541$	−4.54406	−	1.47646i	−0.195365	−	0.0634778i	0.209700	−	0.977766i	$-0.432751\pi$
$541$	−4.54406	−	1.47646i	−0.195365	−	0.0634778i	−0.405065	+	0.914288i	$0.632751\pi$
$542$	14.0799	−	17.8282i	0.604785	−	0.765787i
$543$	18.2961	+	13.2929i	0.785161	+	0.570453i
$544$	−8.96493	+	1.02131i	−0.384368	+	0.0437884i
$545$	4.75981	+	14.6492i	0.203888	+	0.627503i
$546$	−35.9616	−	13.3027i	−1.53901	−	0.569303i
$547$	23.8299	+	32.7991i	1.01889	+	1.40239i	0.912976	+	0.408013i	$0.133778\pi$
$547$	23.8299	+	32.7991i	1.01889	+	1.40239i	0.105919	+	0.994375i	$0.466222\pi$
$548$	−1.39046	−	5.83666i	−0.0593974	−	0.249330i
$549$		−	1.79337i		−	0.0765390i
$550$		0			0
$551$	30.6274			1.30477
$552$	−11.8095	+	6.57296i	−0.502645	+	0.279764i
$553$	−9.93818	+	7.22051i	−0.422615	+	0.307047i
$554$	2.74647	−	7.42460i	0.116686	−	0.315441i
$555$	−3.04346	+	0.988881i	−0.129188	+	0.0419757i
$556$	−11.0286	+	12.8672i	−0.467719	+	0.545691i
$557$	14.3507	−	19.7520i	0.608057	−	0.836919i	−0.388359	−	0.921508i	$-0.626958\pi$
$557$	14.3507	−	19.7520i	0.608057	−	0.836919i	0.996416	+	0.0845892i	$0.0269578\pi$
$558$	2.60371	−	3.29685i	0.110224	−	0.139567i
$559$	−4.52012	+	13.9115i	−0.191181	+	0.588394i
$560$	48.7386	+	25.0489i	2.05958	+	1.05851i
$561$		0			0
$562$	−31.4558	+	8.84175i	−1.32688	+	0.372967i
$563$	17.3235	+	5.62873i	0.730097	+	0.237223i	0.650395	−	0.759596i	$-0.274603\pi$
$563$	17.3235	+	5.62873i	0.730097	+	0.237223i	0.0797014	+	0.996819i	$0.474603\pi$
$564$	13.1378	+	5.46881i	0.553201	+	0.230279i
$565$	7.28819	−	10.0313i	0.306616	−	0.422021i
$566$	20.9940	−	14.0012i	0.882446	−	0.588515i
$567$	−6.93556	−	21.3454i	−0.291266	−	0.896424i
$568$	−28.9048	+	5.67068i	−1.21282	+	0.237936i
$569$	−11.3923	+	8.27702i	−0.477592	+	0.346991i	−0.800393	−	0.599476i	$-0.795376\pi$
$569$	−11.3923	+	8.27702i	−0.477592	+	0.346991i	0.322801	+	0.946467i	$0.395376\pi$
$570$	30.6987	+	1.23306i	1.28583	+	0.0516474i
$571$			40.3881i			1.69019i	0.534618	+	0.845094i	$0.320456\pi$
$571$			40.3881i			1.69019i	−0.534618	+	0.845094i	$0.679544\pi$
$572$		0			0
$573$		−	17.7882i		−	0.743114i
$574$	−2.03189	+	50.5866i	−0.0848097	+	2.11144i
$575$	−20.0866	+	14.5938i	−0.837670	+	0.608603i
$576$	−3.49244	+	5.63254i	−0.145518	+	0.234689i
$577$	−7.83146	−	24.1028i	−0.326028	−	1.00341i	−0.970974	−	0.239183i	$-0.923120\pi$
$577$	−7.83146	−	24.1028i	−0.326028	−	1.00341i	0.644946	−	0.764228i	$-0.276880\pi$
$578$	−11.3430	−	17.0082i	−0.471807	−	0.707448i
$579$	−2.76317	+	3.80318i	−0.114833	+	0.158055i
$580$	20.2101	−	48.5510i	0.839179	−	2.01597i
$581$	46.2083	+	15.0140i	1.91704	+	0.622885i
$582$	−9.66700	−	34.3918i	−0.400710	−	1.42559i
$583$		0			0
$584$	−17.8995	+	19.2619i	−0.740686	+	0.797062i
$585$	4.35149	−	13.3925i	0.179912	−	0.553712i
$586$	3.31236	+	2.61596i	0.136833	+	0.108064i
$587$	3.88504	−	5.34730i	0.160353	−	0.220707i	−0.721279	−	0.692645i	$-0.756445\pi$
$587$	3.88504	−	5.34730i	0.160353	−	0.220707i	0.881632	+	0.471938i	$0.156445\pi$
$588$	−15.0150	+	17.5181i	−0.619207	+	0.722434i
$589$	−14.1317	+	4.59168i	−0.582288	+	0.189197i
$590$	−26.6217	−	9.84776i	−1.09600	−	0.405426i
$591$	−18.6920	+	13.5806i	−0.768887	+	0.558629i
$592$	−1.73249	+	1.72041i	−0.0712050	+	0.0707082i
$593$	−21.7832			−0.894531			−0.447265	−	0.894401i	$-0.647602\pi$
$593$	−21.7832			−0.894531			−0.447265	+	0.894401i	$0.647602\pi$
$594$		0			0
$595$		−	21.8516i		−	0.895826i
$596$	−37.3324	+	8.89363i	−1.52919	+	0.364297i
$597$	−14.5764	−	20.0627i	−0.596571	−	0.821110i
$598$	7.60158	−	20.5496i	0.310852	−	0.840335i
$599$	13.2165	+	40.6763i	0.540012	+	1.66199i	0.732562	+	0.680700i	$0.238324\pi$
$599$	13.2165	+	40.6763i	0.540012	+	1.66199i	−0.192550	+	0.981287i	$0.561676\pi$
$600$	13.4372	−	28.9474i	0.548571	−	1.18177i
$601$	−21.4943	−	15.6165i	−0.876769	−	0.637010i	0.0556256	−	0.998452i	$-0.482285\pi$
$601$	−21.4943	−	15.6165i	−0.876769	−	0.637010i	−0.932395	+	0.361442i	$0.882285\pi$
$602$	13.0839	+	10.3331i	0.533260	+	0.421146i
$603$	1.16104	+	0.377245i	0.0472813	+	0.0153626i
$604$	13.1474	−	8.02509i	0.534958	−	0.326536i
$605$		0			0
$606$	9.58579	−	2.69442i	0.389396	−	0.109453i
$607$	10.0971	−	31.0756i	0.409828	−	1.26132i	−0.506968	−	0.861965i	$-0.669234\pi$
$607$	10.0971	−	31.0756i	0.409828	−	1.26132i	0.916796	−	0.399356i	$-0.130766\pi$
$608$	21.3307	−	9.72065i	0.865075	−	0.394224i
$609$	33.9311	+	24.6524i	1.37496	+	0.998965i
$610$	6.04313	+	9.06134i	0.244679	+	0.366883i
$611$	−21.9407	+	7.12896i	−0.887625	+	0.288407i
$612$	2.63424	+	0.211959i	0.106483	+	0.00856793i
$613$	11.2335	+	15.4616i	0.453718	+	0.624490i	0.973191	−	0.229997i	$-0.0738717\pi$
$613$	11.2335	+	15.4616i	0.453718	+	0.624490i	−0.519473	+	0.854487i	$0.673872\pi$
$614$	−39.7220	−	1.59550i	−1.60305	−	0.0643891i
$615$	48.7386			1.96533
$616$		0			0
$617$	13.7990			0.555526			0.277763	−	0.960650i	$-0.410407\pi$
$617$	13.7990			0.555526			0.277763	+	0.960650i	$0.410407\pi$
$618$	19.3943	+	0.779005i	0.780154	+	0.0313362i
$619$	1.58374	+	2.17983i	0.0636558	+	0.0876147i	0.839658	−	0.543116i	$-0.182755\pi$
$619$	1.58374	+	2.17983i	0.0636558	+	0.0876147i	−0.776002	+	0.630730i	$0.782755\pi$
$620$	−2.04632	+	25.4317i	−0.0821820	+	1.02136i
$621$	17.3985	−	5.65313i	0.698179	−	0.226852i
$622$	8.22744	+	12.3366i	0.329890	+	0.494652i
$623$	33.1997	+	24.1210i	1.33012	+	0.966387i
$624$	4.30833	+	27.8319i	0.172471	+	1.11417i
$625$	−1.43905	+	4.42893i	−0.0575619	+	0.177157i
$626$	−2.48932	+	0.699709i	−0.0994931	+	0.0279660i
$627$		0			0
$628$	−14.1924	−	23.2511i	−0.566338	−	0.927821i
$629$	0.925955	+	0.300861i	0.0369202	+	0.0119961i
$630$	−12.5958	−	9.94759i	−0.501828	−	0.396322i
$631$	−5.35183	−	3.88833i	−0.213053	−	0.154792i	0.476141	−	0.879369i	$-0.342035\pi$
$631$	−5.35183	−	3.88833i	−0.213053	−	0.154792i	−0.689194	+	0.724577i	$0.742035\pi$
$632$	8.18415	+	3.79903i	0.325548	+	0.151117i
$633$	10.5054	+	32.3323i	0.417553	+	1.28510i
$634$	0.898462	−	2.42884i	0.0356825	−	0.0964615i
$635$	−30.8283	−	42.4315i	−1.22338	−	1.68384i
$636$	−2.84679	−	11.9499i	−0.112883	−	0.473843i
$637$		−	37.4035i		−	1.48198i
$638$		0			0
$639$	8.62742			0.341295
$640$	−1.33380	−	40.2281i	−0.0527231	−	1.59015i
$641$	−1.75684	+	1.27642i	−0.0693910	+	0.0504155i	−0.621940	−	0.783065i	$-0.713655\pi$
$641$	−1.75684	+	1.27642i	−0.0693910	+	0.0504155i	0.552549	+	0.833480i	$0.313655\pi$
$642$	14.0834	+	5.20964i	0.555827	+	0.205608i
$643$	−38.5207	+	12.5161i	−1.51911	+	0.493588i	−0.945522	−	0.325559i	$-0.894448\pi$
$643$	−38.5207	+	12.5161i	−1.51911	+	0.493588i	−0.573585	+	0.819146i	$0.694448\pi$
$644$	−18.9614	−	16.2521i	−0.747186	−	0.640422i
$645$	9.43406	−	12.9849i	0.371466	−	0.511278i
$646$	−7.33562	−	5.79336i	−0.288616	−	0.227937i
$647$	8.46236	−	26.0445i	0.332690	−	1.02391i	−0.635159	−	0.772381i	$-0.719065\pi$
$647$	8.46236	−	26.0445i	0.332690	−	1.02391i	0.967849	−	0.251532i	$-0.0809345\pi$
$648$	−11.2220	+	12.0761i	−0.440840	+	0.474394i
$649$		0			0
$650$	14.0000	+	49.8071i	0.549125	+	1.95359i
$651$	−19.3520	−	6.28784i	−0.758464	−	0.246440i
$652$	−37.1593	−	15.4681i	−1.45527	−	0.605779i
$653$	1.79391	−	2.46910i	0.0702011	−	0.0966235i	−0.772473	−	0.635048i	$-0.780980\pi$
$653$	1.79391	−	2.46910i	0.0702011	−	0.0966235i	0.842674	+	0.538425i	$0.180980\pi$
$654$	5.00630	+	7.50666i	0.195762	+	0.293534i
$655$	−11.6954	−	35.9946i	−0.456976	−	1.40643i
$656$	33.1922	−	16.7661i	1.29594	−	0.654608i
$657$	6.23068	−	4.52685i	0.243082	−	0.176609i
$658$	−1.05532	+	26.2735i	−0.0411406	+	1.02425i
$659$			49.2011i			1.91660i	0.285763	+	0.958300i	$0.407753\pi$
$659$			49.2011i			1.91660i	−0.285763	+	0.958300i	$0.592247\pi$
$660$		0			0
$661$			28.5659i			1.11108i	0.831488	+	0.555542i	$0.187489\pi$
$661$			28.5659i			1.11108i	−0.831488	+	0.555542i	$0.812511\pi$
$662$	18.0265	+	0.724065i	0.700621	+	0.0281416i
$663$	9.08562	−	6.60109i	0.352856	−	0.256365i
$664$	−6.87029	−	35.0195i	−0.266619	−	1.35902i
$665$	17.5428	+	53.9911i	0.680279	+	2.09368i
$666$	0.594951	−	0.396781i	0.0230539	−	0.0153749i
$667$	−14.0871	+	19.3893i	−0.545456	+	0.750756i
$668$	−2.95970	+	7.11013i	−0.114514	+	0.275099i
$669$	36.0577	+	11.7159i	1.39407	+	0.452961i
$670$	−7.13761	+	2.00627i	−0.275750	+	0.0775090i
$671$		0			0
$672$	31.4558	+	6.40017i	1.21344	+	0.246892i
$673$	−2.95737	+	9.10184i	−0.113998	+	0.350850i	−0.991737	−	0.128290i	$-0.959051\pi$
$673$	−2.95737	+	9.10184i	−0.113998	+	0.350850i	0.877739	+	0.479140i	$0.159051\pi$
$674$	−5.35236	+	6.77723i	−0.206165	+	0.261049i
$675$	−25.3908	+	34.9475i	−0.977293	+	1.34513i
$676$	−14.9248	−	12.7922i	−0.574032	−	0.492010i
$677$	31.4552	−	10.2204i	1.20892	−	0.392802i	0.365886	−	0.930660i	$-0.380766\pi$
$677$	31.4552	−	10.2204i	1.20892	−	0.392802i	0.843036	+	0.537857i	$0.180766\pi$
$678$	2.51995	−	6.81226i	0.0967781	−	0.261623i
$679$	53.4035	−	38.7999i	2.04944	−	1.48901i
$680$	−14.0243	+	7.80566i	−0.537806	+	0.299334i
$681$	4.23779			0.162393
$682$		0			0
$683$		−	16.6722i		−	0.637943i	−0.947764	−	0.318971i	$-0.896663\pi$
$683$		−	16.6722i		−	0.637943i	0.947764	−	0.318971i	$-0.103337\pi$
$684$	−6.67886	+	1.59109i	−0.255373	+	0.0608370i
$685$	−6.27340	−	8.63459i	−0.239694	−	0.329911i
$686$	−4.23124	−	1.56520i	−0.161550	−	0.0597595i
$687$	−9.44243	−	29.0608i	−0.360251	−	1.10874i
$688$	1.95800	−	12.0883i	0.0746482	−	0.460863i
$689$	16.1112	+	11.7055i	0.613788	+	0.445943i
$690$	−14.9005	+	18.8673i	−0.567254	+	0.718265i
$691$	−22.1836	−	7.20788i	−0.843902	−	0.274201i	−0.145013	−	0.989430i	$-0.546322\pi$
$691$	−22.1836	−	7.20788i	−0.843902	−	0.274201i	−0.698890	+	0.715229i	$0.746322\pi$
$692$	−5.44581	−	8.92177i	−0.207019	−	0.339155i
$693$		0			0
$694$	−0.414214	−	1.47363i	−0.0157233	−	0.0559381i
$695$	−9.31546	+	28.6700i	−0.353356	+	1.08752i
$696$	3.70118	−	30.5830i	0.140293	−	1.15925i
$697$	−11.9964	−	8.71593i	−0.454398	−	0.330139i
$698$	−21.9585	+	14.6444i	−0.831143	+	0.554301i
$699$	−15.2646	+	4.95978i	−0.577361	+	0.187596i
$700$	58.7796	+	4.72959i	2.22166	+	0.178762i
$701$	−16.3685	−	22.5293i	−0.618229	−	0.850919i	0.378994	−	0.925399i	$-0.376270\pi$
$701$	−16.3685	−	22.5293i	−0.618229	−	0.850919i	−0.997222	+	0.0744806i	$0.976270\pi$
$702$	1.52995	−	38.0900i	0.0577441	−	1.43761i
$703$	−2.52939			−0.0953979
$704$		0			0
$705$	25.3137			0.953369
$706$	−0.953484	+	23.7382i	−0.0358849	+	0.893400i
$707$	10.8144	+	14.8848i	0.406719	+	0.559801i
$708$	−16.5739	−	1.33358i	−0.622883	−	0.0501191i
$709$	7.34757	−	2.38737i	0.275944	−	0.0896595i	−0.167776	−	0.985825i	$-0.553659\pi$
$709$	7.34757	−	2.38737i	0.275944	−	0.0896595i	0.443720	+	0.896166i	$0.353659\pi$
$710$	−43.5918	+	29.0719i	−1.63597	+	1.09105i
$711$	−2.13803	−	1.55337i	−0.0801824	−	0.0582559i
$712$	3.62140	−	29.9238i	0.135718	−	1.12144i
$713$	3.59307	−	11.0583i	0.134562	−	0.414138i
$714$	−3.46375	−	12.3228i	−0.129628	−	0.461169i
$715$		0			0
$716$	20.7071	+	33.9241i	0.773861	+	1.26780i
$717$	32.3812	+	10.5213i	1.20930	+	0.392924i
$718$	−15.7179	+	19.9022i	−0.586585	+	0.742742i
$719$	28.7895	+	20.9168i	1.07367	+	0.780065i	0.976568	−	0.215210i	$-0.0690435\pi$
$719$	28.7895	+	20.9168i	1.07367	+	0.780065i	0.0970995	+	0.995275i	$0.469043\pi$
$720$	−1.88496	+	11.6373i	−0.0702482	+	0.433698i
$721$	11.0829	+	34.1096i	0.412748	+	1.27031i
$722$	−2.42518	−	0.897108i	−0.0902558	−	0.0333869i
$723$	−25.5390	−	35.1514i	−0.949805	−	1.30730i
$724$	29.8577	−	7.11296i	1.10965	−	0.264351i
$725$		−	56.5921i		−	2.10178i
$726$		0			0
$727$	−8.07107			−0.299339			−0.149670	−	0.988736i	$-0.547821\pi$
$727$	−8.07107			−0.299339			−0.149670	+	0.988736i	$0.547821\pi$
$728$	−45.4706	+	25.3082i	−1.68525	+	0.937983i
$729$	24.0841	−	17.4981i	0.892003	−	0.648078i
$730$	−16.2276	+	43.8684i	−0.600609	+	1.62364i
$731$	−4.64417	+	1.50898i	−0.171771	+	0.0558117i
$732$	4.84425	+	4.15207i	0.179049	+	0.153465i
$733$	−3.81729	+	5.25404i	−0.140995	+	0.194062i	−0.873674	−	0.486511i	$-0.838269\pi$
$733$	−3.81729	+	5.25404i	−0.140995	+	0.194062i	0.732680	+	0.680574i	$0.238269\pi$
$734$	5.19672	−	6.58016i	0.191815	−	0.242878i
$735$	−12.6826	+	39.0329i	−0.467803	+	1.43975i
$736$	−3.65726	+	17.9749i	−0.134808	+	0.662562i
$737$		0			0
$738$	−10.4853	+	2.94725i	−0.385969	+	0.108490i
$739$	−21.9407	−	7.12896i	−0.807101	−	0.262243i	−0.123731	−	0.992316i	$-0.539486\pi$
$739$	−21.9407	−	7.12896i	−0.807101	−	0.262243i	−0.683369	+	0.730073i	$0.739486\pi$
$740$	−1.66907	+	4.00963i	−0.0613563	+	0.147397i
$741$	−17.1494	+	23.6041i	−0.629999	+	0.867119i
$742$	18.8840	−	12.5940i	0.693255	−	0.462341i
$743$	−11.8995	−	36.6230i	−0.436552	−	1.34357i	−0.891488	−	0.453044i	$-0.850338\pi$
$743$	−11.8995	−	36.6230i	−0.436552	−	1.34357i	0.454937	−	0.890524i	$-0.349662\pi$
$744$	2.87727	+	14.6661i	0.105486	+	0.537687i
$745$	−55.2285	+	40.1258i	−2.02341	+	1.47010i
$746$	40.6179	+	1.63149i	1.48713	+	0.0597330i
$747$			10.4525i			0.382437i
$748$		0			0
$749$			27.7461i			1.01382i
$750$	0.790584	−	19.6826i	0.0288681	−	0.718707i
$751$	−11.9390	+	8.67416i	−0.435659	+	0.316525i	−0.783908	−	0.620878i	$-0.786776\pi$
$751$	−11.9390	+	8.67416i	−0.435659	+	0.316525i	0.348249	+	0.937402i	$0.386776\pi$
$752$	17.2392	−	8.70795i	0.628650	−	0.317546i
$753$	6.59539	+	20.2985i	0.240350	+	0.739720i
$754$	27.7095	+	41.5488i	1.00912	+	1.51312i
$755$	16.1049	−	22.1665i	0.586119	−	0.806723i
$756$	−40.1130	−	16.6977i	−1.45889	−	0.607288i
$757$	−46.8884	−	15.2350i	−1.70419	−	0.553724i	−0.714840	−	0.699289i	$-0.753500\pi$
$757$	−46.8884	−	15.2350i	−1.70419	−	0.553724i	−0.989349	+	0.145564i	$0.953500\pi$
$758$	−1.03111	−	3.66832i	−0.0374516	−	0.133239i
$759$		0			0
$760$	28.3848	−	30.5452i	1.02962	−	1.10799i
$761$	−9.02673	+	27.7814i	−0.327219	+	1.00708i	0.643210	+	0.765690i	$0.277602\pi$
$761$	−9.02673	+	27.7814i	−0.327219	+	1.00708i	−0.970429	+	0.241386i	$0.922398\pi$
$762$	−24.1110	−	19.0418i	−0.873449	−	0.689812i
$763$	−9.79966	+	13.4881i	−0.354771	+	0.488301i
$764$	−18.3304	−	15.7112i	−0.663169	−	0.568410i
$765$	4.47090	−	1.45268i	0.161646	−	0.0525219i
$766$	−1.64821	−	0.609695i	−0.0595521	−	0.0220292i
$767$	21.8074	−	15.8440i	0.787418	−	0.572093i
$768$	−7.12883	−	22.4745i	−0.257240	−	0.810978i
$769$	−40.1027			−1.44614			−0.723071	−	0.690774i	$-0.757270\pi$
$769$	−40.1027			−1.44614			−0.723071	+	0.690774i	$0.757270\pi$
$770$		0			0
$771$			27.2404i			0.981039i
$772$	1.47856	+	6.20648i	0.0532145	+	0.223376i
$773$	28.5583	+	39.3071i	1.02717	+	1.41378i	0.907052	+	0.421019i	$0.138328\pi$
$773$	28.5583	+	39.3071i	1.02717	+	1.41378i	0.120119	+	0.992760i	$0.461672\pi$
$774$	−1.24437	+	3.36395i	−0.0447281	+	0.120915i
$775$	8.48432	+	26.1121i	0.304766	+	0.937973i
$776$	−43.9781	−	20.4144i	−1.57872	−	0.732833i
$777$	−2.80223	−	2.03594i	−0.100529	−	0.0730389i
$778$	−18.3872	−	14.5214i	−0.659213	−	0.520618i
$779$	36.6382	+	11.9045i	1.31270	+	0.426522i
$780$	26.1012	+	42.7611i	0.934572	+	1.53109i
$781$		0			0
$782$	7.04163	−	1.97929i	0.251808	−	0.0707794i
$783$	−12.8853	+	39.6569i	−0.460484	+	1.41722i
$784$	4.79025	+	30.9451i	0.171080	+	1.10518i
$785$	−39.2016	−	28.4816i	−1.39917	−	1.01655i
$786$	−12.3010	−	18.4447i	−0.438762	−	0.657900i
$787$	0.852796	−	0.277090i	0.0303989	−	0.00987720i	−0.293778	−	0.955874i	$-0.594913\pi$
$787$	0.852796	−	0.277090i	0.0303989	−	0.00987720i	0.324177	+	0.945996i	$0.394913\pi$
$788$	−2.51499	+	31.2565i	−0.0895930	+	1.11347i
$789$	6.09861	+	8.39402i	0.217116	+	0.298835i
$790$	16.0372	+	0.644162i	0.570579	+	0.0229183i
$791$	13.4210			0.477196
$792$		0			0
$793$	−10.3431			−0.367296
$794$	50.9867	+	2.04797i	1.80945	+	0.0726796i
$795$	−12.8440	−	17.6783i	−0.455530	−	0.626984i
$796$	−33.5484	−	2.69941i	−1.18909	−	0.0956781i
$797$	−5.70561	+	1.85386i	−0.202103	+	0.0656672i	−0.408319	−	0.912839i	$-0.633885\pi$
$797$	−5.70561	+	1.85386i	−0.202103	+	0.0656672i	0.206216	+	0.978506i	$0.433885\pi$
$798$	18.4512	+	27.6665i	0.653165	+	0.979385i
$799$	−6.23068	−	4.52685i	−0.220425	−	0.160148i
$800$	−17.9614	−	39.4140i	−0.635032	−	1.39350i
$801$	−2.72813	+	8.39633i	−0.0963939	+	0.296670i
$802$	−15.5966	+	4.38396i	−0.550735	+	0.154803i
$803$		0			0
$804$	−3.70711	+	2.26280i	−0.130740	+	0.0798029i
$805$	−42.2489	−	13.7275i	−1.48908	−	0.483831i
$806$	−19.0144	−	15.0167i	−0.669753	−	0.528942i
$807$	−9.08562	−	6.60109i	−0.319829	−	0.232369i
$808$	5.68996	−	12.2577i	0.200172	−	0.431225i
$809$	2.87280	+	8.84157i	0.101002	+	0.310853i	0.988771	−	0.149436i	$-0.0477458\pi$
$809$	2.87280	+	8.84157i	0.101002	+	0.310853i	−0.887769	+	0.460289i	$0.847746\pi$
$810$	−10.1738	+	27.5030i	−0.357469	+	0.966357i
$811$	−1.58117	−	2.17630i	−0.0555224	−	0.0764201i	0.780353	−	0.625339i	$-0.215039\pi$
$811$	−1.58117	−	2.17630i	−0.0555224	−	0.0764201i	−0.835875	+	0.548919i	$0.815039\pi$
$812$	55.3728	−	13.1914i	1.94320	−	0.462926i
$813$		−	23.6720i		−	0.830213i
$814$		0			0
$815$	−71.5980			−2.50797
$816$	−6.67143	+	6.62489i	−0.233547	+	0.231917i
$817$	10.2634	−	7.45682i	0.359072	−	0.260881i
$818$	8.46248	+	3.13039i	0.295884	+	0.109452i
$819$	14.4959	−	4.71001i	0.506529	−	0.164581i
$820$	43.0476	−	50.2240i	1.50329	−	1.75390i
$821$	−1.05411	+	1.45086i	−0.0367888	+	0.0506355i	−0.827015	−	0.562180i	$-0.809963\pi$
$821$	−1.05411	+	1.45086i	−0.0367888	+	0.0506355i	0.790226	+	0.612815i	$0.209963\pi$
$822$	−4.90646	−	3.87491i	−0.171133	−	0.135153i
$823$	−0.702111	+	2.16087i	−0.0244740	+	0.0753234i	−0.962548	−	0.271113i	$-0.912608\pi$
$823$	−0.702111	+	2.16087i	−0.0244740	+	0.0753234i	0.938074	+	0.346436i	$0.112608\pi$
$824$	17.9325	−	19.2974i	0.624707	−	0.672255i
$825$		0			0
$826$	−8.31371	−	29.5772i	−0.289271	−	1.02912i
$827$	−21.7641	−	7.07157i	−0.756810	−	0.245903i	−0.0949013	−	0.995487i	$-0.530254\pi$
$827$	−21.7641	−	7.07157i	−0.756810	−	0.245903i	−0.661909	+	0.749584i	$0.730254\pi$
$828$	2.06468	−	4.96001i	0.0717527	−	0.172372i
$829$	−18.5230	+	25.4947i	−0.643329	+	0.885467i	−0.998788	−	0.0492253i	$-0.984325\pi$
$829$	−18.5230	+	25.4947i	−0.643329	+	0.885467i	0.355458	+	0.934692i	$0.384325\pi$
$830$	−35.2220	−	52.8134i	−1.22257	−	1.83318i
$831$	−2.54904	−	7.84514i	−0.0884253	−	0.272145i
$832$	32.4854	+	20.1425i	1.12623	+	0.698314i
$833$	10.1019	−	7.33948i	0.350011	−	0.254298i
$834$	−0.708724	+	17.6446i	−0.0245411	+	0.610982i
$835$			13.6997i			0.474097i
$836$		0			0
$837$		−	20.2298i		−	0.699245i
$838$	16.6587	+	0.669126i	0.575467	+	0.0231146i
$839$	4.24139	−	3.08155i	0.146429	−	0.106387i	−0.512159	−	0.858891i	$-0.671154\pi$
$839$	4.24139	−	3.08155i	0.146429	−	0.106387i	0.658588	+	0.752504i	$0.271154\pi$
$840$	56.0327	−	10.9928i	1.93331	−	0.379286i
$841$	−7.91931	−	24.3731i	−0.273080	−	0.840452i
$842$	4.90396	−	3.27052i	0.169002	−	0.112710i
$843$	−20.0127	+	27.5451i	−0.689272	+	0.948702i
$844$	42.5964	+	17.7314i	1.46623	+	0.610341i
$845$	−33.2547	−	10.8051i	−1.14400	−	0.371707i
$846$	−5.44581	+	1.53073i	−0.187231	+	0.0526277i
$847$		0			0
$848$	−14.8284	−	7.62096i	−0.509210	−	0.261705i
$849$	8.12551	−	25.0077i	0.278867	−	0.858264i
$850$	−10.7047	+	13.5545i	−0.367169	+	0.464914i
$851$	1.16340	−	1.60128i	0.0398808	−	0.0548913i
$852$	−19.9745	+	23.3044i	−0.684316	+	0.798397i
$853$	30.5292	−	9.91955i	1.04530	−	0.339639i	0.264479	−	0.964392i	$-0.414800\pi$
$853$	30.5292	−	9.91955i	1.04530	−	0.339639i	0.780823	+	0.624753i	$0.214800\pi$
$854$	−4.09005	+	11.0568i	−0.139959	+	0.378355i
$855$	−9.88052	+	7.17862i	−0.337907	+	0.245504i
$856$	17.8073	−	9.91126i	0.608642	−	0.338760i
$857$	−24.9733			−0.853073			−0.426536	−	0.904470i	$-0.640266\pi$
$857$	−24.9733			−0.853073			−0.426536	+	0.904470i	$0.640266\pi$
$858$		0			0
$859$			49.5542i			1.69077i	0.534159	+	0.845384i	$0.320628\pi$
$859$			49.5542i			1.69077i	−0.534159	+	0.845384i	$0.679372\pi$
$860$	−5.04812	−	21.1902i	−0.172139	−	0.722581i
$861$	31.0082	+	42.6791i	1.05676	+	1.45450i
$862$	34.0003	+	12.5772i	1.15805	+	0.428381i
$863$	10.3566	+	31.8744i	0.352543	+	1.08502i	0.957420	+	0.288698i	$0.0932223\pi$
$863$	10.3566	+	31.8744i	0.352543	+	1.08502i	−0.604877	+	0.796319i	$0.706778\pi$
$864$	3.61238	+	31.7090i	0.122896	+	1.07876i
$865$	−15.0422	−	10.9288i	−0.511450	−	0.371590i
$866$	2.93028	−	3.71035i	0.0995748	−	0.126083i
$867$	−20.2599	−	6.58284i	−0.688062	−	0.223565i
$868$	−23.5718	+	14.3881i	−0.800079	+	0.488365i
$869$		0			0
$870$	−14.8284	−	52.7543i	−0.502731	−	1.78854i
$871$	2.17574	−	6.69625i	0.0737222	−	0.226894i
$872$	12.1572	+	1.47127i	0.411694	+	0.0498235i
$873$	11.4889	+	8.34714i	0.388839	+	0.282508i
$874$	−15.8095	+	10.5436i	−0.534765	+	0.356642i
$875$	34.6166	−	11.2476i	1.17025	−	0.380239i
$876$	−2.19754	+	27.3111i	−0.0742478	+	0.922756i
$877$	−8.20684	−	11.2957i	−0.277125	−	0.381430i	0.647654	−	0.761935i	$-0.275750\pi$
$877$	−8.20684	−	11.2957i	−0.277125	−	0.381430i	−0.924779	+	0.380504i	$0.875750\pi$
$878$	−0.256063	+	6.37502i	−0.00864172	+	0.215147i
$879$	4.39810			0.148344
$880$		0			0
$881$	−24.1716			−0.814361			−0.407180	−	0.913348i	$-0.633488\pi$
$881$	−24.1716			−0.814361			−0.407180	+	0.913348i	$0.633488\pi$
$882$	0.368094	−	9.16418i	0.0123944	−	0.308574i
$883$	15.7143	+	21.6288i	0.528827	+	0.727868i	0.986951	−	0.161020i	$-0.0514783\pi$
$883$	15.7143	+	21.6288i	0.528827	+	0.727868i	−0.458124	+	0.888888i	$0.651478\pi$
$884$	1.22246	−	15.1928i	0.0411158	−	0.510990i
$885$	−28.1296	+	9.13987i	−0.945567	+	0.307233i
$886$	7.23273	−	4.82360i	0.242988	−	0.162052i
$887$	33.7342	+	24.5093i	1.13268	+	0.822943i	0.986083	−	0.166253i	$-0.0531667\pi$
$887$	33.7342	+	24.5093i	1.13268	+	0.822943i	0.146601	+	0.989196i	$0.453167\pi$
$888$	−0.305666	+	2.52573i	−0.0102575	+	0.0847579i
$889$	17.5428	−	53.9911i	0.588365	−	1.81080i
$890$	−14.5088	−	51.6172i	−0.486336	−	1.73021i
$891$		0			0
$892$	43.9203	−	26.8088i	1.47056	−	0.897624i
$893$	19.0290	+	6.18291i	0.636783	+	0.206903i
$894$	−24.7847	+	31.3827i	−0.828923	+	1.04959i
$895$	57.1963	+	41.5555i	1.91186	+	1.38905i
$896$	34.3781	−	26.7616i	1.14849	−	0.894044i
$897$	−7.05515	−	21.7135i	−0.235565	−	0.724994i
$898$	−23.0035	−	8.50932i	−0.767637	−	0.283960i
$899$	15.5779	+	21.4411i	0.519551	+	0.715101i
$900$	2.93996	+	12.3409i	0.0979987	+	0.411364i
$901$			6.64820i			0.221484i
$902$		0			0
$903$	17.3726			0.578123
$904$	−4.79416	−	8.61356i	−0.159452	−	0.286483i
$905$	44.1707	−	32.0919i	1.46828	−	1.06677i
$906$	5.56841	−	15.0533i	0.184998	−	0.500111i
$907$	42.9244	−	13.9470i	1.42528	−	0.463102i	0.508005	−	0.861354i	$-0.330383\pi$
$907$	42.9244	−	13.9470i	1.42528	−	0.463102i	0.917276	+	0.398253i	$0.130383\pi$
$908$	3.74296	−	4.36694i	0.124215	−	0.144922i
$909$	−2.32654	+	3.20221i	−0.0771665	+	0.106211i
$910$	−57.3722	+	72.6455i	−1.90187	+	2.40817i
$911$	−7.16041	+	22.0375i	−0.237235	+	0.730134i	0.759582	+	0.650411i	$0.225403\pi$
$911$	−7.16041	+	22.0375i	−0.237235	+	0.730134i	−0.996817	+	0.0797227i	$0.974597\pi$
$912$	11.1653	−	21.7248i	0.369720	−	0.719379i
$913$		0			0
$914$	35.7990	−	10.0625i	1.18413	−	0.332839i
$915$	10.7937	+	3.50709i	0.356829	+	0.115941i
$916$	−38.2863	−	15.9373i	−1.26502	−	0.526583i
$917$	24.0788	−	33.1416i	0.795152	−	1.09443i
$918$	10.5875	−	7.06096i	0.349440	−	0.233047i
$919$	−10.0971	−	31.0756i	−0.333072	−	1.02509i	−0.967664	−	0.252243i	$-0.918832\pi$
$919$	−10.0971	−	31.0756i	−0.333072	−	1.02509i	0.634592	−	0.772848i	$-0.281168\pi$
$920$	6.28160	+	32.0189i	0.207098	+	1.05563i
$921$	−33.5128	+	24.3485i	−1.10428	+	0.802310i
$922$	6.86024	+	0.275553i	0.225930	+	0.00907485i
$923$		−	49.7582i		−	1.63781i
$924$		0			0
$925$			4.67371i			0.153671i
$926$	0.438625	−	10.9201i	0.0144141	−	0.358858i
$927$	−6.24216	+	4.53519i	−0.205019	+	0.148955i
$928$	−28.2461	−	30.8259i	−0.927222	−	1.01191i
$929$	17.9487	+	55.2405i	0.588878	+	1.81238i	0.583104	+	0.812398i	$0.301838\pi$
$929$	17.9487	+	55.2405i	0.588878	+	1.81238i	0.00577421	+	0.999983i	$0.498162\pi$
$930$	14.7509	+	22.1182i	0.483702	+	0.725284i
$931$	−19.0677	+	26.2444i	−0.624919	+	0.860127i
$932$	−8.37130	+	20.1105i	−0.274211	+	0.658740i
$933$	14.6951	+	4.77474i	0.481097	+	0.156318i
$934$	−10.9884	−	39.0928i	−0.359551	−	1.27915i
$935$		0			0
$936$	−8.20101	−	7.62096i	−0.268058	−	0.249099i
$937$	−11.9841	+	36.8833i	−0.391503	+	1.20492i	0.540148	+	0.841570i	$0.318368\pi$
$937$	−11.9841	+	36.8833i	−0.391503	+	1.20492i	−0.931651	+	0.363354i	$0.881632\pi$
$938$	−6.29789	−	4.97380i	−0.205633	−	0.162400i
$939$	−1.58374	+	2.17983i	−0.0516834	+	0.0711360i
$940$	22.3579	−	26.0852i	0.729235	−	0.850804i
$941$	−50.0578	+	16.2648i	−1.63184	+	0.530217i	−0.974693	−	0.223547i	$-0.928237\pi$
$941$	−50.0578	+	16.2648i	−1.63184	+	0.530217i	−0.657146	+	0.753763i	$0.728237\pi$
$942$	−26.6217	−	9.84776i	−0.867383	−	0.320857i
$943$	−24.3882	+	17.7191i	−0.794189	+	0.577012i
$944$	−16.0128	+	15.9011i	−0.521173	+	0.517536i
$945$	−77.2891			−2.51421
$946$		0			0
$947$		−	29.9348i		−	0.972750i	−0.873750	−	0.486375i	$-0.838319\pi$
$947$		−	29.9348i		−	0.972750i	0.873750	−	0.486375i	$-0.161681\pi$
$948$	9.14602	−	2.17884i	0.297049	−	0.0707655i
$949$	−26.1084	−	35.9351i	−0.847514	−	1.16650i
$950$	15.5676	−	42.0844i	0.505080	−	1.36540i
$951$	−0.833878	−	2.56641i	−0.0270403	−	0.0832216i
$952$	−15.7576	−	7.31460i	−0.510708	−	0.237067i
$953$	−36.0936	−	26.2236i	−1.16919	−	0.849465i	−0.178276	−	0.983980i	$-0.557052\pi$
$953$	−36.0936	−	26.2236i	−1.16919	−	0.849465i	−0.990911	+	0.134516i	$0.957052\pi$
$954$	3.83219	+	3.02649i	0.124072	+	0.0979863i
$955$	−40.8427	−	13.2706i	−1.32164	−	0.429427i
$956$	39.4421	−	24.0753i	1.27565	−	0.778650i
$957$		0			0
$958$	−5.24264	+	1.47363i	−0.169382	+	0.0476107i
$959$	3.56986	−	10.9869i	0.115277	−	0.354785i
$960$	−27.0707	−	32.0349i	−0.873704	−	1.03392i
$961$	14.6773	+	10.6637i	0.473461	+	0.343990i
$962$	−2.28841	−	3.43135i	−0.0737813	−	0.110631i
$963$	−5.67694	+	1.84455i	−0.182937	+	0.0594398i
$964$	−58.7796	−	4.72959i	−1.89316	−	0.152330i
$965$	6.67088	+	9.18168i	0.214743	+	0.295569i
$966$	−26.0015	−	1.04439i	−0.836585	−	0.0336028i
$967$	−33.9962			−1.09325			−0.546623	−	0.837379i	$-0.684087\pi$
$967$	−33.9962			−1.09325			−0.546623	+	0.837379i	$0.684087\pi$
$968$		0			0
$969$	−9.74012			−0.312898
$970$	−86.1773	−	3.46145i	−2.76699	−	0.111141i
$971$	−14.4278	−	19.8581i	−0.463009	−	0.637277i	0.512121	−	0.858914i	$-0.328860\pi$
$971$	−14.4278	−	19.8581i	−0.463009	−	0.637277i	−0.975129	+	0.221637i	$0.928860\pi$
$972$	1.33717	−	16.6185i	0.0428898	−	0.533037i
$973$	−31.0322	+	10.0830i	−0.994848	+	0.323246i
$974$	−27.3844	−	41.0614i	−0.877454	−	1.31569i
$975$	43.6147	+	31.6880i	1.39679	+	1.01483i
$976$	8.55722	−	1.32464i	0.273910	−	0.0424007i
$977$	−18.6380	+	57.3617i	−0.596281	+	1.83516i	−0.0480386	+	0.998845i	$0.515297\pi$
$977$	−18.6380	+	57.3617i	−0.596281	+	1.83516i	−0.548243	+	0.836319i	$0.684703\pi$
$978$	−40.3764	+	11.3492i	−1.29110	+	0.362907i
$979$		0			0
$980$	29.0208	+	47.5443i	0.927036	+	1.51875i
$981$	−3.41119	−	1.10836i	−0.108911	−	0.0353873i
$982$	26.0160	+	20.5463i	0.830203	+	0.655658i
$983$	−35.3766	−	25.7026i	−1.12834	−	0.819787i	−0.142887	−	0.989739i	$-0.545639\pi$
$983$	−35.3766	−	25.7026i	−1.12834	−	0.819787i	−0.985452	+	0.169952i	$0.945639\pi$
$984$	16.3148	−	35.1465i	0.520096	−	1.12043i
$985$	17.2368	+	53.0494i	0.549210	+	1.69030i
$986$	−5.78421	+	15.6366i	−0.184207	+	0.497972i
$987$	16.1049	+	22.1665i	0.512626	+	0.705569i
$988$	9.17656	+	38.5200i	0.291945	+	1.22548i
$989$			9.92724i			0.315668i
$990$		0			0
$991$	−39.4558			−1.25336			−0.626678	−	0.779278i	$-0.715586\pi$
$991$	−39.4558			−1.25336			−0.626678	+	0.779278i	$0.715586\pi$
$992$	17.6544	+	9.98867i	0.560528	+	0.317141i
$993$	15.2087	−	11.0498i	0.482634	−	0.350654i
$994$	−53.1912	−	19.6762i	−1.68712	−	0.624091i
$995$	−56.9394	+	18.5007i	−1.80510	+	0.586512i
$996$	−28.2344	−	24.2000i	−0.894641	−	0.766808i
$997$	−7.15273	+	9.84488i	−0.226529	+	0.311791i	−0.907119	−	0.420874i	$-0.861724\pi$
$997$	−7.15273	+	9.84488i	−0.226529	+	0.311791i	0.680590	+	0.732664i	$0.261724\pi$
$998$	−35.4195	−	27.9728i	−1.12119	−	0.885463i
$999$	1.06415	−	3.27511i	0.0336681	−	0.103620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.c.493.5		32
8.5	even	2	inner	968.2.o.c.493.7		32
11.2	odd	10	inner	968.2.o.c.245.6		32
11.3	even	5	inner	968.2.o.c.565.2		32
11.4	even	5		968.2.c.c.485.7	yes	8
11.5	even	5	inner	968.2.o.c.269.7		32
11.6	odd	10	inner	968.2.o.c.269.2		32
11.7	odd	10		968.2.c.c.485.2	yes	8
11.8	odd	10	inner	968.2.o.c.565.7		32
11.9	even	5	inner	968.2.o.c.245.3		32
11.10	odd	2	inner	968.2.o.c.493.4		32
44.7	even	10		3872.2.c.c.1937.4		8
44.15	odd	10		3872.2.c.c.1937.3		8
88.5	even	10	inner	968.2.o.c.269.5		32
88.13	odd	10	inner	968.2.o.c.245.7		32
88.21	odd	2	inner	968.2.o.c.493.2		32
88.29	odd	10		968.2.c.c.485.1	✓	8
88.37	even	10		968.2.c.c.485.8	yes	8
88.51	even	10		3872.2.c.c.1937.6		8
88.53	even	10	inner	968.2.o.c.245.2		32
88.59	odd	10		3872.2.c.c.1937.5		8
88.61	odd	10	inner	968.2.o.c.269.4		32
88.69	even	10	inner	968.2.o.c.565.3		32
88.85	odd	10	inner	968.2.o.c.565.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.2.c.c.485.1	✓	8	88.29	odd	10
968.2.c.c.485.2	yes	8	11.7	odd	10
968.2.c.c.485.7	yes	8	11.4	even	5
968.2.c.c.485.8	yes	8	88.37	even	10
968.2.o.c.245.2		32	88.53	even	10	inner
968.2.o.c.245.3		32	11.9	even	5	inner
968.2.o.c.245.6		32	11.2	odd	10	inner
968.2.o.c.245.7		32	88.13	odd	10	inner
968.2.o.c.269.2		32	11.6	odd	10	inner
968.2.o.c.269.4		32	88.61	odd	10	inner
968.2.o.c.269.5		32	88.5	even	10	inner
968.2.o.c.269.7		32	11.5	even	5	inner
968.2.o.c.493.2		32	88.21	odd	2	inner
968.2.o.c.493.4		32	11.10	odd	2	inner
968.2.o.c.493.5		32	1.1	even	1	trivial
968.2.o.c.493.7		32	8.5	even	2	inner
968.2.o.c.565.2		32	11.3	even	5	inner
968.2.o.c.565.3		32	88.69	even	10	inner
968.2.o.c.565.6		32	88.85	odd	10	inner
968.2.o.c.565.7		32	11.8	odd	10	inner
3872.2.c.c.1937.3		8	44.15	odd	10
3872.2.c.c.1937.4		8	44.7	even	10
3872.2.c.c.1937.5		8	88.59	odd	10
3872.2.c.c.1937.6		8	88.51	even	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0567584 - 1.41307i) q^{2} +(-0.866175 - 1.19219i) q^{3} +(-1.99356 - 0.160408i) q^{4} +(-3.38352 + 1.09937i) q^{5} +(-1.73381 + 1.15630i) q^{6} +(-3.11534 - 2.26343i) q^{7} +(-0.339819 + 2.80794i) q^{8} +(0.255998 - 0.787881i) q^{9} +(1.36145 + 4.84357i) q^{10} +(1.53553 + 2.51564i) q^{12} +(-4.54406 - 1.47646i) q^{13} +(-3.37521 + 4.27374i) q^{14} +(4.24139 + 3.08155i) q^{15} +(3.94854 + 0.639564i) q^{16} +(-0.492895 - 1.51697i) q^{17} +(-1.09880 - 0.406463i) q^{18} +(2.43570 + 3.35245i) q^{19} +(6.92160 - 1.64892i) q^{20} +5.67459i q^{21} -3.24264 q^{23} +(3.64194 - 2.02704i) q^{24} +(6.19453 - 4.50059i) q^{25} +(-2.34425 + 6.33730i) q^{26} +(-5.36555 + 1.74337i) q^{27} +(5.84753 + 5.01199i) q^{28} +(4.34434 - 5.97947i) q^{29} +(4.59519 - 5.81849i) q^{30} +(-1.10807 + 3.41029i) q^{31} +(1.12786 - 5.54328i) q^{32} +(-2.17157 + 0.610396i) q^{34} +(13.0292 + 4.23343i) q^{35} +(-0.636729 + 1.52962i) q^{36} +(-0.358782 + 0.493821i) q^{37} +(4.87551 - 3.25154i) q^{38} +(2.17574 + 6.69625i) q^{39} +(-1.93719 - 9.87432i) q^{40} +(7.52109 - 5.46439i) q^{41} +(8.01862 + 0.322081i) q^{42} -3.06147i q^{43} +2.94725i q^{45} +(-0.184047 + 4.58209i) q^{46} +(3.90628 - 2.83808i) q^{47} +(-2.65765 - 5.26138i) q^{48} +(2.41912 + 7.44528i) q^{49} +(-6.00807 - 9.00877i) q^{50} +(-1.38159 + 1.90159i) q^{51} +(8.82201 + 3.67230i) q^{52} +(-3.96404 - 1.28800i) q^{53} +(2.15897 + 7.68087i) q^{54} +(7.41421 - 7.97852i) q^{56} +(1.88701 - 5.80763i) q^{57} +(-8.20286 - 6.47826i) q^{58} +(-3.31609 + 4.56421i) q^{59} +(-7.96114 - 6.82359i) q^{60} +(2.05883 - 0.668955i) q^{61} +(4.75609 + 1.75935i) q^{62} +(-2.58083 + 1.87508i) q^{63} +(-7.76905 - 1.90838i) q^{64} +16.9981 q^{65} +1.47363i q^{67} +(0.739279 + 3.10324i) q^{68} +(2.80870 + 3.86584i) q^{69} +(6.72167 - 18.1709i) q^{70} +(3.21817 + 9.90451i) q^{71} +(2.12533 + 0.986564i) q^{72} +(7.52109 + 5.46439i) q^{73} +(0.677441 + 0.535014i) q^{74} +(-10.7311 - 3.48674i) q^{75} +(-4.31795 - 7.07401i) q^{76} +(9.58579 - 2.69442i) q^{78} +(0.985790 - 3.03395i) q^{79} +(-14.0631 + 2.17694i) q^{80} +(4.71530 + 3.42586i) q^{81} +(-7.29471 - 10.9380i) q^{82} +(-11.9998 + 3.89896i) q^{83} +(0.910249 - 11.3126i) q^{84} +(3.33544 + 4.59084i) q^{85} +(-4.32608 - 0.173764i) q^{86} -10.8916 q^{87} -10.6569 q^{89} +(4.16468 + 0.167281i) q^{90} +(10.8144 + 14.8848i) q^{91} +(6.46439 + 0.520145i) q^{92} +(5.02548 - 1.63288i) q^{93} +(-3.78870 - 5.68095i) q^{94} +(-11.9268 - 8.66536i) q^{95} +(-7.58556 + 3.45682i) q^{96} +(-5.29721 + 16.3031i) q^{97} +(10.6580 - 2.99581i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{4} + 16 q^{9} - 64 q^{12} - 8 q^{14} + 8 q^{15} + 8 q^{16} - 24 q^{20} + 32 q^{23} + 16 q^{25} - 8 q^{26} + 40 q^{31} - 160 q^{34} + 24 q^{38} - 40 q^{42} + 16 q^{47} - 8 q^{48} - 40 q^{49}+ \cdots + 24 q^{97}+O(q^{100}) \) 32 * q - 8 * q^4 + 16 * q^9 - 64 * q^12 - 8 * q^14 + 8 * q^15 + 8 * q^16 - 24 * q^20 + 32 * q^23 + 16 * q^25 - 8 * q^26 + 40 * q^31 - 160 * q^34 + 24 * q^38 - 40 * q^42 + 16 * q^47 - 8 * q^48 - 40 * q^49 + 192 * q^56 + 32 * q^60 + 16 * q^64 - 8 * q^70 - 72 * q^71 + 352 * q^78 - 56 * q^80 + 24 * q^81 + 56 * q^82 + 32 * q^86 - 160 * q^89 + 16 * q^92 + 24 * q^97

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