LMFDB - Embedded newform 1089.2.e.o.364.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, 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:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			364.11
Character	$\chi$	$=$	1089.364
Dual form			1089.2.e.o.727.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.288906 + 0.500400i) q^{2} +(-1.33220 + 1.10691i) q^{3} +(0.833067 - 1.44291i) q^{4} +(-1.50221 + 2.60191i) q^{5} +(-0.938776 - 0.346842i) q^{6} +(-0.582160 - 1.00833i) q^{7} +2.11834 q^{8} +(0.549521 - 2.94924i) q^{9} -1.73599 q^{10} +(0.487356 + 2.84438i) q^{12} +(-1.97309 + 3.41748i) q^{13} +(0.336379 - 0.582626i) q^{14} +(-0.878818 - 5.12908i) q^{15} +(-1.05413 - 1.82581i) q^{16} +0.314191 q^{17} +(1.63456 - 0.577073i) q^{18} -6.36839 q^{19} +(2.50289 + 4.33513i) q^{20} +(1.89168 + 0.698904i) q^{21} +(0.0427501 - 0.0740453i) q^{23} +(-2.82205 + 2.34480i) q^{24} +(-2.01329 - 3.48713i) q^{25} -2.28015 q^{26} +(2.53246 + 4.53725i) q^{27} -1.93991 q^{28} +(-3.84991 - 6.66824i) q^{29} +(2.31269 - 1.92158i) q^{30} +(-3.26442 + 5.65414i) q^{31} +(2.72743 - 4.72404i) q^{32} +(0.0907715 + 0.157221i) q^{34} +3.49812 q^{35} +(-3.79771 - 3.24983i) q^{36} -6.24309 q^{37} +(-1.83987 - 3.18674i) q^{38} +(-1.15428 - 6.73680i) q^{39} +(-3.18219 + 5.51172i) q^{40} +(2.90454 - 5.03080i) q^{41} +(0.196787 + 1.14851i) q^{42} +(-3.39229 - 5.87562i) q^{43} +(6.84817 + 5.86020i) q^{45} +0.0494030 q^{46} +(0.163868 + 0.283827i) q^{47} +(3.42532 + 1.26552i) q^{48} +(2.82218 - 4.88816i) q^{49} +(1.16331 - 2.01490i) q^{50} +(-0.418565 + 0.347779i) q^{51} +(3.28742 + 5.69398i) q^{52} -2.42269 q^{53} +(-1.53880 + 2.57808i) q^{54} +(-1.23321 - 2.13598i) q^{56} +(8.48398 - 7.04920i) q^{57} +(2.22452 - 3.85299i) q^{58} +(1.14802 - 1.98842i) q^{59} +(-8.13293 - 3.00481i) q^{60} +(-6.84360 - 11.8535i) q^{61} -3.77244 q^{62} +(-3.29372 + 1.16283i) q^{63} -1.06465 q^{64} +(-5.92799 - 10.2676i) q^{65} +(-5.83989 + 10.1150i) q^{67} +(0.261742 - 0.453350i) q^{68} +(0.0250094 + 0.145964i) q^{69} +(1.01063 + 1.75046i) q^{70} +8.71765 q^{71} +(1.16407 - 6.24749i) q^{72} -2.94656 q^{73} +(-1.80367 - 3.12404i) q^{74} +(6.54203 + 2.41703i) q^{75} +(-5.30529 + 9.18904i) q^{76} +(3.03761 - 2.52391i) q^{78} +(-4.44360 - 7.69654i) q^{79} +6.33413 q^{80} +(-8.39605 - 3.24134i) q^{81} +3.35655 q^{82} +(2.47889 + 4.29357i) q^{83} +(2.58435 - 2.14730i) q^{84} +(-0.471981 + 0.817496i) q^{85} +(1.96011 - 3.39500i) q^{86} +(12.5100 + 4.62195i) q^{87} +2.12862 q^{89} +(-0.953966 + 5.11987i) q^{90} +4.59461 q^{91} +(-0.0712273 - 0.123369i) q^{92} +(-1.90973 - 11.1459i) q^{93} +(-0.0946848 + 0.163999i) q^{94} +(9.56668 - 16.5700i) q^{95} +(1.59559 + 9.31238i) q^{96} +(0.0444196 + 0.0769370i) q^{97} +3.26138 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} + 3 q^{13} - 5 q^{15} + 8 q^{16} + 40 q^{17} - 17 q^{18} + 6 q^{19} + 5 q^{20} + 8 q^{21} + 10 q^{23}+ \cdots + 164 q^{98}+O(q^{100}) $ 36 * q - 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 + q^6 + q^7 + 12 * q^8 - q^9 + 4 * q^10 - 8 * q^12 + 3 * q^13 - 5 * q^15 + 8 * q^16 + 40 * q^17 - 17 * q^18 + 6 * q^19 + 5 * q^20 + 8 * q^21 + 10 * q^23 + 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 - 38 * q^28 - 21 * q^29 - 12 * q^30 - 6 * q^31 - 9 * q^32 + 4 * q^34 + 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 - 42 * q^39 - 20 * q^41 + 18 * q^42 + 4 * q^43 + 20 * q^45 - 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 - 25 * q^50 + 4 * q^51 - 19 * q^52 + 62 * q^53 - 17 * q^54 + 57 * q^56 + 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 - 16 * q^61 + 38 * q^62 - 5 * q^63 - 32 * q^64 - 42 * q^65 + 5 * q^67 - 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 - 51 * q^72 - 9 * q^74 - 16 * q^75 - 8 * q^76 - 32 * q^78 - 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 - 36 * q^83 - 60 * q^84 + 25 * q^85 - 26 * q^86 + 60 * q^87 - 28 * q^89 - 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 + 4 * q^94 - 64 * q^95 + 21 * q^96 + 16 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.288906	+	0.500400i	0.204287	+	0.353836i	0.949905	−	0.312537i	$-0.101179\pi$
$2$	0.288906	+	0.500400i	0.204287	+	0.353836i	−0.745618	+	0.666374i	$0.767846\pi$
$3$	−1.33220	+	1.10691i	−0.769147	+	0.639072i
$3$	−1.33220	+	1.10691i	−0.769147	+	0.639072i
$4$	0.833067	−	1.44291i	0.416533	−	0.721457i
$5$	−1.50221	+	2.60191i	−0.671810	+	1.16361i	0.305580	+	0.952166i	$0.401150\pi$
$5$	−1.50221	+	2.60191i	−0.671810	+	1.16361i	−0.977390	+	0.211443i	$0.932184\pi$
$6$	−0.938776	−	0.346842i	−0.383254	−	0.141598i
$7$	−0.582160	−	1.00833i	−0.220036	−	0.381113i	0.734783	−	0.678303i	$-0.237284\pi$
$7$	−0.582160	−	1.00833i	−0.220036	−	0.381113i	−0.954819	+	0.297189i	$0.903951\pi$
$8$	2.11834			0.748945
$9$	0.549521	−	2.94924i	0.183174	−	0.983081i
$10$	−1.73599			−0.548970
$11$		0			0
$11$		0			0
$12$	0.487356	+	2.84438i	0.140688	+	0.821101i
$13$	−1.97309	+	3.41748i	−0.547236	+	0.947840i	0.451227	+	0.892409i	$0.350986\pi$
$13$	−1.97309	+	3.41748i	−0.547236	+	0.947840i	−0.998463	+	0.0554305i	$0.982347\pi$
$14$	0.336379	−	0.582626i	0.0899011	−	0.155713i
$15$	−0.878818	−	5.12908i	−0.226910	−	1.32432i
$16$	−1.05413	−	1.82581i	−0.263533	−	0.456453i
$17$	0.314191			0.0762024			0.0381012	−	0.999274i	$-0.487869\pi$
$17$	0.314191			0.0762024			0.0381012	+	0.999274i	$0.487869\pi$
$18$	1.63456	−	0.577073i	0.385270	−	0.136018i
$19$	−6.36839			−1.46101			−0.730504	−	0.682908i	$-0.760715\pi$
$19$	−6.36839			−1.46101			−0.730504	+	0.682908i	$0.760715\pi$
$20$	2.50289	+	4.33513i	0.559663	+	0.969365i
$21$	1.89168	+	0.698904i	0.412799	+	0.152513i
$22$		0			0
$23$	0.0427501	−	0.0740453i	0.00891401	−	0.0154395i	−0.861534	−	0.507700i	$-0.830496\pi$
$23$	0.0427501	−	0.0740453i	0.00891401	−	0.0154395i	0.870448	+	0.492260i	$0.163829\pi$
$24$	−2.82205	+	2.34480i	−0.576049	+	0.478630i
$25$	−2.01329	−	3.48713i	−0.402659	−	0.697425i
$26$	−2.28015			−0.447173
$27$	2.53246	+	4.53725i	0.487372	+	0.873195i
$28$	−1.93991			−0.366609
$29$	−3.84991	−	6.66824i	−0.714910	−	1.23826i	−0.962994	−	0.269522i	$-0.913134\pi$
$29$	−3.84991	−	6.66824i	−0.714910	−	1.23826i	0.248084	−	0.968739i	$-0.420199\pi$
$30$	2.31269	−	1.92158i	0.422238	−	0.350831i
$31$	−3.26442	+	5.65414i	−0.586307	+	1.01551i	0.408404	+	0.912801i	$0.366085\pi$
$31$	−3.26442	+	5.65414i	−0.586307	+	1.01551i	−0.994711	+	0.102712i	$0.967248\pi$
$32$	2.72743	−	4.72404i	0.482146	−	0.835101i
$33$		0			0
$34$	0.0907715	+	0.157221i	0.0155672	+	0.0269632i
$35$	3.49812			0.591290
$36$	−3.79771	−	3.24983i	−0.632952	−	0.541638i
$37$	−6.24309			−1.02636			−0.513179	−	0.858282i	$-0.671532\pi$
$37$	−6.24309			−1.02636			−0.513179	+	0.858282i	$0.671532\pi$
$38$	−1.83987	−	3.18674i	−0.298466	−	0.516958i
$39$	−1.15428	−	6.73680i	−0.184833	−	1.07875i
$40$	−3.18219	+	5.51172i	−0.503149	+	0.871480i
$41$	2.90454	−	5.03080i	0.453612	−	0.785679i	−0.544995	−	0.838439i	$-0.683468\pi$
$41$	2.90454	−	5.03080i	0.453612	−	0.785679i	0.998607	+	0.0527599i	$0.0168018\pi$
$42$	0.196787	+	1.14851i	0.0303649	+	0.177220i
$43$	−3.39229	−	5.87562i	−0.517320	−	0.896024i	−0.999798	−	0.0201157i	$-0.993597\pi$
$43$	−3.39229	−	5.87562i	−0.517320	−	0.896024i	0.482478	−	0.875908i	$-0.339737\pi$
$44$		0			0
$45$	6.84817	+	5.86020i	1.02086	+	0.873587i
$46$	0.0494030			0.00728408
$47$	0.163868	+	0.283827i	0.0239026	+	0.0414005i	0.877729	−	0.479157i	$-0.159058\pi$
$47$	0.163868	+	0.283827i	0.0239026	+	0.0414005i	−0.853827	+	0.520557i	$0.825724\pi$
$48$	3.42532	+	1.26552i	0.494402	+	0.182663i
$49$	2.82218	−	4.88816i	0.403168	−	0.698308i
$50$	1.16331	−	2.01490i	0.164516	−	0.284950i
$51$	−0.418565	+	0.347779i	−0.0586108	+	0.0486988i
$52$	3.28742	+	5.69398i	0.455884	+	0.789614i
$53$	−2.42269			−0.332782			−0.166391	−	0.986060i	$-0.553211\pi$
$53$	−2.42269			−0.332782			−0.166391	+	0.986060i	$0.553211\pi$
$54$	−1.53880	+	2.57808i	−0.209404	+	0.350832i
$55$		0			0
$56$	−1.23321	−	2.13598i	−0.164795	−	0.285433i
$57$	8.48398	−	7.04920i	1.12373	−	0.933690i
$58$	2.22452	−	3.85299i	0.292094	−	0.505922i
$59$	1.14802	−	1.98842i	0.149459	−	0.258870i	−0.781569	−	0.623819i	$-0.785580\pi$
$59$	1.14802	−	1.98842i	0.149459	−	0.258870i	0.931028	+	0.364949i	$0.118913\pi$
$60$	−8.13293	−	3.00481i	−1.04996	−	0.387919i
$61$	−6.84360	−	11.8535i	−0.876233	−	1.51768i	−0.855443	−	0.517897i	$-0.826715\pi$
$61$	−6.84360	−	11.8535i	−0.876233	−	1.51768i	−0.0207900	−	0.999784i	$-0.506618\pi$
$62$	−3.77244			−0.479100
$63$	−3.29372	+	1.16283i	−0.414970	+	0.146503i
$64$	−1.06465			−0.133081
$65$	−5.92799	−	10.2676i	−0.735277	−	1.27354i
$66$		0			0
$67$	−5.83989	+	10.1150i	−0.713456	+	1.23574i	0.250096	+	0.968221i	$0.419538\pi$
$67$	−5.83989	+	10.1150i	−0.713456	+	1.23574i	−0.963552	+	0.267521i	$0.913795\pi$
$68$	0.261742	−	0.453350i	0.0317408	−	0.0549767i
$69$	0.0250094	+	0.145964i	0.00301078	+	0.0175719i
$70$	1.01063	+	1.75046i	0.120793	+	0.209220i
$71$	8.71765			1.03459			0.517297	−	0.855806i	$-0.326938\pi$
$71$	8.71765			1.03459			0.517297	+	0.855806i	$0.326938\pi$
$72$	1.16407	−	6.24749i	0.137187	−	0.736273i
$73$	−2.94656			−0.344869			−0.172434	−	0.985021i	$-0.555163\pi$
$73$	−2.94656			−0.344869			−0.172434	+	0.985021i	$0.555163\pi$
$74$	−1.80367	−	3.12404i	−0.209672	−	0.363162i
$75$	6.54203	+	2.41703i	0.755409	+	0.279095i
$76$	−5.30529	+	9.18904i	−0.608559	+	1.05405i
$77$		0			0
$78$	3.03761	−	2.52391i	0.343942	−	0.285776i
$79$	−4.44360	−	7.69654i	−0.499944	−	0.865928i	0.500056	−	0.865993i	$-0.333313\pi$
$79$	−4.44360	−	7.69654i	−0.499944	−	0.865928i	−1.00000		6.50093e-5i	$0.999979\pi$
$80$	6.33413			0.708178
$81$	−8.39605	−	3.24134i	−0.932895	−	0.360149i
$82$	3.35655			0.370669
$83$	2.47889	+	4.29357i	0.272094	+	0.471280i	0.969398	−	0.245495i	$-0.0789506\pi$
$83$	2.47889	+	4.29357i	0.272094	+	0.471280i	−0.697304	+	0.716775i	$0.745617\pi$
$84$	2.58435	−	2.14730i	0.281976	−	0.234290i
$85$	−0.471981	+	0.817496i	−0.0511936	+	0.0886699i
$86$	1.96011	−	3.39500i	0.211364	−	0.366093i
$87$	12.5100	+	4.62195i	1.34121	+	0.495525i
$88$		0			0
$89$	2.12862			0.225634			0.112817	−	0.993616i	$-0.464013\pi$
$89$	2.12862			0.225634			0.112817	+	0.993616i	$0.464013\pi$
$90$	−0.953966	+	5.11987i	−0.100557	+	0.539681i
$91$	4.59461			0.481646
$92$	−0.0712273	−	0.123369i	−0.00742596	−	0.0128621i
$93$	−1.90973	−	11.1459i	−0.198030	−	1.15577i
$94$	−0.0946848	+	0.163999i	−0.00976599	+	0.0169152i
$95$	9.56668	−	16.5700i	0.981521	−	1.70004i
$96$	1.59559	+	9.31238i	0.162849	+	0.950441i
$97$	0.0444196	+	0.0769370i	0.00451013	+	0.00781177i	0.868272	−	0.496089i	$-0.165231\pi$
$97$	0.0444196	+	0.0769370i	0.00451013	+	0.00781177i	−0.863762	+	0.503901i	$0.831898\pi$
$98$	3.26138			0.329449
$99$		0			0
$100$	−6.70883			−0.670883
$101$	−1.02824	−	1.78097i	−0.102314	−	0.177213i	0.810324	−	0.585983i	$-0.199291\pi$
$101$	−1.02824	−	1.78097i	−0.102314	−	0.177213i	−0.912638	+	0.408770i	$0.865958\pi$
$102$	−0.294955	−	0.108974i	−0.0292049	−	0.0107901i
$103$	1.50836	−	2.61255i	0.148623	−	0.257422i	−0.782096	−	0.623158i	$-0.785849\pi$
$103$	1.50836	−	2.61255i	0.148623	−	0.257422i	0.930719	+	0.365736i	$0.119183\pi$
$104$	−4.17966	+	7.23938i	−0.409849	+	0.709880i
$105$	−4.66020	+	3.87208i	−0.454788	+	0.377877i
$106$	−0.699931	−	1.21232i	−0.0679833	−	0.117750i
$107$	−11.9929			−1.15939			−0.579697	−	0.814832i	$-0.696829\pi$
$107$	−11.9929			−1.15939			−0.579697	+	0.814832i	$0.696829\pi$
$108$	8.65657	+	0.125714i	0.832979	+	0.0120968i
$109$	−5.20013			−0.498082			−0.249041	−	0.968493i	$-0.580115\pi$
$109$	−5.20013			−0.498082			−0.249041	+	0.968493i	$0.580115\pi$
$110$		0			0
$111$	8.31705	−	6.91051i	0.789420	−	0.655916i
$112$	−1.22735	+	2.12583i	−0.115974	+	0.200872i
$113$	−9.61378	+	16.6515i	−0.904388	+	1.56645i	−0.0826514	+	0.996579i	$0.526339\pi$
$113$	−9.61378	+	16.6515i	−0.904388	+	1.56645i	−0.821737	+	0.569867i	$0.806995\pi$
$114$	5.97849	+	2.20882i	0.559937	+	0.206875i
$115$	0.128440	+	0.222464i	0.0119770	+	0.0207449i
$116$	−12.8289			−1.19114
$117$	8.99474	+	7.69709i	0.831564	+	0.711596i
$118$	1.32667			0.122130
$119$	−0.182909	−	0.316808i	−0.0167673	−	0.0290417i
$120$	−1.86163	−	10.8651i	−0.169943	−	0.991844i
$121$		0			0
$122$	3.95432	−	6.84907i	0.358007	−	0.620086i
$123$	1.69920	+	9.91709i	0.153211	+	0.894194i
$124$	5.43896	+	9.42055i	0.488433	+	0.845990i
$125$	−2.92455			−0.261580
$126$	−1.53346	−	1.31223i	−0.136611	−	0.116903i
$127$	13.1829			1.16980			0.584898	−	0.811107i	$-0.301135\pi$
$127$	13.1829			1.16980			0.584898	+	0.811107i	$0.301135\pi$
$128$	−5.76244	−	9.98084i	−0.509332	−	0.882190i
$129$	11.0230	+	4.07256i	0.970518	+	0.358569i
$130$	3.42527	−	5.93274i	0.300416	−	0.520335i
$131$	−8.98588	+	15.5640i	−0.785100	+	1.35983i	0.143839	+	0.989601i	$0.454055\pi$
$131$	−8.98588	+	15.5640i	−0.785100	+	1.35983i	−0.928939	+	0.370233i	$0.879278\pi$
$132$		0			0
$133$	3.70742	+	6.42144i	0.321474	+	0.556810i
$134$	−6.74872			−0.583001
$135$	−15.6098	−	0.226691i	−1.34348	−	0.0195105i
$136$	0.665561			0.0570714
$137$	8.20087	+	14.2043i	0.700648	+	1.21356i	0.968239	+	0.250025i	$0.0804388\pi$
$137$	8.20087	+	14.2043i	0.700648	+	1.21356i	−0.267592	+	0.963532i	$0.586228\pi$
$138$	−0.0658148	+	0.0546845i	−0.00560253	+	0.00465505i
$139$	−5.95080	+	10.3071i	−0.504740	+	0.874236i	0.495245	+	0.868754i	$0.335078\pi$
$139$	−5.95080	+	10.3071i	−0.504740	+	0.874236i	−0.999985	+	0.00548243i	$0.998255\pi$
$140$	2.91416	−	5.04748i	0.246292	−	0.426590i
$141$	−0.532475	−	0.196729i	−0.0448425	−	0.0165676i
$142$	2.51858	+	4.36231i	0.211355	+	0.366077i
$143$		0			0
$144$	−5.96403	+	2.10557i	−0.497002	+	0.175464i
$145$	23.1336			1.92114
$146$	−0.851279	−	1.47446i	−0.0704524	−	0.122027i
$147$	1.65102	+	9.63590i	0.136174	+	0.794755i
$148$	−5.20091	+	9.00824i	−0.427512	+	0.740473i
$149$	−2.26586	+	3.92458i	−0.185626	+	0.321514i	−0.943787	−	0.330553i	$-0.892765\pi$
$149$	−2.26586	+	3.92458i	−0.185626	+	0.321514i	0.758161	+	0.652067i	$0.226098\pi$
$150$	0.680551	+	3.97193i	0.0555667	+	0.324306i
$151$	−1.46543	−	2.53820i	−0.119255	−	0.206556i	0.800218	−	0.599710i	$-0.204717\pi$
$151$	−1.46543	−	2.53820i	−0.119255	−	0.206556i	−0.919473	+	0.393154i	$0.871384\pi$
$152$	−13.4904			−1.09422
$153$	0.172654	−	0.926624i	0.0139583	−	0.0749131i
$154$		0			0
$155$	−9.80771	−	16.9874i	−0.787774	−	1.36446i
$156$	−10.6822	−	3.94667i	−0.855261	−	0.315986i
$157$	9.02682	−	15.6349i	0.720419	−	1.24780i	−0.240413	−	0.970671i	$-0.577283\pi$
$157$	9.02682	−	15.6349i	0.720419	−	1.24780i	0.960832	−	0.277131i	$-0.0893837\pi$
$158$	2.56756	−	4.44715i	0.204264	−	0.353796i
$159$	3.22752	−	2.68169i	0.255959	−	0.212672i
$160$	8.19436	+	14.1930i	0.647821	+	1.12206i
$161$	−0.0995496			−0.00784561
$162$	−0.803704	−	5.13783i	−0.0631449	−	0.403666i
$163$	−5.82347			−0.456130			−0.228065	−	0.973646i	$-0.573240\pi$
$163$	−5.82347			−0.456130			−0.228065	+	0.973646i	$0.573240\pi$
$164$	−4.83934	−	8.38199i	−0.377889	−	0.654523i
$165$		0			0
$166$	−1.43233	+	2.48087i	−0.111171	+	0.192553i
$167$	−2.51086	+	4.34894i	−0.194296	+	0.336531i	−0.946670	−	0.322206i	$-0.895576\pi$
$167$	−2.51086	+	4.34894i	−0.194296	+	0.336531i	0.752373	+	0.658737i	$0.228909\pi$
$168$	4.00722	+	1.48051i	0.309163	+	0.114224i
$169$	−1.28613	−	2.22765i	−0.0989334	−	0.171358i
$170$	−0.545433			−0.0418328
$171$	−3.49956	+	18.7819i	−0.267618	+	1.43629i
$172$	−11.3040			−0.861923
$173$	−7.79493	−	13.5012i	−0.592638	−	1.02648i	−0.993876	−	0.110505i	$-0.964753\pi$
$173$	−7.79493	−	13.5012i	−0.592638	−	1.02648i	0.401238	−	0.915974i	$-0.368580\pi$
$174$	1.30138	+	7.59530i	0.0986574	+	0.575798i
$175$	−2.34412	+	4.06013i	−0.177199	+	0.306917i
$176$		0			0
$177$	0.671606	+	3.91972i	0.0504810	+	0.294624i
$178$	0.614972	+	1.06516i	0.0460941	+	0.0798373i
$179$	7.04887			0.526857			0.263428	−	0.964679i	$-0.415147\pi$
$179$	7.04887			0.526857			0.263428	+	0.964679i	$0.415147\pi$
$180$	14.1607	−	4.99938i	1.05548	−	0.372632i
$181$	2.49770			0.185652			0.0928262	−	0.995682i	$-0.470410\pi$
$181$	2.49770			0.185652			0.0928262	+	0.995682i	$0.470410\pi$
$182$	1.32741	+	2.29914i	0.0983942	+	0.170424i
$183$	22.2377	+	8.21598i	1.64386	+	0.607343i
$184$	0.0905590	−	0.156853i	0.00667610	−	0.0115633i
$185$	9.37845	−	16.2440i	0.689518	−	1.19428i
$186$	5.02565	−	4.17573i	0.368499	−	0.306180i
$187$		0			0
$188$	0.546051			0.0398249
$189$	3.10075	−	5.19496i	0.225547	−	0.377878i
$190$	11.0555			0.802050
$191$	5.91149	+	10.2390i	0.427740	+	0.740868i	0.996672	−	0.0815168i	$-0.0259764\pi$
$191$	5.91149	+	10.2390i	0.427740	+	0.740868i	−0.568932	+	0.822385i	$0.692643\pi$
$192$	1.41833	−	1.17847i	0.102359	−	0.0850486i
$193$	3.37333	−	5.84278i	0.242817	−	0.420572i	−0.718698	−	0.695322i	$-0.755262\pi$
$193$	3.37333	−	5.84278i	0.242817	−	0.420572i	0.961516	+	0.274750i	$0.0885951\pi$
$194$	−0.0256662	+	0.0444551i	−0.00184272	+	0.00319169i
$195$	19.2625	+	7.11676i	1.37942	+	0.509642i
$196$	−4.70213	−	8.14432i	−0.335866	−	0.581737i
$197$	20.6474			1.47107			0.735534	−	0.677488i	$-0.236931\pi$
$197$	20.6474			1.47107			0.735534	+	0.677488i	$0.236931\pi$
$198$		0			0
$199$	−13.2862			−0.941832			−0.470916	−	0.882178i	$-0.656077\pi$
$199$	−13.2862			−0.941832			−0.470916	+	0.882178i	$0.656077\pi$
$200$	−4.26483	−	7.38691i	−0.301569	−	0.522333i
$201$	−3.41642	−	19.9394i	−0.240976	−	1.40642i
$202$	0.594131	−	1.02906i	0.0418029	−	0.0724047i
$203$	−4.48253	+	7.76397i	−0.314612	+	0.544924i
$204$	0.153123	+	0.893676i	0.0107207	+	0.0625699i
$205$	8.72647	+	15.1147i	0.609483	+	1.05566i
$206$	1.74309			0.121447
$207$	−0.194885	−	0.166770i	−0.0135455	−	0.0115913i
$208$	8.31958			0.576859
$209$		0			0
$210$	−3.28395	−	1.21329i	−0.226614	−	0.0837252i
$211$	−4.17251	+	7.22700i	−0.287247	+	0.497527i	−0.973152	−	0.230165i	$-0.926074\pi$
$211$	−4.17251	+	7.22700i	−0.287247	+	0.497527i	0.685904	+	0.727692i	$0.259407\pi$
$212$	−2.01826	+	3.49574i	−0.138615	+	0.240088i
$213$	−11.6137	+	9.64961i	−0.795755	+	0.661180i
$214$	−3.46481	−	6.00123i	−0.236850	−	0.410235i
$215$	20.3838			1.39016
$216$	5.36460	+	9.61142i	0.365015	+	0.653975i
$217$	7.60166			0.516034
$218$	−1.50235	−	2.60214i	−0.101752	−	0.176239i
$219$	3.92541	−	3.26156i	0.265255	−	0.220396i
$220$		0			0
$221$	−0.619925	+	1.07374i	−0.0417007	+	0.0722277i
$222$	5.86086	+	2.16536i	0.393355	+	0.145330i
$223$	0.191828	+	0.332255i	0.0128457	+	0.0222495i	0.872377	−	0.488834i	$-0.162578\pi$
$223$	0.191828	+	0.332255i	0.0128457	+	0.0222495i	−0.859531	+	0.511083i	$0.829244\pi$
$224$	−6.35120			−0.424357
$225$	−11.3907	+	4.02144i	−0.759382	+	0.268096i
$226$	−11.1099			−0.739020
$227$	9.00701	+	15.6006i	0.597817	+	1.03545i	0.993143	+	0.116908i	$0.0372982\pi$
$227$	9.00701	+	15.6006i	0.597817	+	1.03545i	−0.395326	+	0.918541i	$0.629368\pi$
$228$	−3.10368	−	18.1141i	−0.205546	−	1.19964i
$229$	−6.71393	+	11.6289i	−0.443669	+	0.768458i	−0.997958	−	0.0638664i	$-0.979657\pi$
$229$	−6.71393	+	11.6289i	−0.443669	+	0.768458i	0.554289	+	0.832324i	$0.312990\pi$
$230$	−0.0742139	+	0.128542i	−0.00489352	+	0.00847583i
$231$		0			0
$232$	−8.15540	−	14.1256i	−0.535428	−	0.927389i
$233$	3.36965			0.220753			0.110377	−	0.993890i	$-0.464794\pi$
$233$	3.36965			0.220753			0.110377	+	0.993890i	$0.464794\pi$
$234$	−1.25299	+	6.72470i	−0.0819104	+	0.439607i
$235$	−0.984658			−0.0642320
$236$	−1.91275	−	3.31298i	−0.124509	−	0.215656i
$237$	14.4391	+	5.33469i	0.937920	+	0.346526i
$238$	0.105687	−	0.183056i	0.00685068	−	0.0118657i
$239$	−11.5984	+	20.0890i	−0.750238	+	1.29945i	0.197469	+	0.980309i	$0.436728\pi$
$239$	−11.5984	+	20.0890i	−0.750238	+	1.29945i	−0.947707	+	0.319141i	$0.896606\pi$
$240$	−8.43834	+	7.01129i	−0.544693	+	0.452577i
$241$	7.58206	+	13.1325i	0.488404	+	0.845940i	0.999911	−	0.0133389i	$-0.00424604\pi$
$241$	7.58206	+	13.1325i	0.488404	+	0.845940i	−0.511507	+	0.859279i	$0.670913\pi$
$242$		0			0
$243$	14.7731	−	4.97552i	0.947694	−	0.319180i
$244$	−22.8047			−1.45992
$245$	8.47903	+	14.6861i	0.541706	+	0.938262i
$246$	−4.47160	+	3.71538i	−0.285099	+	0.236884i
$247$	12.5654	−	21.7639i	0.799516	−	1.38480i
$248$	−6.91513	+	11.9774i	−0.439111	+	0.760563i
$249$	−8.05495	−	2.97600i	−0.510462	−	0.188596i
$250$	−0.844920	−	1.46344i	−0.0534375	−	0.0925564i
$251$	−0.582306			−0.0367548			−0.0183774	−	0.999831i	$-0.505850\pi$
$251$	−0.582306			−0.0367548			−0.0183774	+	0.999831i	$0.505850\pi$
$252$	−1.06602	+	5.72127i	−0.0671531	+	0.360406i
$253$		0			0
$254$	3.80863	+	6.59673i	0.238974	+	0.413916i
$255$	−0.276116	−	1.61151i	−0.0172911	−	0.100917i
$256$	2.26495	−	3.92302i	0.141560	−	0.245189i
$257$	5.48571	−	9.50153i	0.342189	−	0.592689i	−0.642650	−	0.766160i	$-0.722165\pi$
$257$	5.48571	−	9.50153i	0.342189	−	0.592689i	0.984839	+	0.173471i	$0.0554983\pi$
$258$	1.14669	+	6.69248i	0.0713899	+	0.416656i
$259$	3.63448	+	6.29510i	0.225835	+	0.391158i
$260$	−19.7537			−1.22507
$261$	−21.7819	+	7.68998i	−1.34826	+	0.475998i
$262$	−10.3843			−0.641544
$263$	−7.19768	−	12.4668i	−0.443828	−	0.768733i	0.554142	−	0.832422i	$-0.313047\pi$
$263$	−7.19768	−	12.4668i	−0.443828	−	0.768733i	−0.997970	+	0.0636896i	$0.979713\pi$
$264$		0			0
$265$	3.63940	−	6.30363i	0.223567	−	0.387229i
$266$	−2.14219	+	3.71039i	−0.131346	+	0.227498i
$267$	−2.83575	+	2.35618i	−0.173545	+	0.144196i
$268$	9.73004	+	16.8529i	0.594357	+	1.02946i
$269$	0.488976			0.0298134			0.0149067	−	0.999889i	$-0.495255\pi$
$269$	0.488976			0.0298134			0.0149067	+	0.999889i	$0.495255\pi$
$270$	−4.39633	−	7.87665i	−0.267552	−	0.479357i
$271$	−21.9389			−1.33270			−0.666348	−	0.745641i	$-0.732143\pi$
$271$	−21.9389			−1.33270			−0.666348	+	0.745641i	$0.732143\pi$
$272$	−0.331199	−	0.573653i	−0.0200819	−	0.0347828i
$273$	−6.12094	+	5.08580i	−0.370456	+	0.307806i
$274$	−4.73856	+	8.20743i	−0.286267	+	0.495829i
$275$		0			0
$276$	0.231447	+	0.0855109i	0.0139315	+	0.00514715i
$277$	1.43476	+	2.48508i	0.0862065	+	0.149314i	0.905905	−	0.423482i	$-0.139192\pi$
$277$	1.43476	+	2.48508i	0.0862065	+	0.149314i	−0.819698	+	0.572796i	$0.805859\pi$
$278$	−6.87689			−0.412448
$279$	14.8816	+	12.7346i	0.890935	+	0.762402i
$280$	7.41019			0.442843
$281$	9.08903	+	15.7427i	0.542206	+	0.939129i	0.998777	+	0.0494416i	$0.0157442\pi$
$281$	9.08903	+	15.7427i	0.542206	+	0.939129i	−0.456571	+	0.889687i	$0.650922\pi$
$282$	−0.0553920	−	0.323287i	−0.00329855	−	0.0192514i
$283$	−10.2686	+	17.7857i	−0.610402	+	1.05725i	0.380770	+	0.924670i	$0.375659\pi$
$283$	−10.2686	+	17.7857i	−0.610402	+	1.05725i	−0.991173	+	0.132578i	$0.957674\pi$
$284$	7.26238	−	12.5788i	0.430943	−	0.746415i
$285$	5.59665	+	32.6640i	0.331517	+	1.93485i
$286$		0			0
$287$	−6.76362			−0.399244
$288$	−12.4336	−	10.6398i	−0.732655	−	0.626956i
$289$	−16.9013			−0.994193
$290$	6.68342	+	11.5760i	0.392464	+	0.679768i
$291$	−0.144338	−	0.0533273i	−0.00846124	−	0.00312610i
$292$	−2.45468	+	4.25163i	−0.143649	+	0.248808i
$293$	0.430033	−	0.744840i	0.0251228	−	0.0435140i	−0.853191	−	0.521599i	$-0.825336\pi$
$293$	0.430033	−	0.744840i	0.0251228	−	0.0435140i	0.878313	+	0.478085i	$0.158669\pi$
$294$	−4.34481	+	3.61004i	−0.253395	+	0.210542i
$295$	3.44913	+	5.97407i	0.200816	+	0.347824i
$296$	−13.2250			−0.768685
$297$		0			0
$298$	−2.61848			−0.151684
$299$	0.168699	+	0.292196i	0.00975612	+	0.0168981i
$300$	8.93751	−	7.42604i	0.516007	−	0.428743i
$301$	−3.94971	+	6.84110i	−0.227658	+	0.394315i
$302$	0.846744	−	1.46660i	0.0487247	−	0.0843936i
$303$	3.34119	+	1.23444i	0.191946	+	0.0709167i
$304$	6.71313	+	11.6275i	0.385024	+	0.666882i
$305$	41.1222			2.35465
$306$	0.513563	−	0.181311i	0.0293585	−	0.0103649i
$307$	−3.48920			−0.199139			−0.0995696	−	0.995031i	$-0.531747\pi$
$307$	−3.48920			−0.199139			−0.0995696	+	0.995031i	$0.531747\pi$
$308$		0			0
$309$	0.882412	+	5.15005i	0.0501986	+	0.292976i
$310$	5.66701	−	9.81555i	0.321865	−	0.557486i
$311$	−5.42265	+	9.39231i	−0.307490	+	0.532589i	−0.977813	−	0.209481i	$-0.932822\pi$
$311$	−5.42265	+	9.39231i	−0.307490	+	0.532589i	0.670322	+	0.742070i	$0.266156\pi$
$312$	−2.44516	−	14.2708i	−0.138430	−	0.807925i
$313$	14.1405	+	24.4921i	0.799270	+	1.38438i	0.920092	+	0.391702i	$0.128114\pi$
$313$	14.1405	+	24.4921i	0.799270	+	1.38438i	−0.120822	+	0.992674i	$0.538553\pi$
$314$	10.4316			0.588690
$315$	1.92229	−	10.3168i	0.108309	−	0.581285i
$316$	−14.8072			−0.832973
$317$	0.556263	+	0.963477i	0.0312429	+	0.0541142i	0.881224	−	0.472699i	$-0.156720\pi$
$317$	0.556263	+	0.963477i	0.0312429	+	0.0541142i	−0.849981	+	0.526813i	$0.823387\pi$
$318$	2.27437	+	0.840291i	0.127540	+	0.0471212i
$319$		0			0
$320$	1.59933	−	2.77013i	0.0894055	−	0.154855i
$321$	15.9769	−	13.2750i	0.891744	−	0.740936i
$322$	−0.0287605	−	0.0498146i	−0.00160276	−	0.00277606i
$323$	−2.00089			−0.111332
$324$	−11.6714	+	9.41453i	−0.648414	+	0.523029i
$325$	15.8896			0.881396
$326$	−1.68244	−	2.91407i	−0.0931816	−	0.161395i
$327$	6.92762	−	5.75605i	0.383098	−	0.318310i
$328$	6.15278	−	10.6569i	0.339731	−	0.588431i
$329$	0.190795	−	0.330466i	0.0105188	−	0.0182192i
$330$		0			0
$331$	6.18915	+	10.7199i	0.340187	+	0.589221i	0.984467	−	0.175569i	$-0.0561764\pi$
$331$	6.18915	+	10.7199i	0.340187	+	0.589221i	−0.644281	+	0.764789i	$0.722843\pi$
$332$	8.26033			0.453344
$333$	−3.43071	+	18.4124i	−0.188002	+	1.00899i
$334$	−2.90161			−0.158769
$335$	−17.5455	−	30.3897i	−0.958615	−	1.66037i
$336$	−0.718017	−	4.19059i	−0.0391710	−	0.228616i
$337$	6.73681	−	11.6685i	0.366977	−	0.635623i	−0.622114	−	0.782927i	$-0.713726\pi$
$337$	6.73681	−	11.6685i	0.366977	−	0.635623i	0.989091	+	0.147303i	$0.0470593\pi$
$338$	0.743144	−	1.28716i	0.0404217	−	0.0700124i
$339$	−5.62420	−	32.8248i	−0.305465	−	1.78280i
$340$	0.786384	+	1.36206i	0.0426477	+	0.0738679i
$341$		0			0
$342$	−10.4095	+	3.67503i	−0.562882	+	0.198723i
$343$	−14.7221			−0.794918
$344$	−7.18601	−	12.4465i	−0.387444	−	0.671072i
$345$	−0.417354	−	0.154196i	−0.0224696	−	0.00830164i
$346$	4.50400	−	7.80117i	0.242137	−	0.419393i
$347$	4.86958	−	8.43437i	0.261413	−	0.452781i	−0.705205	−	0.709004i	$-0.749145\pi$
$347$	4.86958	−	8.43437i	0.261413	−	0.452781i	0.966618	+	0.256223i	$0.0824782\pi$
$348$	17.0907	−	14.2004i	0.916158	−	0.761222i
$349$	−2.22010	−	3.84532i	−0.118839	−	0.205835i	0.800469	−	0.599374i	$-0.204584\pi$
$349$	−2.22010	−	3.84532i	−0.118839	−	0.205835i	−0.919308	+	0.393539i	$0.871251\pi$
$350$	−2.70892			−0.144798
$351$	−20.5027	−	0.297748i	−1.09436	−	0.0158926i
$352$		0			0
$353$	−16.2618	−	28.1662i	−0.865527	−	1.49914i	−0.866523	−	0.499137i	$-0.833651\pi$
$353$	−16.2618	−	28.1662i	−0.865527	−	1.49914i	0.000996749	−	1.00000i	$-0.499683\pi$
$354$	−1.76740	+	1.46850i	−0.0939361	+	0.0780501i
$355$	−13.0958	+	22.6825i	−0.695051	+	1.20386i
$356$	1.77328	−	3.07142i	0.0939839	−	0.162785i
$357$	0.594348	+	0.219589i	0.0314563	+	0.0116219i
$358$	2.03646	+	3.52725i	0.107630	+	0.186421i
$359$	27.7701			1.46565			0.732825	−	0.680417i	$-0.238201\pi$
$359$	27.7701			1.46565			0.732825	+	0.680417i	$0.238201\pi$
$360$	14.5067	+	12.4139i	0.764571	+	0.654268i
$361$	21.5564			1.13455
$362$	0.721600	+	1.24985i	0.0379264	+	0.0656905i
$363$		0			0
$364$	3.82761	−	6.62962i	0.200621	−	0.347487i
$365$	4.42637	−	7.66669i	0.231687	−	0.401293i
$366$	2.31333	+	13.5014i	0.120920	+	0.705729i
$367$	−0.586098	−	1.01515i	−0.0305941	−	0.0529905i	0.850323	−	0.526261i	$-0.176407\pi$
$367$	−0.586098	−	1.01515i	−0.0305941	−	0.0529905i	−0.880917	+	0.473271i	$0.843073\pi$
$368$	−0.180257			−0.00939655
$369$	−13.2409	−	11.3307i	−0.689296	−	0.589853i
$370$	10.8380			0.563439
$371$	1.41040	+	2.44288i	0.0732241	+	0.126828i
$372$	−17.6734	−	6.52966i	−0.916325	−	0.338547i
$373$	10.8834	−	18.8506i	0.563520	−	0.976046i	−0.433665	−	0.901074i	$-0.642780\pi$
$373$	10.8834	−	18.8506i	0.563520	−	0.976046i	0.997186	−	0.0749719i	$-0.0238867\pi$
$374$		0			0
$375$	3.89609	−	3.23720i	0.201193	−	0.167168i
$376$	0.347127	+	0.601242i	0.0179017	+	0.0310067i
$377$	30.3848			1.56490
$378$	3.49539	+	0.0507612i	0.179783	+	0.00261087i
$379$	−16.2469			−0.834545			−0.417273	−	0.908781i	$-0.637014\pi$
$379$	−16.2469			−0.834545			−0.417273	+	0.908781i	$0.637014\pi$
$380$	−15.9394	−	27.6078i	−0.817672	−	1.41625i
$381$	−17.5623	+	14.5922i	−0.899744	+	0.747584i
$382$	−3.41573	+	5.91622i	−0.174764	+	0.302700i
$383$	−3.09667	+	5.36360i	−0.158233	+	0.274067i	−0.934231	−	0.356667i	$-0.883913\pi$
$383$	−3.09667	+	5.36360i	−0.158233	+	0.274067i	0.775999	+	0.630734i	$0.217246\pi$
$384$	18.7246	+	6.91801i	0.955534	+	0.353033i
$385$		0			0
$386$	3.89830			0.198418
$387$	−19.1928	+	6.77591i	−0.975623	+	0.344439i
$388$	0.148018			0.00751447
$389$	0.361607	+	0.626321i	0.0183342	+	0.0317557i	0.875047	−	0.484038i	$-0.160830\pi$
$389$	0.361607	+	0.626321i	0.0183342	+	0.0317557i	−0.856713	+	0.515794i	$0.827497\pi$
$390$	2.00383	+	11.6950i	0.101468	+	0.592202i
$391$	0.0134317	−	0.0232643i	0.000679269	−	0.00117653i
$392$	5.97832	−	10.3548i	0.301951	−	0.522994i
$393$	−5.25688	−	30.6809i	−0.265174	−	1.54765i
$394$	5.96517	+	10.3320i	0.300521	+	0.520517i
$395$	26.7009			1.34347
$396$		0			0
$397$	4.08994			0.205268			0.102634	−	0.994719i	$-0.467273\pi$
$397$	4.08994			0.205268			0.102634	+	0.994719i	$0.467273\pi$
$398$	−3.83846	−	6.64840i	−0.192404	−	0.333254i
$399$	−12.0470	−	4.45089i	−0.603103	−	0.222823i
$400$	−4.24456	+	7.35179i	−0.212228	+	0.367590i
$401$	2.82313	−	4.88981i	0.140981	−	0.244185i	−0.786886	−	0.617099i	$-0.788308\pi$
$401$	2.82313	−	4.88981i	0.140981	−	0.244185i	0.927866	+	0.372913i	$0.121641\pi$
$402$	8.99065	−	7.47019i	0.448413	−	0.372579i
$403$	−12.8820	−	22.3122i	−0.641696	−	1.11145i
$404$	−3.42638			−0.170469
$405$	21.0463	−	16.9766i	1.04580	−	0.843574i
$406$	−5.18012			−0.257085
$407$		0			0
$408$	−0.886662	+	0.736713i	−0.0438963	+	0.0364727i
$409$	4.72439	−	8.18288i	0.233606	−	0.404617i	−0.725261	−	0.688474i	$-0.758281\pi$
$409$	4.72439	−	8.18288i	0.233606	−	0.404617i	0.958867	+	0.283857i	$0.0916141\pi$
$410$	−5.04226	+	8.73345i	−0.249019	+	0.431314i
$411$	−26.6481	−	9.84543i	−1.31445	−	0.485639i
$412$	−2.51312	−	4.35286i	−0.123813	−	0.214450i
$413$	−2.67332			−0.131545
$414$	0.0271480	−	0.145701i	0.00133425	−	0.00716084i
$415$	−14.8953			−0.731182
$416$	10.7629	+	18.6419i	0.527694	+	0.913993i
$417$	−3.48131	−	20.3181i	−0.170480	−	0.994981i
$418$		0			0
$419$	−0.0757820	+	0.131258i	−0.00370219	+	0.00641238i	−0.867871	−	0.496790i	$-0.834512\pi$
$419$	−0.0757820	+	0.131258i	−0.00370219	+	0.00641238i	0.864168	+	0.503203i	$0.167845\pi$
$420$	1.70483	+	9.94996i	0.0831871	+	0.485508i
$421$	−8.48828	−	14.7021i	−0.413693	−	0.716538i	0.581597	−	0.813477i	$-0.302428\pi$
$421$	−8.48828	−	14.7021i	−0.413693	−	0.716538i	−0.995290	+	0.0969391i	$0.969095\pi$
$422$	−4.82185			−0.234724
$423$	0.927124	−	0.327317i	0.0450783	−	0.0159147i
$424$	−5.13208			−0.249236
$425$	−0.632558	−	1.09562i	−0.0306836	−	0.0531455i
$426$	−8.18392	−	3.02364i	−0.396512	−	0.146496i
$427$	−7.96814	+	13.8012i	−0.385605	+	0.667888i
$428$	−9.99085	+	17.3047i	−0.482926	+	0.836453i
$429$		0			0
$430$	5.88900	+	10.2000i	0.283993	+	0.491890i
$431$	25.3694			1.22200			0.610999	−	0.791631i	$-0.290768\pi$
$431$	25.3694			1.22200			0.610999	+	0.791631i	$0.290768\pi$
$432$	5.61462	−	9.40666i	0.270134	−	0.452578i
$433$	16.5347			0.794607			0.397303	−	0.917687i	$-0.369946\pi$
$433$	16.5347			0.794607			0.397303	+	0.917687i	$0.369946\pi$
$434$	2.19616	+	3.80387i	0.105419	+	0.182592i
$435$	−30.8185	+	25.6067i	−1.47764	+	1.22774i
$436$	−4.33205	+	7.50333i	−0.207468	+	0.359344i
$437$	−0.272249	+	0.471549i	−0.0130234	+	0.0225573i
$438$	2.76616	+	1.02199i	0.132172	+	0.0488326i
$439$	−19.6207	−	33.9840i	−0.936443	−	1.62197i	−0.772040	−	0.635574i	$-0.780763\pi$
$439$	−19.6207	−	33.9840i	−0.936443	−	1.62197i	−0.164403	−	0.986393i	$-0.552570\pi$
$440$		0			0
$441$	−12.8655	−	11.0094i	−0.612643	−	0.524259i
$442$	−0.716400			−0.0340757
$443$	−16.0947	−	27.8768i	−0.764681	−	1.32447i	−0.940415	−	0.340029i	$-0.889563\pi$
$443$	−16.0947	−	27.8768i	−0.764681	−	1.32447i	0.175734	−	0.984438i	$-0.443770\pi$
$444$	−3.04261	−	17.7577i	−0.144396	−	0.842743i
$445$	−3.19765	+	5.53849i	−0.151583	+	0.262549i
$446$	−0.110840	+	0.191981i	−0.00524845	+	0.00909057i
$447$	−1.32556	−	7.73642i	−0.0626969	−	0.365920i
$448$	0.619798	+	1.07352i	0.0292827	+	0.0507191i
$449$	−25.8443			−1.21967			−0.609833	−	0.792530i	$-0.708764\pi$
$449$	−25.8443			−1.21967			−0.609833	+	0.792530i	$0.708764\pi$
$450$	−5.30318	−	4.53810i	−0.249994	−	0.213928i
$451$		0			0
$452$	16.0178	+	27.7437i	0.753415	+	1.30495i
$453$	4.76180	+	1.75930i	0.223729	+	0.0826592i
$454$	−5.20436	+	9.01422i	−0.244253	+	0.423058i
$455$	−6.90208	+	11.9548i	−0.323575	+	0.560448i
$456$	17.9719	−	14.9326i	0.841612	−	0.699282i
$457$	−6.35814	−	11.0126i	−0.297421	−	0.515149i	0.678124	−	0.734947i	$-0.262793\pi$
$457$	−6.35814	−	11.0126i	−0.297421	−	0.515149i	−0.975545	+	0.219799i	$0.929460\pi$
$458$	−7.75879			−0.362544
$459$	0.795675	+	1.42556i	0.0371389	+	0.0665395i
$460$	0.427995			0.0199554
$461$	−9.51087	−	16.4733i	−0.442965	−	0.767238i	0.554943	−	0.831889i	$-0.312740\pi$
$461$	−9.51087	−	16.4733i	−0.442965	−	0.767238i	−0.997908	+	0.0646502i	$0.979407\pi$
$462$		0			0
$463$	11.4334	−	19.8032i	0.531353	−	0.920331i	−0.467977	−	0.883741i	$-0.655017\pi$
$463$	11.4334	−	19.8032i	0.531353	−	0.920331i	0.999330	−	0.0365903i	$-0.0116497\pi$
$464$	−8.11663	+	14.0584i	−0.376805	+	0.652646i
$465$	31.8693	+	11.7745i	1.47791	+	0.546029i
$466$	0.973513	+	1.68617i	0.0450971	+	0.0781105i
$467$	15.9228			0.736821			0.368411	−	0.929663i	$-0.379902\pi$
$467$	15.9228			0.736821			0.368411	+	0.929663i	$0.379902\pi$
$468$	18.5994	−	6.56644i	0.859760	−	0.303534i
$469$	13.5990			0.627944
$470$	−0.284474	−	0.492723i	−0.0131218	−	0.0227276i
$471$	5.28082	+	30.8207i	0.243328	+	1.42014i
$472$	2.43188	−	4.21215i	0.111936	−	0.193880i
$473$		0			0
$474$	1.50206	+	8.76655i	0.0689920	+	0.402661i
$475$	12.8214	+	22.2074i	0.588288	+	1.01894i
$476$	−0.609502			−0.0279365
$477$	−1.33132	+	7.14511i	−0.0609570	+	0.327152i
$478$	−13.4034			−0.613057
$479$	−8.19498	−	14.1941i	−0.374438	−	0.648546i	0.615805	−	0.787899i	$-0.288831\pi$
$479$	−8.19498	−	14.1941i	−0.374438	−	0.648546i	−0.990243	+	0.139353i	$0.955498\pi$
$480$	−26.6269	−	9.83761i	−1.21535	−	0.449024i
$481$	12.3181	−	21.3357i	0.561659	−	0.972822i
$482$	−4.38101	+	7.58813i	−0.199549	+	0.345630i
$483$	0.132620	−	0.110192i	0.00603442	−	0.00501391i
$484$		0			0
$485$	−0.266911			−0.0121198
$486$	6.75778	+	5.95500i	0.306539	+	0.270124i
$487$	22.7865			1.03256			0.516278	−	0.856421i	$-0.327317\pi$
$487$	22.7865			1.03256			0.516278	+	0.856421i	$0.327317\pi$
$488$	−14.4970	−	25.1096i	−0.656250	−	1.13666i
$489$	7.75804	−	6.44603i	0.350831	−	0.291500i
$490$	−4.89929	+	8.48582i	−0.221327	+	0.383350i
$491$	−21.8215	+	37.7960i	−0.984791	+	1.70571i	−0.341928	+	0.939726i	$0.611080\pi$
$491$	−21.8215	+	37.7960i	−0.984791	+	1.70571i	−0.642863	+	0.765981i	$0.722253\pi$
$492$	15.7250	+	5.80980i	0.708940	+	0.261926i
$493$	−1.20961	−	2.09510i	−0.0544779	−	0.0943585i
$494$	14.5209			0.653324
$495$		0			0
$496$	13.7645			0.618045
$497$	−5.07507	−	8.79027i	−0.227648	−	0.394298i
$498$	−0.837937	−	4.89048i	−0.0375488	−	0.219148i
$499$	10.0518	−	17.4102i	0.449978	−	0.779385i	−0.548406	−	0.836212i	$-0.684765\pi$
$499$	10.0518	−	17.4102i	0.449978	−	0.779385i	0.998384	+	0.0568270i	$0.0180983\pi$
$500$	−2.43635	+	4.21987i	−0.108957	+	0.188718i
$501$	−1.46889	−	8.57296i	−0.0656253	−	0.383011i
$502$	−0.168232	−	0.291386i	−0.00750854	−	0.0130052i
$503$	10.6083			0.473001			0.236500	−	0.971631i	$-0.424000\pi$
$503$	10.6083			0.473001			0.236500	+	0.971631i	$0.424000\pi$
$504$	−6.97721	+	2.46327i	−0.310790	+	0.109723i
$505$	6.17856			0.274942
$506$		0			0
$507$	4.17919	+	1.54405i	0.185604	+	0.0685736i
$508$	10.9823	−	19.0218i	0.487259	−	0.843957i
$509$	22.2342	−	38.5107i	0.985513	−	1.70696i	0.345878	−	0.938280i	$-0.387581\pi$
$509$	22.2342	−	38.5107i	0.985513	−	1.70696i	0.639635	−	0.768679i	$-0.279086\pi$
$510$	0.726627	−	0.603743i	0.0321756	−	0.0267342i
$511$	1.71537	+	2.97111i	0.0758835	+	0.131434i
$512$	−20.4323			−0.902989
$513$	−16.1277	−	28.8950i	−0.712055	−	1.27574i
$514$	6.33942			0.279620
$515$	4.53175	+	7.84922i	0.199693	+	0.345878i
$516$	15.0592	−	12.5125i	0.662946	−	0.550831i
$517$		0			0
$518$	−2.10004	+	3.63738i	−0.0922707	+	0.159817i
$519$	25.3290	+	9.35809i	1.11182	+	0.410774i
$520$	−12.5575	−	21.7502i	−0.550682	−	0.953809i
$521$	16.9511			0.742643			0.371322	−	0.928504i	$-0.378905\pi$
$521$	16.9511			0.742643			0.371322	+	0.928504i	$0.378905\pi$
$522$	−10.1410	−	8.67796i	−0.443858	−	0.379824i
$523$	−30.2142			−1.32117			−0.660587	−	0.750749i	$-0.729693\pi$
$523$	−30.2142			−1.32117			−0.660587	+	0.750749i	$0.729693\pi$
$524$	14.9717	+	25.9317i	0.654041	+	1.13283i
$525$	−1.37134	−	8.00363i	−0.0598504	−	0.349307i
$526$	4.15891	−	7.20344i	0.181337	−	0.314085i
$527$	−1.02565	+	1.77648i	−0.0446780	+	0.0773845i
$528$		0			0
$529$	11.4963	+	19.9123i	0.499841	+	0.865750i
$530$	4.20578			0.182688
$531$	−5.23348	−	4.47846i	−0.227114	−	0.194348i
$532$	12.3541			0.535619
$533$	11.4618	+	19.8524i	0.496465	+	0.859903i
$534$	−1.99830	−	0.738296i	−0.0864750	−	0.0319492i
$535$	18.0158	−	31.2044i	0.778893	−	1.34908i
$536$	−12.3709	+	21.4269i	−0.534339	+	0.925503i
$537$	−9.39051	+	7.80243i	−0.405230	+	0.336700i
$538$	0.141268	+	0.244683i	0.00609050	+	0.0105491i
$539$		0			0
$540$	−13.3311	+	22.3348i	−0.573680	+	0.961136i
$541$	−11.8312			−0.508663			−0.254332	−	0.967117i	$-0.581855\pi$
$541$	−11.8312			−0.508663			−0.254332	+	0.967117i	$0.581855\pi$
$542$	−6.33829	−	10.9782i	−0.272253	−	0.471556i
$543$	−3.32744	+	2.76471i	−0.142794	+	0.118645i
$544$	0.856932	−	1.48425i	0.0367406	−	0.0636367i
$545$	7.81170	−	13.5303i	0.334617	−	0.579573i
$546$	−4.31331	−	1.59360i	−0.184593	−	0.0681999i
$547$	1.27290	+	2.20474i	0.0544255	+	0.0942677i	0.891955	−	0.452125i	$-0.149334\pi$
$547$	1.27290	+	2.20474i	0.0544255	+	0.0942677i	−0.837529	+	0.546393i	$0.816001\pi$
$548$	27.3275			1.16737
$549$	−38.7194	+	13.6697i	−1.65251	+	0.583409i
$550$		0			0
$551$	24.5177	+	42.4659i	1.04449	+	1.80911i
$552$	0.0529784	+	0.309200i	0.00225491	+	0.0131604i
$553$	−5.17377	+	8.96123i	−0.220011	+	0.381070i
$554$	−0.829023	+	1.43591i	−0.0352218	+	0.0610060i
$555$	5.48654	+	32.0213i	0.232890	+	1.35923i
$556$	9.91483	+	17.1730i	0.420482	+	0.728297i
$557$	−9.67543			−0.409961			−0.204981	−	0.978766i	$-0.565713\pi$
$557$	−9.67543			−0.409961			−0.204981	+	0.978766i	$0.565713\pi$
$558$	−2.07304	+	11.1258i	−0.0877586	+	0.470994i
$559$	26.7731			1.13238
$560$	−3.68748	−	6.38690i	−0.155824	−	0.269896i
$561$		0			0
$562$	−5.25175	+	9.09630i	−0.221532	+	0.383704i
$563$	−11.9936	+	20.7735i	−0.505470	+	0.875501i	0.494510	+	0.869172i	$0.335348\pi$
$563$	−11.9936	+	20.7735i	−0.505470	+	0.875501i	−0.999980	+	0.00632830i	$0.997986\pi$
$564$	−0.727450	+	0.604427i	−0.0306312	+	0.0254510i
$565$	−28.8839	−	50.0284i	−1.21515	−	2.10471i
$566$	−11.8666			−0.498790
$567$	1.61950	+	10.3530i	0.0680127	+	0.434784i
$568$	18.4669			0.774854
$569$	−18.8096	−	32.5791i	−0.788538	−	1.36579i	−0.926863	−	0.375401i	$-0.877505\pi$
$569$	−18.8096	−	32.5791i	−0.788538	−	1.36579i	0.138325	−	0.990387i	$-0.455828\pi$
$570$	−14.7281	+	12.2374i	−0.616894	+	0.512568i
$571$	−7.37740	+	12.7780i	−0.308735	+	0.534744i	−0.978086	−	0.208202i	$-0.933239\pi$
$571$	−7.37740	+	12.7780i	−0.308735	+	0.534744i	0.669351	+	0.742946i	$0.266572\pi$
$572$		0			0
$573$	−19.2089	−	7.09695i	−0.802463	−	0.296479i
$574$	−1.95405	−	3.38451i	−0.0815605	−	0.141267i
$575$	−0.344274			−0.0143572
$576$	−0.585049	+	3.13992i	−0.0243770	+	0.130830i
$577$	−22.3068			−0.928644			−0.464322	−	0.885667i	$-0.653702\pi$
$577$	−22.3068			−0.928644			−0.464322	+	0.885667i	$0.653702\pi$
$578$	−4.88288	−	8.45740i	−0.203101	−	0.351782i
$579$	1.97345	+	11.5177i	0.0820137	+	0.478660i
$580$	19.2718	−	33.3797i	0.800217	−	1.38602i
$581$	2.88622	−	4.99909i	0.119741	−	0.207397i
$582$	−0.0150151	−	0.0876332i	−0.000622396	−	0.00363251i
$583$		0			0
$584$	−6.24181			−0.258288
$585$	−33.5391	+	11.8408i	−1.38667	+	0.489558i
$586$	0.496957			0.0205291
$587$	1.25008	+	2.16521i	0.0515965	+	0.0893677i	0.890670	−	0.454650i	$-0.150236\pi$
$587$	1.25008	+	2.16521i	0.0515965	+	0.0893677i	−0.839074	+	0.544018i	$0.816902\pi$
$588$	15.2792	+	5.64507i	0.630102	+	0.232799i
$589$	20.7891	−	36.0078i	0.856599	−	1.48367i
$590$	−1.99295	+	3.45189i	−0.0820484	+	0.142112i
$591$	−27.5065	+	22.8547i	−1.13147	+	0.940119i
$592$	6.58105	+	11.3987i	0.270479	+	0.468484i
$593$	10.8953			0.447417			0.223708	−	0.974656i	$-0.428184\pi$
$593$	10.8953			0.447417			0.223708	+	0.974656i	$0.428184\pi$
$594$		0			0
$595$	1.09907			0.0450577
$596$	3.77522	+	6.53887i	0.154639	+	0.267843i
$597$	17.6999	−	14.7065i	0.724407	−	0.601899i
$598$	−0.0974764	+	0.168834i	−0.00398611	+	0.00690414i
$599$	18.4190	−	31.9027i	0.752582	−	1.30351i	−0.193986	−	0.981004i	$-0.562142\pi$
$599$	18.4190	−	31.9027i	0.752582	−	1.30351i	0.946568	−	0.322506i	$-0.104525\pi$
$600$	13.8582	+	5.12008i	0.565759	+	0.209026i
$601$	−7.72714	−	13.3838i	−0.315197	−	0.545937i	0.664283	−	0.747482i	$-0.268737\pi$
$601$	−7.72714	−	13.3838i	−0.315197	−	0.545937i	−0.979479	+	0.201545i	$0.935404\pi$
$602$	−4.56438			−0.186030
$603$	26.6224	+	22.7816i	1.08415	+	0.927740i
$604$	−4.88321			−0.198695
$605$		0			0
$606$	0.347575	+	2.02857i	0.0141193	+	0.0824049i
$607$	−12.7385	+	22.0636i	−0.517038	+	0.895536i	0.482766	+	0.875749i	$0.339632\pi$
$607$	−12.7385	+	22.0636i	−0.517038	+	0.895536i	−0.999804	+	0.0197865i	$0.993701\pi$
$608$	−17.3693	+	30.0845i	−0.704419	+	1.22009i
$609$	−2.62235	−	15.3049i	−0.106263	−	0.620186i
$610$	11.8805	+	20.5776i	0.481026	+	0.833161i
$611$	−1.29330			−0.0523214
$612$	−1.19321	−	1.02106i	−0.0482325	−	0.0412741i
$613$	37.7740			1.52568			0.762839	−	0.646588i	$-0.223805\pi$
$613$	37.7740			1.52568			0.762839	+	0.646588i	$0.223805\pi$
$614$	−1.00805	−	1.74600i	−0.0406816	−	0.0704626i
$615$	−28.3559	−	10.4764i	−1.14342	−	0.422450i
$616$		0			0
$617$	−20.9464	+	36.2802i	−0.843271	+	1.46059i	0.0438437	+	0.999038i	$0.486040\pi$
$617$	−20.9464	+	36.2802i	−0.843271	+	1.46059i	−0.887115	+	0.461549i	$0.847294\pi$
$618$	−2.32215	+	1.92944i	−0.0934107	+	0.0776135i
$619$	2.99480	+	5.18715i	0.120371	+	0.208489i	0.919914	−	0.392120i	$-0.128258\pi$
$619$	2.99480	+	5.18715i	0.120371	+	0.208489i	−0.799543	+	0.600609i	$0.794925\pi$
$620$	−32.6819			−1.31254
$621$	0.444225	+	0.00645119i	0.0178261	+	0.000258877i
$622$	−6.26655			−0.251266
$623$	−1.23920	−	2.14636i	−0.0496475	−	0.0859920i
$624$	−11.0834	+	9.20899i	−0.443689	+	0.368655i
$625$	14.4598	−	25.0451i	0.578391	−	1.00180i
$626$	−8.17057	+	14.1518i	−0.326562	+	0.565621i
$627$		0			0
$628$	−15.0399	−	26.0498i	−0.600157	−	1.03950i
$629$	−1.96152			−0.0782109
$630$	5.71788	−	2.01867i	0.227806	−	0.0804257i
$631$	−21.4994			−0.855878			−0.427939	−	0.903808i	$-0.640760\pi$
$631$	−21.4994			−0.855878			−0.427939	+	0.903808i	$0.640760\pi$
$632$	−9.41303	−	16.3038i	−0.374430	−	0.648532i
$633$	−2.44098	−	14.2464i	−0.0970202	−	0.566243i
$634$	−0.321416	+	0.556708i	−0.0127651	+	0.0221097i
$635$	−19.8036	+	34.3008i	−0.785881	+	1.36119i
$636$	−1.18071	−	6.89105i	−0.0468184	−	0.273248i
$637$	11.1368	+	19.2895i	0.441256	+	0.764278i
$638$		0			0
$639$	4.79053	−	25.7104i	0.189510	−	1.01709i
$640$	34.6257			1.36870
$641$	−6.41850	−	11.1172i	−0.253516	−	0.439102i	0.710976	−	0.703217i	$-0.248254\pi$
$641$	−6.41850	−	11.1172i	−0.253516	−	0.439102i	−0.964491	+	0.264115i	$0.914920\pi$
$642$	11.2586	+	4.15963i	0.444342	+	0.164167i
$643$	−14.1778	+	24.5566i	−0.559117	+	0.968419i	0.438453	+	0.898754i	$0.355527\pi$
$643$	−14.1778	+	24.5566i	−0.559117	+	0.968419i	−0.997570	+	0.0696654i	$0.977807\pi$
$644$	−0.0829314	+	0.143641i	−0.00326796	+	0.00566027i
$645$	−27.1553	+	22.5629i	−1.06924	+	0.888414i
$646$	−0.578069	−	1.00124i	−0.0227438	−	0.0393934i
$647$	−17.4948			−0.687792			−0.343896	−	0.939008i	$-0.611747\pi$
$647$	−17.4948			−0.687792			−0.343896	+	0.939008i	$0.611747\pi$
$648$	−17.7857	−	6.86625i	−0.698687	−	0.269732i
$649$		0			0
$650$	4.59060	+	7.95116i	0.180058	+	0.311870i
$651$	−10.1269	+	8.41431i	−0.396906	+	0.329783i
$652$	−4.85134	+	8.40277i	−0.189993	+	0.329078i
$653$	14.6511	−	25.3765i	0.573342	−	0.993058i	−0.422877	−	0.906187i	$-0.638980\pi$
$653$	14.6511	−	25.3765i	0.573342	−	0.993058i	0.996220	−	0.0868708i	$-0.0276867\pi$
$654$	4.88176	+	1.80362i	0.190892	+	0.0705272i
$655$	−26.9974	−	46.7609i	−1.05488	−	1.82710i
$656$	−12.2471			−0.478168
$657$	−1.61920	+	8.69012i	−0.0631709	+	0.339034i
$658$	0.220487			0.00859547
$659$	13.7935	+	23.8911i	0.537319	+	0.930664i	0.999047	+	0.0436422i	$0.0138961\pi$
$659$	13.7935	+	23.8911i	0.537319	+	0.930664i	−0.461728	+	0.887021i	$0.652771\pi$
$660$		0			0
$661$	−14.8776	+	25.7688i	−0.578672	+	1.00229i	0.416960	+	0.908925i	$0.363096\pi$
$661$	−14.8776	+	25.7688i	−0.578672	+	1.00229i	−0.995632	+	0.0933649i	$0.970238\pi$
$662$	−3.57617	+	6.19410i	−0.138992	+	0.240741i
$663$	−0.362665	−	2.11664i	−0.0140848	−	0.0822034i
$664$	5.25113	+	9.09522i	0.203783	+	0.352963i
$665$	−22.2774			−0.863879
$666$	−10.2047	+	3.60272i	−0.395424	+	0.139603i
$667$	−0.658336			−0.0254909
$668$	4.18343	+	7.24592i	0.161862	+	0.280353i
$669$	−0.623329	−	0.230296i	−0.0240993	−	0.00890376i
$670$	10.1380	−	17.5596i	0.391666	−	0.678385i
$671$		0			0
$672$	8.46107	−	7.03017i	0.326393	−	0.271195i
$673$	4.82684	+	8.36033i	0.186061	+	0.322267i	0.943934	−	0.330136i	$-0.107094\pi$
$673$	4.82684	+	8.36033i	0.186061	+	0.322267i	−0.757873	+	0.652403i	$0.773761\pi$
$674$	7.78522			0.299875
$675$	10.7234	−	17.9658i	0.412743	−	0.691505i
$676$	−4.28574			−0.164836
$677$	−0.0490576	−	0.0849702i	−0.00188544	−	0.00326567i	0.865081	−	0.501632i	$-0.167267\pi$
$677$	−0.0490576	−	0.0849702i	−0.00188544	−	0.00326567i	−0.866967	+	0.498366i	$0.833933\pi$
$678$	14.8006	−	12.2976i	0.568415	−	0.472287i
$679$	0.0517187	−	0.0895793i	0.00198478	−	0.00343774i
$680$	−0.999815	+	1.73173i	−0.0383412	+	0.0664088i
$681$	−29.2676	−	10.8132i	−1.12153	−	0.414364i
$682$		0			0
$683$	30.5246			1.16799			0.583996	−	0.811756i	$-0.301488\pi$
$683$	30.5246			1.16799			0.583996	+	0.811756i	$0.301488\pi$
$684$	24.1853	+	20.6962i	0.924749	+	0.791337i
$685$	−49.2778			−1.88281
$686$	−4.25330	−	7.36693i	−0.162392	−	0.281271i
$687$	−3.92775	−	22.9237i	−0.149853	−	0.874593i
$688$	−7.15185	+	12.3874i	−0.272662	+	0.472264i
$689$	4.78018	−	8.27952i	0.182110	−	0.315424i
$690$	−0.0434163	−	0.253392i	−0.00165283	−	0.00964647i
$691$	−16.4008	−	28.4071i	−0.623918	−	1.08066i	−0.988749	−	0.149583i	$-0.952207\pi$
$691$	−16.4008	−	28.4071i	−0.623918	−	1.08066i	0.364832	−	0.931074i	$-0.381127\pi$
$692$	−25.9748			−0.987413
$693$		0			0
$694$	5.62741			0.213614
$695$	−17.8788	−	30.9669i	−0.678180	−	1.17464i
$696$	26.5003	+	9.79085i	1.00449	+	0.371121i
$697$	0.912577	−	1.58063i	0.0345663	−	0.0598707i
$698$	1.28280	−	2.22187i	0.0485547	−	0.0840991i
$699$	−4.48906	+	3.72989i	−0.169792	+	0.141077i
$700$	3.90561	+	6.76472i	0.147618	+	0.255682i
$701$	8.74920			0.330453			0.165226	−	0.986256i	$-0.447165\pi$
$701$	8.74920			0.330453			0.165226	+	0.986256i	$0.447165\pi$
$702$	−5.77437	−	10.3456i	−0.217940	−	0.390469i
$703$	39.7584			1.49952
$704$		0			0
$705$	1.31176	−	1.08992i	0.0494039	−	0.0410489i
$706$	9.39625	−	16.2748i	0.353632	−	0.612509i
$707$	−1.19720	+	2.07362i	−0.0450254	+	0.0779863i
$708$	6.21531	+	2.29632i	0.233586	+	0.0863010i
$709$	−13.3879	−	23.1886i	−0.502795	−	0.870866i	−0.999995	−	0.00322996i	$-0.998972\pi$
$709$	−13.3879	−	23.1886i	−0.502795	−	0.870866i	0.497200	−	0.867636i	$-0.334361\pi$
$710$	−15.1338			−0.567961
$711$	−25.1408	+	8.87583i	−0.942853	+	0.332870i
$712$	4.50914			0.168987
$713$	0.279108	+	0.483430i	0.0104527	+	0.0181046i
$714$	0.0618286	+	0.360852i	0.00231388	+	0.0135046i
$715$		0			0
$716$	5.87217	−	10.1709i	0.219453	−	0.380105i
$717$	−6.78524	−	39.6009i	−0.253399	−	1.47892i
$718$	8.02295	+	13.8962i	0.299414	+	0.518600i
$719$	−15.0047			−0.559582			−0.279791	−	0.960061i	$-0.590265\pi$
$719$	−15.0047			−0.559582			−0.279791	+	0.960061i	$0.590265\pi$
$720$	3.48074	−	18.6809i	0.129720	−	0.696196i
$721$	−3.51242			−0.130809
$722$	6.22777	+	10.7868i	0.231774	+	0.401444i
$723$	−24.6373	−	9.10253i	−0.916271	−	0.338527i
$724$	2.08075	−	3.60396i	0.0773304	−	0.133940i
$725$	−15.5020	+	26.8502i	−0.575730	+	0.997193i
$726$		0			0
$727$	−13.7663	−	23.8438i	−0.510562	−	0.884319i	−0.999925	−	0.0122391i	$-0.996104\pi$
$727$	−13.7663	−	23.8438i	−0.510562	−	0.884319i	0.489363	−	0.872080i	$-0.337229\pi$
$728$	9.73292			0.360726
$729$	−14.1733	+	22.9808i	−0.524937	+	0.851141i
$730$	5.11522			0.189323
$731$	−1.06583	−	1.84606i	−0.0394210	−	0.0682792i
$732$	30.3805	−	25.2426i	1.12289	−	0.932995i
$733$	23.8698	−	41.3438i	0.881653	−	1.52707i	0.0321496	−	0.999483i	$-0.489765\pi$
$733$	23.8698	−	41.3438i	0.881653	−	1.52707i	0.849503	−	0.527584i	$-0.176902\pi$
$734$	0.338655	−	0.586567i	0.0125000	−	0.0216506i
$735$	−27.5519	−	10.1794i	−1.01627	−	0.375472i
$736$	−0.233195	−	0.403906i	−0.00859570	−	0.0148882i
$737$		0			0
$738$	1.84450	−	9.89928i	0.0678968	−	0.364398i
$739$	−1.48849			−0.0547549			−0.0273774	−	0.999625i	$-0.508716\pi$
$739$	−1.48849			−0.0547549			−0.0273774	+	0.999625i	$0.508716\pi$
$740$	−15.6258	−	27.0646i	−0.574414	−	0.994914i
$741$	7.35093	+	42.9025i	0.270043	+	1.57606i
$742$	−0.814943	+	1.41152i	−0.0299175	+	0.0518187i
$743$	−9.08009	+	15.7272i	−0.333116	+	0.576974i	−0.983121	−	0.182956i	$-0.941433\pi$
$743$	−9.08009	+	15.7272i	−0.333116	+	0.576974i	0.650005	+	0.759930i	$0.274767\pi$
$744$	−4.04546	−	23.6107i	−0.148314	−	0.865609i
$745$	−6.80761	−	11.7911i	−0.249411	−	0.431993i
$746$	12.5771			0.460481
$747$	14.0250	−	4.95145i	0.513147	−	0.181164i
$748$		0			0
$749$	6.98177	+	12.0928i	0.255108	+	0.441860i
$750$	2.74550	+	1.01436i	0.100251	+	0.0370391i
$751$	2.19733	−	3.80588i	0.0801816	−	0.138879i	−0.823146	−	0.567829i	$-0.807783\pi$
$751$	2.19733	−	3.80588i	0.0801816	−	0.138879i	0.903328	+	0.428951i	$0.141117\pi$
$752$	0.345477	−	0.598384i	0.0125983	−	0.0218208i
$753$	0.775748	−	0.644557i	0.0282698	−	0.0234890i
$754$	8.77835	+	15.2046i	0.319689	+	0.553717i
$755$	8.80557			0.320467
$756$	−4.91275	−	8.80187i	−0.178675	−	0.320121i
$757$	−13.7659			−0.500331			−0.250165	−	0.968203i	$-0.580485\pi$
$757$	−13.7659			−0.500331			−0.250165	+	0.968203i	$0.580485\pi$
$758$	−4.69382	−	8.12993i	−0.170487	−	0.295292i
$759$		0			0
$760$	20.2655	−	35.1008i	0.735105	−	1.27324i
$761$	−15.5531	+	26.9387i	−0.563798	+	0.976526i	0.433363	+	0.901220i	$0.357327\pi$
$761$	−15.5531	+	26.9387i	−0.563798	+	0.976526i	−0.997160	+	0.0753068i	$0.976006\pi$
$762$	−12.3758	−	4.57239i	−0.448329	−	0.165640i
$763$	3.02731	+	5.24345i	0.109596	+	0.189826i
$764$	19.6987			0.712672
$765$	2.15163	+	1.84122i	0.0777923	+	0.0665694i
$766$	−3.57859			−0.129300
$767$	4.53027	+	7.84665i	0.163578	+	0.283326i
$768$	1.32503	+	7.73334i	0.0478130	+	0.279053i
$769$	10.9677	−	18.9966i	0.395504	−	0.685034i	−0.597661	−	0.801749i	$-0.703903\pi$
$769$	10.9677	−	18.9966i	0.395504	−	0.685034i	0.993165	+	0.116715i	$0.0372365\pi$
$770$		0			0
$771$	3.20922	+	18.7301i	0.115577	+	0.674549i
$772$	−5.62041	−	9.73484i	−0.202283	−	0.350365i
$773$	−12.7166			−0.457385			−0.228693	−	0.973499i	$-0.573445\pi$
$773$	−12.7166			−0.457385			−0.228693	+	0.973499i	$0.573445\pi$
$774$	−8.93557	−	7.64646i	−0.321182	−	0.274846i
$775$	26.2889			0.944326
$776$	0.0940957	+	0.162978i	0.00337784	+	0.00585059i
$777$	−11.8099	−	4.36332i	−0.423679	−	0.156533i
$778$	−0.208941	+	0.361896i	−0.00749089	+	0.0129746i
$779$	−18.4972	+	32.0381i	−0.662731	+	1.14788i
$780$	26.3158	−	21.8654i	0.942258	−	0.782908i
$781$		0			0
$782$	0.0155220			0.000555064
$783$	20.5057	−	34.3550i	0.732815	−	1.22775i
$784$	−11.8998			−0.424993
$785$	27.1204	+	46.9740i	0.967970	+	1.67657i
$786$	13.8340	−	11.4944i	0.493442	−	0.409993i
$787$	−8.63083	+	14.9490i	−0.307656	+	0.532875i	−0.977849	−	0.209311i	$-0.932878\pi$
$787$	−8.63083	+	14.9490i	−0.307656	+	0.532875i	0.670193	+	0.742187i	$0.266211\pi$
$788$	17.2007	−	29.7924i	0.612749	−	1.06131i
$789$	23.3883	+	8.64107i	0.832645	+	0.307630i
$790$	7.71406	+	13.3611i	0.274454	+	0.475368i
$791$	22.3870			0.795991
$792$		0			0
$793$	54.0120			1.91802
$794$	1.18161	+	2.04660i	0.0419337	+	0.0726312i
$795$	2.12911	+	12.4262i	0.0755116	+	0.440711i
$796$	−11.0683	+	19.1708i	−0.392304	+	0.679491i
$797$	−17.6008	+	30.4854i	−0.623451	+	1.07985i	0.365388	+	0.930855i	$0.380936\pi$
$797$	−17.6008	+	30.4854i	−0.623451	+	1.07985i	−0.988838	+	0.148993i	$0.952397\pi$
$798$	−1.25322	−	7.31419i	−0.0443633	−	0.258920i
$799$	0.0514857	+	0.0891759i	0.00182143	+	0.00315482i
$800$	−21.9644			−0.776560
$801$	1.16972	−	6.27782i	0.0413301	−	0.221816i
$802$	3.26248			0.115202
$803$		0			0
$804$	−31.6170	−	11.6812i	−1.11504	−	0.411966i
$805$	0.149545	−	0.259019i	0.00527076	−	0.00912922i
$806$	7.44335	−	12.8923i	0.262181	−	0.454110i
$807$	−0.651414	+	0.541250i	−0.0229309	+	0.0190529i
$808$	−2.17816	−	3.77269i	−0.0766275	−	0.132723i
$809$	19.0808			0.670845			0.335423	−	0.942068i	$-0.391121\pi$
$809$	19.0808			0.670845			0.335423	+	0.942068i	$0.391121\pi$
$810$	14.5755	+	5.62695i	0.512131	+	0.197711i
$811$	31.0588			1.09062			0.545311	−	0.838234i	$-0.316412\pi$
$811$	31.0588			1.09062			0.545311	+	0.838234i	$0.316412\pi$
$812$	7.46849	+	12.9358i	0.262093	+	0.453958i
$813$	29.2271	−	24.2843i	1.02504	−	0.851688i
$814$		0			0
$815$	8.74810	−	15.1522i	0.306433	−	0.530757i
$816$	1.07620	+	0.397616i	0.0376746	+	0.0139193i
$817$	21.6034	+	37.4182i	0.755808	+	1.30910i
$818$	5.45961			0.190891
$819$	2.52483	−	13.5506i	0.0882248	−	0.473497i
$820$	29.0789			1.01548
$821$	17.0043	+	29.4522i	0.593453	+	1.02789i	0.993763	+	0.111511i	$0.0355689\pi$
$821$	17.0043	+	29.4522i	0.593453	+	1.02789i	−0.400311	+	0.916380i	$0.631098\pi$
$822$	−2.77213	−	16.1791i	−0.0966891	−	0.564311i
$823$	−7.77800	+	13.4719i	−0.271124	+	0.469601i	−0.969150	−	0.246472i	$-0.920729\pi$
$823$	−7.77800	+	13.4719i	−0.271124	+	0.469601i	0.698026	+	0.716073i	$0.254062\pi$
$824$	3.19521	−	5.53426i	0.111310	−	0.192795i
$825$		0			0
$826$	−0.772337	−	1.33773i	−0.0268730	−	0.0465455i
$827$	−16.0277			−0.557337			−0.278669	−	0.960387i	$-0.589893\pi$
$827$	−16.0277			−0.557337			−0.278669	+	0.960387i	$0.589893\pi$
$828$	−0.402987	+	0.142273i	−0.0140048	+	0.00494431i
$829$	19.0994			0.663351			0.331675	−	0.943394i	$-0.392386\pi$
$829$	19.0994			0.663351			0.331675	+	0.943394i	$0.392386\pi$
$830$	−4.30334	−	7.45361i	−0.149371	−	0.258719i
$831$	−4.66214	−	1.72248i	−0.161728	−	0.0597523i
$832$	2.10065	−	3.63843i	0.0728269	−	0.126140i
$833$	0.886702	−	1.53581i	0.0307224	−	0.0532128i
$834$	9.16140	−	7.61207i	0.317233	−	0.263584i
$835$	−7.54371	−	13.0661i	−0.261061	−	0.452171i
$836$		0			0
$837$	−33.9213	−	0.492616i	−1.17249	−	0.0170273i
$838$	−0.0875755			−0.00302524
$839$	−0.743960	−	1.28858i	−0.0256844	−	0.0444866i	0.852898	−	0.522078i	$-0.174843\pi$
$839$	−0.743960	−	1.28858i	−0.0256844	−	0.0444866i	−0.878582	+	0.477592i	$0.841510\pi$
$840$	−9.87186	+	8.20237i	−0.340612	+	0.283009i
$841$	−15.1436	+	26.2295i	−0.522193	+	0.904465i
$842$	4.90463	−	8.49507i	0.169025	−	0.292759i
$843$	−29.5341	−	10.9117i	−1.01721	−	0.375819i
$844$	6.95196	+	12.0411i	0.239296	+	0.414473i
$845$	7.72819			0.265858
$846$	0.431641	+	0.369369i	0.0148401	+	0.0126992i
$847$		0			0
$848$	2.55384	+	4.42338i	0.0876993	+	0.151900i
$849$	−6.00726	−	35.0604i	−0.206169	−	1.20327i
$850$	0.365500	−	0.633064i	0.0125365	−	0.0217139i
$851$	−0.266893	+	0.462271i	−0.00914896	+	0.0158465i
$852$	4.24860	+	24.7963i	0.145555	+	0.849506i
$853$	18.9010	+	32.7376i	0.647159	+	1.12091i	0.983798	+	0.179279i	$0.0573765\pi$
$853$	18.9010	+	32.7376i	0.647159	+	1.12091i	−0.336639	+	0.941634i	$0.609290\pi$
$854$	−9.20818			−0.315097
$855$	−43.6118	−	37.3200i	−1.49149	−	1.27632i
$856$	−25.4049			−0.868322
$857$	9.91348	+	17.1706i	0.338638	+	0.586538i	0.984177	−	0.177189i	$-0.0567005\pi$
$857$	9.91348	+	17.1706i	0.338638	+	0.586538i	−0.645539	+	0.763727i	$0.723367\pi$
$858$		0			0
$859$	7.85764	−	13.6098i	0.268099	−	0.464362i	−0.700272	−	0.713876i	$-0.746938\pi$
$859$	7.85764	−	13.6098i	0.268099	−	0.464362i	0.968371	+	0.249515i	$0.0802711\pi$
$860$	16.9811	−	29.4120i	0.579049	−	1.00294i
$861$	9.01050	−	7.48668i	0.307077	−	0.255146i
$862$	7.32936	+	12.6948i	0.249639	+	0.432387i
$863$	8.12774			0.276671			0.138336	−	0.990385i	$-0.455825\pi$
$863$	8.12774			0.276671			0.138336	+	0.990385i	$0.455825\pi$
$864$	28.3413	+	0.411581i	0.964189	+	0.0140023i
$865$	46.8386			1.59256
$866$	4.77697	+	8.27396i	0.162328	+	0.281161i
$867$	22.5159	−	18.7081i	0.764681	−	0.635361i
$868$	6.33269	−	10.9685i	0.214945	−	0.372296i
$869$		0			0
$870$	−21.7172	−	8.02368i	−0.736283	−	0.272028i
$871$	−23.0452	−	39.9155i	−0.780857	−	1.35248i
$872$	−11.0156			−0.373036
$873$	0.251315	−	0.0887257i	0.00850574	−	0.00300291i
$874$	−0.314618			−0.0106421
$875$	1.70256	+	2.94891i	0.0575569	+	0.0996915i
$876$	−1.43603	−	8.38113i	−0.0485188	−	0.283172i
$877$	−1.26676	+	2.19410i	−0.0427756	+	0.0740895i	−0.886621	−	0.462498i	$-0.846953\pi$
$877$	−1.26676	+	2.19410i	−0.0427756	+	0.0740895i	0.843845	+	0.536587i	$0.180287\pi$
$878$	11.3371	−	19.6364i	0.382607	−	0.662695i
$879$	0.251576	+	1.46828i	0.00848544	+	0.0495239i
$880$		0			0
$881$	−47.4109			−1.59731			−0.798657	−	0.601786i	$-0.794456\pi$
$881$	−47.4109			−1.59731			−0.798657	+	0.601786i	$0.794456\pi$
$882$	1.79220	−	9.61859i	0.0603464	−	0.323875i
$883$	26.5129			0.892231			0.446116	−	0.894975i	$-0.352807\pi$
$883$	26.5129			0.892231			0.446116	+	0.894975i	$0.352807\pi$
$884$	1.03288	+	1.78900i	0.0347394	+	0.0601705i
$885$	−11.2077	−	4.14080i	−0.376742	−	0.139192i
$886$	9.29970	−	16.1076i	0.312430	−	0.541144i
$887$	−23.9147	+	41.4214i	−0.802976	+	1.39080i	0.114673	+	0.993403i	$0.463418\pi$
$887$	−23.9147	+	41.4214i	−0.802976	+	1.39080i	−0.917649	+	0.397392i	$0.869915\pi$
$888$	17.6183	−	14.6388i	0.591232	−	0.491245i
$889$	−7.67457	−	13.2927i	−0.257397	−	0.445825i
$890$	−3.69528			−0.123866
$891$		0			0
$892$	0.639221			0.0214027
$893$	−1.04357	−	1.80752i	−0.0349219	−	0.0604865i
$894$	3.48834	−	2.89841i	0.116668	−	0.0969373i
$895$	−10.5889	+	18.3405i	−0.353948	+	0.613056i
$896$	−6.70932	+	11.6209i	−0.224143	+	0.388227i
$897$	−0.548174	−	0.202529i	−0.0183030	−	0.00676226i
$898$	−7.46657	−	12.9325i	−0.249163	−	0.431562i
$899$	50.2709			1.67663
$900$	−3.68664	+	19.7860i	−0.122888	+	0.659532i
$901$	−0.761187			−0.0253588
$902$		0			0
$903$	−2.31064	−	13.4857i	−0.0768933	−	0.448776i
$904$	−20.3652	+	35.2736i	−0.677337	+	1.17318i
$905$	−3.75208	+	6.49879i	−0.124723	+	0.216027i
$906$	0.495358	+	2.89108i	0.0164572	+	0.0960496i
$907$	−23.7292	−	41.1001i	−0.787914	−	1.36471i	−0.927243	−	0.374461i	$-0.877828\pi$
$907$	−23.7292	−	41.1001i	−0.787914	−	1.36471i	0.139328	−	0.990246i	$-0.455506\pi$
$908$	30.0138			0.996042
$909$	−5.81754	+	2.05385i	−0.192956	+	0.0681221i
$910$	−7.97621			−0.264409
$911$	14.2161	+	24.6230i	0.471001	+	0.815797i	0.999450	−	0.0331677i	$-0.0105595\pi$
$911$	14.2161	+	24.6230i	0.471001	+	0.815797i	−0.528449	+	0.848965i	$0.677226\pi$
$912$	−21.8138	−	8.05935i	−0.722326	−	0.266872i
$913$		0			0
$914$	3.67381	−	6.36322i	0.121519	−	0.210477i
$915$	−54.7831	+	45.5184i	−1.81107	+	1.50479i
$916$	11.1863	+	19.3753i	0.369606	+	0.640176i
$917$	20.9249			0.691001
$918$	−0.483476	+	0.810009i	−0.0159571	+	0.0267343i
$919$	−38.3728			−1.26580			−0.632901	−	0.774233i	$-0.718136\pi$
$919$	−38.3728			−1.26580			−0.632901	+	0.774233i	$0.718136\pi$
$920$	0.272078	+	0.471253i	0.00897015	+	0.0155368i
$921$	4.64832	−	3.86221i	0.153167	−	0.127264i
$922$	5.49549	−	9.51848i	0.180984	−	0.313474i
$923$	−17.2007	+	29.7924i	−0.566167	+	0.980629i
$924$		0			0
$925$	12.5692	+	21.7704i	0.413272	+	0.715808i
$926$	13.2127			0.434195
$927$	−6.87617	−	5.88416i	−0.225843	−	0.193261i
$928$	−42.0014			−1.37876
$929$	−6.69383	−	11.5941i	−0.219618	−	0.380389i	0.735073	−	0.677987i	$-0.237148\pi$
$929$	−6.69383	−	11.5941i	−0.219618	−	0.380389i	−0.954691	+	0.297599i	$0.903814\pi$
$930$	3.31529	+	19.3491i	0.108713	+	0.634483i
$931$	−17.9727	+	31.1297i	−0.589033	+	1.02023i
$932$	2.80715	−	4.86212i	0.0919511	−	0.159264i
$933$	−3.17233	−	18.5148i	−0.103857	−	0.606147i
$934$	4.60021	+	7.96779i	0.150523	+	0.260714i
$935$		0			0
$936$	19.0539	+	16.3050i	0.622795	+	0.532946i
$937$	24.6705			0.805950			0.402975	−	0.915211i	$-0.367976\pi$
$937$	24.6705			0.805950			0.402975	+	0.915211i	$0.367976\pi$
$938$	3.92884	+	6.80494i	0.128281	+	0.222189i
$939$	−45.9485	−	16.9762i	−1.49947	−	0.553998i
$940$	−0.820286	+	1.42078i	−0.0267548	+	0.0463406i
$941$	4.15115	−	7.19000i	0.135324	−	0.234387i	−0.790397	−	0.612594i	$-0.790126\pi$
$941$	4.15115	−	7.19000i	0.135324	−	0.234387i	0.925721	+	0.378207i	$0.123459\pi$
$942$	−13.8970	+	11.5468i	−0.452789	+	0.376215i
$943$	−0.248338	−	0.430134i	−0.00808701	−	0.0140071i
$944$	−4.84065			−0.157550
$945$	8.85883	+	15.8718i	0.288178	+	0.516311i
$946$		0			0
$947$	−18.9748	−	32.8653i	−0.616598	−	1.06798i	−0.990102	−	0.140351i	$-0.955177\pi$
$947$	−18.9748	−	32.8653i	−0.616598	−	1.06798i	0.373503	−	0.927629i	$-0.378156\pi$
$948$	19.7262	−	16.3902i	0.640678	−	0.532330i
$949$	5.81382	−	10.0698i	0.188725	−	0.326880i
$950$	−7.40838	+	12.8317i	−0.240360	+	0.416315i
$951$	−1.80753	−	0.667814i	−0.0586133	−	0.0216553i
$952$	−0.387463	−	0.671106i	−0.0125578	−	0.0217507i
$953$	48.6705			1.57659			0.788297	−	0.615295i	$-0.210963\pi$
$953$	48.6705			1.57659			0.788297	+	0.615295i	$0.210963\pi$
$954$	−3.96004	+	1.39807i	−0.128211	+	0.0452642i
$955$	−35.5213			−1.14944
$956$	19.3245	+	33.4710i	0.624998	+	1.08253i
$957$		0			0
$958$	4.73516	−	8.20154i	0.152986	−	0.264980i
$959$	9.54844	−	16.5384i	0.308335	−	0.534052i
$960$	0.935635	+	5.46068i	0.0301975	+	0.176243i
$961$	−5.81285	−	10.0682i	−0.187511	−	0.324779i
$962$	14.2352			0.458960
$963$	−6.59033	+	35.3698i	−0.212370	+	1.13978i
$964$	25.2655			0.813746
$965$	10.1349	+	17.5542i	0.326255	+	0.565090i
$966$	0.0934548	+	0.0345280i	0.00300686	+	0.00111092i
$967$	5.48901	−	9.50724i	0.176515	−	0.305732i	−0.764170	−	0.645015i	$-0.776851\pi$
$967$	5.48901	−	9.50724i	0.176515	−	0.305732i	0.940684	+	0.339283i	$0.110184\pi$
$968$		0			0
$969$	2.66559	−	2.21479i	0.0856309	−	0.0711494i
$970$	−0.0771122	−	0.133562i	−0.00247592	−	0.00428843i
$971$	13.0636			0.419231			0.209615	−	0.977784i	$-0.432779\pi$
$971$	13.0636			0.419231			0.209615	+	0.977784i	$0.432779\pi$
$972$	5.12773	−	25.4612i	0.164472	−	0.816669i
$973$	13.8573			0.444244
$974$	6.58316	+	11.4024i	0.210938	+	0.365355i
$975$	−21.1681	+	17.5883i	−0.677923	+	0.563276i
$976$	−14.4281	+	24.9903i	−0.461833	+	0.799919i
$977$	5.53815	−	9.59236i	0.177181	−	0.306887i	−0.763733	−	0.645533i	$-0.776635\pi$
$977$	5.53815	−	9.59236i	0.177181	−	0.306887i	0.940914	+	0.338646i	$0.109969\pi$
$978$	5.46694	+	2.01982i	0.174813	+	0.0645869i
$979$		0			0
$980$	28.2544			0.902554
$981$	−2.85758	+	15.3364i	−0.0912355	+	0.489655i
$982$	−25.2175			−0.804721
$983$	13.2157	+	22.8903i	0.421517	+	0.730088i	0.996088	−	0.0883661i	$-0.0281645\pi$
$983$	13.2157	+	22.8903i	0.421517	+	0.730088i	−0.574571	+	0.818455i	$0.694831\pi$
$984$	3.59947	+	21.0077i	0.114747	+	0.669702i
$985$	−31.0168	+	53.7228i	−0.988279	+	1.71175i
$986$	0.698925	−	1.21057i	0.0222583	−	0.0385525i
$987$	0.111618	+	0.651439i	0.00355283	+	0.0207355i
$988$	−20.9356	−	36.2615i	−0.666050	−	1.15363i
$989$	−0.580083			−0.0184456
$990$		0			0
$991$	−18.9911			−0.603272			−0.301636	−	0.953423i	$-0.597533\pi$
$991$	−18.9911			−0.603272			−0.301636	+	0.953423i	$0.597533\pi$
$992$	17.8069	+	30.8425i	0.565370	+	0.979250i
$993$	−20.1111	−	7.43030i	−0.638208	−	0.235793i
$994$	2.93243	−	5.07913i	0.0930112	−	0.161100i
$995$	19.9587	−	34.5694i	0.632733	−	1.09593i
$996$	−11.0044	+	9.14340i	−0.348688	+	0.289720i
$997$	11.0566	+	19.1506i	0.350165	+	0.606504i	0.986278	−	0.165092i	$-0.0527921\pi$
$997$	11.0566	+	19.1506i	0.350165	+	0.606504i	−0.636113	+	0.771596i	$0.719459\pi$
$998$	11.6161			0.367700
$999$	−15.8104	−	28.3265i	−0.500218	−	0.896210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.o.364.11		36
9.4	even	3		9801.2.a.co.1.8		18
9.5	odd	6		9801.2.a.cn.1.11		18
9.7	even	3	inner	1089.2.e.o.727.11		36
11.2	odd	10		99.2.m.b.4.4	✓	72
11.6	odd	10		99.2.m.b.58.6	yes	72
11.10	odd	2		1089.2.e.p.364.8		36
33.2	even	10		297.2.n.b.37.6		72
33.17	even	10		297.2.n.b.91.4		72
99.2	even	30		297.2.n.b.235.4		72
99.13	odd	30		891.2.f.f.730.4		36
99.32	even	6		9801.2.a.cp.1.8		18
99.43	odd	6		1089.2.e.p.727.8		36
99.50	even	30		891.2.f.e.487.6		36
99.61	odd	30		99.2.m.b.25.4	yes	72
99.68	even	30		891.2.f.e.730.6		36
99.76	odd	6		9801.2.a.cm.1.11		18
99.79	odd	30		99.2.m.b.70.6	yes	72
99.83	even	30		297.2.n.b.289.6		72
99.94	odd	30		891.2.f.f.487.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.4	✓	72	11.2	odd	10
99.2.m.b.25.4	yes	72	99.61	odd	30
99.2.m.b.58.6	yes	72	11.6	odd	10
99.2.m.b.70.6	yes	72	99.79	odd	30
297.2.n.b.37.6		72	33.2	even	10
297.2.n.b.91.4		72	33.17	even	10
297.2.n.b.235.4		72	99.2	even	30
297.2.n.b.289.6		72	99.83	even	30
891.2.f.e.487.6		36	99.50	even	30
891.2.f.e.730.6		36	99.68	even	30
891.2.f.f.487.4		36	99.94	odd	30
891.2.f.f.730.4		36	99.13	odd	30
1089.2.e.o.364.11		36	1.1	even	1	trivial
1089.2.e.o.727.11		36	9.7	even	3	inner
1089.2.e.p.364.8		36	11.10	odd	2
1089.2.e.p.727.8		36	99.43	odd	6
9801.2.a.cm.1.11		18	99.76	odd	6
9801.2.a.cn.1.11		18	9.5	odd	6
9801.2.a.co.1.8		18	9.4	even	3
9801.2.a.cp.1.8		18	99.32	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.288906 + 0.500400i) q^{2} +(-1.33220 + 1.10691i) q^{3} +(0.833067 - 1.44291i) q^{4} +(-1.50221 + 2.60191i) q^{5} +(-0.938776 - 0.346842i) q^{6} +(-0.582160 - 1.00833i) q^{7} +2.11834 q^{8} +(0.549521 - 2.94924i) q^{9} -1.73599 q^{10} +(0.487356 + 2.84438i) q^{12} +(-1.97309 + 3.41748i) q^{13} +(0.336379 - 0.582626i) q^{14} +(-0.878818 - 5.12908i) q^{15} +(-1.05413 - 1.82581i) q^{16} +0.314191 q^{17} +(1.63456 - 0.577073i) q^{18} -6.36839 q^{19} +(2.50289 + 4.33513i) q^{20} +(1.89168 + 0.698904i) q^{21} +(0.0427501 - 0.0740453i) q^{23} +(-2.82205 + 2.34480i) q^{24} +(-2.01329 - 3.48713i) q^{25} -2.28015 q^{26} +(2.53246 + 4.53725i) q^{27} -1.93991 q^{28} +(-3.84991 - 6.66824i) q^{29} +(2.31269 - 1.92158i) q^{30} +(-3.26442 + 5.65414i) q^{31} +(2.72743 - 4.72404i) q^{32} +(0.0907715 + 0.157221i) q^{34} +3.49812 q^{35} +(-3.79771 - 3.24983i) q^{36} -6.24309 q^{37} +(-1.83987 - 3.18674i) q^{38} +(-1.15428 - 6.73680i) q^{39} +(-3.18219 + 5.51172i) q^{40} +(2.90454 - 5.03080i) q^{41} +(0.196787 + 1.14851i) q^{42} +(-3.39229 - 5.87562i) q^{43} +(6.84817 + 5.86020i) q^{45} +0.0494030 q^{46} +(0.163868 + 0.283827i) q^{47} +(3.42532 + 1.26552i) q^{48} +(2.82218 - 4.88816i) q^{49} +(1.16331 - 2.01490i) q^{50} +(-0.418565 + 0.347779i) q^{51} +(3.28742 + 5.69398i) q^{52} -2.42269 q^{53} +(-1.53880 + 2.57808i) q^{54} +(-1.23321 - 2.13598i) q^{56} +(8.48398 - 7.04920i) q^{57} +(2.22452 - 3.85299i) q^{58} +(1.14802 - 1.98842i) q^{59} +(-8.13293 - 3.00481i) q^{60} +(-6.84360 - 11.8535i) q^{61} -3.77244 q^{62} +(-3.29372 + 1.16283i) q^{63} -1.06465 q^{64} +(-5.92799 - 10.2676i) q^{65} +(-5.83989 + 10.1150i) q^{67} +(0.261742 - 0.453350i) q^{68} +(0.0250094 + 0.145964i) q^{69} +(1.01063 + 1.75046i) q^{70} +8.71765 q^{71} +(1.16407 - 6.24749i) q^{72} -2.94656 q^{73} +(-1.80367 - 3.12404i) q^{74} +(6.54203 + 2.41703i) q^{75} +(-5.30529 + 9.18904i) q^{76} +(3.03761 - 2.52391i) q^{78} +(-4.44360 - 7.69654i) q^{79} +6.33413 q^{80} +(-8.39605 - 3.24134i) q^{81} +3.35655 q^{82} +(2.47889 + 4.29357i) q^{83} +(2.58435 - 2.14730i) q^{84} +(-0.471981 + 0.817496i) q^{85} +(1.96011 - 3.39500i) q^{86} +(12.5100 + 4.62195i) q^{87} +2.12862 q^{89} +(-0.953966 + 5.11987i) q^{90} +4.59461 q^{91} +(-0.0712273 - 0.123369i) q^{92} +(-1.90973 - 11.1459i) q^{93} +(-0.0946848 + 0.163999i) q^{94} +(9.56668 - 16.5700i) q^{95} +(1.59559 + 9.31238i) q^{96} +(0.0444196 + 0.0769370i) q^{97} +3.26138 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} + 3 q^{13} - 5 q^{15} + 8 q^{16} + 40 q^{17} - 17 q^{18} + 6 q^{19} + 5 q^{20} + 8 q^{21} + 10 q^{23}+ \cdots + 164 q^{98}+O(q^{100}) \) 36 * q - 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 + q^6 + q^7 + 12 * q^8 - q^9 + 4 * q^10 - 8 * q^12 + 3 * q^13 - 5 * q^15 + 8 * q^16 + 40 * q^17 - 17 * q^18 + 6 * q^19 + 5 * q^20 + 8 * q^21 + 10 * q^23 + 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 - 38 * q^28 - 21 * q^29 - 12 * q^30 - 6 * q^31 - 9 * q^32 + 4 * q^34 + 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 - 42 * q^39 - 20 * q^41 + 18 * q^42 + 4 * q^43 + 20 * q^45 - 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 - 25 * q^50 + 4 * q^51 - 19 * q^52 + 62 * q^53 - 17 * q^54 + 57 * q^56 + 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 - 16 * q^61 + 38 * q^62 - 5 * q^63 - 32 * q^64 - 42 * q^65 + 5 * q^67 - 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 - 51 * q^72 - 9 * q^74 - 16 * q^75 - 8 * q^76 - 32 * q^78 - 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 - 36 * q^83 - 60 * q^84 + 25 * q^85 - 26 * q^86 + 60 * q^87 - 28 * q^89 - 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 + 4 * q^94 - 64 * q^95 + 21 * q^96 + 16 * q^97 + 164 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more