LMFDB - Embedded newform 841.2.d.g.571.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(190,841)] 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("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-1,1,1,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	12.0.4413675765625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2x^{10} - 3x^{9} + 5x^{8} - 8x^{7} + 13x^{6} + 8x^{5} + 5x^{4} + 3x^{3} + 2x^{2} + x + 1 $ x^12 - x^11 + 2x^10 - 3x^9 + 5x^8 - 8x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			571.1
Root			$1.45780 - 0.702039i$ of defining polynomial
Character	$\chi$	$=$	841.571
Dual form			841.2.d.g.190.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.45780 + 0.702039i) q^{2} +(-1.00883 - 1.26503i) q^{3} +(0.385338 - 0.483198i) q^{4} +(2.57146 - 1.23835i) q^{5} +(2.35877 + 1.13592i) q^{6} +(1.39417 + 1.74823i) q^{7} +(0.497572 - 2.18001i) q^{8} +(0.0849954 - 0.372389i) q^{9} +(-2.87930 + 3.61052i) q^{10} +(-0.805088 - 3.52732i) q^{11} -1.00000 q^{12} +(-0.942614 - 4.12986i) q^{13} +(-3.25974 - 1.56981i) q^{14} +(-4.16070 - 2.00369i) q^{15} +(1.08014 + 4.73240i) q^{16} +6.61803 q^{17} +(0.137526 + 0.602539i) q^{18} +(-1.15601 + 1.44960i) q^{19} +(0.392512 - 1.71971i) q^{20} +(0.805088 - 3.52732i) q^{21} +(3.64997 + 4.57692i) q^{22} +(-2.91560 - 1.40408i) q^{23} +(-3.25974 + 1.56981i) q^{24} +(1.96144 - 2.45956i) q^{25} +(4.27346 + 5.35875i) q^{26} +(-4.93022 + 2.37427i) q^{27} +1.38197 q^{28} +7.47214 q^{30} +(0.982209 - 0.473007i) q^{31} +(-2.10862 - 2.64413i) q^{32} +(-3.64997 + 4.57692i) q^{33} +(-9.64776 + 4.64612i) q^{34} +(5.74995 + 2.76903i) q^{35} +(-0.147186 - 0.184565i) q^{36} +(-1.93776 + 8.48987i) q^{37} +(0.667563 - 2.92478i) q^{38} +(-4.27346 + 5.35875i) q^{39} +(-1.42012 - 6.22196i) q^{40} +2.85410 q^{41} +(1.30266 + 5.70733i) q^{42} +(-2.49022 - 1.19923i) q^{43} +(-2.01463 - 0.970194i) q^{44} +(-0.242586 - 1.06284i) q^{45} +5.23607 q^{46} +(-1.55765 - 6.82450i) q^{47} +(4.89695 - 6.14058i) q^{48} +(0.445042 - 1.94986i) q^{49} +(-1.13267 + 4.96255i) q^{50} +(-6.67646 - 8.37201i) q^{51} +(-2.35877 - 1.13592i) q^{52} +(1.80194 - 0.867767i) q^{53} +(5.52044 - 6.92242i) q^{54} +(-6.43830 - 8.07338i) q^{55} +(4.50484 - 2.16942i) q^{56} +3.00000 q^{57} -5.09017 q^{59} +(-2.57146 + 1.23835i) q^{60} +(-1.00883 - 1.26503i) q^{61} +(-1.09979 + 1.37910i) q^{62} +(0.769519 - 0.370581i) q^{63} +(-3.81657 - 1.83796i) q^{64} +(-7.53810 - 9.45248i) q^{65} +(2.10775 - 9.23465i) q^{66} +(2.33027 - 10.2096i) q^{67} +(2.55018 - 3.19782i) q^{68} +(1.16513 + 5.10479i) q^{69} -10.3262 q^{70} +(-0.339982 - 1.48956i) q^{71} +(-0.769519 - 0.370581i) q^{72} +(-0.262899 - 0.126606i) q^{73} +(-3.13536 - 13.7369i) q^{74} -5.09017 q^{75} +(0.254986 + 1.11717i) q^{76} +(5.04414 - 6.32515i) q^{77} +(2.46779 - 10.8121i) q^{78} +(1.13267 - 4.96255i) q^{79} +(8.63789 + 10.8316i) q^{80} +(6.94485 + 3.34446i) q^{81} +(-4.16070 + 2.00369i) q^{82} +(4.95317 - 6.21108i) q^{83} +(-1.39417 - 1.74823i) q^{84} +(17.0180 - 8.19543i) q^{85} +4.47214 q^{86} -8.09017 q^{88} +(-7.84582 + 3.77835i) q^{89} +(1.09979 + 1.37910i) q^{90} +(5.90578 - 7.40561i) q^{91} +(-1.80194 + 0.867767i) q^{92} +(-1.58925 - 0.765341i) q^{93} +(7.06179 + 8.85521i) q^{94} +(-1.17754 + 5.15912i) q^{95} +(-1.21766 + 5.33494i) q^{96} +(10.3264 - 12.9489i) q^{97} +(0.720093 + 3.15493i) q^{98} -1.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9} + 7 q^{10} - 5 q^{11} - 12 q^{12} - 4 q^{13} - 5 q^{14} - 7 q^{15} + 3 q^{16} + 66 q^{17} - q^{18} - 3 q^{19} + 8 q^{20} + 5 q^{21} - 5 q^{22}+ \cdots - 30 q^{99}+O(q^{100}) $ 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9 + 7 * q^10 - 5 * q^11 - 12 * q^12 - 4 * q^13 - 5 * q^14 - 7 * q^15 + 3 * q^16 + 66 * q^17 - q^18 - 3 * q^19 + 8 * q^20 + 5 * q^21 - 5 * q^22 - 2 * q^23 - 5 * q^24 - 13 * q^25 - 7 * q^26 - 2 * q^27 + 30 * q^28 + 36 * q^30 - 9 * q^31 + 9 * q^32 + 5 * q^33 - 8 * q^34 + 15 * q^35 - 4 * q^36 - 4 * q^37 + 6 * q^38 + 7 * q^39 - 15 * q^40 - 6 * q^41 + 5 * q^42 - 10 * q^43 + 9 * q^45 + 36 * q^46 - 14 * q^47 - 9 * q^48 + 4 * q^49 + q^50 + 8 * q^51 - 3 * q^52 + 4 * q^53 - 11 * q^54 + 5 * q^55 + 10 * q^56 + 36 * q^57 + 6 * q^59 + q^60 + q^61 + 8 * q^62 - 5 * q^63 - 4 * q^64 + 13 * q^65 + 10 * q^66 + 12 * q^67 + 3 * q^68 + 6 * q^69 - 30 * q^70 - 12 * q^71 + 5 * q^72 - 14 * q^73 - 17 * q^74 + 6 * q^75 + 9 * q^76 - 5 * q^77 + 11 * q^78 - q^79 - 21 * q^80 + 2 * q^81 - 7 * q^82 + 2 * q^83 + 2 * q^85 - 30 * q^88 - 4 * q^89 - 8 * q^90 - 10 * q^91 - 4 * q^92 - 8 * q^93 - 7 * q^94 - 24 * q^95 - 2 * q^96 - 13 * q^97 + 2 * q^98 - 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	−1.45780	+	0.702039i	−1.03082	+	0.496416i	−0.871286	−	0.490776i	$-0.836713\pi$
$2$	−1.45780	+	0.702039i	−1.03082	+	0.496416i	−0.159533	+	0.987193i	$0.550999\pi$
$3$	−1.00883	−	1.26503i	−0.582447	−	0.730365i	0.400081	−	0.916480i	$-0.368982\pi$
$3$	−1.00883	−	1.26503i	−0.582447	−	0.730365i	−0.982528	+	0.186114i	$0.940411\pi$
$4$	0.385338	−	0.483198i	0.192669	−	0.241599i
$5$	2.57146	−	1.23835i	1.14999	−	0.553806i	0.240960	−	0.970535i	$-0.422538\pi$
$5$	2.57146	−	1.23835i	1.14999	−	0.553806i	0.909031	+	0.416729i	$0.136824\pi$
$6$	2.35877	+	1.13592i	0.962963	+	0.463738i
$7$	1.39417	+	1.74823i	0.526945	+	0.660768i	0.972067	−	0.234702i	$-0.0754113\pi$
$7$	1.39417	+	1.74823i	0.526945	+	0.660768i	−0.445122	+	0.895470i	$0.646840\pi$
$8$	0.497572	−	2.18001i	0.175918	−	0.770748i
$9$	0.0849954	−	0.372389i	0.0283318	−	0.124130i
$10$	−2.87930	+	3.61052i	−0.910514	+	1.14175i
$11$	−0.805088	−	3.52732i	−0.242743	−	1.06353i	−0.938508	−	0.345258i	$-0.887791\pi$
$11$	−0.805088	−	3.52732i	−0.242743	−	1.06353i	0.695765	−	0.718270i	$-0.255066\pi$
$12$	−1.00000			−0.288675
$13$	−0.942614	−	4.12986i	−0.261434	−	1.14542i	−0.919697	−	0.392629i	$-0.871566\pi$
$13$	−0.942614	−	4.12986i	−0.261434	−	1.14542i	0.658263	−	0.752788i	$-0.271292\pi$
$14$	−3.25974	−	1.56981i	−0.871201	−	0.419548i
$15$	−4.16070	−	2.00369i	−1.07429	−	0.517350i
$16$	1.08014	+	4.73240i	0.270035	+	1.18310i
$17$	6.61803			1.60511			0.802555	−	0.596579i	$-0.203474\pi$
$17$	6.61803			1.60511			0.802555	+	0.596579i	$0.203474\pi$
$18$	0.137526	+	0.602539i	0.0324151	+	0.142020i
$19$	−1.15601	+	1.44960i	−0.265208	+	0.332560i	−0.896549	−	0.442946i	$-0.853933\pi$
$19$	−1.15601	+	1.44960i	−0.265208	+	0.332560i	0.631341	+	0.775506i	$0.282505\pi$
$20$	0.392512	−	1.71971i	0.0877683	−	0.384538i
$21$	0.805088	−	3.52732i	0.175685	−	0.769725i
$22$	3.64997	+	4.57692i	0.778177	+	0.975803i
$23$	−2.91560	−	1.40408i	−0.607944	−	0.292770i	0.104472	−	0.994528i	$-0.466685\pi$
$23$	−2.91560	−	1.40408i	−0.607944	−	0.292770i	−0.712416	+	0.701757i	$0.752399\pi$
$24$	−3.25974	+	1.56981i	−0.665391	+	0.320435i
$25$	1.96144	−	2.45956i	0.392287	−	0.491912i
$26$	4.27346	+	5.35875i	0.838095	+	1.05094i
$27$	−4.93022	+	2.37427i	−0.948822	+	0.456929i
$28$	1.38197			0.261167
$29$		0			0
$29$		0			0
$30$	7.47214			1.36422
$31$	0.982209	−	0.473007i	0.176410	−	0.0849546i	−0.343594	−	0.939118i	$-0.611645\pi$
$31$	0.982209	−	0.473007i	0.176410	−	0.0849546i	0.520004	+	0.854164i	$0.325930\pi$
$32$	−2.10862	−	2.64413i	−0.372755	−	0.467420i
$33$	−3.64997	+	4.57692i	−0.635379	+	0.796740i
$34$	−9.64776	+	4.64612i	−1.65458	+	0.796802i
$35$	5.74995	+	2.76903i	0.971919	+	0.468052i
$36$	−0.147186	−	0.184565i	−0.0245310	−	0.0307609i
$37$	−1.93776	+	8.48987i	−0.318565	+	1.39573i	0.521505	+	0.853248i	$0.325371\pi$
$37$	−1.93776	+	8.48987i	−0.318565	+	1.39573i	−0.840070	+	0.542478i	$0.817486\pi$
$38$	0.667563	−	2.92478i	0.108293	−	0.474463i
$39$	−4.27346	+	5.35875i	−0.684302	+	0.858087i
$40$	−1.42012	−	6.22196i	−0.224541	−	0.983778i
$41$	2.85410			0.445736			0.222868	−	0.974849i	$-0.428458\pi$
$41$	2.85410			0.445736			0.222868	+	0.974849i	$0.428458\pi$
$42$	1.30266	+	5.70733i	0.201005	+	0.880660i
$43$	−2.49022	−	1.19923i	−0.379754	−	0.182880i	0.234262	−	0.972174i	$-0.424733\pi$
$43$	−2.49022	−	1.19923i	−0.379754	−	0.182880i	−0.614016	+	0.789293i	$0.710447\pi$
$44$	−2.01463	−	0.970194i	−0.303717	−	0.146262i
$45$	−0.242586	−	1.06284i	−0.0361625	−	0.158438i
$46$	5.23607			0.772016
$47$	−1.55765	−	6.82450i	−0.227206	−	0.995455i	−0.951906	−	0.306390i	$-0.900879\pi$
$47$	−1.55765	−	6.82450i	−0.227206	−	0.995455i	0.724700	−	0.689065i	$-0.241978\pi$
$48$	4.89695	−	6.14058i	0.706814	−	0.886317i
$49$	0.445042	−	1.94986i	0.0635774	−	0.278551i
$50$	−1.13267	+	4.96255i	−0.160184	+	0.701810i
$51$	−6.67646	−	8.37201i	−0.934891	−	1.17232i
$52$	−2.35877	−	1.13592i	−0.327102	−	0.157524i
$53$	1.80194	−	0.867767i	0.247515	−	0.119197i	−0.306013	−	0.952027i	$-0.598995\pi$
$53$	1.80194	−	0.867767i	0.247515	−	0.119197i	0.553529	+	0.832830i	$0.313281\pi$
$54$	5.52044	−	6.92242i	0.751237	−	0.942021i
$55$	−6.43830	−	8.07338i	−0.868141	−	1.08861i
$56$	4.50484	−	2.16942i	0.601985	−	0.289901i
$57$	3.00000			0.397360
$58$		0			0
$59$	−5.09017			−0.662684			−0.331342	−	0.943511i	$-0.607501\pi$
$59$	−5.09017			−0.662684			−0.331342	+	0.943511i	$0.607501\pi$
$60$	−2.57146	+	1.23835i	−0.331974	+	0.159870i
$61$	−1.00883	−	1.26503i	−0.129167	−	0.161970i	0.713042	−	0.701121i	$-0.247317\pi$
$61$	−1.00883	−	1.26503i	−0.129167	−	0.161970i	−0.842209	+	0.539151i	$0.818745\pi$
$62$	−1.09979	+	1.37910i	−0.139674	+	0.175146i
$63$	0.769519	−	0.370581i	0.0969503	−	0.0466888i
$64$	−3.81657	−	1.83796i	−0.477071	−	0.229745i
$65$	−7.53810	−	9.45248i	−0.934986	−	1.17244i
$66$	2.10775	−	9.23465i	0.259446	−	1.13671i
$67$	2.33027	−	10.2096i	0.284688	−	1.24730i	−0.607020	−	0.794687i	$-0.707635\pi$
$67$	2.33027	−	10.2096i	0.284688	−	1.24730i	0.891708	−	0.452612i	$-0.149508\pi$
$68$	2.55018	−	3.19782i	0.309255	−	0.387793i
$69$	1.16513	+	5.10479i	0.140266	+	0.614544i
$70$	−10.3262			−1.23422
$71$	−0.339982	−	1.48956i	−0.0403484	−	0.176778i	0.950739	−	0.309993i	$-0.100327\pi$
$71$	−0.339982	−	1.48956i	−0.0403484	−	0.176778i	−0.991087	+	0.133216i	$0.957470\pi$
$72$	−0.769519	−	0.370581i	−0.0906887	−	0.0436734i
$73$	−0.262899	−	0.126606i	−0.0307700	−	0.0148181i	0.418435	−	0.908247i	$-0.362579\pi$
$73$	−0.262899	−	0.126606i	−0.0307700	−	0.0148181i	−0.449205	+	0.893428i	$0.648293\pi$
$74$	−3.13536	−	13.7369i	−0.364478	−	1.59688i
$75$	−5.09017			−0.587762
$76$	0.254986	+	1.11717i	0.0292489	+	0.128148i
$77$	5.04414	−	6.32515i	0.574833	−	0.720818i
$78$	2.46779	−	10.8121i	0.279423	−	1.22423i
$79$	1.13267	−	4.96255i	0.127435	−	0.558330i	−0.870387	−	0.492368i	$-0.836131\pi$
$79$	1.13267	−	4.96255i	0.127435	−	0.558330i	0.997822	−	0.0659619i	$-0.0210116\pi$
$80$	8.63789	+	10.8316i	0.965746	+	1.21101i
$81$	6.94485	+	3.34446i	0.771650	+	0.371607i
$82$	−4.16070	+	2.00369i	−0.459473	+	0.221271i
$83$	4.95317	−	6.21108i	0.543681	−	0.681755i	−0.431767	−	0.901985i	$-0.642110\pi$
$83$	4.95317	−	6.21108i	0.543681	−	0.681755i	0.975448	+	0.220231i	$0.0706810\pi$
$84$	−1.39417	−	1.74823i	−0.152116	−	0.190747i
$85$	17.0180	−	8.19543i	1.84586	−	0.888919i
$86$	4.47214			0.482243
$87$		0			0
$88$	−8.09017			−0.862415
$89$	−7.84582	+	3.77835i	−0.831655	+	0.400504i	−0.800736	−	0.599018i	$-0.795558\pi$
$89$	−7.84582	+	3.77835i	−0.831655	+	0.400504i	−0.0309196	+	0.999522i	$0.509844\pi$
$90$	1.09979	+	1.37910i	0.115928	+	0.145370i
$91$	5.90578	−	7.40561i	0.619094	−	0.776319i
$92$	−1.80194	+	0.867767i	−0.187865	+	0.0904710i
$93$	−1.58925	−	0.765341i	−0.164797	−	0.0793622i
$94$	7.06179	+	8.85521i	0.728368	+	0.913345i
$95$	−1.17754	+	5.15912i	−0.120813	+	0.529315i
$96$	−1.21766	+	5.33494i	−0.124277	+	0.544495i
$97$	10.3264	−	12.9489i	1.04849	−	1.31476i	0.101033	−	0.994883i	$-0.467785\pi$
$97$	10.3264	−	12.9489i	1.04849	−	1.31476i	0.947457	−	0.319882i	$-0.103643\pi$
$98$	0.720093	+	3.15493i	0.0727404	+	0.318696i
$99$	−1.38197			−0.138893
$100$	−0.432641	−	1.89552i	−0.0432641	−	0.189552i
$101$	1.45780	+	0.702039i	0.145056	+	0.0698555i	0.505004	−	0.863117i	$-0.331491\pi$
$101$	1.45780	+	0.702039i	0.145056	+	0.0698555i	−0.359947	+	0.932973i	$0.617205\pi$
$102$	15.6104	+	7.51757i	1.54566	+	0.744351i
$103$	2.93290	+	12.8499i	0.288987	+	1.26614i	0.885917	+	0.463843i	$0.153530\pi$
$103$	2.93290	+	12.8499i	0.288987	+	1.26614i	−0.596930	+	0.802293i	$0.703613\pi$
$104$	−9.47214			−0.928819
$105$	−2.29780	−	10.0673i	−0.224243	−	0.982472i
$106$	−2.01766	+	2.53006i	−0.195972	+	0.245741i
$107$	−2.50026	+	10.9544i	−0.241709	+	1.05900i	0.697751	+	0.716340i	$0.254184\pi$
$107$	−2.50026	+	10.9544i	−0.241709	+	1.05900i	−0.939460	+	0.342657i	$0.888673\pi$
$108$	−0.752558	+	3.29717i	−0.0724149	+	0.317271i
$109$	−10.3612	−	12.9925i	−0.992421	−	1.24446i	−0.969595	−	0.244717i	$-0.921305\pi$
$109$	−10.3612	−	12.9925i	−0.992421	−	1.24446i	−0.0228259	−	0.999739i	$-0.507266\pi$
$110$	15.0536	+	7.24942i	1.43530	+	0.691205i
$111$	12.6948	−	6.11350i	1.20494	−	0.580267i
$112$	−6.76742	+	8.48608i	−0.639461	+	0.801859i
$113$	6.20015	+	7.77474i	0.583261	+	0.731386i	0.982665	−	0.185389i	$-0.0593544\pi$
$113$	6.20015	+	7.77474i	0.583261	+	0.731386i	−0.399404	+	0.916775i	$0.630783\pi$
$114$	−4.37339	+	2.10612i	−0.409606	+	0.197256i
$115$	−9.23607			−0.861268
$116$		0			0
$117$	−1.61803			−0.149587
$118$	7.42044	−	3.57350i	0.683107	−	0.328967i
$119$	9.22664	+	11.5698i	0.845804	+	1.06060i
$120$	−6.43830	+	8.07338i	−0.587734	+	0.736995i
$121$	−1.88318	+	0.906891i	−0.171198	+	0.0824446i
$122$	2.35877	+	1.13592i	0.213553	+	0.102842i
$123$	−2.87930	−	3.61052i	−0.259617	−	0.325550i
$124$	0.149926	−	0.656869i	0.0134638	−	0.0589886i
$125$	−1.17754	+	5.15912i	−0.105322	+	0.461446i
$126$	−0.861642	+	1.08046i	−0.0767611	+	0.0962554i
$127$	−0.432641	−	1.89552i	−0.0383907	−	0.168201i	0.952098	−	0.305792i	$-0.0989211\pi$
$127$	−0.432641	−	1.89552i	−0.0383907	−	0.168201i	−0.990489	+	0.137591i	$0.956064\pi$
$128$	13.6180			1.20368
$129$	0.995144	+	4.36001i	0.0876175	+	0.383877i
$130$	17.6250	+	8.48777i	1.54582	+	0.744426i
$131$	−1.19490	−	0.575433i	−0.104399	−	0.0502758i	0.380956	−	0.924593i	$-0.375595\pi$
$131$	−1.19490	−	0.575433i	−0.104399	−	0.0502758i	−0.485354	+	0.874318i	$0.661309\pi$
$132$	0.805088	+	3.52732i	0.0700739	+	0.307014i
$133$	−4.14590			−0.359495
$134$	3.77046	+	16.5194i	0.325718	+	1.42706i
$135$	−9.73768	+	12.2107i	−0.838086	+	1.05093i
$136$	3.29295	−	14.4273i	0.282368	−	1.23713i
$137$	3.08283	−	13.5068i	0.263384	−	1.15396i	−0.654170	−	0.756348i	$-0.726982\pi$
$137$	3.08283	−	13.5068i	0.263384	−	1.15396i	0.917554	−	0.397612i	$-0.130161\pi$
$138$	−5.28229	−	6.62378i	−0.449658	−	0.563854i
$139$	−13.2516	−	6.38165i	−1.12399	−	0.541285i	−0.222866	−	0.974849i	$-0.571541\pi$
$139$	−13.2516	−	6.38165i	−1.12399	−	0.541285i	−0.901123	+	0.433564i	$0.857256\pi$
$140$	3.55367	−	1.71136i	0.300340	−	0.144636i
$141$	−7.06179	+	8.85521i	−0.594710	+	0.745743i
$142$	1.54135	+	1.93279i	0.129347	+	0.162196i
$143$	−13.8085	+	6.64981i	−1.15472	+	0.556085i
$144$	1.85410			0.154508
$145$		0			0
$146$	0.472136			0.0390742
$147$	−2.91560	+	1.40408i	−0.240474	+	0.115806i
$148$	3.35560	+	4.20779i	0.275829	+	0.345878i
$149$	4.60258	−	5.77145i	0.377058	−	0.472816i	−0.556704	−	0.830711i	$-0.687934\pi$
$149$	4.60258	−	5.77145i	0.377058	−	0.472816i	0.933762	+	0.357895i	$0.116506\pi$
$150$	7.42044	−	3.57350i	0.605876	−	0.291775i
$151$	−16.5114	−	7.95146i	−1.34368	−	0.647080i	−0.382742	−	0.923855i	$-0.625020\pi$
$151$	−16.5114	−	7.95146i	−1.34368	−	0.647080i	−0.960935	+	0.276775i	$0.910734\pi$
$152$	2.58493	+	3.24139i	0.209665	+	0.262912i
$153$	0.562503	−	2.46449i	0.0454756	−	0.199242i
$154$	−2.91284	+	12.7620i	−0.234723	+	1.02839i
$155$	1.93996	−	2.43263i	0.155821	−	0.195394i
$156$	0.942614	+	4.12986i	0.0754695	+	0.330654i
$157$	5.56231			0.443920			0.221960	−	0.975056i	$-0.428755\pi$
$157$	5.56231			0.443920			0.221960	+	0.975056i	$0.428755\pi$
$158$	1.83270	+	8.02957i	0.145802	+	0.638798i
$159$	−2.91560	−	1.40408i	−0.231222	−	0.111351i
$160$	−8.69658	−	4.18805i	−0.687525	−	0.331095i
$161$	−1.61018	−	7.05464i	−0.126900	−	0.555984i
$162$	−12.4721			−0.979904
$163$	5.12565	+	22.4569i	0.401472	+	1.75896i	0.621447	+	0.783456i	$0.286545\pi$
$163$	5.12565	+	22.4569i	0.401472	+	1.75896i	−0.219975	+	0.975505i	$0.570598\pi$
$164$	1.09979	−	1.37910i	0.0858795	−	0.107689i
$165$	−3.71793	+	16.2893i	−0.289440	+	1.26812i
$166$	−2.86031	+	12.5318i	−0.222003	+	0.972658i
$167$	12.1407	+	15.2239i	0.939474	+	1.17806i	0.983840	+	0.179048i	$0.0573016\pi$
$167$	12.1407	+	15.2239i	0.939474	+	1.17806i	−0.0443665	+	0.999015i	$0.514127\pi$
$168$	−7.28899	−	3.51019i	−0.562358	−	0.270817i
$169$	−4.45464	+	2.14524i	−0.342664	+	0.165018i
$170$	−19.0553	+	23.8946i	−1.46147	+	1.83263i
$171$	0.441558	+	0.553696i	0.0337668	+	0.0423422i
$172$	−1.53904	+	0.741162i	−0.117351	+	0.0565131i
$173$	−7.09017			−0.539056			−0.269528	−	0.962993i	$-0.586868\pi$
$173$	−7.09017			−0.539056			−0.269528	+	0.962993i	$0.586868\pi$
$174$		0			0
$175$	7.03444			0.531754
$176$	15.8231	−	7.62000i	1.19271	−	0.574379i
$177$	5.13510	+	6.43922i	0.385978	+	0.484001i
$178$	8.78508	−	11.0161i	0.658469	−	0.825694i
$179$	14.4155	−	6.94214i	1.07747	−	0.518880i	0.190960	−	0.981598i	$-0.438840\pi$
$179$	14.4155	−	6.94214i	1.07747	−	0.518880i	0.886506	+	0.462718i	$0.153126\pi$
$180$	−0.607039	−	0.292334i	−0.0452460	−	0.0217893i
$181$	−7.44713	−	9.33841i	−0.553541	−	0.694118i	0.423808	−	0.905752i	$-0.360693\pi$
$181$	−7.44713	−	9.33841i	−0.553541	−	0.694118i	−0.977349	+	0.211634i	$0.932122\pi$
$182$	−3.41041	+	14.9420i	−0.252796	+	1.10757i
$183$	−0.582567	+	2.55239i	−0.0430646	+	0.188678i
$184$	−4.51161	+	5.65739i	−0.332601	+	0.417068i
$185$	5.53056	+	24.2310i	0.406615	+	1.78150i
$186$	2.85410			0.209273
$187$	−5.32810	−	23.3439i	−0.389629	−	1.70708i
$188$	−3.89781	−	1.87708i	−0.284277	−	0.136900i
$189$	−11.0243	−	5.30903i	−0.801901	−	0.386175i
$190$	−1.90529	−	8.34763i	−0.138224	−	0.605601i
$191$	12.0344			0.870782			0.435391	−	0.900242i	$-0.356610\pi$
$191$	12.0344			0.870782			0.435391	+	0.900242i	$0.356610\pi$
$192$	1.52518	+	6.68226i	0.110070	+	0.482250i
$193$	−2.19959	+	2.75820i	−0.158330	+	0.198539i	−0.854669	−	0.519174i	$-0.826240\pi$
$193$	−2.19959	+	2.75820i	−0.158330	+	0.198539i	0.696339	+	0.717713i	$0.254811\pi$
$194$	−5.96320	+	26.1265i	−0.428133	+	1.87577i
$195$	−4.35302	+	19.0718i	−0.311726	+	1.36576i
$196$	−0.770676	−	0.966397i	−0.0550483	−	0.0690283i
$197$	17.7565	+	8.55107i	1.26510	+	0.609238i	0.941518	−	0.336963i	$-0.109400\pi$
$197$	17.7565	+	8.55107i	1.26510	+	0.609238i	0.323579	+	0.946201i	$0.395114\pi$
$198$	2.01463	−	0.970194i	0.143173	−	0.0689487i
$199$	0.532524	−	0.667764i	0.0377496	−	0.0473365i	−0.762598	−	0.646872i	$-0.776077\pi$
$199$	0.532524	−	0.667764i	0.0377496	−	0.0473365i	0.800348	+	0.599536i	$0.204648\pi$
$200$	−4.38590	−	5.49975i	−0.310130	−	0.388891i
$201$	−15.2663	+	7.35184i	−1.07680	+	0.518559i
$202$	−2.61803			−0.184204
$203$		0			0
$204$	−6.61803			−0.463355
$205$	7.33920	−	3.53437i	0.512592	−	0.246851i
$206$	−13.2967	−	16.6735i	−0.926424	−	1.16170i
$207$	−0.770676	+	0.966397i	−0.0535657	+	0.0671692i
$208$	18.5260	−	8.92165i	1.28455	−	0.618605i
$209$	6.04388	+	2.91058i	0.418064	+	0.201329i
$210$	10.4174	+	13.0630i	0.718869	+	0.901433i
$211$	4.37309	−	19.1597i	0.301056	−	1.31901i	−0.567481	−	0.823387i	$-0.692082\pi$
$211$	4.37309	−	19.1597i	0.301056	−	1.31901i	0.868537	−	0.495625i	$-0.165061\pi$
$212$	0.275051	−	1.20508i	0.0188906	−	0.0827650i
$213$	−1.54135	+	1.93279i	−0.105612	+	0.132433i
$214$	−4.04551	−	17.7245i	−0.276545	−	1.21162i
$215$	−7.88854			−0.537994
$216$	2.72278	+	11.9293i	0.185262	+	0.811685i
$217$	2.19629	+	1.05768i	0.149094	+	0.0717997i
$218$	24.2257	+	11.6665i	1.64077	+	0.790155i
$219$	0.105060	+	0.460299i	0.00709931	+	0.0311041i
$220$	−6.38197			−0.430272
$221$	−6.23825	−	27.3316i	−0.419630	−	1.83852i
$222$	−14.2146	+	17.8245i	−0.954018	+	1.19630i
$223$	−4.07797	+	17.8668i	−0.273081	+	1.19645i	0.633273	+	0.773928i	$0.281711\pi$
$223$	−4.07797	+	17.8668i	−0.273081	+	1.19645i	−0.906354	+	0.422518i	$0.861146\pi$
$224$	1.68277	−	7.37270i	0.112435	−	0.492609i
$225$	−0.749202	−	0.939469i	−0.0499468	−	0.0626313i
$226$	−14.4967	−	6.98126i	−0.964309	−	0.464387i
$227$	−13.4141	+	6.45990i	−0.890326	+	0.428758i	−0.822385	−	0.568931i	$-0.807357\pi$
$227$	−13.4141	+	6.45990i	−0.890326	+	0.428758i	−0.0679407	+	0.997689i	$0.521643\pi$
$228$	1.15601	−	1.44960i	0.0765589	−	0.0960018i
$229$	−9.79390	−	12.2812i	−0.647199	−	0.811562i	0.344683	−	0.938719i	$-0.387986\pi$
$229$	−9.79390	−	12.2812i	−0.647199	−	0.811562i	−0.991883	+	0.127157i	$0.959415\pi$
$230$	13.4643	−	6.48408i	0.887811	−	0.427547i
$231$	−13.0902			−0.861270
$232$		0			0
$233$	10.7639			0.705169			0.352584	−	0.935780i	$-0.385303\pi$
$233$	10.7639			0.705169			0.352584	+	0.935780i	$0.385303\pi$
$234$	2.35877	−	1.13592i	0.154197	−	0.0742576i
$235$	−12.4565	−	15.6200i	−0.812574	−	1.01894i
$236$	−1.96144	+	2.45956i	−0.127679	+	0.160104i
$237$	−7.42044	+	3.57350i	−0.482009	+	0.232124i
$238$	−21.5730	−	10.3890i	−1.39837	−	0.673421i
$239$	9.19189	+	11.5263i	0.594574	+	0.745572i	0.984521	−	0.175265i	$-0.0560782\pi$
$239$	9.19189	+	11.5263i	0.594574	+	0.745572i	−0.389947	+	0.920837i	$0.627507\pi$
$240$	4.98812	−	21.8544i	0.321982	−	1.41069i
$241$	−5.93073	+	25.9842i	−0.382032	+	1.67379i	0.309073	+	0.951038i	$0.399981\pi$
$241$	−5.93073	+	25.9842i	−0.382032	+	1.67379i	−0.691105	+	0.722754i	$0.742876\pi$
$242$	2.10862	−	2.64413i	0.135547	−	0.169971i
$243$	0.877683	+	3.84538i	0.0563034	+	0.246681i
$244$	−1.00000			−0.0640184
$245$	−1.27019	−	5.56509i	−0.0811498	−	0.355540i
$246$	6.73216	+	3.24204i	0.429227	+	0.206705i
$247$	7.07630	+	3.40777i	0.450254	+	0.216831i
$248$	−0.542438	−	2.37658i	−0.0344448	−	0.150913i
$249$	−12.8541			−0.814596
$250$	−1.90529	−	8.34763i	−0.120501	−	0.527951i
$251$	−7.26520	+	9.11027i	−0.458575	+	0.575035i	−0.956332	−	0.292281i	$-0.905586\pi$
$251$	−7.26520	+	9.11027i	−0.458575	+	0.575035i	0.497757	+	0.867316i	$0.334157\pi$
$252$	0.117461	−	0.514629i	0.00739933	−	0.0324186i
$253$	−2.60532	+	11.4147i	−0.163795	+	0.717633i
$254$	1.96144	+	2.45956i	0.123071	+	0.154327i
$255$	−27.5357	−	13.2605i	−1.72435	−	0.830404i
$256$	−12.2192	+	5.88446i	−0.763701	+	0.367779i
$257$	−0.511050	+	0.640836i	−0.0318784	+	0.0399743i	−0.797515	−	0.603299i	$-0.793853\pi$
$257$	−0.511050	+	0.640836i	−0.0318784	+	0.0399743i	0.765637	+	0.643273i	$0.222424\pi$
$258$	−4.51161	−	5.65739i	−0.280881	−	0.352213i
$259$	−17.5438	+	8.44864i	−1.09012	+	0.524973i
$260$	−7.47214			−0.463402
$261$		0			0
$262$	2.14590			0.132574
$263$	−2.96581	+	1.42826i	−0.182879	+	0.0880701i	−0.523083	−	0.852282i	$-0.675218\pi$
$263$	−2.96581	+	1.42826i	−0.182879	+	0.0880701i	0.340204	+	0.940352i	$0.389504\pi$
$264$	8.16159	+	10.2343i	0.502311	+	0.629878i
$265$	3.55901	−	4.46285i	0.218628	−	0.274151i
$266$	6.04388	−	2.91058i	0.370574	−	0.178459i
$267$	12.6948	+	6.11350i	0.776909	+	0.374140i
$268$	−4.03531	−	5.06012i	−0.246496	−	0.309096i
$269$	−1.33513	+	5.84957i	−0.0814040	+	0.356654i	−0.999182	−	0.0404396i	$-0.987124\pi$
$269$	−1.33513	+	5.84957i	−0.0814040	+	0.356654i	0.917778	+	0.397094i	$0.129981\pi$
$270$	5.62322	−	24.6369i	0.342218	−	1.49936i
$271$	7.59432	−	9.52297i	0.461322	−	0.578479i	−0.495700	−	0.868494i	$-0.665089\pi$
$271$	7.59432	−	9.52297i	0.461322	−	0.578479i	0.957022	+	0.290014i	$0.0936600\pi$
$272$	7.14840	+	31.3192i	0.433435	+	1.89900i
$273$	−15.3262			−0.927586
$274$	4.98812	+	21.8544i	0.301343	+	1.32027i
$275$	−10.2548	−	4.93845i	−0.618388	−	0.297800i
$276$	2.91560	+	1.40408i	0.175498	+	0.0845155i
$277$	5.25551	+	23.0259i	0.315773	+	1.38349i	0.844889	+	0.534942i	$0.179666\pi$
$277$	5.25551	+	23.0259i	0.315773	+	1.38349i	−0.529116	+	0.848549i	$0.677476\pi$
$278$	23.7984			1.42733
$279$	−0.0926595	−	0.405968i	−0.00554738	−	0.0243046i
$280$	8.89752	−	11.1571i	0.531728	−	0.666766i
$281$	3.81058	−	16.6953i	0.227320	−	0.995956i	−0.724494	−	0.689281i	$-0.757926\pi$
$281$	3.81058	−	16.6953i	0.227320	−	0.995956i	0.951814	−	0.306675i	$-0.0992164\pi$
$282$	4.07797	−	17.8668i	0.242840	−	1.06395i
$283$	−0.476304	−	0.597266i	−0.0283133	−	0.0355038i	0.767473	−	0.641081i	$-0.221514\pi$
$283$	−0.476304	−	0.597266i	−0.0283133	−	0.0355038i	−0.795787	+	0.605577i	$0.792942\pi$
$284$	−0.850760	−	0.409704i	−0.0504833	−	0.0243115i
$285$	7.71437	−	3.71505i	0.456960	−	0.220060i
$286$	15.4615	−	19.3881i	0.914260	−	1.14645i
$287$	3.97909	+	4.98962i	0.234878	+	0.294528i
$288$	−1.16387	+	0.560489i	−0.0685816	+	0.0330271i
$289$	26.7984			1.57637
$290$		0			0
$291$	−26.7984			−1.57095
$292$	−0.162481	+	0.0782465i	−0.00950846	+	0.00457903i
$293$	−10.8937	−	13.6603i	−0.636417	−	0.798041i	0.354133	−	0.935195i	$-0.384776\pi$
$293$	−10.8937	−	13.6603i	−0.636417	−	0.798041i	−0.990550	+	0.137154i	$0.956205\pi$
$294$	3.26463	−	4.09372i	0.190397	−	0.238751i
$295$	−13.0892	+	6.30340i	−0.762080	+	0.366998i
$296$	17.5438	+	8.44864i	1.01971	+	0.491067i
$297$	12.3441	+	15.4790i	0.716276	+	0.898182i
$298$	−2.65785	+	11.6448i	−0.153965	+	0.674565i
$299$	−3.05036	+	13.3645i	−0.176407	+	0.772890i
$300$	−1.96144	+	2.45956i	−0.113244	+	0.142003i
$301$	−1.37526	−	6.02539i	−0.0792684	−	0.347297i
$302$	29.6525			1.70631
$303$	−0.582567	−	2.55239i	−0.0334676	−	0.146631i
$304$	−8.10872	−	3.90495i	−0.465067	−	0.223964i
$305$	−4.16070	−	2.00369i	−0.238241	−	0.114731i
$306$	0.910148	+	3.98762i	0.0520297	+	0.227957i
$307$	−3.18034			−0.181512			−0.0907558	−	0.995873i	$-0.528928\pi$
$307$	−3.18034			−0.181512			−0.0907558	+	0.995873i	$0.528928\pi$
$308$	−1.11260	−	4.87464i	−0.0633965	−	0.277758i
$309$	13.2967	−	16.6735i	0.756422	−	0.948524i
$310$	−1.12027	+	4.90822i	−0.0636270	+	0.278768i
$311$	−2.02275	+	8.86226i	−0.114700	+	0.502533i	0.884642	+	0.466270i	$0.154402\pi$
$311$	−2.02275	+	8.86226i	−0.114700	+	0.502533i	−0.999342	+	0.0362627i	$0.988455\pi$
$312$	9.55575	+	11.9825i	0.540988	+	0.678377i
$313$	21.7045	+	10.4523i	1.22681	+	0.590801i	0.931200	−	0.364508i	$-0.118763\pi$
$313$	21.7045	+	10.4523i	1.22681	+	0.590801i	0.295610	+	0.955309i	$0.404477\pi$
$314$	−8.10872	+	3.90495i	−0.457602	+	0.220369i
$315$	1.51988	−	1.90587i	0.0856354	−	0.107383i
$316$	−1.96144	−	2.45956i	−0.110339	−	0.138361i
$317$	12.8765	−	6.20098i	0.723214	−	0.348282i	−0.0357971	−	0.999359i	$-0.511397\pi$
$317$	12.8765	−	6.20098i	0.723214	−	0.348282i	0.759011	+	0.651077i	$0.225683\pi$
$318$	5.23607			0.293624
$319$		0			0
$320$	−12.0902			−0.675861
$321$	16.3799	−	7.88815i	0.914238	−	0.440274i
$322$	7.29995	+	9.15384i	0.406810	+	0.510124i
$323$	−7.65054	+	9.59347i	−0.425687	+	0.533795i
$324$	4.29215	−	2.06699i	0.238453	−	0.114833i
$325$	−12.0065	−	5.78204i	−0.666002	−	0.320730i
$326$	−23.2378	−	29.1393i	−1.28702	−	1.61387i
$327$	−5.98326	+	26.2144i	−0.330875	+	1.44966i
$328$	1.42012	−	6.22196i	0.0784131	−	0.343550i
$329$	9.75916	−	12.2376i	0.538040	−	0.674681i
$330$	−6.01573	−	26.3566i	−0.331155	−	1.45088i
$331$	1.18034			0.0648773			0.0324387	−	0.999474i	$-0.489673\pi$
$331$	1.18034			0.0648773			0.0324387	+	0.999474i	$0.489673\pi$
$332$	−1.09254	−	4.78673i	−0.0599609	−	0.262706i
$333$	2.99684	+	1.44320i	0.164226	+	0.0790869i
$334$	−28.3864	−	13.6702i	−1.55324	−	0.748000i
$335$	−6.65083	−	29.1392i	−0.363373	−	1.59204i
$336$	17.5623			0.958102
$337$	5.35583	+	23.4654i	0.291751	+	1.27824i	0.882087	+	0.471086i	$0.156138\pi$
$337$	5.35583	+	23.4654i	0.291751	+	1.27824i	−0.590337	+	0.807157i	$0.701005\pi$
$338$	4.98792	−	6.25465i	0.271307	−	0.340208i
$339$	3.58040	−	15.6868i	0.194461	−	0.851988i
$340$	2.59766	−	11.3811i	0.140878	−	0.617226i
$341$	−2.45921	−	3.08376i	−0.133174	−	0.166995i
$342$	−1.03242	−	0.497187i	−0.0558268	−	0.0268848i
$343$	18.1316	−	8.73174i	0.979017	−	0.471470i
$344$	−3.85338	+	4.83198i	−0.207760	+	0.260523i
$345$	9.31760	+	11.6839i	0.501643	+	0.629040i
$346$	10.3360	−	4.97757i	0.555669	−	0.267596i
$347$	8.12461			0.436152			0.218076	−	0.975932i	$-0.430022\pi$
$347$	8.12461			0.436152			0.218076	+	0.975932i	$0.430022\pi$
$348$		0			0
$349$	13.4721			0.721147			0.360573	−	0.932731i	$-0.382581\pi$
$349$	13.4721			0.721147			0.360573	+	0.932731i	$0.382581\pi$
$350$	−10.2548	+	4.93845i	−0.548142	+	0.263971i
$351$	14.4527	+	18.1231i	0.771428	+	0.967341i
$352$	−7.62906	+	9.56654i	−0.406630	+	0.509898i
$353$	−19.0326	+	9.16563i	−1.01300	+	0.487837i	−0.865332	−	0.501199i	$-0.832892\pi$
$353$	−19.0326	+	9.16563i	−1.01300	+	0.487837i	−0.147672	+	0.989036i	$0.547178\pi$
$354$	−12.0065	−	5.78204i	−0.638140	−	0.307312i
$355$	−2.71884	−	3.40932i	−0.144301	−	0.180948i
$356$	−1.19760	+	5.24703i	−0.0634727	+	0.278092i
$357$	5.32810	−	23.3439i	0.281993	−	1.23549i
$358$	−16.1412	+	20.2405i	−0.853091	+	1.06974i
$359$	−6.28312	−	27.5281i	−0.331610	−	1.45288i	−0.816013	−	0.578034i	$-0.803820\pi$
$359$	−6.28312	−	27.5281i	−0.331610	−	1.45288i	0.484403	−	0.874845i	$-0.339037\pi$
$360$	−2.43769			−0.128478
$361$	3.46294	+	15.1721i	0.182260	+	0.798533i
$362$	17.4123	+	8.38534i	0.915172	+	0.440724i
$363$	3.04705	+	1.46738i	0.159928	+	0.0770175i
$364$	−1.30266	−	5.70733i	−0.0682779	−	0.299145i
$365$	−0.832816			−0.0435916
$366$	−0.942614	−	4.12986i	−0.0492712	−	0.215871i
$367$	3.90960	−	4.90248i	0.204079	−	0.255907i	−0.669250	−	0.743037i	$-0.733385\pi$
$367$	3.90960	−	4.90248i	0.204079	−	0.255907i	0.873330	+	0.487130i	$0.161956\pi$
$368$	3.49540	−	15.3144i	0.182211	−	0.798317i
$369$	0.242586	−	1.06284i	0.0126285	−	0.0553291i
$370$	−25.0735	−	31.4412i	−1.30351	−	1.63455i
$371$	4.02926	+	1.94039i	0.209189	+	0.100740i
$372$	−0.982209	+	0.473007i	−0.0509252	+	0.0245243i
$373$	11.4610	−	14.3716i	0.593426	−	0.744133i	−0.390911	−	0.920429i	$-0.627840\pi$
$373$	11.4610	−	14.3716i	0.593426	−	0.744133i	0.984337	+	0.176295i	$0.0564114\pi$
$374$	24.1556	+	30.2902i	1.24906	+	1.56627i
$375$	7.71437	−	3.71505i	0.398368	−	0.191844i
$376$	−15.6525			−0.807215
$377$		0			0
$378$	19.7984			1.01832
$379$	−33.9739	+	16.3610i	−1.74512	+	0.840407i	−0.764468	+	0.644661i	$0.776998\pi$
$379$	−33.9739	+	16.3610i	−1.74512	+	0.840407i	−0.980655	+	0.195745i	$0.937287\pi$
$380$	2.03913	+	2.55699i	0.104605	+	0.131171i
$381$	−1.96144	+	2.45956i	−0.100487	+	0.126007i
$382$	−17.5438	+	8.44864i	−0.897618	+	0.432270i
$383$	19.9528	+	9.60875i	1.01954	+	0.490984i	0.867525	−	0.497394i	$-0.165710\pi$
$383$	19.9528	+	9.60875i	1.01954	+	0.490984i	0.152014	+	0.988378i	$0.451424\pi$
$384$	−13.7382	−	17.2272i	−0.701077	−	0.879123i
$385$	5.13805	−	22.5113i	0.261859	−	1.14728i
$386$	1.27019	−	5.56509i	0.0646512	−	0.283255i
$387$	−0.658236	+	0.825401i	−0.0334600	+	0.0419575i
$388$	−2.27774	−	9.97943i	−0.115635	−	0.506629i
$389$	−21.1246			−1.07106			−0.535530	−	0.844516i	$-0.679888\pi$
$389$	−21.1246			−1.07106			−0.535530	+	0.844516i	$0.679888\pi$
$390$	−7.04334	−	30.8589i	−0.356653	−	1.56260i
$391$	−19.2955	−	9.29223i	−0.975816	−	0.469928i
$392$	−4.02926	−	1.94039i	−0.203508	−	0.0980043i
$393$	0.477507	+	2.09210i	0.0240871	+	0.105532i
$394$	−31.8885			−1.60652
$395$	−3.23275	−	14.1636i	−0.162658	−	0.712649i
$396$	−0.532524	+	0.667764i	−0.0267603	+	0.0335564i
$397$	7.10827	−	31.1434i	0.356754	−	1.56304i	−0.404470	−	0.914551i	$-0.632544\pi$
$397$	7.10827	−	31.1434i	0.356754	−	1.56304i	0.761224	−	0.648489i	$-0.224599\pi$
$398$	−0.307516	+	1.34732i	−0.0154144	+	0.0675349i
$399$	4.18250	+	5.24469i	0.209387	+	0.262563i
$400$	13.7583	+	6.62563i	0.687913	+	0.331281i
$401$	29.7940	−	14.3481i	1.48784	−	0.716507i	0.499158	−	0.866511i	$-0.333643\pi$
$401$	29.7940	−	14.3481i	1.48784	−	0.716507i	0.988685	+	0.150004i	$0.0479286\pi$
$402$	17.0939	−	21.4350i	0.852564	−	1.06908i
$403$	−2.87930	−	3.61052i	−0.143428	−	0.179853i
$404$	0.900969	−	0.433884i	0.0448249	−	0.0215865i
$405$	22.0000			1.09319
$406$		0			0
$407$	31.5066			1.56172
$408$	−21.5730	+	10.3890i	−1.06802	+	0.514334i
$409$	−0.363864	−	0.456271i	−0.0179919	−	0.0225611i	0.772754	−	0.634705i	$-0.218879\pi$
$409$	−0.363864	−	0.456271i	−0.0179919	−	0.0225611i	−0.790746	+	0.612144i	$0.790307\pi$
$410$	−8.21781	+	10.3048i	−0.405849	+	0.508918i
$411$	−20.1965	+	9.72611i	−0.996219	+	0.479754i
$412$	7.33920	+	3.53437i	0.361576	+	0.174126i
$413$	−7.09654	−	8.89878i	−0.349198	−	0.437880i
$414$	0.445042	−	1.94986i	0.0218726	−	0.0958302i
$415$	5.04539	−	22.1053i	0.247668	−	1.08511i
$416$	−8.93226	+	11.2007i	−0.437940	+	0.549160i
$417$	5.29564	+	23.2017i	0.259328	+	1.13619i
$418$	−10.8541			−0.530891
$419$	−0.570167	−	2.49806i	−0.0278545	−	0.122038i	0.959089	−	0.283104i	$-0.0913641\pi$
$419$	−0.570167	−	2.49806i	−0.0278545	−	0.122038i	−0.986944	+	0.161065i	$0.948507\pi$
$420$	−5.74995	−	2.76903i	−0.280569	−	0.135115i
$421$	−1.77091	−	0.852824i	−0.0863087	−	0.0415641i	0.390231	−	0.920717i	$-0.372395\pi$
$421$	−1.77091	−	0.852824i	−0.0863087	−	0.0415641i	−0.476540	+	0.879153i	$0.658109\pi$
$422$	7.07580	+	31.0011i	0.344445	+	1.50911i
$423$	−2.67376			−0.130003
$424$	−0.995144	−	4.36001i	−0.0483285	−	0.211741i
$425$	12.9808	−	16.2775i	0.629664	−	0.789573i
$426$	0.890084	−	3.89971i	0.0431247	−	0.188942i
$427$	0.805088	−	3.52732i	0.0389610	−	0.170699i
$428$	4.32968	+	5.42925i	0.209283	+	0.262433i
$429$	22.3426	+	10.7596i	1.07871	+	0.519479i
$430$	11.4999	−	5.53806i	0.554575	−	0.267069i
$431$	−21.5707	+	27.0488i	−1.03902	+	1.30290i	−0.0872211	+	0.996189i	$0.527799\pi$
$431$	−21.5707	+	27.0488i	−1.03902	+	1.30290i	−0.951804	+	0.306707i	$0.900773\pi$
$432$	−16.5613	−	20.7672i	−0.796807	−	0.999165i
$433$	11.3685	−	5.47476i	0.546333	−	0.263100i	−0.140294	−	0.990110i	$-0.544805\pi$
$433$	11.3685	−	5.47476i	0.546333	−	0.263100i	0.686627	+	0.727010i	$0.259091\pi$
$434$	−3.94427			−0.189331
$435$		0			0
$436$	−10.2705			−0.491868
$437$	5.40581	−	2.60330i	0.258595	−	0.124533i
$438$	−0.476304	−	0.597266i	−0.0227587	−	0.0285385i
$439$	−1.90522	+	2.38906i	−0.0909310	+	0.114024i	−0.825216	−	0.564818i	$-0.808946\pi$
$439$	−1.90522	+	2.38906i	−0.0909310	+	0.114024i	0.734285	+	0.678842i	$0.237518\pi$
$440$	−20.8035	+	10.0184i	−0.991769	+	0.477611i
$441$	−0.688279	−	0.331458i	−0.0327752	−	0.0157837i
$442$	28.2819	+	35.4644i	1.34523	+	1.68687i
$443$	−2.91284	+	12.7620i	−0.138393	+	0.606340i	0.857395	+	0.514658i	$0.172081\pi$
$443$	−2.91284	+	12.7620i	−0.138393	+	0.606340i	−0.995788	+	0.0916812i	$0.970776\pi$
$444$	1.93776	−	8.48987i	0.0919619	−	0.402911i
$445$	−15.4963	+	19.4317i	−0.734594	+	0.921152i
$446$	−6.59830	−	28.9090i	−0.312438	−	1.36888i
$447$	−11.9443			−0.564945
$448$	−2.10775	−	9.23465i	−0.0995818	−	0.436296i
$449$	12.7258	+	6.12844i	0.600569	+	0.289219i	0.709361	−	0.704846i	$-0.248984\pi$
$449$	12.7258	+	6.12844i	0.600569	+	0.289219i	−0.108791	+	0.994065i	$0.534698\pi$
$450$	1.75173	+	0.843588i	0.0825773	+	0.0397671i
$451$	−2.29780	−	10.0673i	−0.108199	−	0.474052i
$452$	6.14590			0.289079
$453$	6.59830	+	28.9090i	0.310015	+	1.35826i
$454$	15.0200	−	18.8345i	0.704922	−	0.883945i
$455$	6.01573	−	26.3566i	0.282022	−	1.23562i
$456$	1.49272	−	6.54002i	0.0699028	−	0.306264i
$457$	3.29938	+	4.13729i	0.154339	+	0.193534i	0.852989	−	0.521929i	$-0.174787\pi$
$457$	3.29938	+	4.13729i	0.154339	+	0.193534i	−0.698651	+	0.715463i	$0.746216\pi$
$458$	22.8994	+	11.0278i	1.07002	+	0.515294i
$459$	−32.6284	+	15.7130i	−1.52296	+	0.733420i
$460$	−3.55901	+	4.46285i	−0.165940	+	0.208082i
$461$	−4.97465	−	6.23801i	−0.231692	−	0.290533i	0.652371	−	0.757900i	$-0.273774\pi$
$461$	−4.97465	−	6.23801i	−0.231692	−	0.290533i	−0.884064	+	0.467366i	$0.845203\pi$
$462$	19.0828	−	9.18981i	0.887813	−	0.427548i
$463$	−2.70820			−0.125861			−0.0629305	−	0.998018i	$-0.520045\pi$
$463$	−2.70820			−0.125861			−0.0629305	+	0.998018i	$0.520045\pi$
$464$		0			0
$465$	−5.03444			−0.233467
$466$	−15.6916	+	7.55670i	−0.726901	+	0.350057i
$467$	0.0347459	+	0.0435700i	0.00160785	+	0.00201618i	0.782635	−	0.622481i	$-0.213875\pi$
$467$	0.0347459	+	0.0435700i	0.00160785	+	0.00201618i	−0.781027	+	0.624497i	$0.785304\pi$
$468$	−0.623490	+	0.781831i	−0.0288208	+	0.0361402i
$469$	21.0975	−	10.1600i	0.974190	−	0.469145i
$470$	29.1249	+	14.0258i	1.34343	+	0.646963i
$471$	−5.61141	−	7.03648i	−0.258560	−	0.324224i
$472$	−2.53273	+	11.0966i	−0.116578	+	0.510762i
$473$	−2.22521	+	9.74928i	−0.102315	+	0.448272i
$474$	8.30877	−	10.4189i	0.381635	−	0.478555i
$475$	1.29792	+	5.68657i	0.0595528	+	0.260918i
$476$	9.14590			0.419202
$477$	−0.169991	−	0.744779i	−0.00778335	−	0.0341011i
$478$	−21.4918	−	10.3499i	−0.983012	−	0.473394i
$479$	10.0731	+	4.85097i	0.460253	+	0.221646i	0.649618	−	0.760260i	$-0.274929\pi$
$479$	10.0731	+	4.85097i	0.460253	+	0.221646i	−0.189365	+	0.981907i	$0.560643\pi$
$480$	3.47534	+	15.2265i	0.158627	+	0.694990i
$481$	36.8885			1.68197
$482$	−9.59613	−	42.0434i	−0.437092	−	1.91502i
$483$	−7.29995	+	9.15384i	−0.332159	+	0.416514i
$484$	−0.287452	+	1.25941i	−0.0130660	+	0.0572458i
$485$	10.5187	−	46.0853i	0.477629	−	2.09263i
$486$	−3.97909	−	4.98962i	−0.180495	−	0.226334i
$487$	−20.2157	−	9.73535i	−0.916059	−	0.441151i	−0.0843966	−	0.996432i	$-0.526896\pi$
$487$	−20.2157	−	9.73535i	−0.916059	−	0.441151i	−0.831663	+	0.555281i	$0.812611\pi$
$488$	−3.25974	+	1.56981i	−0.147561	+	0.0710618i
$489$	23.2378	−	29.1393i	1.05085	−	1.31772i
$490$	5.75859	+	7.22105i	0.260147	+	0.326214i
$491$	22.6365	−	10.9012i	1.02157	−	0.491962i	0.153366	−	0.988169i	$-0.450989\pi$
$491$	22.6365	−	10.9012i	1.02157	−	0.491962i	0.868204	+	0.496207i	$0.165274\pi$
$492$	−2.85410			−0.128673
$493$		0			0
$494$	−12.7082			−0.571769
$495$	−3.55367	+	1.71136i	−0.159725	+	0.0769197i
$496$	3.29938	+	4.13729i	0.148147	+	0.185770i
$497$	2.13010	−	2.67106i	0.0955478	−	0.119813i
$498$	18.7387	−	9.02408i	0.839701	−	0.404379i
$499$	32.1528	+	15.4840i	1.43936	+	0.693158i	0.980711	−	0.195461i	$-0.0626204\pi$
$499$	32.1528	+	15.4840i	1.43936	+	0.693158i	0.458646	+	0.888619i	$0.348335\pi$
$500$	2.03913	+	2.55699i	0.0911926	+	0.114352i
$501$	7.01087	−	30.7166i	0.313223	−	1.37232i
$502$	4.19543	−	18.3814i	0.187251	−	0.820402i
$503$	12.0150	−	15.0663i	0.535721	−	0.671773i	−0.438143	−	0.898905i	$-0.644364\pi$
$503$	12.0150	−	15.0663i	0.535721	−	0.671773i	0.973864	+	0.227133i	$0.0729351\pi$
$504$	−0.424977	−	1.86195i	−0.0189300	−	0.0829377i
$505$	4.61803			0.205500
$506$	−4.21550	−	18.4693i	−0.187402	−	0.821061i
$507$	7.20775	+	3.47107i	0.320107	+	0.154156i
$508$	−1.08263	−	0.521366i	−0.0480338	−	0.0231319i
$509$	−2.54513	−	11.1509i	−0.112811	−	0.494256i	−0.999492	−	0.0318747i	$-0.989852\pi$
$509$	−2.54513	−	11.1509i	−0.112811	−	0.494256i	0.886681	−	0.462381i	$-0.153005\pi$
$510$	49.4508			2.18972
$511$	−0.145190	−	0.636117i	−0.00642281	−	0.0281402i
$512$	−3.29938	+	4.13729i	−0.145813	+	0.182844i
$513$	2.25767	−	9.89152i	0.0996788	−	0.436721i
$514$	0.295116	−	1.29299i	0.0130170	−	0.0570312i
$515$	23.4545	+	29.4110i	1.03353	+	1.29600i
$516$	2.49022	+	1.19923i	0.109626	+	0.0527929i
$517$	−22.8182	+	10.9886i	−1.00354	+	0.483280i
$518$	19.6440	−	24.6328i	0.863109	−	1.08230i
$519$	7.15276	+	8.96928i	0.313971	+	0.393708i
$520$	−24.3572	+	11.7298i	−1.06813	+	0.514386i
$521$	−7.09017			−0.310626			−0.155313	−	0.987865i	$-0.549639\pi$
$521$	−7.09017			−0.310626			−0.155313	+	0.987865i	$0.549639\pi$
$522$		0			0
$523$	−22.6180			−0.989018			−0.494509	−	0.869173i	$-0.664652\pi$
$523$	−22.6180			−0.989018			−0.494509	+	0.869173i	$0.664652\pi$
$524$	−0.738488	+	0.355637i	−0.0322610	+	0.0155361i
$525$	−7.09654	−	8.89878i	−0.309718	−	0.388375i
$526$	3.32086	−	4.16422i	0.144796	−	0.181569i
$527$	6.50029	−	3.13038i	0.283157	−	0.136361i
$528$	−25.6023	−	12.3294i	−1.11420	−	0.536569i
$529$	−7.81100	−	9.79468i	−0.339608	−	0.425856i
$530$	−2.05522	+	9.00450i	−0.0892730	+	0.391131i
$531$	−0.432641	+	1.89552i	−0.0187750	+	0.0822588i
$532$	−1.59757	+	2.00329i	−0.0692635	+	0.0868537i
$533$	−2.69032	−	11.7870i	−0.116531	−	0.510554i
$534$	−22.7984			−0.986582
$535$	7.13600	+	31.2648i	0.308516	+	1.35170i
$536$	−21.0975	−	10.1600i	−0.911271	−	0.438845i
$537$	−23.3248	−	11.2326i	−1.00654	−	0.484723i
$538$	−2.16028	−	9.46480i	−0.0931362	−	0.408056i
$539$	−7.23607			−0.311680
$540$	2.14788	+	9.41047i	0.0924299	+	0.404962i
$541$	−21.5707	+	27.0488i	−0.927398	+	1.16292i	0.0589529	+	0.998261i	$0.481224\pi$
$541$	−21.5707	+	27.0488i	−0.927398	+	1.16292i	−0.986351	+	0.164659i	$0.947348\pi$
$542$	−4.38549	+	19.2141i	−0.188373	+	0.825315i
$543$	−4.30049	+	18.8417i	−0.184552	+	0.808574i
$544$	−13.9549	−	17.4989i	−0.598313	−	0.750260i
$545$	−42.7326	−	20.5789i	−1.83046	−	0.881504i
$546$	22.3426	−	10.7596i	0.956173	−	0.460469i
$547$	5.99675	−	7.51968i	0.256402	−	0.321518i	−0.636924	−	0.770926i	$-0.719794\pi$
$547$	5.99675	−	7.51968i	0.256402	−	0.321518i	0.893327	+	0.449408i	$0.148365\pi$
$548$	−5.33851	−	6.69428i	−0.228050	−	0.285965i
$549$	−0.556829	+	0.268155i	−0.0237649	+	0.0114446i
$550$	18.4164			0.785278
$551$		0			0
$552$	11.7082			0.498334
$553$	10.2548	−	4.93845i	0.436078	−	0.210004i
$554$	−23.8265	−	29.8775i	−1.01229	−	1.26937i
$555$	25.0735	−	31.4412i	1.06431	−	1.33460i
$556$	−8.18996	+	3.94408i	−0.347332	+	0.167266i
$557$	−29.2874	−	14.1041i	−1.24095	−	0.597609i	−0.305877	−	0.952071i	$-0.598950\pi$
$557$	−29.2874	−	14.1041i	−1.24095	−	0.597609i	−0.935070	+	0.354462i	$0.884664\pi$
$558$	0.420084	+	0.526768i	0.0177836	+	0.0222999i
$559$	−2.60532	+	11.4147i	−0.110193	+	0.482788i
$560$	−6.89341	+	30.2020i	−0.291300	+	1.27627i
$561$	−24.1556	+	30.2902i	−1.01985	+	1.27885i
$562$	6.16566	+	27.0135i	0.260082	+	1.13950i
$563$	45.3951			1.91318			0.956588	−	0.291443i	$-0.0941354\pi$
$563$	45.3951			1.91318			0.956588	+	0.291443i	$0.0941354\pi$
$564$	1.55765	+	6.82450i	0.0655888	+	0.287363i
$565$	25.5713	+	12.3145i	1.07579	+	0.518074i
$566$	1.11366	+	0.536310i	0.0468106	+	0.0225428i
$567$	3.83539	+	16.8039i	0.161071	+	0.705698i
$568$	−3.41641			−0.143349
$569$	3.54793	+	15.5445i	0.148737	+	0.651660i	0.993237	+	0.116104i	$0.0370407\pi$
$569$	3.54793	+	15.5445i	0.148737	+	0.651660i	−0.844500	+	0.535556i	$0.820102\pi$
$570$	−8.63789	+	10.8316i	−0.361801	+	0.453685i
$571$	−0.780287	+	3.41866i	−0.0326540	+	0.143066i	−0.988627	−	0.150388i	$-0.951948\pi$
$571$	−0.780287	+	3.41866i	−0.0326540	+	0.143066i	0.955973	+	0.293454i	$0.0948049\pi$
$572$	−2.10775	+	9.23465i	−0.0881294	+	0.386120i
$573$	−12.1407	−	15.2239i	−0.507184	−	0.635989i
$574$	−9.30362	−	4.48039i	−0.388326	−	0.187008i
$575$	−9.17217	+	4.41708i	−0.382506	+	0.184205i
$576$	−1.00883	+	1.26503i	−0.0420345	+	0.0527096i
$577$	4.51161	+	5.65739i	0.187821	+	0.235520i	0.866823	−	0.498617i	$-0.166158\pi$
$577$	4.51161	+	5.65739i	0.187821	+	0.235520i	−0.679002	+	0.734137i	$0.737587\pi$
$578$	−39.0666	+	18.8135i	−1.62496	+	0.782538i
$579$	5.70820			0.237225
$580$		0			0
$581$	17.7639			0.736972
$582$	39.0666	−	18.8135i	1.61936	−	0.779844i
$583$	−4.51161	−	5.65739i	−0.186852	−	0.234305i
$584$	−0.406812	+	0.510126i	−0.0168340	+	0.0211092i
$585$	−4.16070	+	2.00369i	−0.172024	+	0.0828424i
$586$	25.4708	+	12.2661i	1.05219	+	0.506709i
$587$	27.6717	+	34.6992i	1.14213	+	1.43219i	0.884863	+	0.465850i	$0.154252\pi$
$587$	27.6717	+	34.6992i	1.14213	+	1.43219i	0.257270	+	0.966340i	$0.417177\pi$
$588$	−0.445042	+	1.94986i	−0.0183532	+	0.0804107i
$589$	−0.449779	+	1.97061i	−0.0185328	+	0.0811975i
$590$	14.6561	−	18.3782i	0.603383	−	0.756618i
$591$	−7.09587	−	31.0890i	−0.291885	−	1.27883i
$592$	−42.2705			−1.73731
$593$	7.69084	+	33.6958i	0.315825	+	1.38372i	0.844800	+	0.535082i	$0.179719\pi$
$593$	7.69084	+	33.6958i	0.315825	+	1.38372i	−0.528975	+	0.848637i	$0.677424\pi$
$594$	−28.8620	−	13.8992i	−1.18422	−	0.570292i
$595$	38.0534	+	18.3255i	1.56004	+	0.751274i
$596$	−1.01521	−	4.44792i	−0.0415846	−	0.182194i
$597$	−1.38197			−0.0565601
$598$	−4.93559	−	21.6242i	−0.201831	−	0.884281i
$599$	28.1000	−	35.2363i	1.14813	−	1.43972i	0.269001	−	0.963140i	$-0.413307\pi$
$599$	28.1000	−	35.2363i	1.14813	−	1.43972i	0.879134	−	0.476575i	$-0.158122\pi$
$600$	−2.53273	+	11.0966i	−0.103398	+	0.453017i
$601$	−8.93623	+	39.1522i	−0.364516	+	1.59705i	0.377064	+	0.926187i	$0.376934\pi$
$601$	−8.93623	+	39.1522i	−0.364516	+	1.59705i	−0.741581	+	0.670864i	$0.765924\pi$
$602$	6.23490	+	7.81831i	0.254115	+	0.318651i
$603$	−3.60388	−	1.73553i	−0.146761	−	0.0706764i
$604$	−10.2046	+	4.91427i	−0.415219	+	0.199959i
$605$	−3.71946	+	4.66406i	−0.151218	+	0.189621i
$606$	2.64115	+	3.31189i	0.107289	+	0.134536i
$607$	−32.4157	+	15.6106i	−1.31571	+	0.633614i	−0.954316	−	0.298798i	$-0.903414\pi$
$607$	−32.4157	+	15.6106i	−1.31571	+	0.633614i	−0.361396	+	0.932412i	$0.617700\pi$
$608$	6.27051			0.254303
$609$		0			0
$610$	7.47214			0.302538
$611$	−26.7160	+	12.8657i	−1.08081	+	0.520492i
$612$	−0.974082	−	1.22146i	−0.0393749	−	0.0493746i
$613$	−24.6534	+	30.9144i	−0.995742	+	1.24862i	−0.0272369	+	0.999629i	$0.508671\pi$
$613$	−24.6534	+	30.9144i	−0.995742	+	1.24862i	−0.968505	+	0.248992i	$0.919901\pi$
$614$	4.63629	−	2.23272i	0.187106	−	0.0901053i
$615$	−11.8751	−	5.71874i	−0.478849	−	0.230602i
$616$	−11.2790	−	14.1435i	−0.454445	−	0.569856i
$617$	1.82030	−	7.97524i	0.0732824	−	0.321071i	−0.924979	−	0.380019i	$-0.875917\pi$
$617$	1.82030	−	7.97524i	0.0732824	−	0.321071i	0.998261	+	0.0589479i	$0.0187746\pi$
$618$	−7.67844	+	33.6414i	−0.308872	+	1.35326i
$619$	−15.5525	+	19.5022i	−0.625108	+	0.783860i	−0.989053	−	0.147560i	$-0.952858\pi$
$619$	−15.5525	+	19.5022i	−0.625108	+	0.783860i	0.363945	+	0.931420i	$0.381429\pi$
$620$	−0.427905	−	1.87477i	−0.0171851	−	0.0752927i
$621$	17.7082			0.710606
$622$	−3.27288	−	14.3394i	−0.131231	−	0.574959i
$623$	−17.5438	−	8.44864i	−0.702877	−	0.338488i
$624$	−29.9757	−	14.4355i	−1.19999	−	0.577884i
$625$	6.86095	+	30.0598i	0.274438	+	1.20239i
$626$	−38.9787			−1.55790
$627$	−2.41526	−	10.5820i	−0.0964564	−	0.422603i
$628$	2.14337	−	2.68770i	0.0855297	−	0.107251i
$629$	−12.8241	+	56.1863i	−0.511332	+	2.24029i
$630$	−0.877683	+	3.84538i	−0.0349677	+	0.153204i
$631$	14.4742	+	18.1500i	0.576208	+	0.722542i	0.981461	−	0.191663i	$-0.0613880\pi$
$631$	14.4742	+	18.1500i	0.576208	+	0.722542i	−0.405253	+	0.914205i	$0.632817\pi$
$632$	−10.2548	−	4.93845i	−0.407914	−	0.196441i
$633$	−28.6493	+	13.7968i	−1.13871	+	0.548373i
$634$	−14.4180	+	18.0795i	−0.572610	+	0.718031i
$635$	−3.45984	−	4.33850i	−0.137300	−	0.172168i
$636$	−1.80194	+	0.867767i	−0.0714515	+	0.0344092i
$637$	−8.47214			−0.335678
$638$		0			0
$639$	−0.583592			−0.0230865
$640$	35.0182	−	16.8639i	1.38422	−	0.666603i
$641$	−18.0465	−	22.6295i	−0.712792	−	0.893813i	0.285114	−	0.958494i	$-0.407969\pi$
$641$	−18.0465	−	22.6295i	−0.712792	−	0.893813i	−0.997906	+	0.0646805i	$0.979397\pi$
$642$	−18.3408	+	22.9987i	−0.723855	+	0.907685i
$643$	9.53549	−	4.59205i	0.376043	−	0.181093i	−0.236309	−	0.971678i	$-0.575938\pi$
$643$	9.53549	−	4.59205i	0.376043	−	0.181093i	0.612352	+	0.790585i	$0.290224\pi$
$644$	−4.02926	−	1.94039i	−0.158775	−	0.0764620i
$645$	7.95818	+	9.97924i	0.313353	+	0.392932i
$646$	4.41795	−	19.3563i	0.173822	−	0.761564i
$647$	8.78338	−	38.4825i	0.345310	−	1.51290i	−0.442378	−	0.896829i	$-0.645865\pi$
$647$	8.78338	−	38.4825i	0.345310	−	1.51290i	0.787688	−	0.616074i	$-0.211278\pi$
$648$	10.7465	−	13.4757i	0.422163	−	0.529376i
$649$	4.09804	+	17.9547i	0.160862	+	0.704782i
$650$	21.5623			0.845743
$651$	−0.877683	−	3.84538i	−0.0343991	−	0.150712i
$652$	12.8263	+	6.17680i	0.502315	+	0.241902i
$653$	−25.2390	−	12.1545i	−0.987678	−	0.475640i	−0.130939	−	0.991390i	$-0.541799\pi$
$653$	−25.2390	−	12.1545i	−0.987678	−	0.475640i	−0.856739	+	0.515750i	$0.827513\pi$
$654$	−9.68112	−	42.4158i	−0.378562	−	1.65859i
$655$	−3.78522			−0.147901
$656$	3.08283	+	13.5068i	0.120364	+	0.527350i
$657$	−0.0694918	+	0.0871400i	−0.00271113	+	0.00339965i
$658$	−5.63562	+	24.6913i	−0.219699	+	0.962565i
$659$	−5.55062	+	24.3189i	−0.216222	+	0.947329i	0.744020	+	0.668158i	$0.232917\pi$
$659$	−5.55062	+	24.3189i	−0.216222	+	0.947329i	−0.960241	+	0.279171i	$0.909940\pi$
$660$	6.43830	+	8.07338i	0.250611	+	0.314256i
$661$	−16.6236	−	8.00552i	−0.646585	−	0.311379i	0.0816964	−	0.996657i	$-0.473966\pi$
$661$	−16.6236	−	8.00552i	−0.646585	−	0.311379i	−0.728281	+	0.685278i	$0.759680\pi$
$662$	−1.72070	+	0.828644i	−0.0668768	+	0.0322062i
$663$	−28.2819	+	35.4644i	−1.09838	+	1.37732i
$664$	−11.0756	−	13.8884i	−0.429818	−	0.538974i
$665$	−10.6610	+	5.13407i	−0.413416	+	0.199091i
$666$	−5.38197			−0.208547
$667$		0			0
$668$	12.0344			0.465627
$669$	26.7160	−	12.8657i	1.03290	−	0.497418i
$670$	30.1524	+	37.8099i	1.16489	+	1.46072i
$671$	−3.64997	+	4.57692i	−0.140906	+	0.176690i
$672$	−11.0243	+	5.30903i	−0.425272	+	0.204800i
$673$	−2.22732	−	1.07262i	−0.0858568	−	0.0413464i	0.390463	−	0.920619i	$-0.372315\pi$
$673$	−2.22732	−	1.07262i	−0.0858568	−	0.0413464i	−0.476319	+	0.879272i	$0.658029\pi$
$674$	−24.2814	−	30.4479i	−0.935283	−	1.17281i
$675$	−3.83065	+	16.7832i	−0.147442	+	0.645985i
$676$	−0.679963	+	2.97911i	−0.0261524	+	0.114581i
$677$	−8.00113	+	10.0331i	−0.307508	+	0.385603i	−0.911440	−	0.411433i	$-0.865029\pi$
$677$	−8.00113	+	10.0331i	−0.307508	+	0.385603i	0.603932	+	0.797036i	$0.293600\pi$
$678$	5.79321	+	25.3817i	0.222487	+	0.974778i
$679$	37.0344			1.42125
$680$	−9.39841	−	41.1771i	−0.360413	−	1.57907i
$681$	21.7045	+	10.4523i	0.831718	+	0.400534i
$682$	5.74995	+	2.76903i	0.220177	+	0.106032i
$683$	−3.14776	−	13.7912i	−0.120446	−	0.527707i	−0.998767	−	0.0496367i	$-0.984194\pi$
$683$	−3.14776	−	13.7912i	−0.120446	−	0.527707i	0.878322	−	0.478070i	$-0.158663\pi$
$684$	0.437694			0.0167357
$685$	−8.79870	−	38.5496i	−0.336181	−	1.47291i
$686$	−20.3023	+	25.4582i	−0.775144	+	0.972000i
$687$	−5.65568	+	24.7792i	−0.215778	+	0.945384i
$688$	2.98543	−	13.0800i	0.113819	−	0.498671i
$689$	−5.28229	−	6.62378i	−0.201239	−	0.252346i
$690$	−21.7857	−	10.4915i	−0.829369	−	0.399403i
$691$	37.6901	−	18.1506i	1.43380	−	0.690481i	0.454098	−	0.890952i	$-0.349962\pi$
$691$	37.6901	−	18.1506i	1.43380	−	0.690481i	0.979700	+	0.200471i	$0.0642473\pi$
$692$	−2.73211	+	3.42596i	−0.103859	+	0.130235i
$693$	−1.92669	−	2.41599i	−0.0731889	−	0.0917760i
$694$	−11.8440	+	5.70379i	−0.449594	+	0.216513i
$695$	−41.9787			−1.59234
$696$		0			0
$697$	18.8885			0.715455
$698$	−19.6397	+	9.45796i	−0.743372	+	0.357989i
$699$	−10.8590	−	13.6167i	−0.410723	−	0.515031i
$700$	2.71064	−	3.39903i	0.102452	−	0.128471i
$701$	35.0876	−	16.8973i	1.32524	−	0.638202i	0.368630	−	0.929576i	$-0.379827\pi$
$701$	35.0876	−	16.8973i	1.32524	−	0.638202i	0.956609	+	0.291374i	$0.0941125\pi$
$702$	−33.7923	−	16.2735i	−1.27541	−	0.614203i
$703$	−10.0668	−	12.6234i	−0.379677	−	0.476099i
$704$	−3.41041	+	14.9420i	−0.128535	+	0.563147i
$705$	−7.19326	+	31.5158i	−0.270914	+	1.18695i
$706$	21.3111	−	26.7233i	0.802054	−	1.00574i
$707$	0.805088	+	3.52732i	0.0302785	+	0.132659i
$708$	5.09017			0.191300
$709$	0.777360	+	3.40583i	0.0291944	+	0.127909i	0.987425	−	0.158087i	$-0.0505327\pi$
$709$	0.777360	+	3.40583i	0.0291944	+	0.127909i	−0.958231	+	0.285996i	$0.907676\pi$
$710$	6.35699	+	3.06137i	0.238574	+	0.114891i
$711$	−1.75173	−	0.843588i	−0.0656949	−	0.0316370i
$712$	4.33296	+	18.9839i	0.162384	+	0.711453i
$713$	−3.52786			−0.132120
$714$	8.62105	+	37.7713i	0.322635	+	1.41355i
$715$	−27.2731	+	34.1994i	−1.01996	+	1.27898i
$716$	2.20041	−	9.64062i	0.0822331	−	0.360287i
$717$	5.30804	−	23.2560i	0.198232	−	0.868512i
$718$	28.4853	+	35.7195i	1.06306	+	1.33304i
$719$	26.5845	+	12.8024i	0.991435	+	0.477450i	0.858023	−	0.513611i	$-0.171692\pi$
$719$	26.5845	+	12.8024i	0.991435	+	0.477450i	0.133412	+	0.991061i	$0.457407\pi$
$720$	4.76774	−	2.29602i	0.177683	−	0.0855678i
$721$	−18.3756	+	23.0422i	−0.684342	+	0.858138i
$722$	−15.6997	−	19.6868i	−0.584282	−	0.732666i
$723$	38.8539	−	18.7111i	1.44499	−	0.695872i
$724$	−7.38197			−0.274349
$725$		0			0
$726$	−5.47214			−0.203090
$727$	41.3944	−	19.9345i	1.53523	−	0.739329i	0.540452	−	0.841375i	$-0.318253\pi$
$727$	41.3944	−	19.9345i	1.53523	−	0.739329i	0.994780	+	0.102046i	$0.0325389\pi$
$728$	−13.2057	−	16.5595i	−0.489437	−	0.613734i
$729$	18.3971	−	23.0692i	0.681372	−	0.854414i
$730$	1.21408	−	0.584669i	0.0449350	−	0.0216396i
$731$	−16.4803	−	7.93651i	−0.609547	−	0.293543i
$732$	1.00883	+	1.26503i	0.0372873	+	0.0467569i
$733$	8.27340	−	36.2482i	0.305585	−	1.33886i	−0.555974	−	0.831199i	$-0.687655\pi$
$733$	8.27340	−	36.2482i	0.305585	−	1.33886i	0.861560	−	0.507657i	$-0.169488\pi$
$734$	−2.25767	+	9.89152i	−0.0833323	+	0.365103i
$735$	−5.75859	+	7.22105i	−0.212409	+	0.266352i
$736$	2.43533	+	10.6699i	0.0897674	+	0.393297i
$737$	−37.8885			−1.39564
$738$	0.392512	+	1.71971i	0.0144486	+	0.0633033i
$739$	7.26981	+	3.50096i	0.267424	+	0.128785i	0.562791	−	0.826599i	$-0.309728\pi$
$739$	7.26981	+	3.50096i	0.267424	+	0.128785i	−0.295367	+	0.955384i	$0.595442\pi$
$740$	13.8395	+	6.66475i	0.508750	+	0.245001i
$741$	−2.82784	−	12.3896i	−0.103883	−	0.455143i
$742$	−7.23607			−0.265644
$743$	6.84562	+	29.9926i	0.251141	+	1.10032i	0.930435	+	0.366456i	$0.119429\pi$
$743$	6.84562	+	29.9926i	0.251141	+	1.10032i	−0.679294	+	0.733866i	$0.737714\pi$
$744$	−2.45921	+	3.08376i	−0.0901591	+	0.113056i
$745$	4.68827	−	20.5406i	0.171765	−	0.752551i
$746$	−6.61836	+	28.9969i	−0.242315	+	1.06165i
$747$	−1.89194	−	2.37242i	−0.0692226	−	0.0868024i
$748$	−13.3329	−	6.42077i	−0.487498	−	0.234767i
$749$	−22.6365	+	10.9012i	−0.827119	+	0.398320i
$750$	−8.63789	+	10.8316i	−0.315411	+	0.395513i
$751$	17.1286	+	21.4786i	0.625031	+	0.783765i	0.989043	−	0.147630i	$-0.0471645\pi$
$751$	17.1286	+	21.4786i	0.625031	+	0.783765i	−0.364011	+	0.931395i	$0.618593\pi$
$752$	30.6138	−	14.7428i	1.11637	−	0.537615i
$753$	18.8541			0.687082
$754$		0			0
$755$	−52.3050			−1.90357
$756$	−6.81340	+	3.28116i	−0.247801	+	0.119335i
$757$	29.2907	+	36.7294i	1.06459	+	1.33495i	0.939401	+	0.342821i	$0.111383\pi$
$757$	29.2907	+	36.7294i	1.06459	+	1.33495i	0.125190	+	0.992133i	$0.460046\pi$
$758$	38.0411	−	47.7020i	1.38171	−	1.73261i
$759$	17.0682	−	8.21961i	0.619536	−	0.298353i
$760$	10.6610	+	5.13407i	0.386715	+	0.186232i
$761$	31.0488	+	38.9339i	1.12552	+	1.41135i	0.899330	+	0.437270i	$0.144055\pi$
$761$	31.0488	+	38.9339i	1.12552	+	1.41135i	0.226187	+	0.974084i	$0.427374\pi$
$762$	1.13267	−	4.96255i	0.0410323	−	0.179774i
$763$	8.26867	−	36.2274i	0.299346	−	1.31152i
$764$	4.63733	−	5.81502i	0.167773	−	0.210380i
$765$	−1.60544	−	7.03389i	−0.0580448	−	0.254311i
$766$	−35.8328			−1.29469
$767$	4.79806	+	21.0217i	0.173248	+	0.759049i
$768$	19.7711	+	9.52126i	0.713428	+	0.343569i
$769$	22.8492	+	11.0036i	0.823963	+	0.396799i	0.797847	−	0.602859i	$-0.205972\pi$
$769$	22.8492	+	11.0036i	0.823963	+	0.396799i	0.0261152	+	0.999659i	$0.491686\pi$
$770$	8.31353	+	36.4240i	0.299599	+	1.31263i
$771$	1.32624			0.0477633
$772$	0.485171	+	2.12567i	0.0174617	+	0.0765047i
$773$	8.72886	−	10.9456i	0.313955	−	0.393687i	−0.599668	−	0.800249i	$-0.704701\pi$
$773$	8.72886	−	10.9456i	0.313955	−	0.393687i	0.913623	+	0.406561i	$0.133272\pi$
$774$	0.380111	−	1.66538i	0.0136628	−	0.0598607i
$775$	0.763150	−	3.34358i	0.0274131	−	0.120105i
$776$	−23.0906	−	28.9547i	−0.828904	−	1.03941i
$777$	28.3864	+	13.6702i	1.01836	+	0.490415i
$778$	30.7954	−	14.8303i	1.10407	−	0.531692i
$779$	−3.29938	+	4.13729i	−0.118213	+	0.148234i
$780$	7.53810	+	9.45248i	0.269907	+	0.338453i
$781$	−4.98043	+	2.39845i	−0.178214	+	0.0858233i
$782$	34.6525			1.23917
$783$		0			0
$784$	9.70820			0.346722
$785$	14.3032	−	6.88807i	0.510504	−	0.245846i
$786$	−2.16484	−	2.71463i	−0.0772173	−	0.0968275i
$787$	−15.8121	+	19.8278i	−0.563641	+	0.706784i	−0.979226	−	0.202770i	$-0.935005\pi$
$787$	−15.8121	+	19.8278i	−0.563641	+	0.706784i	0.415585	+	0.909554i	$0.363577\pi$
$788$	10.9741	−	5.28485i	0.390936	−	0.188265i
$789$	4.79877	+	2.31097i	0.170841	+	0.0822726i
$790$	14.6561	+	18.3782i	0.521441	+	0.653866i
$791$	−4.94799	+	21.6786i	−0.175930	+	0.770801i
$792$	−0.687628	+	3.01269i	−0.0244338	+	0.107051i
$793$	−4.27346	+	5.35875i	−0.151755	+	0.190295i
$794$	11.5014	+	50.3910i	0.408170	+	1.78831i
$795$	−9.23607			−0.327570
$796$	−0.117461	−	0.514629i	−0.00416329	−	0.0182406i
$797$	18.7579	+	9.03331i	0.664438	+	0.319976i	0.735529	−	0.677494i	$-0.236934\pi$
$797$	18.7579	+	9.03331i	0.664438	+	0.319976i	−0.0710911	+	0.997470i	$0.522648\pi$
$798$	−9.77921	−	4.70942i	−0.346180	−	0.166712i
$799$	−10.3086	−	45.1647i	−0.364691	−	1.59781i
$800$	−10.6393			−0.376157
$801$	0.740158	+	3.24284i	0.0261522	+	0.114580i
$802$	−33.3608	+	41.8331i	−1.17801	+	1.47718i
$803$	−0.234922	+	1.02926i	−0.00829020	+	0.0363218i
$804$	−2.33027	+	10.2096i	−0.0821823	+	0.360064i
$805$	−12.8766	−	16.1468i	−0.453841	−	0.569098i
$806$	6.73216	+	3.24204i	0.237130	+	0.114196i
$807$	8.74679	−	4.21223i	0.307902	−	0.148278i
$808$	2.25581	−	2.82869i	0.0793590	−	0.0995131i
$809$	−9.39530	−	11.7813i	−0.330321	−	0.414209i	0.588741	−	0.808321i	$-0.299624\pi$
$809$	−9.39530	−	11.7813i	−0.330321	−	0.414209i	−0.919062	+	0.394112i	$0.871052\pi$
$810$	−32.0716	+	15.4449i	−1.12688	+	0.542677i
$811$	−25.6525			−0.900780			−0.450390	−	0.892832i	$-0.648715\pi$
$811$	−25.6525			−0.900780			−0.450390	+	0.892832i	$0.648715\pi$
$812$		0			0
$813$	−19.7082			−0.691197
$814$	−45.9302	+	22.1188i	−1.60985	+	0.775265i
$815$	40.9899	+	51.3997i	1.43581	+	1.80045i
$816$	32.4082	−	40.6386i	1.13451	−	1.42264i
$817$	4.61712	−	2.22349i	0.161532	−	0.0777899i
$818$	0.850760	+	0.409704i	0.0297461	+	0.0143250i
$819$	−2.25581	−	2.82869i	−0.0788243	−	0.0988425i
$820$	1.12027	−	4.90822i	0.0391215	−	0.171402i
$821$	−7.88089	+	34.5284i	−0.275045	+	1.20505i	0.628929	+	0.777463i	$0.283494\pi$
$821$	−7.88089	+	34.5284i	−0.275045	+	1.20505i	−0.903974	+	0.427588i	$0.859363\pi$
$822$	22.6143	−	28.3574i	0.788764	−	0.989079i
$823$	0.772623	+	3.38508i	0.0269319	+	0.117997i	0.986607	−	0.163115i	$-0.0521541\pi$
$823$	0.772623	+	3.38508i	0.0269319	+	0.117997i	−0.959675	+	0.281111i	$0.909297\pi$
$824$	29.4721			1.02671
$825$	4.09804	+	17.9547i	0.142675	+	0.625101i
$826$	16.5926	+	7.99058i	0.577331	+	0.278028i
$827$	50.4853	+	24.3124i	1.75555	+	0.845426i	0.975593	+	0.219588i	$0.0704712\pi$
$827$	50.4853	+	24.3124i	1.75555	+	0.845426i	0.779953	+	0.625838i	$0.215243\pi$
$828$	0.169991	+	0.744779i	0.00590759	+	0.0258828i
$829$	−8.20163			−0.284854			−0.142427	−	0.989805i	$-0.545491\pi$
$829$	−8.20163			−0.284854			−0.142427	+	0.989805i	$0.545491\pi$
$830$	8.16361	+	35.7671i	0.283363	+	1.24149i
$831$	23.8265	−	29.8775i	0.826533	−	1.03644i
$832$	−3.99298	+	17.4944i	−0.138432	+	0.606508i
$833$	2.94530	−	12.9042i	0.102049	−	0.447104i
$834$	−24.0085	−	30.1057i	−0.831345	−	1.04247i
$835$	50.0718	+	24.1133i	1.73280	+	0.834475i
$836$	3.73533	−	1.79884i	0.129189	−	0.0622141i
$837$	−3.71946	+	4.66406i	−0.128564	+	0.161214i
$838$	2.58493	+	3.24139i	0.0892948	+	0.111972i
$839$	2.89642	−	1.39484i	0.0999955	−	0.0481553i	−0.383217	−	0.923658i	$-0.625184\pi$
$839$	2.89642	−	1.39484i	0.0999955	−	0.0481553i	0.483213	+	0.875503i	$0.339470\pi$
$840$	−23.0902			−0.796687
$841$		0			0
$842$	3.18034			0.109602
$843$	−24.9642	+	12.0221i	−0.859814	+	0.414064i
$844$	−7.57284	−	9.49605i	−0.260668	−	0.326867i
$845$	−8.79835	+	11.0328i	−0.302672	+	0.379539i
$846$	3.89781	−	1.87708i	0.134009	−	0.0645355i
$847$	−4.21091	−	2.02787i	−0.144689	−	0.0696784i
$848$	6.05297	+	7.59018i	0.207860	+	0.260648i
$849$	−0.275051	+	1.20508i	−0.00943973	+	0.0413581i
$850$	−7.49604	+	32.8423i	−0.257112	+	1.12648i
$851$	17.5702	−	22.0323i	0.602297	−	0.755257i
$852$	0.339982	+	1.48956i	0.0116476	+	0.0510314i
$853$	45.0000			1.54077			0.770385	−	0.637579i	$-0.220064\pi$
$853$	45.0000			1.54077			0.770385	+	0.637579i	$0.220064\pi$
$854$	1.30266	+	5.70733i	0.0445761	+	0.195301i
$855$	1.82112	+	0.877003i	0.0622809	+	0.0299929i
$856$	22.6365	+	10.9012i	0.773699	+	0.372594i
$857$	6.60303	+	28.9298i	0.225555	+	0.988222i	0.953217	+	0.302286i	$0.0977499\pi$
$857$	6.60303	+	28.9298i	0.225555	+	0.988222i	−0.727662	+	0.685936i	$0.759393\pi$
$858$	−40.1246			−1.36983
$859$	4.29283	+	18.8081i	0.146469	+	0.641724i	0.993850	+	0.110738i	$0.0353214\pi$
$859$	4.29283	+	18.8081i	0.146469	+	0.641724i	−0.847380	+	0.530987i	$0.821821\pi$
$860$	−3.03975	+	3.81173i	−0.103655	+	0.129979i
$861$	2.29780	−	10.0673i	0.0783090	−	0.343094i
$862$	12.4564	−	54.5752i	0.424268	−	1.85884i
$863$	−15.4268	−	19.3446i	−0.525134	−	0.658497i	0.446556	−	0.894756i	$-0.352650\pi$
$863$	−15.4268	−	19.3446i	−0.525134	−	0.658497i	−0.971690	+	0.236258i	$0.924079\pi$
$864$	16.6739	+	8.02970i	0.567256	+	0.273176i
$865$	−18.2321	+	8.78010i	−0.619909	+	0.298532i
$866$	−12.7294	+	15.9622i	−0.432563	+	0.542417i
$867$	−27.0349	−	33.9007i	−0.918155	−	1.15133i
$868$	1.35738	−	0.653680i	0.0460725	−	0.0221873i
$869$	−18.4164			−0.624734
$870$		0			0
$871$	−44.3607			−1.50310
$872$	−33.4792	+	16.1227i	−1.13375	+	0.545984i
$873$	−3.94434	−	4.94605i	−0.133496	−	0.167398i
$874$	−6.05297	+	7.59018i	−0.204745	+	0.256742i
$875$	−10.6610	+	5.13407i	−0.360408	+	0.173563i
$876$	0.262899	+	0.126606i	0.00888254	+	0.00427761i
$877$	4.12628	+	5.17419i	0.139334	+	0.174720i	0.846603	−	0.532225i	$-0.178644\pi$
$877$	4.12628	+	5.17419i	0.139334	+	0.174720i	−0.707268	+	0.706945i	$0.750073\pi$
$878$	1.10020	−	4.82031i	0.0371301	−	0.162678i
$879$	−6.29078	+	27.5617i	−0.212183	+	0.929633i
$880$	31.2522	−	39.1890i	1.05351	−	1.32106i
$881$	−6.51330	−	28.5366i	−0.219439	−	0.961424i	−0.957894	−	0.287121i	$-0.907302\pi$
$881$	−6.51330	−	28.5366i	−0.219439	−	0.961424i	0.738455	−	0.674302i	$-0.235555\pi$
$882$	1.23607			0.0416206
$883$	−8.83117	−	38.6919i	−0.297193	−	1.30209i	−0.874287	−	0.485408i	$-0.838671\pi$
$883$	−8.83117	−	38.6919i	−0.297193	−	1.30209i	0.577095	−	0.816677i	$-0.304186\pi$
$884$	−15.6104	−	7.51757i	−0.525035	−	0.252843i
$885$	21.1787	+	10.1991i	0.711914	+	0.342840i
$886$	−4.71307	−	20.6493i	−0.158339	−	0.693727i
$887$	−20.0689			−0.673847			−0.336924	−	0.941532i	$-0.609386\pi$
$887$	−20.0689			−0.673847			−0.336924	+	0.941532i	$0.609386\pi$
$888$	−7.01087	−	30.7166i	−0.235269	−	1.03078i
$889$	2.71064	−	3.39903i	0.0909118	−	0.114000i
$890$	8.94863	−	39.2065i	0.299959	−	1.31421i
$891$	6.20578	−	27.1893i	0.207902	−	0.910876i
$892$	7.06179	+	8.85521i	0.236446	+	0.296494i
$893$	11.6934	+	5.63125i	0.391305	+	0.188443i
$894$	17.4123	−	8.38534i	0.582356	−	0.280448i
$895$	28.4721	−	35.7028i	0.951716	−	1.19341i
$896$	18.9858	+	23.8074i	0.634271	+	0.795351i
$897$	19.9838	−	9.62369i	0.667240	−	0.321326i
$898$	−22.8541			−0.762651
$899$		0			0
$900$	−0.742646			−0.0247549
$901$	11.9253	−	5.74291i	0.397289	−	0.191324i
$902$	10.4174	+	13.0630i	0.346861	+	0.434950i
$903$	−6.23490	+	7.81831i	−0.207484	+	0.260177i
$904$	20.0340	−	9.64787i	0.666321	−	0.320883i
$905$	−30.7142	−	14.7912i	−1.02097	−	0.491675i
$906$	−29.9142	−	37.5113i	−0.993834	−	1.24623i
$907$	3.16782	−	13.8791i	0.105186	−	0.460849i	−0.894713	−	0.446641i	$-0.852620\pi$
$907$	3.16782	−	13.8791i	0.105186	−	0.460849i	0.999899	−	0.0142082i	$-0.00452276\pi$
$908$	−2.04755	+	8.97092i	−0.0679505	+	0.297711i
$909$	0.385338	−	0.483198i	0.0127809	−	0.0160267i
$910$	9.73365	+	42.6459i	0.322668	+	1.41370i
$911$	−6.94427			−0.230074			−0.115037	−	0.993361i	$-0.536699\pi$
$911$	−6.94427			−0.230074			−0.115037	+	0.993361i	$0.536699\pi$
$912$	3.24042	+	14.1972i	0.107301	+	0.470116i
$913$	−25.8962	−	12.4710i	−0.857040	−	0.412729i
$914$	−7.71437	−	3.71505i	−0.255169	−	0.122883i
$915$	1.66271	+	7.28479i	0.0549674	+	0.240828i
$916$	−9.70820			−0.320768
$917$	−0.659899	−	2.89121i	−0.0217918	−	0.0954760i
$918$	36.5345	−	45.8128i	1.20582	−	1.51205i
$919$	6.96601	−	30.5201i	0.229787	−	1.00676i	−0.720026	−	0.693947i	$-0.755870\pi$
$919$	6.96601	−	30.5201i	0.229787	−	1.00676i	0.949813	−	0.312817i	$-0.101273\pi$
$920$	−4.59561	+	20.1347i	−0.151513	+	0.663821i
$921$	3.20841	+	4.02323i	0.105721	+	0.132570i
$922$	11.6314	+	5.60137i	0.383058	+	0.184471i
$923$	−5.83119	+	2.80815i	−0.191936	+	0.0924315i
$924$	−5.04414	+	6.32515i	−0.165940	+	0.208082i
$925$	17.0806	+	21.4184i	0.561606	+	0.704232i
$926$	3.94801	−	1.90126i	0.129740	−	0.0624794i
$927$	5.03444			0.165353
$928$		0			0
$929$	27.6525			0.907248			0.453624	−	0.891193i	$-0.350131\pi$
$929$	27.6525			0.907248			0.453624	+	0.891193i	$0.350131\pi$
$930$	7.33920	−	3.53437i	0.240662	−	0.115897i
$931$	2.31203	+	2.89919i	0.0757736	+	0.0950171i
$932$	4.14775	−	5.20112i	0.135864	−	0.170368i
$933$	13.2516	−	6.38165i	0.433839	−	0.208926i
$934$	−0.0812403	−	0.0391233i	−0.00265826	−	0.00128015i
$935$	−42.6089	−	53.4299i	−1.39346	−	1.74734i
$936$	−0.805088	+	3.52732i	−0.0263151	+	0.115294i
$937$	5.48569	−	24.0344i	0.179210	−	0.785169i	−0.802786	−	0.596267i	$-0.796650\pi$
$937$	5.48569	−	24.0344i	0.179210	−	0.785169i	0.981996	−	0.188902i	$-0.0604929\pi$
$938$	−23.6231	+	29.6225i	−0.771322	+	0.967207i
$939$	−8.67358	−	38.0014i	−0.283052	−	1.24013i
$940$	−12.3475			−0.402732
$941$	−0.197720	−	0.866266i	−0.00644547	−	0.0282395i	0.971603	−	0.236617i	$-0.0760388\pi$
$941$	−0.197720	−	0.866266i	−0.00644547	−	0.0282395i	−0.978048	+	0.208378i	$0.933182\pi$
$942$	13.1202	+	6.31835i	0.427479	+	0.205863i
$943$	−8.32141	−	4.00738i	−0.270982	−	0.130498i
$944$	−5.49809	−	24.0887i	−0.178948	−	0.784021i
$945$	−34.9230			−1.13604
$946$	−3.60046	−	15.7747i	−0.117061	−	0.512879i
$947$	−8.70738	+	10.9187i	−0.282952	+	0.354810i	−0.902914	−	0.429821i	$-0.858577\pi$
$947$	−8.70738	+	10.9187i	−0.282952	+	0.354810i	0.619962	+	0.784632i	$0.287148\pi$
$948$	−1.13267	+	4.96255i	−0.0367874	+	0.161176i
$949$	−0.275051	+	1.20508i	−0.00892853	+	0.0391185i
$950$	−5.88431	−	7.37869i	−0.190912	−	0.239396i
$951$	−20.8346	−	10.0334i	−0.675607	−	0.325355i
$952$	29.8132	−	14.3573i	0.966252	−	0.465322i
$953$	−22.2157	+	27.8576i	−0.719637	+	0.902396i	−0.998317	−	0.0579881i	$-0.981531\pi$
$953$	−22.2157	+	27.8576i	−0.719637	+	0.902396i	0.278681	+	0.960384i	$0.410103\pi$
$954$	0.770676	+	0.966397i	0.0249515	+	0.0312883i
$955$	30.9460	−	14.9028i	1.00139	−	0.482244i
$956$	9.11146			0.294686
$957$		0			0
$958$	−18.0902			−0.584467
$959$	27.9109	−	13.4412i	0.901289	−	0.434038i
$960$	12.1969	+	15.2944i	0.393653	+	0.493625i
$961$	−18.5872	+	23.3076i	−0.599587	+	0.751858i
$962$	−53.7761	+	25.8972i	−1.73381	+	0.834959i
$963$	3.86677	+	1.86214i	0.124605	+	0.0600066i
$964$	10.2702	+	12.8784i	0.330781	+	0.414786i
$965$	−2.24054	+	9.81644i	−0.0721255	+	0.316002i
$966$	4.21550	−	18.4693i	0.135631	−	0.594240i
$967$	10.3264	−	12.9489i	0.332076	−	0.416410i	−0.587561	−	0.809180i	$-0.699912\pi$
$967$	10.3264	−	12.9489i	0.332076	−	0.416410i	0.919637	+	0.392770i	$0.128483\pi$
$968$	1.04001	+	4.55658i	0.0334272	+	0.146454i
$969$	19.8541			0.637806
$970$	17.0196	+	74.5676i	0.546466	+	2.39422i
$971$	16.6739	+	8.02970i	0.535089	+	0.257685i	0.681857	−	0.731486i	$-0.261173\pi$
$971$	16.6739	+	8.02970i	0.535089	+	0.257685i	−0.146768	+	0.989171i	$0.546887\pi$
$972$	2.19629	+	1.05768i	0.0704459	+	0.0339250i
$973$	−7.31839	−	32.0640i	−0.234617	−	1.02792i
$974$	36.3050			1.16329
$975$	4.79806	+	21.0217i	0.153661	+	0.673233i
$976$	4.89695	−	6.14058i	0.156748	−	0.196555i
$977$	−1.38292	+	6.05896i	−0.0442435	+	0.193843i	−0.992220	−	0.124497i	$-0.960268\pi$
$977$	−1.38292	+	6.05896i	−0.0442435	+	0.193843i	0.947976	+	0.318340i	$0.103125\pi$
$978$	−13.4191	+	58.7930i	−0.429096	+	1.87999i
$979$	19.6440	+	24.6328i	0.627826	+	0.787269i
$980$	−3.17850	−	1.53068i	−0.101533	−	0.0488959i
$981$	−5.71892	+	2.75409i	−0.182591	+	0.0879312i
$982$	−25.3464	+	31.7834i	−0.808836	+	1.01425i
$983$	−4.32968	−	5.42925i	−0.138095	−	0.173166i	0.707975	−	0.706238i	$-0.249609\pi$
$983$	−4.32968	−	5.42925i	−0.138095	−	0.173166i	−0.846070	+	0.533072i	$0.821038\pi$
$984$	−9.30362	+	4.48039i	−0.296589	+	0.142830i
$985$	56.2492			1.79225
$986$		0			0
$987$	−25.3262			−0.806143
$988$	4.37339	−	2.10612i	0.139136	−	0.0670045i
$989$	5.57666	+	6.99291i	0.177328	+	0.222362i
$990$	3.97909	−	4.98962i	0.126464	−	0.158581i
$991$	−34.8247	+	16.7707i	−1.10624	+	0.532738i	−0.895616	−	0.444828i	$-0.853265\pi$
$991$	−34.8247	+	16.7707i	−1.10624	+	0.532738i	−0.210627	+	0.977567i	$0.567550\pi$
$992$	−3.32180	−	1.59969i	−0.105467	−	0.0507903i
$993$	−1.19076	−	1.49317i	−0.0377876	−	0.0473842i
$994$	−1.23007	+	5.38927i	−0.0390153	+	0.170937i
$995$	0.542438	−	2.37658i	0.0171964	−	0.0753425i
$996$	−4.95317	+	6.21108i	−0.156947	+	0.196806i
$997$	6.25065	+	27.3859i	0.197960	+	0.867320i	0.972149	+	0.234365i	$0.0753010\pi$
$997$	6.25065	+	27.3859i	0.197960	+	0.867320i	−0.774189	+	0.632955i	$0.781842\pi$
$998$	−57.7426			−1.82781
$999$	−10.6037	−	46.4577i	−0.335485	−	1.46986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.g.571.1		12
29.2	odd	28		841.2.e.j.196.1		24
29.3	odd	28		841.2.e.j.267.1		24
29.4	even	14		841.2.a.a.1.1	✓	2
29.5	even	14		841.2.d.i.645.2		12
29.6	even	14		841.2.d.i.778.1		12
29.7	even	7	inner	841.2.d.g.574.2		12
29.8	odd	28		841.2.e.j.236.1		24
29.9	even	14		841.2.d.i.605.2		12
29.10	odd	28		841.2.b.b.840.4		4
29.11	odd	28		841.2.e.j.651.1		24
29.12	odd	4		841.2.e.j.270.1		24
29.13	even	14		841.2.d.i.190.2		12
29.14	odd	28		841.2.e.j.63.4		24
29.15	odd	28		841.2.e.j.63.1		24
29.16	even	7	inner	841.2.d.g.190.1		12
29.17	odd	4		841.2.e.j.270.4		24
29.18	odd	28		841.2.e.j.651.4		24
29.19	odd	28		841.2.b.b.840.1		4
29.20	even	7	inner	841.2.d.g.605.1		12
29.21	odd	28		841.2.e.j.236.4		24
29.22	even	14		841.2.d.i.574.1		12
29.23	even	7	inner	841.2.d.g.778.2		12
29.24	even	7	inner	841.2.d.g.645.1		12
29.25	even	7		841.2.a.c.1.2	yes	2
29.26	odd	28		841.2.e.j.267.4		24
29.27	odd	28		841.2.e.j.196.4		24
29.28	even	2		841.2.d.i.571.2		12
87.62	odd	14		7569.2.a.l.1.2		2
87.83	odd	14		7569.2.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.a.1.1	✓	2	29.4	even	14
841.2.a.c.1.2	yes	2	29.25	even	7
841.2.b.b.840.1		4	29.19	odd	28
841.2.b.b.840.4		4	29.10	odd	28
841.2.d.g.190.1		12	29.16	even	7	inner
841.2.d.g.571.1		12	1.1	even	1	trivial
841.2.d.g.574.2		12	29.7	even	7	inner
841.2.d.g.605.1		12	29.20	even	7	inner
841.2.d.g.645.1		12	29.24	even	7	inner
841.2.d.g.778.2		12	29.23	even	7	inner
841.2.d.i.190.2		12	29.13	even	14
841.2.d.i.571.2		12	29.28	even	2
841.2.d.i.574.1		12	29.22	even	14
841.2.d.i.605.2		12	29.9	even	14
841.2.d.i.645.2		12	29.5	even	14
841.2.d.i.778.1		12	29.6	even	14
841.2.e.j.63.1		24	29.15	odd	28
841.2.e.j.63.4		24	29.14	odd	28
841.2.e.j.196.1		24	29.2	odd	28
841.2.e.j.196.4		24	29.27	odd	28
841.2.e.j.236.1		24	29.8	odd	28
841.2.e.j.236.4		24	29.21	odd	28
841.2.e.j.267.1		24	29.3	odd	28
841.2.e.j.267.4		24	29.26	odd	28
841.2.e.j.270.1		24	29.12	odd	4
841.2.e.j.270.4		24	29.17	odd	4
841.2.e.j.651.1		24	29.11	odd	28
841.2.e.j.651.4		24	29.18	odd	28
7569.2.a.d.1.1		2	87.83	odd	14
7569.2.a.l.1.2		2	87.62	odd	14

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.45780 + 0.702039i) q^{2} +(-1.00883 - 1.26503i) q^{3} +(0.385338 - 0.483198i) q^{4} +(2.57146 - 1.23835i) q^{5} +(2.35877 + 1.13592i) q^{6} +(1.39417 + 1.74823i) q^{7} +(0.497572 - 2.18001i) q^{8} +(0.0849954 - 0.372389i) q^{9} +(-2.87930 + 3.61052i) q^{10} +(-0.805088 - 3.52732i) q^{11} -1.00000 q^{12} +(-0.942614 - 4.12986i) q^{13} +(-3.25974 - 1.56981i) q^{14} +(-4.16070 - 2.00369i) q^{15} +(1.08014 + 4.73240i) q^{16} +6.61803 q^{17} +(0.137526 + 0.602539i) q^{18} +(-1.15601 + 1.44960i) q^{19} +(0.392512 - 1.71971i) q^{20} +(0.805088 - 3.52732i) q^{21} +(3.64997 + 4.57692i) q^{22} +(-2.91560 - 1.40408i) q^{23} +(-3.25974 + 1.56981i) q^{24} +(1.96144 - 2.45956i) q^{25} +(4.27346 + 5.35875i) q^{26} +(-4.93022 + 2.37427i) q^{27} +1.38197 q^{28} +7.47214 q^{30} +(0.982209 - 0.473007i) q^{31} +(-2.10862 - 2.64413i) q^{32} +(-3.64997 + 4.57692i) q^{33} +(-9.64776 + 4.64612i) q^{34} +(5.74995 + 2.76903i) q^{35} +(-0.147186 - 0.184565i) q^{36} +(-1.93776 + 8.48987i) q^{37} +(0.667563 - 2.92478i) q^{38} +(-4.27346 + 5.35875i) q^{39} +(-1.42012 - 6.22196i) q^{40} +2.85410 q^{41} +(1.30266 + 5.70733i) q^{42} +(-2.49022 - 1.19923i) q^{43} +(-2.01463 - 0.970194i) q^{44} +(-0.242586 - 1.06284i) q^{45} +5.23607 q^{46} +(-1.55765 - 6.82450i) q^{47} +(4.89695 - 6.14058i) q^{48} +(0.445042 - 1.94986i) q^{49} +(-1.13267 + 4.96255i) q^{50} +(-6.67646 - 8.37201i) q^{51} +(-2.35877 - 1.13592i) q^{52} +(1.80194 - 0.867767i) q^{53} +(5.52044 - 6.92242i) q^{54} +(-6.43830 - 8.07338i) q^{55} +(4.50484 - 2.16942i) q^{56} +3.00000 q^{57} -5.09017 q^{59} +(-2.57146 + 1.23835i) q^{60} +(-1.00883 - 1.26503i) q^{61} +(-1.09979 + 1.37910i) q^{62} +(0.769519 - 0.370581i) q^{63} +(-3.81657 - 1.83796i) q^{64} +(-7.53810 - 9.45248i) q^{65} +(2.10775 - 9.23465i) q^{66} +(2.33027 - 10.2096i) q^{67} +(2.55018 - 3.19782i) q^{68} +(1.16513 + 5.10479i) q^{69} -10.3262 q^{70} +(-0.339982 - 1.48956i) q^{71} +(-0.769519 - 0.370581i) q^{72} +(-0.262899 - 0.126606i) q^{73} +(-3.13536 - 13.7369i) q^{74} -5.09017 q^{75} +(0.254986 + 1.11717i) q^{76} +(5.04414 - 6.32515i) q^{77} +(2.46779 - 10.8121i) q^{78} +(1.13267 - 4.96255i) q^{79} +(8.63789 + 10.8316i) q^{80} +(6.94485 + 3.34446i) q^{81} +(-4.16070 + 2.00369i) q^{82} +(4.95317 - 6.21108i) q^{83} +(-1.39417 - 1.74823i) q^{84} +(17.0180 - 8.19543i) q^{85} +4.47214 q^{86} -8.09017 q^{88} +(-7.84582 + 3.77835i) q^{89} +(1.09979 + 1.37910i) q^{90} +(5.90578 - 7.40561i) q^{91} +(-1.80194 + 0.867767i) q^{92} +(-1.58925 - 0.765341i) q^{93} +(7.06179 + 8.85521i) q^{94} +(-1.17754 + 5.15912i) q^{95} +(-1.21766 + 5.33494i) q^{96} +(10.3264 - 12.9489i) q^{97} +(0.720093 + 3.15493i) q^{98} -1.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9} + 7 q^{10} - 5 q^{11} - 12 q^{12} - 4 q^{13} - 5 q^{14} - 7 q^{15} + 3 q^{16} + 66 q^{17} - q^{18} - 3 q^{19} + 8 q^{20} + 5 q^{21} - 5 q^{22}+ \cdots - 30 q^{99}+O(q^{100}) \) 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9 + 7 * q^10 - 5 * q^11 - 12 * q^12 - 4 * q^13 - 5 * q^14 - 7 * q^15 + 3 * q^16 + 66 * q^17 - q^18 - 3 * q^19 + 8 * q^20 + 5 * q^21 - 5 * q^22 - 2 * q^23 - 5 * q^24 - 13 * q^25 - 7 * q^26 - 2 * q^27 + 30 * q^28 + 36 * q^30 - 9 * q^31 + 9 * q^32 + 5 * q^33 - 8 * q^34 + 15 * q^35 - 4 * q^36 - 4 * q^37 + 6 * q^38 + 7 * q^39 - 15 * q^40 - 6 * q^41 + 5 * q^42 - 10 * q^43 + 9 * q^45 + 36 * q^46 - 14 * q^47 - 9 * q^48 + 4 * q^49 + q^50 + 8 * q^51 - 3 * q^52 + 4 * q^53 - 11 * q^54 + 5 * q^55 + 10 * q^56 + 36 * q^57 + 6 * q^59 + q^60 + q^61 + 8 * q^62 - 5 * q^63 - 4 * q^64 + 13 * q^65 + 10 * q^66 + 12 * q^67 + 3 * q^68 + 6 * q^69 - 30 * q^70 - 12 * q^71 + 5 * q^72 - 14 * q^73 - 17 * q^74 + 6 * q^75 + 9 * q^76 - 5 * q^77 + 11 * q^78 - q^79 - 21 * q^80 + 2 * q^81 - 7 * q^82 + 2 * q^83 + 2 * q^85 - 30 * q^88 - 4 * q^89 - 8 * q^90 - 10 * q^91 - 4 * q^92 - 8 * q^93 - 7 * q^94 - 24 * q^95 - 2 * q^96 - 13 * q^97 + 2 * q^98 - 30 * q^99

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