LMFDB - Embedded newform 1089.2.e.o.727.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1089,2,Mod(364,1089)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [36,-2,9,-12,1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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			727.7
Character	$\chi$	$=$	1089.727
Dual form			1089.2.e.o.364.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.584430 + 1.01226i) q^{2} +(-1.73005 + 0.0832210i) q^{3} +(0.316882 + 0.548856i) q^{4} +(1.58346 + 2.74264i) q^{5} +(0.926852 - 1.79990i) q^{6} +(0.124437 - 0.215531i) q^{7} -3.07850 q^{8} +(2.98615 - 0.287953i) q^{9} -3.70170 q^{10} +(-0.593899 - 0.923178i) q^{12} +(2.56539 + 4.44339i) q^{13} +(0.145449 + 0.251925i) q^{14} +(-2.96772 - 4.61313i) q^{15} +(1.16541 - 2.01854i) q^{16} -4.60302 q^{17} +(-1.45371 + 3.19106i) q^{18} -0.797165 q^{19} +(-1.00354 + 1.73819i) q^{20} +(-0.197345 + 0.383234i) q^{21} +(2.46653 + 4.27215i) q^{23} +(5.32597 - 0.256196i) q^{24} +(-2.51472 + 4.35562i) q^{25} -5.99717 q^{26} +(-5.14222 + 0.746684i) q^{27} +0.157727 q^{28} +(-0.785949 + 1.36130i) q^{29} +(6.40413 - 0.308059i) q^{30} +(4.20351 + 7.28069i) q^{31} +(-1.71631 - 2.97273i) q^{32} +(2.69014 - 4.65947i) q^{34} +0.788164 q^{35} +(1.10430 + 1.54772i) q^{36} -0.473896 q^{37} +(0.465887 - 0.806941i) q^{38} +(-4.80804 - 7.47379i) q^{39} +(-4.87470 - 8.44323i) q^{40} +(0.0469859 + 0.0813819i) q^{41} +(-0.272600 - 0.423739i) q^{42} +(5.01977 - 8.69450i) q^{43} +(5.51821 + 7.73397i) q^{45} -5.76606 q^{46} +(1.56389 - 2.70873i) q^{47} +(-1.84823 + 3.58917i) q^{48} +(3.46903 + 6.00854i) q^{49} +(-2.93936 - 5.09112i) q^{50} +(7.96345 - 0.383068i) q^{51} +(-1.62585 + 2.81606i) q^{52} -11.6119 q^{53} +(2.24943 - 5.64167i) q^{54} +(-0.383079 + 0.663512i) q^{56} +(1.37914 - 0.0663409i) q^{57} +(-0.918665 - 1.59117i) q^{58} +(-1.24991 - 2.16491i) q^{59} +(1.59153 - 3.09067i) q^{60} +(-2.00563 + 3.47385i) q^{61} -9.82663 q^{62} +(0.309523 - 0.679438i) q^{63} +8.67387 q^{64} +(-8.12442 + 14.0719i) q^{65} +(-2.07692 - 3.59733i) q^{67} +(-1.45861 - 2.52639i) q^{68} +(-4.62275 - 7.18577i) q^{69} +(-0.460627 + 0.797829i) q^{70} +0.369763 q^{71} +(-9.19287 + 0.886465i) q^{72} -10.1834 q^{73} +(0.276959 - 0.479707i) q^{74} +(3.98811 - 7.74473i) q^{75} +(-0.252607 - 0.437529i) q^{76} +(10.3754 - 0.499091i) q^{78} +(5.85175 - 10.1355i) q^{79} +7.38152 q^{80} +(8.83417 - 1.71974i) q^{81} -0.109840 q^{82} +(-0.532585 + 0.922464i) q^{83} +(-0.272876 + 0.0131262i) q^{84} +(-7.28872 - 12.6244i) q^{85} +(5.86742 + 10.1627i) q^{86} +(1.24644 - 2.42053i) q^{87} -8.39173 q^{89} +(-11.0538 + 1.06592i) q^{90} +1.27691 q^{91} +(-1.56320 + 2.70754i) q^{92} +(-7.87819 - 12.2461i) q^{93} +(1.82796 + 3.16613i) q^{94} +(-1.26228 - 2.18634i) q^{95} +(3.21669 + 5.00014i) q^{96} +(5.54336 - 9.60139i) q^{97} -8.10963 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 $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.584430	+	1.01226i	−0.413255	+	0.715778i	−0.995243	−	0.0974187i	$-0.968941\pi$
$2$	−0.584430	+	1.01226i	−0.413255	+	0.715778i	0.581989	+	0.813197i	$0.302275\pi$
$3$	−1.73005	+	0.0832210i	−0.998845	+	0.0480477i
$3$	−1.73005	+	0.0832210i	−0.998845	+	0.0480477i
$4$	0.316882	+	0.548856i	0.158441	+	0.274428i
$5$	1.58346	+	2.74264i	0.708147	+	1.22655i	0.965544	+	0.260241i	$0.0838019\pi$
$5$	1.58346	+	2.74264i	0.708147	+	1.22655i	−0.257397	+	0.966306i	$0.582865\pi$
$6$	0.926852	−	1.79990i	0.378386	−	0.734807i
$7$	0.124437	−	0.215531i	0.0470326	−	0.0814629i	−0.841551	−	0.540178i	$-0.818357\pi$
$7$	0.124437	−	0.215531i	0.0470326	−	0.0814629i	0.888583	+	0.458715i	$0.151690\pi$
$8$	−3.07850			−1.08842
$9$	2.98615	−	0.287953i	0.995383	−	0.0959844i
$10$	−3.70170			−1.17058
$11$		0			0
$11$		0			0
$12$	−0.593899	−	0.923178i	−0.171444	−	0.266498i
$13$	2.56539	+	4.44339i	0.711512	+	1.23237i	0.964290	+	0.264850i	$0.0853225\pi$
$13$	2.56539	+	4.44339i	0.711512	+	1.23237i	−0.252778	+	0.967524i	$0.581344\pi$
$14$	0.145449	+	0.251925i	0.0388729	+	0.0673298i
$15$	−2.96772	−	4.61313i	−0.766262	−	1.19111i
$16$	1.16541	−	2.01854i	0.291352	−	0.504636i
$17$	−4.60302			−1.11640			−0.558198	−	0.829708i	$-0.688507\pi$
$17$	−4.60302			−1.11640			−0.558198	+	0.829708i	$0.688507\pi$
$18$	−1.45371	+	3.19106i	−0.342643	+	0.752139i
$19$	−0.797165			−0.182882			−0.0914411	−	0.995810i	$-0.529147\pi$
$19$	−0.797165			−0.182882			−0.0914411	+	0.995810i	$0.529147\pi$
$20$	−1.00354	+	1.73819i	−0.224399	+	0.388671i
$21$	−0.197345	+	0.383234i	−0.0430642	+	0.0836286i
$22$		0			0
$23$	2.46653	+	4.27215i	0.514307	+	0.890805i	0.999862	+	0.0165995i	$0.00528403\pi$
$23$	2.46653	+	4.27215i	0.514307	+	0.890805i	−0.485556	+	0.874206i	$0.661383\pi$
$24$	5.32597	−	0.256196i	1.08716	−	0.0522958i
$25$	−2.51472	+	4.35562i	−0.502944	+	0.871125i
$26$	−5.99717			−1.17614
$27$	−5.14222	+	0.746684i	−0.989621	+	0.143699i
$28$	0.157727			0.0298076
$29$	−0.785949	+	1.36130i	−0.145947	+	0.252788i	−0.929726	−	0.368252i	$-0.879956\pi$
$29$	−0.785949	+	1.36130i	−0.145947	+	0.252788i	0.783779	+	0.621040i	$0.213290\pi$
$30$	6.40413	−	0.308059i	1.16923	−	0.0562437i
$31$	4.20351	+	7.28069i	0.754973	+	1.30765i	0.945388	+	0.325947i	$0.105683\pi$
$31$	4.20351	+	7.28069i	0.754973	+	1.30765i	−0.190415	+	0.981704i	$0.560984\pi$
$32$	−1.71631	−	2.97273i	−0.303403	−	0.525509i
$33$		0			0
$34$	2.69014	−	4.65947i	0.461356	−	0.799092i
$35$	0.788164			0.133224
$36$	1.10430	+	1.54772i	0.184050	+	0.257953i
$37$	−0.473896			−0.0779080			−0.0389540	−	0.999241i	$-0.512403\pi$
$37$	−0.473896			−0.0779080			−0.0389540	+	0.999241i	$0.512403\pi$
$38$	0.465887	−	0.806941i	0.0755769	−	0.130903i
$39$	−4.80804	−	7.47379i	−0.769903	−	1.19676i
$40$	−4.87470	−	8.44323i	−0.770758	−	1.33499i
$41$	0.0469859	+	0.0813819i	0.00733796	+	0.0127097i	0.869671	−	0.493632i	$-0.164331\pi$
$41$	0.0469859	+	0.0813819i	0.00733796	+	0.0127097i	−0.862333	+	0.506341i	$0.830998\pi$
$42$	−0.272600	−	0.423739i	−0.0420630	−	0.0653843i
$43$	5.01977	−	8.69450i	0.765508	−	1.32590i	−0.174469	−	0.984663i	$-0.555821\pi$
$43$	5.01977	−	8.69450i	0.765508	−	1.32590i	0.939977	−	0.341237i	$-0.110846\pi$
$44$		0			0
$45$	5.51821	+	7.73397i	0.822607	+	1.15291i
$46$	−5.76606			−0.850159
$47$	1.56389	−	2.70873i	0.228116	−	0.395109i	−0.729134	−	0.684371i	$-0.760077\pi$
$47$	1.56389	−	2.70873i	0.228116	−	0.395109i	0.957250	+	0.289263i	$0.0934101\pi$
$48$	−1.84823	+	3.58917i	−0.266769	+	0.518052i
$49$	3.46903	+	6.00854i	0.495576	+	0.858363i
$50$	−2.93936	−	5.09112i	−0.415688	−	0.719993i
$51$	7.96345	−	0.383068i	1.11511	−	0.0536402i
$52$	−1.62585	+	2.81606i	−0.225465	+	0.390518i
$53$	−11.6119			−1.59502			−0.797508	−	0.603309i	$-0.793849\pi$
$53$	−11.6119			−1.59502			−0.797508	+	0.603309i	$0.793849\pi$
$54$	2.24943	−	5.64167i	0.306109	−	0.767734i
$55$		0			0
$56$	−0.383079	+	0.663512i	−0.0511910	+	0.0886655i
$57$	1.37914	−	0.0663409i	0.182671	−	0.00878707i
$58$	−0.918665	−	1.59117i	−0.120627	−	0.208931i
$59$	−1.24991	−	2.16491i	−0.162724	−	0.281847i	0.773121	−	0.634259i	$-0.218695\pi$
$59$	−1.24991	−	2.16491i	−0.162724	−	0.281847i	−0.935845	+	0.352412i	$0.885361\pi$
$60$	1.59153	−	3.09067i	0.205465	−	0.399004i
$61$	−2.00563	+	3.47385i	−0.256794	+	0.444781i	−0.965381	−	0.260842i	$-0.916000\pi$
$61$	−2.00563	+	3.47385i	−0.256794	+	0.444781i	0.708587	+	0.705624i	$0.249333\pi$
$62$	−9.82663			−1.24798
$63$	0.309523	−	0.679438i	0.0389963	−	0.0856011i
$64$	8.67387			1.08423
$65$	−8.12442	+	14.0719i	−1.00771	+	1.74540i
$66$		0			0
$67$	−2.07692	−	3.59733i	−0.253736	−	0.439483i	0.710816	−	0.703378i	$-0.248326\pi$
$67$	−2.07692	−	3.59733i	−0.253736	−	0.439483i	−0.964551	+	0.263895i	$0.914993\pi$
$68$	−1.45861	−	2.52639i	−0.176883	−	0.306370i
$69$	−4.62275	−	7.18577i	−0.556514	−	0.865065i
$70$	−0.460627	+	0.797829i	−0.0550554	+	0.0953588i
$71$	0.369763			0.0438828			0.0219414	−	0.999759i	$-0.493015\pi$
$71$	0.369763			0.0438828			0.0219414	+	0.999759i	$0.493015\pi$
$72$	−9.19287	+	0.886465i	−1.08339	+	0.104471i
$73$	−10.1834			−1.19188			−0.595940	−	0.803029i	$-0.703220\pi$
$73$	−10.1834			−1.19188			−0.595940	+	0.803029i	$0.703220\pi$
$74$	0.276959	−	0.479707i	0.0321958	−	0.0557648i
$75$	3.98811	−	7.74473i	0.460508	−	0.894284i
$76$	−0.252607	−	0.437529i	−0.0289761	−	0.0501880i
$77$		0			0
$78$	10.3754	−	0.499091i	1.17478	−	0.0565109i
$79$	5.85175	−	10.1355i	0.658374	−	1.14034i	−0.322663	−	0.946514i	$-0.604578\pi$
$79$	5.85175	−	10.1355i	0.658374	−	1.14034i	0.981037	−	0.193823i	$-0.0620887\pi$
$80$	7.38152			0.825279
$81$	8.83417	−	1.71974i	0.981574	−	0.191082i
$82$	−0.109840			−0.0121298
$83$	−0.532585	+	0.922464i	−0.0584588	+	0.101254i	−0.893774	−	0.448518i	$-0.851952\pi$
$83$	−0.532585	+	0.922464i	−0.0584588	+	0.101254i	0.835315	+	0.549772i	$0.185285\pi$
$84$	−0.272876	+	0.0131262i	−0.0297732	+	0.00143219i
$85$	−7.28872	−	12.6244i	−0.790572	−	1.36931i
$86$	5.86742	+	10.1627i	0.632700	+	1.09587i
$87$	1.24644	−	2.42053i	0.133633	−	0.259508i
$88$		0			0
$89$	−8.39173			−0.889521			−0.444761	−	0.895650i	$-0.646711\pi$
$89$	−8.39173			−0.889521			−0.444761	+	0.895650i	$0.646711\pi$
$90$	−11.0538	+	1.06592i	−1.16518	+	0.112357i
$91$	1.27691			0.133857
$92$	−1.56320	+	2.70754i	−0.162975	+	0.282280i
$93$	−7.87819	−	12.2461i	−0.816930	−	1.26987i
$94$	1.82796	+	3.16613i	0.188540	+	0.326561i
$95$	−1.26228	−	2.18634i	−0.129507	−	0.224314i
$96$	3.21669	+	5.00014i	0.328302	+	0.510324i
$97$	5.54336	−	9.60139i	0.562843	−	0.974873i	−0.434403	−	0.900718i	$-0.643041\pi$
$97$	5.54336	−	9.60139i	0.562843	−	0.974873i	0.997247	−	0.0741548i	$-0.0236259\pi$
$98$	−8.10963			−0.819196
$99$		0			0
$100$	−3.18748			−0.318748
$101$	−3.30574	+	5.72571i	−0.328933	+	0.569729i	−0.982300	−	0.187312i	$-0.940022\pi$
$101$	−3.30574	+	5.72571i	−0.328933	+	0.569729i	0.653367	+	0.757041i	$0.273356\pi$
$102$	−4.26632	+	8.28499i	−0.422428	+	0.820336i
$103$	−4.26163	−	7.38137i	−0.419911	−	0.727308i	0.576019	−	0.817436i	$-0.304605\pi$
$103$	−4.26163	−	7.38137i	−0.419911	−	0.727308i	−0.995930	+	0.0901287i	$0.971272\pi$
$104$	−7.89757	−	13.6790i	−0.774421	−	1.34134i
$105$	−1.36356	+	0.0655918i	−0.133070	+	0.00640110i
$106$	6.78634	−	11.7543i	0.659148	−	1.14168i
$107$	3.92040			0.378999			0.189500	−	0.981881i	$-0.439313\pi$
$107$	3.92040			0.378999			0.189500	+	0.981881i	$0.439313\pi$
$108$	−2.03930	−	2.58573i	−0.196232	−	0.248812i
$109$	−3.83554			−0.367379			−0.183689	−	0.982984i	$-0.558804\pi$
$109$	−3.83554			−0.367379			−0.183689	+	0.982984i	$0.558804\pi$
$110$		0			0
$111$	0.819863	−	0.0394381i	0.0778180	−	0.00374330i
$112$	−0.290038	−	0.502361i	−0.0274061	−	0.0474687i
$113$	−4.53726	−	7.85876i	−0.426829	−	0.739290i	0.569760	−	0.821811i	$-0.307036\pi$
$113$	−4.53726	−	7.85876i	−0.426829	−	0.739290i	−0.996589	+	0.0825212i	$0.973703\pi$
$114$	−0.738854	+	1.43482i	−0.0692001	+	0.134383i
$115$	−7.81132	+	13.5296i	−0.728409	+	1.26164i
$116$	−0.996214			−0.0924961
$117$	8.94013	+	12.5299i	0.826515	+	1.15839i
$118$	2.92194			0.268986
$119$	−0.572784	+	0.992091i	−0.0525070	+	0.0909448i
$120$	9.13613	+	14.2015i	0.834011	+	1.29642i
$121$		0			0
$122$	−2.34430	−	4.06045i	−0.212243	−	0.367616i
$123$	−0.0880606	−	0.136885i	−0.00794015	−	0.0123425i
$124$	−2.66404	+	4.61424i	−0.239237	+	0.414371i
$125$	−0.0932375			−0.00833941
$126$	0.506875	+	0.710403i	0.0451560	+	0.0632878i
$127$	−1.77330			−0.157355			−0.0786777	−	0.996900i	$-0.525070\pi$
$127$	−1.77330			−0.157355			−0.0786777	+	0.996900i	$0.525070\pi$
$128$	−1.63666	+	2.83478i	−0.144662	+	0.250562i
$129$	−7.96090	+	15.4597i	−0.700918	+	1.36115i
$130$	−9.49631	−	16.4481i	−0.832882	−	1.44259i
$131$	−0.162082	−	0.280734i	−0.0141611	−	0.0245278i	0.858858	−	0.512214i	$-0.171174\pi$
$131$	−0.162082	−	0.280734i	−0.0141611	−	0.0245278i	−0.873019	+	0.487686i	$0.837841\pi$
$132$		0			0
$133$	−0.0991965	+	0.171813i	−0.00860143	+	0.0148981i
$134$	4.85526			0.419430
$135$	−10.1904	−	12.9209i	−0.877051	−	1.11206i
$136$	14.1704			1.21510
$137$	−2.58835	+	4.48316i	−0.221138	+	0.383022i	−0.955154	−	0.296110i	$-0.904310\pi$
$137$	−2.58835	+	4.48316i	−0.221138	+	0.383022i	0.734016	+	0.679132i	$0.237644\pi$
$138$	9.97557	−	0.479857i	0.849177	−	0.0408481i
$139$	−6.16090	−	10.6710i	−0.522561	−	0.905102i	−0.999655	−	0.0262500i	$-0.991643\pi$
$139$	−6.16090	−	10.6710i	−0.522561	−	0.905102i	0.477095	−	0.878852i	$-0.341690\pi$
$140$	0.249755	+	0.432589i	0.0211082	+	0.0365604i
$141$	−2.48018	+	4.81639i	−0.208869	+	0.405613i
$142$	−0.216101	+	0.374297i	−0.0181348	+	0.0314103i
$143$		0			0
$144$	2.89883	−	6.36325i	0.241569	−	0.530271i
$145$	−4.97809			−0.413408
$146$	5.95150	−	10.3083i	0.492550	−	0.853121i
$147$	−6.50164	−	10.1064i	−0.536246	−	0.833560i
$148$	−0.150169	−	0.260101i	−0.0123438	−	0.0213801i
$149$	10.1028	+	17.4986i	0.827655	+	1.43354i	0.899873	+	0.436152i	$0.143659\pi$
$149$	10.1028	+	17.4986i	0.827655	+	1.43354i	−0.0722175	+	0.997389i	$0.523008\pi$
$150$	5.50893	+	8.56327i	0.449802	+	0.699188i
$151$	6.04314	−	10.4670i	0.491784	−	0.851794i	−0.508172	−	0.861256i	$-0.669678\pi$
$151$	6.04314	−	10.4670i	0.491784	−	0.851794i	0.999955	+	0.00946167i	$0.00301179\pi$
$152$	2.45408			0.199052
$153$	−13.7453	+	1.32545i	−1.11124	+	0.107157i
$154$		0			0
$155$	−13.3122	+	23.0574i	−1.06926	+	1.85202i
$156$	2.57845	−	5.00724i	0.206442	−	0.400900i
$157$	5.52618	+	9.57162i	0.441037	+	0.763898i	0.997767	−	0.0667952i	$-0.0212774\pi$
$157$	5.52618	+	9.57162i	0.441037	+	0.763898i	−0.556730	+	0.830694i	$0.687944\pi$
$158$	6.83989	+	11.8470i	0.544152	+	0.942499i
$159$	20.0892	−	0.966353i	1.59317	−	0.0766368i
$160$	5.43542	−	9.41442i	0.429708	−	0.744275i
$161$	1.22771			0.0967568
$162$	−3.42212	+	9.94757i	−0.268867	+	0.781555i
$163$	−15.3517			−1.20244			−0.601219	−	0.799084i	$-0.705318\pi$
$163$	−15.3517			−1.20244			−0.601219	+	0.799084i	$0.705318\pi$
$164$	−0.0297780	+	0.0515770i	−0.00232527	+	0.00402748i
$165$		0			0
$166$	−0.622518	−	1.07823i	−0.0483168	−	0.0836871i
$167$	1.30290	+	2.25668i	0.100821	+	0.174627i	0.912023	−	0.410139i	$-0.134520\pi$
$167$	1.30290	+	2.25668i	0.100821	+	0.174627i	−0.811202	+	0.584766i	$0.801186\pi$
$168$	0.607527	−	1.17979i	0.0468717	−	0.0910227i
$169$	−6.66248	+	11.5397i	−0.512498	+	0.887673i
$170$	17.0390			1.30683
$171$	−2.38045	+	0.229546i	−0.182038	+	0.0175538i
$172$	6.36271			0.485152
$173$	−9.63816	+	16.6938i	−0.732776	+	1.26920i	0.222917	+	0.974838i	$0.428442\pi$
$173$	−9.63816	+	16.6938i	−0.732776	+	1.26920i	−0.955692	+	0.294367i	$0.904891\pi$
$174$	1.72176	+	2.67636i	0.130526	+	0.202894i
$175$	0.625847	+	1.08400i	0.0473096	+	0.0819425i
$176$		0			0
$177$	2.34257	+	3.64138i	0.176078	+	0.273703i
$178$	4.90438	−	8.49463i	0.367599	−	0.636700i
$179$	18.0866			1.35186			0.675928	−	0.736967i	$-0.263743\pi$
$179$	18.0866			1.35186			0.675928	+	0.736967i	$0.263743\pi$
$180$	−2.49621	+	5.47946i	−0.186057	+	0.408415i
$181$	22.5500			1.67613			0.838064	−	0.545573i	$-0.183688\pi$
$181$	22.5500			1.67613			0.838064	+	0.545573i	$0.183688\pi$
$182$	−0.746268	+	1.29257i	−0.0553170	+	0.0958119i
$183$	3.18074	−	6.17685i	0.235127	−	0.456606i
$184$	−7.59322	−	13.1518i	−0.559779	−	0.969566i
$185$	−0.750397	−	1.29973i	−0.0551703	−	0.0955577i
$186$	17.0006	−	0.817782i	1.24654	−	0.0599627i
$187$		0			0
$188$	1.98227			0.144572
$189$	−0.478948	+	1.20122i	−0.0348383	+	0.0873760i
$190$	2.95087			0.214078
$191$	4.76976	−	8.26147i	0.345128	−	0.597779i	−0.640249	−	0.768167i	$-0.721169\pi$
$191$	4.76976	−	8.26147i	0.345128	−	0.597779i	0.985377	+	0.170388i	$0.0545021\pi$
$192$	−15.0062	+	0.721848i	−1.08298	+	0.0520949i
$193$	9.55458	+	16.5490i	0.687754	+	1.19122i	0.972563	+	0.232640i	$0.0747365\pi$
$193$	9.55458	+	16.5490i	0.687754	+	1.19122i	−0.284809	+	0.958584i	$0.591930\pi$
$194$	6.47942	+	11.2227i	0.465195	+	0.805742i
$195$	12.8846	−	25.0212i	0.922683	−	1.79181i
$196$	−2.19855	+	3.80800i	−0.157039	+	0.272000i
$197$	17.7425			1.26410			0.632049	−	0.774928i	$-0.282214\pi$
$197$	17.7425			1.26410			0.632049	+	0.774928i	$0.282214\pi$
$198$		0			0
$199$	10.2632			0.727539			0.363770	−	0.931489i	$-0.381490\pi$
$199$	10.2632			0.727539			0.363770	+	0.931489i	$0.381490\pi$
$200$	7.74158	−	13.4088i	0.547412	−	0.948146i
$201$	3.89255	+	6.05071i	0.274559	+	0.426784i
$202$	−3.86395	−	6.69255i	−0.271866	−	0.470886i
$203$	0.195602	+	0.338792i	0.0137285	+	0.0237785i
$204$	2.73373	+	4.24940i	0.191399	+	0.297518i
$205$	−0.148801	+	0.257731i	−0.0103927	+	0.0180007i
$206$	9.96251			0.694121
$207$	8.59560	+	12.0470i	0.597435	+	0.837327i
$208$	11.9589			0.829201
$209$		0			0
$210$	0.730512	−	1.41862i	0.0504101	−	0.0978940i
$211$	7.51248	+	13.0120i	0.517181	+	0.895783i	0.999801	+	0.0199534i	$0.00635179\pi$
$211$	7.51248	+	13.0120i	0.517181	+	0.895783i	−0.482620	+	0.875830i	$0.660315\pi$
$212$	−3.67960	−	6.37326i	−0.252716	−	0.437717i
$213$	−0.639709	+	0.0307721i	−0.0438321	+	0.00210847i
$214$	−2.29120	+	3.96847i	−0.156623	+	0.271279i
$215$	31.7945			2.16837
$216$	15.8304	−	2.29867i	1.07712	−	0.156405i
$217$	2.09228			0.142033
$218$	2.24161	−	3.88258i	0.151821	−	0.262962i
$219$	17.6178	−	0.847475i	1.19050	−	0.0572670i
$220$		0			0
$221$	−11.8085	−	20.4530i	−0.794329	−	1.37582i
$222$	−0.439231	+	0.852966i	−0.0294793	+	0.0572473i
$223$	−1.10758	+	1.91839i	−0.0741694	+	0.128465i	−0.900725	−	0.434390i	$-0.856964\pi$
$223$	−1.10758	+	1.91839i	−0.0741694	+	0.128465i	0.826555	+	0.562855i	$0.190297\pi$
$224$	−0.854285			−0.0570793
$225$	−6.25511	+	13.7307i	−0.417008	+	0.915377i
$226$	10.6068			0.705557
$227$	−13.0265	+	22.5625i	−0.864597	+	1.49753i	0.00284954	+	0.999996i	$0.499093\pi$
$227$	−13.0265	+	22.5625i	−0.864597	+	1.49753i	−0.867447	+	0.497530i	$0.834240\pi$
$228$	0.473435	+	0.735925i	0.0313540	+	0.0487378i
$229$	3.17552	+	5.50017i	0.209845	+	0.363461i	0.951665	−	0.307137i	$-0.0993709\pi$
$229$	3.17552	+	5.50017i	0.209845	+	0.363461i	−0.741821	+	0.670598i	$0.766038\pi$
$230$	−9.13035	−	15.8142i	−0.602037	−	1.04276i
$231$		0			0
$232$	2.41955	−	4.19078i	0.158851	−	0.275138i
$233$	−5.29654			−0.346988			−0.173494	−	0.984835i	$-0.555506\pi$
$233$	−5.29654			−0.346988			−0.173494	+	0.984835i	$0.555506\pi$
$234$	−17.9084	+	1.72690i	−1.17071	+	0.112891i
$235$	9.90543			0.646159
$236$	0.792148	−	1.37204i	0.0515644	−	0.0893122i
$237$	−9.28034	+	18.0220i	−0.602823	+	1.17065i
$238$	−0.669505	−	1.15962i	−0.0433975	−	0.0751667i
$239$	−5.80550	−	10.0554i	−0.375527	−	0.650431i	0.614879	−	0.788621i	$-0.289205\pi$
$239$	−5.80550	−	10.0554i	−0.375527	−	0.650431i	−0.990406	+	0.138190i	$0.955872\pi$
$240$	−12.7704	+	0.614298i	−0.824326	+	0.0396527i
$241$	3.66269	−	6.34397i	0.235935	−	0.408651i	−0.723609	−	0.690210i	$-0.757518\pi$
$241$	3.66269	−	6.34397i	0.235935	−	0.408651i	0.959544	+	0.281559i	$0.0908515\pi$
$242$		0			0
$243$	−15.1404	+	3.71043i	−0.971259	+	0.238024i
$244$	−2.54219			−0.162747
$245$	−10.9862	+	19.0286i	−0.701881	+	1.21569i
$246$	0.190028	−	0.00914098i	0.0121158	−	0.000582808i
$247$	−2.04504	−	3.54212i	−0.130123	−	0.225379i
$248$	−12.9405	−	22.4136i	−0.821724	−	1.42327i
$249$	0.844631	−	1.64023i	0.0535263	−	0.103945i
$250$	0.0544908	−	0.0943809i	0.00344630	−	0.00596917i
$251$	−19.0874			−1.20479			−0.602394	−	0.798199i	$-0.705786\pi$
$251$	−19.0874			−1.20479			−0.602394	+	0.798199i	$0.705786\pi$
$252$	0.470996	−	0.0454180i	0.0296700	−	0.00286106i
$253$		0			0
$254$	1.03637	−	1.79505i	0.0650278	−	0.112632i
$255$	13.6605	+	21.2343i	0.855451	+	1.32974i
$256$	6.76084	+	11.7101i	0.422553	+	0.731883i
$257$	5.01499	+	8.68622i	0.312827	+	0.541831i	0.978973	−	0.203989i	$-0.0653908\pi$
$257$	5.01499	+	8.68622i	0.312827	+	0.541831i	−0.666147	+	0.745821i	$0.732057\pi$
$258$	−10.9967	−	17.0936i	−0.684623	−	1.06420i
$259$	−0.0589700	+	0.102139i	−0.00366421	+	0.00634661i
$260$	−10.2979			−0.638651
$261$	−1.95497	+	4.29137i	−0.121010	+	0.265629i
$262$	0.378902			0.0234086
$263$	−7.00714	+	12.1367i	−0.432079	+	0.748383i	−0.997052	−	0.0767265i	$-0.975553\pi$
$263$	−7.00714	+	12.1367i	−0.432079	+	0.748383i	0.564973	+	0.825109i	$0.308886\pi$
$264$		0			0
$265$	−18.3870	−	31.8472i	−1.12951	−	1.95636i
$266$	−0.115947	−	0.200826i	−0.00710916	−	0.0123134i
$267$	14.5181	−	0.698368i	0.888494	−	0.0427394i
$268$	1.31628	−	2.27986i	0.0804044	−	0.139265i
$269$	1.15556			0.0704555			0.0352278	−	0.999379i	$-0.488784\pi$
$269$	1.15556			0.0704555			0.0352278	+	0.999379i	$0.488784\pi$
$270$	19.0350	−	2.76400i	1.15843	−	0.168212i
$271$	29.2424			1.77635			0.888174	−	0.459507i	$-0.151974\pi$
$271$	29.2424			1.77635			0.888174	+	0.459507i	$0.151974\pi$
$272$	−5.36439	+	9.29139i	−0.325264	+	0.563373i
$273$	−2.20913	+	0.106266i	−0.133702	+	0.00643152i
$274$	−3.02542	−	5.24019i	−0.182773	−	0.316571i
$275$		0			0
$276$	2.47909	−	4.81427i	0.149224	−	0.289785i
$277$	−11.3658	+	19.6862i	−0.682907	+	1.18283i	0.291183	+	0.956667i	$0.405951\pi$
$277$	−11.3658	+	19.6862i	−0.682907	+	1.18283i	−0.974090	+	0.226162i	$0.927382\pi$
$278$	14.4025			0.863803
$279$	14.6488	+	20.5308i	0.877001	+	1.22915i
$280$	−2.42637			−0.145003
$281$	8.45940	−	14.6521i	0.504645	−	0.874071i	−0.495340	−	0.868699i	$-0.664957\pi$
$281$	8.45940	−	14.6521i	0.504645	−	0.874071i	0.999986	−	0.00537218i	$-0.00171003\pi$
$282$	−3.42596	−	5.32544i	−0.204013	−	0.317125i
$283$	14.2782	+	24.7306i	0.848752	+	1.47008i	0.882323	+	0.470645i	$0.155979\pi$
$283$	14.2782	+	24.7306i	0.848752	+	1.47008i	−0.0335710	+	0.999436i	$0.510688\pi$
$284$	0.117171	+	0.202947i	0.00695284	+	0.0120427i
$285$	2.36576	+	3.67743i	0.140136	+	0.217832i
$286$		0			0
$287$	0.0233870			0.00138049
$288$	−5.98115	−	8.38279i	−0.352443	−	0.493961i
$289$	4.18777			0.246340
$290$	2.90935	−	5.03914i	0.170843	−	0.295908i
$291$	−8.79126	+	17.0722i	−0.515353	+	1.00079i
$292$	−3.22695	−	5.58923i	−0.188843	−	0.327085i
$293$	8.08895	+	14.0105i	0.472561	+	0.818500i	0.999507	−	0.0313988i	$-0.00999619\pi$
$293$	8.08895	+	14.0105i	0.472561	+	0.818500i	−0.526946	+	0.849899i	$0.676663\pi$
$294$	14.0301	−	0.674892i	0.818250	−	0.0393605i
$295$	3.95837	−	6.85610i	0.230465	−	0.399178i
$296$	1.45889			0.0847962
$297$		0			0
$298$	−23.6176			−1.36813
$299$	−12.6552	+	21.9195i	−0.731871	+	1.26764i
$300$	5.51450	−	0.265265i	0.318380	−	0.0153151i
$301$	−1.24929	−	2.16383i	−0.0720077	−	0.124721i
$302$	7.06359	+	12.2345i	0.406464	+	0.704016i
$303$	5.24259	−	10.1809i	0.301179	−	0.584876i
$304$	−0.929022	+	1.60911i	−0.0532830	+	0.0922889i
$305$	−12.7034			−0.727393
$306$	6.69146	−	14.6885i	0.382525	−	0.839685i
$307$	−14.3499			−0.818989			−0.409495	−	0.912312i	$-0.634295\pi$
$307$	−14.3499			−0.818989			−0.409495	+	0.912312i	$0.634295\pi$
$308$		0			0
$309$	7.98713	+	12.4155i	0.454372	+	0.706292i
$310$	−15.5601	−	26.9509i	−0.883756	−	1.53071i
$311$	−1.78864	−	3.09801i	−0.101424	−	0.175672i	0.810847	−	0.585258i	$-0.199007\pi$
$311$	−1.78864	−	3.09801i	−0.101424	−	0.175672i	−0.912272	+	0.409586i	$0.865673\pi$
$312$	14.8016	+	23.0081i	0.837974	+	1.30258i
$313$	−5.54353	+	9.60167i	−0.313339	+	0.542719i	−0.979083	−	0.203461i	$-0.934781\pi$
$313$	−5.54353	+	9.60167i	−0.313339	+	0.542719i	0.665744	+	0.746180i	$0.268114\pi$
$314$	−12.9187			−0.729042
$315$	2.35357	−	0.226954i	0.132609	−	0.0127874i
$316$	7.41727			0.417254
$317$	6.03393	−	10.4511i	0.338899	−	0.586991i	−0.645327	−	0.763907i	$-0.723279\pi$
$317$	6.03393	−	10.4511i	0.338899	−	0.586991i	0.984226	+	0.176916i	$0.0566121\pi$
$318$	−10.7625	+	20.9003i	−0.603531	+	1.17203i
$319$		0			0
$320$	13.7348	+	23.7893i	0.767797	+	1.32986i
$321$	−6.78249	+	0.326260i	−0.378562	+	0.0182100i
$322$	−0.717508	+	1.24276i	−0.0399852	+	0.0692564i
$323$	3.66937			0.204169
$324$	3.74328	+	4.30373i	0.207960	+	0.239096i
$325$	−25.8050			−1.43140
$326$	8.97201	−	15.5400i	0.496913	−	0.860679i
$327$	6.63569	−	0.319198i	0.366954	−	0.0176517i
$328$	−0.144646	−	0.250534i	−0.00798675	−	0.0138335i
$329$	−0.389209	−	0.674130i	−0.0214578	−	0.0371660i
$330$		0			0
$331$	1.03329	−	1.78971i	0.0567948	−	0.0983716i	−0.836230	−	0.548379i	$-0.815245\pi$
$331$	1.03329	−	1.78971i	0.0567948	−	0.0983716i	0.893025	+	0.450007i	$0.148579\pi$
$332$	−0.675067			−0.0370491
$333$	−1.41512	+	0.136460i	−0.0775482	+	0.00747795i
$334$	−3.04581			−0.166659
$335$	6.57745	−	11.3925i	0.359365	−	0.622438i
$336$	0.543588	+	0.844973i	0.0296552	+	0.0460971i
$337$	0.274688	+	0.475774i	0.0149632	+	0.0259170i	0.873410	−	0.486985i	$-0.161904\pi$
$337$	0.274688	+	0.475774i	0.0149632	+	0.0259170i	−0.858447	+	0.512903i	$0.828570\pi$
$338$	−7.78751	−	13.4884i	−0.423584	−	0.733670i
$339$	8.50370	+	13.2185i	0.461857	+	0.717928i
$340$	4.61933	−	8.00091i	0.250518	−	0.433910i
$341$		0			0
$342$	1.15885	−	2.54380i	0.0626633	−	0.137553i
$343$	3.46881			0.187298
$344$	−15.4534	+	26.7661i	−0.833191	+	1.44313i
$345$	12.3880	−	24.0570i	0.666949	−	1.29518i
$346$	−11.2657	−	19.5127i	−0.605646	−	1.04901i
$347$	7.12154	+	12.3349i	0.382304	+	0.662171i	0.991391	−	0.130933i	$-0.0417972\pi$
$347$	7.12154	+	12.3349i	0.382304	+	0.662171i	−0.609087	+	0.793104i	$0.708464\pi$
$348$	1.72350	−	0.0829059i	0.0923893	−	0.00444422i
$349$	−10.4148	+	18.0390i	−0.557493	+	0.965606i	0.440212	+	0.897894i	$0.354903\pi$
$349$	−10.4148	+	18.0390i	−0.557493	+	0.965606i	−0.997705	+	0.0677122i	$0.978430\pi$
$350$	−1.46305			−0.0782036
$351$	−16.5096	−	20.9334i	−0.881219	−	1.11734i
$352$		0			0
$353$	10.2296	−	17.7181i	0.544465	−	0.943042i	−0.454175	−	0.890912i	$-0.650066\pi$
$353$	10.2296	−	17.7181i	0.544465	−	0.943042i	0.998640	−	0.0521291i	$-0.0166007\pi$
$354$	−5.05510	+	0.243167i	−0.268676	+	0.0129242i
$355$	0.585507	+	1.01413i	0.0310755	+	0.0538243i
$356$	−2.65919	−	4.60585i	−0.140937	−	0.244110i
$357$	0.908382	−	1.76403i	0.0480767	−	0.0933626i
$358$	−10.5704	+	18.3084i	−0.558661	+	0.967629i
$359$	−18.9964			−1.00259			−0.501297	−	0.865275i	$-0.667144\pi$
$359$	−18.9964			−1.00259			−0.501297	+	0.865275i	$0.667144\pi$
$360$	−16.9878	−	23.8091i	−0.895338	−	1.25485i
$361$	−18.3645			−0.966554
$362$	−13.1789	+	22.8265i	−0.692667	+	1.19974i
$363$		0			0
$364$	0.404632	+	0.700843i	0.0212085	+	0.0367341i
$365$	−16.1251	−	27.9295i	−0.844026	−	1.46190i
$366$	4.39367	+	6.82969i	0.229661	+	0.356993i
$367$	−1.92400	+	3.33247i	−0.100432	+	0.173953i	−0.911863	−	0.410495i	$-0.865356\pi$
$367$	−1.92400	+	3.33247i	−0.100432	+	0.173953i	0.811431	+	0.584449i	$0.198689\pi$
$368$	11.4980			0.599376
$369$	0.163741	+	0.229489i	0.00852401	+	0.0119467i
$370$	1.75422			0.0911975
$371$	−1.44494	+	2.50272i	−0.0750177	+	0.129935i
$372$	4.22491	−	8.20458i	0.219052	−	0.425388i
$373$	−4.55186	−	7.88405i	−0.235686	−	0.408221i	0.723786	−	0.690025i	$-0.242400\pi$
$373$	−4.55186	−	7.88405i	−0.235686	−	0.408221i	−0.959472	+	0.281804i	$0.909067\pi$
$374$		0			0
$375$	0.161306	−	0.00775932i	0.00832978	−	0.000400689i
$376$	−4.81443	+	8.33884i	−0.248285	+	0.430043i
$377$	−8.06507			−0.415372
$378$	−0.936040	−	1.18685i	−0.0481447	−	0.0610450i
$379$	−26.6856			−1.37075			−0.685375	−	0.728190i	$-0.740362\pi$
$379$	−26.6856			−1.37075			−0.685375	+	0.728190i	$0.740362\pi$
$380$	0.799990	−	1.38562i	0.0410386	−	0.0710810i
$381$	3.06791	−	0.147576i	0.157174	−	0.00756056i
$382$	5.57519	+	9.65651i	0.285252	+	0.494070i
$383$	2.22159	+	3.84790i	0.113518	+	0.196618i	0.917186	−	0.398459i	$-0.130455\pi$
$383$	2.22159	+	3.84790i	0.113518	+	0.196618i	−0.803669	+	0.595077i	$0.797121\pi$
$384$	2.59559	−	5.04052i	0.132456	−	0.257223i
$385$		0			0
$386$	−22.3360			−1.13687
$387$	12.4862	−	27.4085i	0.634708	−	1.39325i
$388$	7.02637			0.356710
$389$	5.83331	−	10.1036i	0.295761	−	0.512272i	−0.679401	−	0.733767i	$-0.737760\pi$
$389$	5.83331	−	10.1036i	0.295761	−	0.512272i	0.975162	+	0.221495i	$0.0710936\pi$
$390$	17.7979	+	27.6657i	0.901233	+	1.40091i
$391$	−11.3535	−	19.6648i	−0.574170	−	0.994491i
$392$	−10.6794	−	18.4973i	−0.539392	−	0.934255i
$393$	0.303772	+	0.472195i	0.0153233	+	0.0238191i
$394$	−10.3692	+	17.9601i	−0.522395	+	0.904814i
$395$	37.0642			1.86490
$396$		0			0
$397$	30.3159			1.52151			0.760756	−	0.649038i	$-0.224828\pi$
$397$	30.3159			1.52151			0.760756	+	0.649038i	$0.224828\pi$
$398$	−5.99813	+	10.3891i	−0.300659	+	0.520757i
$399$	0.157316	−	0.305501i	0.00787567	−	0.0152942i
$400$	5.86134	+	10.1521i	0.293067	+	0.507607i
$401$	−7.98042	−	13.8225i	−0.398523	−	0.690262i	0.595021	−	0.803710i	$-0.297144\pi$
$401$	−7.98042	−	13.8225i	−0.398523	−	0.690262i	−0.993544	+	0.113448i	$0.963810\pi$
$402$	−8.39984	+	0.404059i	−0.418946	+	0.0201526i
$403$	−21.5673	+	37.3557i	−1.07434	+	1.86082i
$404$	−4.19012			−0.208466
$405$	18.7052	+	21.5058i	0.929470	+	1.06863i
$406$	−0.457262			−0.0226935
$407$		0			0
$408$	−24.5155	+	1.17928i	−1.21370	+	0.0583829i
$409$	5.65111	+	9.78800i	0.279429	+	0.483986i	0.971243	−	0.238090i	$-0.0765214\pi$
$409$	5.65111	+	9.78800i	0.279429	+	0.483986i	−0.691814	+	0.722076i	$0.743188\pi$
$410$	−0.173927	−	0.301251i	−0.00858967	−	0.0148777i
$411$	4.10489	−	7.97149i	0.202479	−	0.393205i
$412$	2.70087	−	4.67805i	0.133062	−	0.230471i
$413$	−0.622138			−0.0306134
$414$	−17.2183	+	1.66035i	−0.846233	+	0.0816019i
$415$	−3.37332			−0.165590
$416$	8.80600	−	15.2524i	0.431749	−	0.747812i
$417$	11.5467	+	17.9486i	0.565445	+	0.878949i
$418$		0			0
$419$	0.927962	+	1.60728i	0.0453339	+	0.0785207i	0.887802	−	0.460226i	$-0.152231\pi$
$419$	0.927962	+	1.60728i	0.0453339	+	0.0785207i	−0.842468	+	0.538746i	$0.818898\pi$
$420$	−0.468089	−	0.727615i	−0.0228404	−	0.0355040i
$421$	−6.12175	+	10.6032i	−0.298356	+	0.516767i	−0.975760	−	0.218844i	$-0.929771\pi$
$421$	−6.12175	+	10.6032i	−0.298356	+	0.516767i	0.677404	+	0.735611i	$0.263105\pi$
$422$	−17.5621			−0.854909
$423$	3.89001	−	8.53900i	0.189139	−	0.415180i
$424$	35.7472			1.73604
$425$	11.5753	−	20.0490i	0.561485	−	0.972520i
$426$	0.342716	−	0.665538i	0.0166046	−	0.0322454i
$427$	0.499147	+	0.864549i	0.0241554	+	0.0418384i
$428$	1.24230	+	2.15174i	0.0600491	+	0.104008i
$429$		0			0
$430$	−18.5817	+	32.1844i	−0.896089	+	1.55207i
$431$	14.1977			0.683880			0.341940	−	0.939722i	$-0.388916\pi$
$431$	14.1977			0.683880			0.341940	+	0.939722i	$0.388916\pi$
$432$	−4.48557	+	11.2500i	−0.215812	+	0.541266i
$433$	−34.7050			−1.66782			−0.833908	−	0.551903i	$-0.813902\pi$
$433$	−34.7050			−1.66782			−0.833908	+	0.551903i	$0.813902\pi$
$434$	−1.22279	+	2.11794i	−0.0586959	+	0.101664i
$435$	8.61235	−	0.414282i	0.412931	−	0.0198633i
$436$	−1.21542	−	2.10516i	−0.0582079	−	0.100819i
$437$	−1.96623	−	3.40561i	−0.0940575	−	0.162912i
$438$	−9.43853	+	18.3292i	−0.450990	+	0.875802i
$439$	−6.29079	+	10.8960i	−0.300243	+	0.520037i	−0.976191	−	0.216913i	$-0.930401\pi$
$439$	−6.29079	+	10.8960i	−0.300243	+	0.520037i	0.675948	+	0.736950i	$0.263735\pi$
$440$		0			0
$441$	12.0892	+	16.9435i	0.575677	+	0.806832i
$442$	27.6051			1.31304
$443$	19.0379	−	32.9746i	0.904518	−	1.56667i	0.0829561	−	0.996553i	$-0.473564\pi$
$443$	19.0379	−	32.9746i	0.904518	−	1.56667i	0.821562	−	0.570119i	$-0.193103\pi$
$444$	0.281446	+	0.437490i	0.0133568	+	0.0207623i
$445$	−13.2880	−	23.0155i	−0.629912	−	1.09104i
$446$	−1.29461	−	2.24233i	−0.0613017	−	0.106178i
$447$	−18.9346	−	29.4327i	−0.895578	−	1.39212i
$448$	1.07935	−	1.86948i	0.0509944	−	0.0883248i
$449$	19.5509			0.922662			0.461331	−	0.887228i	$-0.347372\pi$
$449$	19.5509			0.922662			0.461331	+	0.887228i	$0.347372\pi$
$450$	−10.2434	−	14.3564i	−0.482877	−	0.676769i
$451$		0			0
$452$	2.87555	−	4.98060i	0.135255	−	0.234268i
$453$	−9.58386	+	18.6114i	−0.450289	+	0.874439i
$454$	−15.2261	−	26.3724i	−0.714598	−	1.23772i
$455$	2.02195	+	3.50212i	0.0947904	+	0.164182i
$456$	−4.24567	+	0.204231i	−0.198822	+	0.00956398i
$457$	−5.67157	+	9.82344i	−0.265305	+	0.459521i	−0.967643	−	0.252322i	$-0.918806\pi$
$457$	−5.67157	+	9.82344i	−0.265305	+	0.459521i	0.702339	+	0.711843i	$0.252139\pi$
$458$	−7.42349			−0.346877
$459$	23.6697	−	3.43700i	1.10481	−	0.160425i
$460$	−9.90108			−0.461640
$461$	12.8991	−	22.3419i	0.600772	−	1.04057i	−0.391933	−	0.919994i	$-0.628193\pi$
$461$	12.8991	−	22.3419i	0.600772	−	1.04057i	0.992704	−	0.120573i	$-0.0384733\pi$
$462$		0			0
$463$	10.2149	+	17.6926i	0.474725	+	0.822247i	0.999581	−	0.0289436i	$-0.00921432\pi$
$463$	10.2149	+	17.6926i	0.474725	+	0.822247i	−0.524856	+	0.851191i	$0.675881\pi$
$464$	1.83190	+	3.17295i	0.0850439	+	0.147300i
$465$	21.1119	−	40.9984i	0.979043	−	1.90125i
$466$	3.09546	−	5.36149i	0.143394	−	0.248366i
$467$	0.863420			0.0399543			0.0199772	−	0.999800i	$-0.493641\pi$
$467$	0.863420			0.0399543			0.0199772	+	0.999800i	$0.493641\pi$
$468$	−4.04415	+	8.87735i	−0.186941	+	0.410356i
$469$	−1.03378			−0.0477354
$470$	−5.78904	+	10.0269i	−0.267028	+	0.462507i
$471$	−10.3571	−	16.0995i	−0.477231	−	0.741825i
$472$	3.84785	+	6.66467i	0.177112	+	0.306766i
$473$		0			0
$474$	−12.8193	−	19.9267i	−0.588809	−	0.915265i
$475$	2.00465	−	3.47215i	0.0919795	−	0.159313i
$476$	−0.726020			−0.0332771
$477$	−34.6748	+	3.34368i	−1.58765	+	0.153097i
$478$	13.5716			0.620753
$479$	−6.58209	+	11.4005i	−0.300743	+	0.520903i	−0.976305	−	0.216401i	$-0.930568\pi$
$479$	−6.58209	+	11.4005i	−0.300743	+	0.520903i	0.675561	+	0.737304i	$0.263901\pi$
$480$	−8.62007	+	16.7398i	−0.393451	+	0.764062i
$481$	−1.21573	−	2.10570i	−0.0554324	−	0.0960118i
$482$	4.28117	+	7.41521i	0.195002	+	0.337754i
$483$	−2.12399	+	0.102171i	−0.0966450	+	0.00464894i
$484$		0			0
$485$	35.1109			1.59430
$486$	5.09260	−	17.4946i	0.231005	−	0.793571i
$487$	−14.1969			−0.643324			−0.321662	−	0.946855i	$-0.604241\pi$
$487$	−14.1969			−0.643324			−0.321662	+	0.946855i	$0.604241\pi$
$488$	6.17434	−	10.6943i	0.279499	−	0.484107i
$489$	26.5592	−	1.27758i	1.20105	−	0.0577744i
$490$	−12.8413	−	22.2418i	−0.580111	−	1.00478i
$491$	4.80586	+	8.32400i	0.216886	+	0.375657i	0.953854	−	0.300270i	$-0.0970768\pi$
$491$	4.80586	+	8.32400i	0.216886	+	0.375657i	−0.736969	+	0.675927i	$0.763743\pi$
$492$	0.0472251	−	0.0917089i	0.00212907	−	0.00413456i
$493$	3.61774	−	6.26611i	0.162935	−	0.282211i
$494$	4.78074			0.215096
$495$		0			0
$496$	19.5952			0.879850
$497$	0.0460121	−	0.0796952i	0.00206392	−	0.00357482i
$498$	1.16672	+	1.81359i	0.0522819	+	0.0812689i
$499$	11.3625	+	19.6804i	0.508653	+	0.881014i	0.999950	+	0.0100212i	$0.00318989\pi$
$499$	11.3625	+	19.6804i	0.508653	+	0.881014i	−0.491296	+	0.870993i	$0.663477\pi$
$500$	−0.0295453	−	0.0511740i	−0.00132131	−	0.00228857i
$501$	−2.44188	−	3.79574i	−0.109095	−	0.169581i
$502$	11.1553	−	19.3215i	0.497884	−	0.862361i
$503$	33.5451			1.49570			0.747851	−	0.663867i	$-0.231086\pi$
$503$	33.5451			1.49570			0.747851	+	0.663867i	$0.231086\pi$
$504$	−0.952869	+	2.09165i	−0.0424442	+	0.0931696i
$505$	−20.9381			−0.931732
$506$		0			0
$507$	10.5661	−	20.5188i	0.469256	−	0.911272i
$508$	−0.561929	−	0.973289i	−0.0249316	−	0.0431827i
$509$	−8.97375	−	15.5430i	−0.397754	−	0.688931i	0.595694	−	0.803211i	$-0.296877\pi$
$509$	−8.97375	−	15.5430i	−0.397754	−	0.688931i	−0.993449	+	0.114281i	$0.963544\pi$
$510$	−29.4783	+	1.41800i	−1.30532	+	0.0627902i
$511$	−1.26719	+	2.19484i	−0.0560572	+	0.0970939i
$512$	−22.3516			−0.987811
$513$	4.09920	−	0.595230i	0.180984	−	0.0262801i
$514$	−11.7237			−0.517108
$515$	13.4963	−	23.3763i	0.594718	−	1.03008i
$516$	−11.0078	+	0.529511i	−0.484592	+	0.0233104i
$517$		0			0
$518$	−0.0689277	−	0.119386i	−0.00302851	−	0.00524553i
$519$	15.2852	−	29.6832i	0.670947	−	1.30295i
$520$	25.0110	−	43.3204i	1.09681	−	1.89973i
$521$	2.95071			0.129273			0.0646364	−	0.997909i	$-0.479411\pi$
$521$	2.95071			0.129273			0.0646364	+	0.997909i	$0.479411\pi$
$522$	−3.20145	−	4.48695i	−0.140124	−	0.196389i
$523$	−20.8217			−0.910470			−0.455235	−	0.890371i	$-0.650445\pi$
$523$	−20.8217			−0.910470			−0.455235	+	0.890371i	$0.650445\pi$
$524$	0.102722	−	0.177919i	0.00448741	−	0.00777243i
$525$	−1.17296	−	1.82329i	−0.0511921	−	0.0795748i
$526$	−8.19037	−	14.1861i	−0.357117	−	0.618545i
$527$	−19.3488	−	33.5132i	−0.842848	−	1.45986i
$528$		0			0
$529$	−0.667523	+	1.15618i	−0.0290228	+	0.0502689i
$530$	42.9837			1.86709
$531$	−4.35580	−	6.10481i	−0.189026	−	0.264926i
$532$	−0.125734			−0.00545128
$533$	−0.241074	+	0.417553i	−0.0104421	+	0.0180862i
$534$	−7.77789	+	15.1043i	−0.336582	+	0.653627i
$535$	6.20781	+	10.7522i	0.268387	+	0.464860i
$536$	6.39380	+	11.0744i	0.276170	+	0.478341i
$537$	−31.2907	+	1.50519i	−1.35030	+	0.0649536i
$538$	−0.675342	+	1.16973i	−0.0291161	+	0.0504305i
$539$		0			0
$540$	3.86257	−	9.68749i	0.166219	−	0.416883i
$541$	0.958892			0.0412260			0.0206130	−	0.999788i	$-0.493438\pi$
$541$	0.958892			0.0412260			0.0206130	+	0.999788i	$0.493438\pi$
$542$	−17.0901	+	29.6010i	−0.734084	+	1.27147i
$543$	−39.0126	+	1.87663i	−1.67419	+	0.0805340i
$544$	7.90019	+	13.6835i	0.338718	+	0.586676i
$545$	−6.07345	−	10.5195i	−0.260158	−	0.450607i
$546$	1.18351	−	2.29832i	0.0506496	−	0.0983591i
$547$	19.5031	−	33.7804i	0.833893	−	1.44435i	−0.0610353	−	0.998136i	$-0.519440\pi$
$547$	19.5031	−	33.7804i	0.833893	−	1.44435i	0.894928	−	0.446210i	$-0.147226\pi$
$548$	−3.28081			−0.140149
$549$	−4.98880	+	10.9510i	−0.212917	+	0.467376i
$550$		0			0
$551$	0.626531	−	1.08518i	0.0266911	−	0.0462304i
$552$	14.2312	+	22.1214i	0.605718	+	0.941550i
$553$	−1.45634	−	2.52246i	−0.0619301	−	0.107266i
$554$	−13.2851	−	23.0104i	−0.564429	−	0.977619i
$555$	1.40639	+	2.18614i	0.0596979	+	0.0927966i
$556$	3.90456	−	6.76290i	0.165590	−	0.286811i
$557$	46.6661			1.97731			0.988653	−	0.150217i	$-0.0479972\pi$
$557$	46.6661			1.97731			0.988653	+	0.150217i	$0.0479972\pi$
$558$	−29.3438	+	2.82961i	−1.24222	+	0.119787i
$559$	51.5108			2.17867
$560$	0.918531	−	1.59094i	0.0388150	−	0.0672296i
$561$		0			0
$562$	9.88786	+	17.1263i	0.417094	+	0.722428i
$563$	−1.28627	−	2.22789i	−0.0542099	−	0.0938942i	0.837647	−	0.546212i	$-0.183931\pi$
$563$	−1.28627	−	2.22789i	−0.0542099	−	0.0938942i	−0.891857	+	0.452318i	$0.850597\pi$
$564$	−3.42943	+	0.164967i	−0.144405	+	0.00694635i
$565$	14.3692	−	24.8881i	0.604516	−	1.04705i
$566$	−33.3785			−1.40300
$567$	0.728637	−	2.11803i	0.0305999	−	0.0889489i
$568$	−1.13832			−0.0477627
$569$	9.19439	−	15.9252i	0.385449	−	0.667617i	−0.606382	−	0.795173i	$-0.707380\pi$
$569$	9.19439	−	15.9252i	0.385449	−	0.667617i	0.991831	+	0.127556i	$0.0407133\pi$
$570$	−5.10515	+	0.245574i	−0.213831	+	0.0102860i
$571$	17.7347	+	30.7173i	0.742173	+	1.28548i	0.951504	+	0.307636i	$0.0995378\pi$
$571$	17.7347	+	30.7173i	0.742173	+	1.28548i	−0.209332	+	0.977845i	$0.567129\pi$
$572$		0			0
$573$	−7.56440	+	14.6897i	−0.316008	+	0.613672i
$574$	−0.0136681	+	0.0236738i	−0.000570495	+	0.000988127i
$575$	−24.8105			−1.03467
$576$	25.9015	−	2.49767i	1.07923	−	0.104070i
$577$	34.4382			1.43368			0.716840	−	0.697238i	$-0.245588\pi$
$577$	34.4382			1.43368			0.716840	+	0.697238i	$0.245588\pi$
$578$	−2.44746	+	4.23913i	−0.101801	+	0.176324i
$579$	−17.9071	−	27.8355i	−0.744195	−	1.15680i
$580$	−1.57747	−	2.73226i	−0.0655008	−	0.113451i
$581$	0.132546	+	0.229577i	0.00549894	+	0.00952445i
$582$	−12.1437	−	18.8766i	−0.503372	−	0.782460i
$583$		0			0
$584$	31.3497			1.29726
$585$	−20.2087	+	44.3602i	−0.835525	+	1.83407i
$586$	−18.9097			−0.781153
$587$	−1.01312	+	1.75477i	−0.0418159	+	0.0724273i	−0.886176	−	0.463349i	$-0.846648\pi$
$587$	−1.01312	+	1.75477i	−0.0418159	+	0.0724273i	0.844360	+	0.535776i	$0.179981\pi$
$588$	3.48669	−	6.77099i	0.143789	−	0.279231i
$589$	−3.35089	−	5.80391i	−0.138071	−	0.239146i
$590$	4.62679	+	8.01383i	0.190482	+	0.329924i
$591$	−30.6954	+	1.47655i	−1.26264	+	0.0607370i
$592$	−0.552281	+	0.956579i	−0.0226986	+	0.0393152i
$593$	7.39127			0.303523			0.151761	−	0.988417i	$-0.451505\pi$
$593$	7.39127			0.303523			0.151761	+	0.988417i	$0.451505\pi$
$594$		0			0
$595$	−3.62793			−0.148731
$596$	−6.40281	+	11.0900i	−0.262269	+	0.454264i
$597$	−17.7559	+	0.854114i	−0.726699	+	0.0349566i
$598$	−14.7922	−	25.6208i	−0.604898	−	1.04771i
$599$	4.65791	+	8.06773i	0.190317	+	0.329639i	0.945355	−	0.326042i	$-0.105715\pi$
$599$	4.65791	+	8.06773i	0.190317	+	0.329639i	−0.755038	+	0.655681i	$0.772382\pi$
$600$	−12.2774	+	23.8422i	−0.501224	+	0.973352i
$601$	−9.77860	+	16.9370i	−0.398877	+	0.690876i	−0.993588	−	0.113064i	$-0.963933\pi$
$601$	−9.77860	+	16.9370i	−0.398877	+	0.690876i	0.594710	+	0.803940i	$0.297267\pi$
$602$	2.92049			0.119030
$603$	−7.23785	−	10.1441i	−0.294748	−	0.413100i
$604$	7.65985			0.311675
$605$		0			0
$606$	7.24179	+	11.2569i	0.294177	+	0.457280i
$607$	−13.8019	−	23.9057i	−0.560204	−	0.970301i	−0.997478	−	0.0709732i	$-0.977390\pi$
$607$	−13.8019	−	23.9057i	−0.560204	−	0.970301i	0.437274	−	0.899328i	$-0.355944\pi$
$608$	1.36818	+	2.36976i	0.0554870	+	0.0961063i
$609$	−0.366595	−	0.569849i	−0.0148552	−	0.0230915i
$610$	7.42424	−	12.8592i	0.300599	−	0.520652i
$611$	16.0479			0.649230
$612$	−5.08312	−	7.12418i	−0.205473	−	0.287978i
$613$	−17.8256			−0.719969			−0.359985	−	0.932958i	$-0.617218\pi$
$613$	−17.8256			−0.719969			−0.359985	+	0.932958i	$0.617218\pi$
$614$	8.38649	−	14.5258i	0.338451	−	0.586215i
$615$	0.235984	−	0.458270i	0.00951581	−	0.0184792i
$616$		0			0
$617$	2.55221	+	4.42056i	0.102748	+	0.177965i	0.912816	−	0.408371i	$-0.133903\pi$
$617$	2.55221	+	4.42056i	0.102748	+	0.177965i	−0.810068	+	0.586336i	$0.800570\pi$
$618$	−17.2357	+	0.829091i	−0.693320	+	0.0333509i
$619$	−1.27452	+	2.20754i	−0.0512273	+	0.0887284i	−0.890502	−	0.454979i	$-0.849647\pi$
$619$	−1.27452	+	2.20754i	−0.0512273	+	0.0887284i	0.839275	+	0.543708i	$0.182980\pi$
$620$	−16.8736			−0.677661
$621$	−15.8734	−	20.1266i	−0.636977	−	0.807654i
$622$	4.18133			0.167656
$623$	−1.04424	+	1.80867i	−0.0418365	+	0.0724629i
$624$	−20.6895	+	0.995232i	−0.828243	+	0.0398412i
$625$	12.4260	+	21.5224i	0.497039	+	0.860896i
$626$	−6.47961	−	11.2230i	−0.258977	−	0.448562i
$627$		0			0
$628$	−3.50230	+	6.06615i	−0.139757	+	0.242066i
$629$	2.18135			0.0869761
$630$	−1.14576	+	2.51508i	−0.0456483	+	0.100203i
$631$	−30.8940			−1.22987			−0.614935	−	0.788578i	$-0.710818\pi$
$631$	−30.8940			−1.22987			−0.614935	+	0.788578i	$0.710818\pi$
$632$	−18.0146	+	31.2023i	−0.716584	+	1.24116i
$633$	−14.0798	−	21.8862i	−0.559624	−	0.869899i
$634$	7.05283	+	12.2159i	0.280103	+	0.485153i
$635$	−2.80797	−	4.86354i	−0.111431	−	0.193004i
$636$	6.89628	+	10.7198i	0.273455	+	0.425069i
$637$	−17.7989	+	30.8285i	−0.705216	+	1.22147i
$638$		0			0
$639$	1.10417	−	0.106474i	0.0436802	−	0.00421206i
$640$	−10.3664			−0.409767
$641$	−16.4823	+	28.5482i	−0.651012	+	1.12759i	0.331866	+	0.943327i	$0.392322\pi$
$641$	−16.4823	+	28.5482i	−0.651012	+	1.12759i	−0.982878	+	0.184259i	$0.941011\pi$
$642$	3.63363	−	7.05634i	0.143408	−	0.278491i
$643$	2.60079	+	4.50471i	0.102565	+	0.177648i	0.912741	−	0.408539i	$-0.133962\pi$
$643$	2.60079	+	4.50471i	0.102565	+	0.177648i	−0.810176	+	0.586187i	$0.800628\pi$
$644$	0.389038	+	0.673834i	0.0153302	+	0.0265528i
$645$	−55.0062	+	2.64597i	−2.16587	+	0.104185i
$646$	−2.14449	+	3.71436i	−0.0843738	+	0.146140i
$647$	−2.20260			−0.0865931			−0.0432965	−	0.999062i	$-0.513786\pi$
$647$	−2.20260			−0.0865931			−0.0432965	+	0.999062i	$0.513786\pi$
$648$	−27.1960	+	5.29423i	−1.06836	+	0.207977i
$649$		0			0
$650$	15.0812	−	26.1214i	0.591534	−	1.02457i
$651$	−3.61975	+	0.174122i	−0.141869	+	0.00682437i
$652$	−4.86468	−	8.42588i	−0.190516	−	0.329983i
$653$	20.2632	+	35.0970i	0.792962	+	1.37345i	0.924125	+	0.382090i	$0.124796\pi$
$653$	20.2632	+	35.0970i	0.792962	+	1.37345i	−0.131163	+	0.991361i	$0.541871\pi$
$654$	−3.55498	+	6.90361i	−0.139011	+	0.269952i
$655$	0.513301	−	0.889063i	0.0200563	−	0.0347386i
$656$	0.219030			0.00855170
$657$	−30.4092	+	2.93235i	−1.18638	+	0.114402i
$658$	0.909863			0.0354702
$659$	−19.7539	+	34.2147i	−0.769501	+	1.33282i	0.168332	+	0.985730i	$0.446162\pi$
$659$	−19.7539	+	34.2147i	−0.769501	+	1.33282i	−0.937834	+	0.347085i	$0.887171\pi$
$660$		0			0
$661$	18.3547	+	31.7912i	0.713914	+	1.23653i	0.963377	+	0.268150i	$0.0864124\pi$
$661$	18.3547	+	31.7912i	0.713914	+	1.23653i	−0.249464	+	0.968384i	$0.580254\pi$
$662$	1.20777	+	2.09193i	0.0469415	+	0.0813050i
$663$	22.1315	+	34.4020i	0.859516	+	1.33606i
$664$	1.63957	−	2.83981i	0.0636275	−	0.110206i
$665$	−0.628297			−0.0243643
$666$	0.688908	−	1.51223i	0.0266946	−	0.0585976i
$667$	−7.75426			−0.300246
$668$	−0.825729	+	1.43020i	−0.0319484	+	0.0553363i
$669$	1.75653	−	3.41109i	0.0679112	−	0.131880i
$670$	7.68813	+	13.3162i	0.297018	+	0.514451i
$671$		0			0
$672$	1.47796	−	0.0710945i	0.0570134	−	0.00274253i
$673$	5.27804	−	9.14183i	0.203453	−	0.352392i	−0.746185	−	0.665738i	$-0.768117\pi$
$673$	5.27804	−	9.14183i	0.203453	−	0.352392i	0.949639	+	0.313346i	$0.101450\pi$
$674$	−0.642144			−0.0247345
$675$	9.67898	−	24.2753i	0.372544	−	0.934356i
$676$	−8.44488			−0.324803
$677$	−3.50815	+	6.07630i	−0.134829	+	0.233531i	−0.925532	−	0.378669i	$-0.876382\pi$
$677$	−3.50815	+	6.07630i	−0.134829	+	0.233531i	0.790703	+	0.612200i	$0.209715\pi$
$678$	−18.3504	+	0.882712i	−0.704742	+	0.0339004i
$679$	−1.37959	−	2.38953i	−0.0529440	−	0.0917017i
$680$	22.4383	+	38.8643i	0.860471	+	1.49038i
$681$	20.6588	−	40.1183i	0.791646	−	1.53734i
$682$		0			0
$683$	−40.0949			−1.53419			−0.767094	−	0.641535i	$-0.778298\pi$
$683$	−40.0949			−1.53419			−0.767094	+	0.641535i	$0.778298\pi$
$684$	−0.880311	−	1.23379i	−0.0336595	−	0.0471750i
$685$	−16.3943			−0.626392
$686$	−2.02728	+	3.51135i	−0.0774018	+	0.134064i
$687$	−5.95155	−	9.25130i	−0.227066	−	0.352959i
$688$	−11.7002	−	20.2653i	−0.446064	−	0.772606i
$689$	−29.7890	−	51.5961i	−1.13487	−	1.96566i
$690$	17.1120	+	26.5996i	0.651444	+	1.01263i
$691$	9.27744	−	16.0690i	0.352931	−	0.611294i	−0.633831	−	0.773472i	$-0.718519\pi$
$691$	9.27744	−	16.0690i	0.352931	−	0.611294i	0.986762	+	0.162178i	$0.0518518\pi$
$692$	−12.2166			−0.464407
$693$		0			0
$694$	−16.6482			−0.631956
$695$	19.5111	−	33.7943i	0.740100	−	1.28189i
$696$	−3.83718	+	7.45162i	−0.145448	+	0.282453i
$697$	−0.216277	−	0.374602i	−0.00819206	−	0.0141891i
$698$	−12.1735	−	21.0851i	−0.460773	−	0.798082i
$699$	9.16328	−	0.440784i	0.346587	−	0.0166720i
$700$	−0.396639	+	0.686999i	−0.0149916	+	0.0259661i
$701$	46.6487			1.76190			0.880949	−	0.473211i	$-0.156905\pi$
$701$	46.6487			1.76190			0.880949	+	0.473211i	$0.156905\pi$
$702$	30.8388	−	4.47799i	1.16394	−	0.169011i
$703$	0.377773			0.0142480
$704$		0			0
$705$	−17.1369	+	0.824340i	−0.645413	+	0.0310464i
$706$	11.9569	+	20.7100i	0.450006	+	0.779433i
$707$	0.822710	+	1.42497i	0.0309412	+	0.0535917i
$708$	−1.25627	+	2.43962i	−0.0472136	+	0.0916866i
$709$	−3.30999	+	5.73306i	−0.124309	+	0.215310i	−0.921463	−	0.388467i	$-0.873005\pi$
$709$	−3.30999	+	5.73306i	−0.124309	+	0.215310i	0.797154	+	0.603777i	$0.206338\pi$
$710$	−1.36875			−0.0513683
$711$	14.5556	−	31.9512i	0.545879	−	1.19827i
$712$	25.8340			0.968169
$713$	−20.7361	+	35.9161i	−0.776575	+	1.34507i
$714$	1.25478	+	1.95048i	0.0469590	+	0.0729948i
$715$		0			0
$716$	5.73133	+	9.92695i	0.214190	+	0.370987i
$717$	10.8806	+	16.9133i	0.406345	+	0.631637i
$718$	11.1021	−	19.2294i	0.414326	−	0.717635i
$719$	13.8341			0.515925			0.257963	−	0.966155i	$-0.416949\pi$
$719$	13.8341			0.515925			0.257963	+	0.966155i	$0.416949\pi$
$720$	22.0423	−	2.12553i	0.821469	−	0.0792139i
$721$	−2.12121			−0.0789981
$722$	10.7328	−	18.5897i	0.399433	−	0.691838i
$723$	−5.80869	+	11.2802i	−0.216027	+	0.419515i
$724$	7.14569	+	12.3767i	0.265567	+	0.459976i
$725$	−3.95289	−	6.84660i	−0.146806	−	0.254276i
$726$		0			0
$727$	10.6621	−	18.4673i	0.395435	−	0.684913i	−0.597722	−	0.801704i	$-0.703927\pi$
$727$	10.6621	−	18.4673i	0.395435	−	0.684913i	0.993157	+	0.116791i	$0.0372606\pi$
$728$	−3.93099			−0.145692
$729$	25.8849	−	7.67923i	0.958701	−	0.284416i
$730$	37.6960			1.39519
$731$	−23.1061	+	40.0210i	−0.854610	+	1.48023i
$732$	4.39812	−	0.211564i	0.162559	−	0.00781963i
$733$	3.83730	+	6.64641i	0.141734	+	0.245491i	0.928150	−	0.372207i	$-0.121399\pi$
$733$	3.83730	+	6.64641i	0.141734	+	0.245491i	−0.786416	+	0.617698i	$0.788066\pi$
$734$	−2.24889	−	3.89519i	−0.0830081	−	0.143774i
$735$	17.4231	−	33.8347i	0.642659	−	1.24801i
$736$	8.46663	−	14.6646i	0.312084	−	0.540546i
$737$		0			0
$738$	−0.327998	+	0.0316287i	−0.0120738	+	0.00116427i
$739$	−18.6267			−0.685193			−0.342597	−	0.939483i	$-0.611306\pi$
$739$	−18.6267			−0.685193			−0.342597	+	0.939483i	$0.611306\pi$
$740$	0.475575	−	0.823720i	0.0174825	−	0.0302805i
$741$	3.83280	+	5.95785i	0.140802	+	0.218867i
$742$	−1.68894	−	2.92533i	−0.0620029	−	0.107392i
$743$	−1.63816	−	2.83738i	−0.0600983	−	0.104093i	0.834411	−	0.551143i	$-0.185808\pi$
$743$	−1.63816	−	2.83738i	−0.0600983	−	0.104093i	−0.894509	+	0.447050i	$0.852475\pi$
$744$	24.2530	+	37.6998i	0.889159	+	1.38214i
$745$	−31.9949	+	55.4168i	−1.17220	+	2.03032i
$746$	10.6410			0.389594
$747$	−1.32475	+	2.90798i	−0.0484701	+	0.106397i
$748$		0			0
$749$	0.487841	−	0.844965i	0.0178253	−	0.0308744i
$750$	−0.0864174	+	0.167818i	−0.00315552	+	0.00612786i
$751$	0.0732705	+	0.126908i	0.00267368	+	0.00463095i	0.867359	−	0.497683i	$-0.165816\pi$
$751$	0.0732705	+	0.126908i	0.00267368	+	0.00463095i	−0.864685	+	0.502314i	$0.832482\pi$
$752$	−3.64513	−	6.31354i	−0.132924	−	0.230231i
$753$	33.0222	−	1.58848i	1.20340	−	0.0578873i
$754$	4.71347	−	8.16398i	0.171655	−	0.297314i
$755$	38.2764			1.39302
$756$	−0.811068	+	0.117772i	−0.0294982	+	0.00428333i
$757$	−13.1974			−0.479666			−0.239833	−	0.970814i	$-0.577093\pi$
$757$	−13.1974			−0.479666			−0.239833	+	0.970814i	$0.577093\pi$
$758$	15.5959	−	27.0129i	0.566469	−	0.981153i
$759$		0			0
$760$	3.88594	+	6.73065i	0.140958	+	0.244146i
$761$	−3.03078	−	5.24946i	−0.109866	−	0.190293i	0.805850	−	0.592120i	$-0.201709\pi$
$761$	−3.03078	−	5.24946i	−0.109866	−	0.190293i	−0.915716	+	0.401827i	$0.868375\pi$
$762$	−1.64359	+	3.19178i	−0.0595410	+	0.115626i
$763$	−0.477282	+	0.826677i	−0.0172788	+	0.0299277i
$764$	6.04582			0.218730
$765$	−25.4004	−	35.5996i	−0.918355	−	1.28711i
$766$	−5.19345			−0.187647
$767$	6.41301	−	11.1077i	0.231560	−	0.401074i
$768$	−12.6711	−	19.6965i	−0.457230	−	0.710735i
$769$	−13.0916	−	22.6754i	−0.472097	−	0.817695i	0.527394	−	0.849621i	$-0.323169\pi$
$769$	−13.0916	−	22.6754i	−0.472097	−	0.817695i	−0.999490	+	0.0319257i	$0.989836\pi$
$770$		0			0
$771$	−9.39906	−	14.6102i	−0.338499	−	0.526175i
$772$	−6.05536	+	10.4882i	−0.217937	+	0.377478i
$773$	22.3999			0.805669			0.402834	−	0.915273i	$-0.368025\pi$
$773$	22.3999			0.805669			0.402834	+	0.915273i	$0.368025\pi$
$774$	20.4474	+	28.6577i	0.734965	+	1.03008i
$775$	−42.2826			−1.51884
$776$	−17.0653	+	29.5579i	−0.612607	+	1.06107i
$777$	0.0935209	−	0.181613i	0.00335504	−	0.00651533i
$778$	6.81833	+	11.8097i	0.244449	+	0.423398i
$779$	−0.0374555	−	0.0648748i	−0.00134198	−	0.00232438i
$780$	17.8159	−	0.857005i	0.637913	−	0.0306857i
$781$		0			0
$782$	26.5413			0.949113
$783$	3.02506	−	7.58698i	0.108107	−	0.271137i
$784$	16.1713			0.577547
$785$	−17.5010	+	30.3126i	−0.624638	+	1.08190i
$786$	−0.655519	+	0.0315326i	−0.0233816	+	0.00112473i
$787$	12.0611	+	20.8904i	0.429931	+	0.744663i	0.996867	−	0.0790993i	$-0.0252044\pi$
$787$	12.0611	+	20.8904i	0.429931	+	0.744663i	−0.566935	+	0.823762i	$0.691871\pi$
$788$	5.62228	+	9.73807i	0.200285	+	0.346904i
$789$	11.1127	−	21.5803i	0.395622	−	0.768279i
$790$	−21.6614	+	37.5187i	−0.770679	+	1.33486i
$791$	−2.25840			−0.0802996
$792$		0			0
$793$	−20.5809			−0.730849
$794$	−17.7175	+	30.6877i	−0.628772	+	1.08907i
$795$	34.4608	+	53.5671i	1.22220	+	1.89983i
$796$	3.25223	+	5.63302i	0.115272	+	0.199657i
$797$	−5.32340	−	9.22041i	−0.188565	−	0.326604i	0.756207	−	0.654332i	$-0.227050\pi$
$797$	−5.32340	−	9.22041i	−0.188565	−	0.326604i	−0.944772	+	0.327729i	$0.893717\pi$
$798$	0.217307	+	0.337790i	0.00769258	+	0.0119576i
$799$	−7.19859	+	12.4683i	−0.254668	+	0.441098i
$800$	17.2641			0.610379
$801$	−25.0589	+	2.41642i	−0.885414	+	0.0853801i
$802$	18.6560			0.658766
$803$		0			0
$804$	−2.08749	+	4.05381i	−0.0736202	+	0.142967i
$805$	1.94403	+	3.36716i	0.0685180	+	0.118677i
$806$	−25.2092	−	43.6636i	−0.887955	−	1.53798i
$807$	−1.99917	+	0.0961666i	−0.0703741	+	0.00338522i
$808$	10.1767	−	17.6266i	0.358016	−	0.620102i
$809$	−21.1939			−0.745136			−0.372568	−	0.928005i	$-0.621523\pi$
$809$	−21.1939			−0.745136			−0.372568	+	0.928005i	$0.621523\pi$
$810$	−32.7014	+	6.36597i	−1.14901	+	0.223677i
$811$	26.8201			0.941781			0.470890	−	0.882192i	$-0.343933\pi$
$811$	26.8201			0.941781			0.470890	+	0.882192i	$0.343933\pi$
$812$	−0.123965	+	0.214714i	−0.00435033	+	0.00753500i
$813$	−50.5908	+	2.43358i	−1.77430	+	0.0853494i
$814$		0			0
$815$	−24.3089	−	42.1042i	−0.851503	−	1.47485i
$816$	8.50742	−	16.5210i	0.297819	−	0.578351i
$817$	−4.00159	+	6.93096i	−0.139998	+	0.242483i
$818$	−13.2107			−0.461902
$819$	3.81306	−	0.367692i	0.133239	−	0.0128482i
$820$	−0.188609			−0.00658653
$821$	15.0278	−	26.0289i	0.524473	−	0.908415i	−0.475121	−	0.879921i	$-0.657596\pi$
$821$	15.0278	−	26.0289i	0.524473	−	0.908415i	0.999594	−	0.0284939i	$-0.00907111\pi$
$822$	5.67023	+	8.81401i	0.197772	+	0.307424i
$823$	−1.66234	−	2.87927i	−0.0579457	−	0.100365i	0.835597	−	0.549342i	$-0.185122\pi$
$823$	−1.66234	−	2.87927i	−0.0579457	−	0.100365i	−0.893543	+	0.448977i	$0.851788\pi$
$824$	13.1195	+	22.7236i	0.457038	+	0.791613i
$825$		0			0
$826$	0.363596	−	0.629767i	0.0126511	−	0.0219124i
$827$	−32.5498			−1.13187			−0.565935	−	0.824450i	$-0.691485\pi$
$827$	−32.5498			−1.13187			−0.565935	+	0.824450i	$0.691485\pi$
$828$	−3.88830	+	8.53524i	−0.135128	+	0.296620i
$829$	−4.91096			−0.170565			−0.0852824	−	0.996357i	$-0.527179\pi$
$829$	−4.91096			−0.170565			−0.0852824	+	0.996357i	$0.527179\pi$
$830$	1.97147	−	3.41469i	0.0684307	−	0.118525i
$831$	18.0252	−	35.0040i	0.625286	−	1.21428i
$832$	22.2519	+	38.5414i	0.771445	+	1.33618i
$833$	−15.9680	−	27.6574i	−0.553259	−	0.958272i
$834$	−24.9170	+	1.19859i	−0.862805	+	0.0415037i
$835$	−4.12618	+	7.14675i	−0.142792	+	0.247324i
$836$		0			0
$837$	−27.0518	−	34.3003i	−0.935046	−	1.18559i
$838$	−2.16932			−0.0749378
$839$	−10.3536	+	17.9329i	−0.357445	+	0.619114i	−0.987533	−	0.157410i	$-0.949686\pi$
$839$	−10.3536	+	17.9329i	−0.357445	+	0.619114i	0.630088	+	0.776524i	$0.283019\pi$
$840$	4.19773	−	0.201925i	0.144836	−	0.00696706i
$841$	13.2646	+	22.9749i	0.457399	+	0.792238i
$842$	−7.15547	−	12.3936i	−0.246594	−	0.427113i
$843$	−13.4158	+	26.0529i	−0.462065	+	0.897309i
$844$	−4.76115	+	8.24655i	−0.163885	+	0.283858i
$845$	−42.1992			−1.45170
$846$	6.37027	+	8.92816i	0.219014	+	0.306956i
$847$		0			0
$848$	−13.5326	+	23.4391i	−0.464710	+	0.804902i
$849$	−26.7601	−	41.5969i	−0.918405	−	1.42760i
$850$	13.5299	+	23.4345i	0.464072	+	0.803797i
$851$	−1.16888	−	2.02455i	−0.0400686	−	0.0694008i
$852$	−0.219602	−	0.341357i	−0.00752343	−	0.0116947i
$853$	24.0608	−	41.6746i	0.823827	−	1.42691i	−0.0789860	−	0.996876i	$-0.525168\pi$
$853$	24.0608	−	41.6746i	0.823827	−	1.42691i	0.902813	−	0.430034i	$-0.141498\pi$
$854$	−1.16687			−0.0399294
$855$	−4.39893	−	6.16525i	−0.150440	−	0.210847i
$856$	−12.0690			−0.412509
$857$	18.4177	−	31.9004i	0.629138	−	1.08970i	−0.358588	−	0.933496i	$-0.616742\pi$
$857$	18.4177	−	31.9004i	0.629138	−	1.08970i	0.987725	−	0.156202i	$-0.0499251\pi$
$858$		0			0
$859$	12.3159	+	21.3318i	0.420214	+	0.727831i	0.995960	−	0.0897969i	$-0.0286218\pi$
$859$	12.3159	+	21.3318i	0.420214	+	0.727831i	−0.575746	+	0.817628i	$0.695288\pi$
$860$	10.0751	+	17.4506i	0.343559	+	0.595062i
$861$	−0.0404608	+	0.00194629i	−0.00137890	+	6.63295e-5i
$862$	−8.29757	+	14.3718i	−0.282617	+	0.489506i
$863$	−12.5279			−0.426453			−0.213227	−	0.977003i	$-0.568397\pi$
$863$	−12.5279			−0.426453			−0.213227	+	0.977003i	$0.568397\pi$
$864$	11.0453	+	14.0049i	0.375769	+	0.476456i
$865$	−61.0467			−2.07565
$866$	20.2827	−	35.1306i	0.689233	−	1.19379i
$867$	−7.24506	+	0.348511i	−0.246055	+	0.0118360i
$868$	0.663007	+	1.14836i	0.0225039	+	0.0389779i
$869$		0			0
$870$	−4.61396	+	8.96008i	−0.156428	+	0.303775i
$871$	10.6562	−	18.4571i	0.361072	−	0.625395i
$872$	11.8077			0.399861
$873$	13.7886	−	30.2674i	0.466672	−	1.02440i
$874$	4.59650			0.155479
$875$	−0.0116022	+	0.0200955i	−0.000392224	+	0.000679353i
$876$	6.04792	+	9.40111i	0.204340	+	0.317634i
$877$	−12.8743	−	22.2989i	−0.434733	−	0.752980i	0.562540	−	0.826770i	$-0.309824\pi$
$877$	−12.8743	−	22.2989i	−0.434733	−	0.752980i	−0.997274	+	0.0737894i	$0.976491\pi$
$878$	−7.35306	−	12.7359i	−0.248154	−	0.429815i
$879$	−15.1603	−	23.5656i	−0.511343	−	0.794849i
$880$		0			0
$881$	36.6362			1.23430			0.617152	−	0.786844i	$-0.288286\pi$
$881$	36.6362			1.23430			0.617152	+	0.786844i	$0.288286\pi$
$882$	−24.2166	+	2.33519i	−0.815414	+	0.0786300i
$883$	19.4248			0.653696			0.326848	−	0.945077i	$-0.394013\pi$
$883$	19.4248			0.653696			0.326848	+	0.945077i	$0.394013\pi$
$884$	7.48384	−	12.9624i	0.251709	−	0.435972i
$885$	−6.27761	+	12.1908i	−0.211020	+	0.409790i
$886$	22.2527	+	38.5427i	0.747593	+	1.29487i
$887$	26.0528	+	45.1247i	0.874767	+	1.51514i	0.857011	+	0.515298i	$0.172319\pi$
$887$	26.0528	+	45.1247i	0.874767	+	1.51514i	0.0177557	+	0.999842i	$0.494348\pi$
$888$	−2.52395	+	0.121410i	−0.0846983	+	0.00407426i
$889$	−0.220664	+	0.382201i	−0.00740083	+	0.0128186i
$890$	31.0636			1.04126
$891$		0			0
$892$	−1.40390			−0.0470059
$893$	−1.24668	+	2.15930i	−0.0417184	+	0.0722584i
$894$	40.8596	−	1.96548i	1.36655	−	0.0657355i
$895$	28.6395	+	49.6051i	0.957313	+	1.65811i
$896$	0.407321	+	0.705501i	0.0136077	+	0.0235691i
$897$	20.0700	−	38.9750i	0.670118	−	1.30134i
$898$	−11.4261	+	19.7906i	−0.381295	+	0.660421i
$899$	−13.2150			−0.440744
$900$	−9.51829	+	0.917845i	−0.317276	+	0.0305948i
$901$	53.4497			1.78067
$902$		0			0
$903$	2.34141	+	3.63957i	0.0779171	+	0.121117i
$904$	13.9680	+	24.1932i	0.464568	+	0.804655i
$905$	35.7071	+	61.8465i	1.18694	+	2.05585i
$906$	−13.2385	−	20.5784i	−0.439821	−	0.683673i
$907$	28.6704	−	49.6586i	0.951984	−	1.64889i	0.210861	−	0.977516i	$-0.432373\pi$
$907$	28.6704	−	49.6586i	0.951984	−	1.64889i	0.741123	−	0.671369i	$-0.234293\pi$
$908$	−16.5114			−0.547951
$909$	−8.22269	+	18.0497i	−0.272729	+	0.598671i
$910$	−4.72675			−0.156690
$911$	−7.32080	+	12.6800i	−0.242549	+	0.420107i	−0.961440	−	0.275016i	$-0.911317\pi$
$911$	−7.32080	+	12.6800i	−0.242549	+	0.420107i	0.718891	+	0.695123i	$0.244650\pi$
$912$	1.47334	−	2.86116i	0.0487872	−	0.0947425i
$913$		0			0
$914$	−6.62927	−	11.4822i	−0.219277	−	0.379799i
$915$	21.9775	−	1.05719i	0.726553	−	0.0349495i
$916$	−2.01253	+	3.48581i	−0.0664960	+	0.115174i
$917$	−0.0806755			−0.00266414
$918$	−10.3542	+	25.9687i	−0.341739	+	0.857095i
$919$	−10.2505			−0.338133			−0.169067	−	0.985605i	$-0.554075\pi$
$919$	−10.2505			−0.338133			−0.169067	+	0.985605i	$0.554075\pi$
$920$	24.0472	−	41.6509i	0.792812	−	1.37319i
$921$	24.8260	−	1.19421i	0.818043	−	0.0393505i
$922$	15.0773	+	26.1146i	0.496544	+	0.860039i
$923$	0.948587	+	1.64300i	0.0312231	+	0.0540800i
$924$		0			0
$925$	1.19171	−	2.06411i	0.0391833	−	0.0678675i
$926$	−23.8795			−0.784729
$927$	−14.8514	−	20.8147i	−0.487783	−	0.683645i
$928$	5.39572			0.177123
$929$	17.7511	−	30.7459i	0.582396	−	1.00874i	−0.412798	−	0.910822i	$-0.635449\pi$
$929$	17.7511	−	30.7459i	0.582396	−	1.00874i	0.995195	−	0.0979172i	$-0.0312180\pi$
$930$	29.1627	+	45.3315i	0.956282	+	1.48648i
$931$	−2.76539	−	4.78980i	−0.0906320	−	0.156979i
$932$	−1.67838	−	2.90704i	−0.0549772	−	0.0952233i
$933$	3.35225	+	5.21086i	0.109748	+	0.170596i
$934$	−0.504609	+	0.874008i	−0.0165113	+	0.0285984i
$935$		0			0
$936$	−27.5222	−	38.5734i	−0.899592	−	1.26081i
$937$	42.9385			1.40274			0.701369	−	0.712798i	$-0.252573\pi$
$937$	42.9385			1.40274			0.701369	+	0.712798i	$0.252573\pi$
$938$	0.604171	−	1.04646i	0.0197269	−	0.0341680i
$939$	8.79152	−	17.0727i	0.286900	−	0.557147i
$940$	3.13886	+	5.43666i	0.102378	+	0.177324i
$941$	3.70673	+	6.42024i	0.120836	+	0.209294i	0.920098	−	0.391689i	$-0.128109\pi$
$941$	3.70673	+	6.42024i	0.120836	+	0.209294i	−0.799262	+	0.600983i	$0.794776\pi$
$942$	22.3499	−	1.07510i	0.728200	−	0.0350288i
$943$	−0.231784	+	0.401461i	−0.00754792	+	0.0130734i
$944$	−5.82661			−0.189640
$945$	−4.05291	+	0.588509i	−0.131841	+	0.0191442i
$946$		0			0
$947$	6.74751	−	11.6870i	0.219265	−	0.379778i	−0.735319	−	0.677722i	$-0.762968\pi$
$947$	6.74751	−	11.6870i	0.219265	−	0.379778i	0.954583	+	0.297944i	$0.0963008\pi$
$948$	−12.8322	+	0.617273i	−0.416772	+	0.0200481i
$949$	−26.1245	−	45.2489i	−0.848036	−	1.46884i
$950$	2.34315	+	4.05846i	0.0760219	+	0.131674i
$951$	−9.56926	+	18.5830i	−0.310304	+	0.602596i
$952$	1.76332	−	3.05416i	0.0571494	−	0.0989857i
$953$	−8.77715			−0.284320			−0.142160	−	0.989844i	$-0.545405\pi$
$953$	−8.77715			−0.284320			−0.142160	+	0.989844i	$0.545405\pi$
$954$	16.8803	−	37.0542i	0.546521	−	1.19967i
$955$	30.2110			0.977605
$956$	3.67932	−	6.37277i	0.118998	−	0.206110i
$957$		0			0
$958$	−7.69355	−	13.3256i	−0.248567	−	0.430531i
$959$	0.644171	+	1.11574i	0.0208014	+	0.0360291i
$960$	−25.7416	−	40.0137i	−0.830807	−	1.29144i
$961$	−19.8390	+	34.3621i	−0.639967	+	1.10846i
$962$	2.84203			0.0916308
$963$	11.7069	−	1.12889i	0.377249	−	0.0363780i
$964$	4.64257			0.149527
$965$	−30.2587	+	52.4096i	−0.974062	+	1.68712i
$966$	1.13790	−	2.20975i	0.0366114	−	0.0710976i
$967$	7.08115	+	12.2649i	0.227714	+	0.394413i	0.957130	−	0.289658i	$-0.0935414\pi$
$967$	7.08115	+	12.2649i	0.227714	+	0.394413i	−0.729416	+	0.684070i	$0.760208\pi$
$968$		0			0
$969$	−6.34819	+	0.305368i	−0.203933	+	0.00980984i
$970$	−20.5199	+	35.5414i	−0.658853	+	1.14117i
$971$	−10.3327			−0.331593			−0.165796	−	0.986160i	$-0.553019\pi$
$971$	−10.3327			−0.331593			−0.165796	+	0.986160i	$0.553019\pi$
$972$	−6.83423	−	7.13415i	−0.219208	−	0.228828i
$973$	−3.06657			−0.0983096
$974$	8.29711	−	14.3710i	0.265857	−	0.460477i
$975$	44.6439	−	2.14752i	1.42975	−	0.0687756i
$976$	4.67475	+	8.09690i	0.149635	+	0.259175i
$977$	−24.0742	−	41.6978i	−0.770202	−	1.33403i	−0.937452	−	0.348115i	$-0.886822\pi$
$977$	−24.0742	−	41.6978i	−0.770202	−	1.33403i	0.167249	−	0.985915i	$-0.446511\pi$
$978$	−14.2288	+	27.6316i	−0.454986	+	0.883561i
$979$		0			0
$980$	−13.9253			−0.444827
$981$	−11.4535	+	1.10446i	−0.365682	+	0.0352626i
$982$	−11.2348			−0.358516
$983$	13.4702	−	23.3311i	0.429633	−	0.744147i	−0.567207	−	0.823575i	$-0.691976\pi$
$983$	13.4702	−	23.3311i	0.429633	−	0.744147i	0.996841	+	0.0794285i	$0.0253095\pi$
$984$	0.271095	+	0.421400i	0.00864219	+	0.0134337i
$985$	28.0946	+	48.6612i	0.895168	+	1.55048i
$986$	4.22863	+	7.32421i	0.134667	+	0.233250i
$987$	0.729453	+	1.13389i	0.0232188	+	0.0360921i
$988$	1.29607	−	2.24487i	0.0412336	−	0.0714187i
$989$	49.5257			1.57482
$990$		0			0
$991$	−33.7506			−1.07212			−0.536062	−	0.844179i	$-0.680089\pi$
$991$	−33.7506			−1.07212			−0.536062	+	0.844179i	$0.680089\pi$
$992$	14.4290	−	24.9918i	0.458122	−	0.793490i
$993$	−1.63870	+	3.18229i	−0.0520027	+	0.100987i
$994$	0.0537817	+	0.0931526i	0.00170585	+	0.00295462i
$995$	16.2514	+	28.1483i	0.515205	+	0.892360i
$996$	1.16790	−	0.0561798i	0.0370063	−	0.00178012i
$997$	24.5282	−	42.4841i	0.776815	−	1.34548i	−0.156953	−	0.987606i	$-0.550167\pi$
$997$	24.5282	−	42.4841i	0.776815	−	1.34548i	0.933769	−	0.357878i	$-0.116499\pi$
$998$	−26.5623			−0.840814
$999$	2.43688	−	0.353850i	0.0770994	−	0.0111953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.o.727.7		36
9.2	odd	6		9801.2.a.cn.1.7		18
9.4	even	3	inner	1089.2.e.o.364.7		36
9.7	even	3		9801.2.a.co.1.12		18
11.2	odd	10		99.2.m.b.70.3	yes	72
11.6	odd	10		99.2.m.b.25.7	yes	72
11.10	odd	2		1089.2.e.p.727.12		36
33.2	even	10		297.2.n.b.235.7		72
33.17	even	10		297.2.n.b.289.3		72
99.2	even	30		891.2.f.e.730.3		36
99.13	odd	30		99.2.m.b.4.7	✓	72
99.43	odd	6		9801.2.a.cm.1.7		18
99.50	even	30		297.2.n.b.91.7		72
99.61	odd	30		891.2.f.f.487.7		36
99.65	even	6		9801.2.a.cp.1.12		18
99.68	even	30		297.2.n.b.37.3		72
99.76	odd	6		1089.2.e.p.364.12		36
99.79	odd	30		891.2.f.f.730.7		36
99.83	even	30		891.2.f.e.487.3		36
99.94	odd	30		99.2.m.b.58.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.7	✓	72	99.13	odd	30
99.2.m.b.25.7	yes	72	11.6	odd	10
99.2.m.b.58.3	yes	72	99.94	odd	30
99.2.m.b.70.3	yes	72	11.2	odd	10
297.2.n.b.37.3		72	99.68	even	30
297.2.n.b.91.7		72	99.50	even	30
297.2.n.b.235.7		72	33.2	even	10
297.2.n.b.289.3		72	33.17	even	10
891.2.f.e.487.3		36	99.83	even	30
891.2.f.e.730.3		36	99.2	even	30
891.2.f.f.487.7		36	99.61	odd	30
891.2.f.f.730.7		36	99.79	odd	30
1089.2.e.o.364.7		36	9.4	even	3	inner
1089.2.e.o.727.7		36	1.1	even	1	trivial
1089.2.e.p.364.12		36	99.76	odd	6
1089.2.e.p.727.12		36	11.10	odd	2
9801.2.a.cm.1.7		18	99.43	odd	6
9801.2.a.cn.1.7		18	9.2	odd	6
9801.2.a.co.1.12		18	9.7	even	3
9801.2.a.cp.1.12		18	99.65	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 $\F_{q}$
Belyi maps

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+(-0.584430 + 1.01226i) q^{2} +(-1.73005 + 0.0832210i) q^{3} +(0.316882 + 0.548856i) q^{4} +(1.58346 + 2.74264i) q^{5} +(0.926852 - 1.79990i) q^{6} +(0.124437 - 0.215531i) q^{7} -3.07850 q^{8} +(2.98615 - 0.287953i) q^{9} -3.70170 q^{10} +(-0.593899 - 0.923178i) q^{12} +(2.56539 + 4.44339i) q^{13} +(0.145449 + 0.251925i) q^{14} +(-2.96772 - 4.61313i) q^{15} +(1.16541 - 2.01854i) q^{16} -4.60302 q^{17} +(-1.45371 + 3.19106i) q^{18} -0.797165 q^{19} +(-1.00354 + 1.73819i) q^{20} +(-0.197345 + 0.383234i) q^{21} +(2.46653 + 4.27215i) q^{23} +(5.32597 - 0.256196i) q^{24} +(-2.51472 + 4.35562i) q^{25} -5.99717 q^{26} +(-5.14222 + 0.746684i) q^{27} +0.157727 q^{28} +(-0.785949 + 1.36130i) q^{29} +(6.40413 - 0.308059i) q^{30} +(4.20351 + 7.28069i) q^{31} +(-1.71631 - 2.97273i) q^{32} +(2.69014 - 4.65947i) q^{34} +0.788164 q^{35} +(1.10430 + 1.54772i) q^{36} -0.473896 q^{37} +(0.465887 - 0.806941i) q^{38} +(-4.80804 - 7.47379i) q^{39} +(-4.87470 - 8.44323i) q^{40} +(0.0469859 + 0.0813819i) q^{41} +(-0.272600 - 0.423739i) q^{42} +(5.01977 - 8.69450i) q^{43} +(5.51821 + 7.73397i) q^{45} -5.76606 q^{46} +(1.56389 - 2.70873i) q^{47} +(-1.84823 + 3.58917i) q^{48} +(3.46903 + 6.00854i) q^{49} +(-2.93936 - 5.09112i) q^{50} +(7.96345 - 0.383068i) q^{51} +(-1.62585 + 2.81606i) q^{52} -11.6119 q^{53} +(2.24943 - 5.64167i) q^{54} +(-0.383079 + 0.663512i) q^{56} +(1.37914 - 0.0663409i) q^{57} +(-0.918665 - 1.59117i) q^{58} +(-1.24991 - 2.16491i) q^{59} +(1.59153 - 3.09067i) q^{60} +(-2.00563 + 3.47385i) q^{61} -9.82663 q^{62} +(0.309523 - 0.679438i) q^{63} +8.67387 q^{64} +(-8.12442 + 14.0719i) q^{65} +(-2.07692 - 3.59733i) q^{67} +(-1.45861 - 2.52639i) q^{68} +(-4.62275 - 7.18577i) q^{69} +(-0.460627 + 0.797829i) q^{70} +0.369763 q^{71} +(-9.19287 + 0.886465i) q^{72} -10.1834 q^{73} +(0.276959 - 0.479707i) q^{74} +(3.98811 - 7.74473i) q^{75} +(-0.252607 - 0.437529i) q^{76} +(10.3754 - 0.499091i) q^{78} +(5.85175 - 10.1355i) q^{79} +7.38152 q^{80} +(8.83417 - 1.71974i) q^{81} -0.109840 q^{82} +(-0.532585 + 0.922464i) q^{83} +(-0.272876 + 0.0131262i) q^{84} +(-7.28872 - 12.6244i) q^{85} +(5.86742 + 10.1627i) q^{86} +(1.24644 - 2.42053i) q^{87} -8.39173 q^{89} +(-11.0538 + 1.06592i) q^{90} +1.27691 q^{91} +(-1.56320 + 2.70754i) q^{92} +(-7.87819 - 12.2461i) q^{93} +(1.82796 + 3.16613i) q^{94} +(-1.26228 - 2.18634i) q^{95} +(3.21669 + 5.00014i) q^{96} +(5.54336 - 9.60139i) q^{97} -8.10963 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

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Database

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