LMFDB - Embedded newform 961.2.c.i.439.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(439,961)] 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("961.439"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,-3,16,-3] 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			439.8
Root			$1.83925i$ of defining polynomial
Character	$\chi$	$=$	961.439
Dual form			961.2.c.i.521.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.30753 q^{2} +(-1.27136 + 2.20206i) q^{3} +3.32468 q^{4} +(1.24923 + 2.16373i) q^{5} +(-2.93370 + 5.08132i) q^{6} +(-0.800939 + 1.38727i) q^{7} +3.05673 q^{8} +(-1.73272 - 3.00116i) q^{9} +(2.88263 + 4.99286i) q^{10} +(0.366828 + 0.635365i) q^{11} +(-4.22687 + 7.32116i) q^{12} +(-0.947988 - 1.64196i) q^{13} +(-1.84819 + 3.20116i) q^{14} -6.35289 q^{15} +0.404135 q^{16} +(-2.18962 + 3.79253i) q^{17} +(-3.99830 - 6.92527i) q^{18} +(2.31901 - 4.01665i) q^{19} +(4.15329 + 7.19371i) q^{20} +(-2.03657 - 3.52744i) q^{21} +(0.846466 + 1.46612i) q^{22} +7.11846 q^{23} +(-3.88622 + 6.73112i) q^{24} +(-0.621150 + 1.07586i) q^{25} +(-2.18751 - 3.78887i) q^{26} +1.18350 q^{27} +(-2.66287 + 4.61222i) q^{28} +0.128939 q^{29} -14.6595 q^{30} -5.18091 q^{32} -1.86549 q^{33} +(-5.05261 + 8.75137i) q^{34} -4.00223 q^{35} +(-5.76075 - 9.97791i) q^{36} +(4.21474 - 7.30014i) q^{37} +(5.35118 - 9.26852i) q^{38} +4.82094 q^{39} +(3.81856 + 6.61394i) q^{40} +(3.68699 + 6.38605i) q^{41} +(-4.69943 - 8.13966i) q^{42} +(0.115246 - 0.199612i) q^{43} +(1.21959 + 2.11239i) q^{44} +(4.32914 - 7.49829i) q^{45} +16.4260 q^{46} -8.03652 q^{47} +(-0.513802 + 0.889932i) q^{48} +(2.21699 + 3.83994i) q^{49} +(-1.43332 + 2.48258i) q^{50} +(-5.56760 - 9.64336i) q^{51} +(-3.15176 - 5.45900i) q^{52} +(2.86712 + 4.96600i) q^{53} +2.73096 q^{54} +(-0.916506 + 1.58743i) q^{55} +(-2.44826 + 4.24051i) q^{56} +(5.89661 + 10.2132i) q^{57} +0.297530 q^{58} +(-4.75186 + 8.23046i) q^{59} -21.1213 q^{60} +7.84044 q^{61} +5.55122 q^{63} -12.7634 q^{64} +(2.36851 - 4.10238i) q^{65} -4.30466 q^{66} +(-2.41329 - 4.17994i) q^{67} +(-7.27978 + 12.6090i) q^{68} +(-9.05014 + 15.6753i) q^{69} -9.23525 q^{70} +(1.70251 + 2.94883i) q^{71} +(-5.29647 - 9.17376i) q^{72} +(1.34602 + 2.33138i) q^{73} +(9.72562 - 16.8453i) q^{74} +(-1.57941 - 2.73562i) q^{75} +(7.70998 - 13.3541i) q^{76} -1.17523 q^{77} +11.1245 q^{78} +(2.26397 - 3.92132i) q^{79} +(0.504858 + 0.874439i) q^{80} +(3.69351 - 6.39735i) q^{81} +(8.50783 + 14.7360i) q^{82} +(1.33517 + 2.31259i) q^{83} +(-6.77093 - 11.7276i) q^{84} -10.9414 q^{85} +(0.265933 - 0.460609i) q^{86} +(-0.163928 + 0.283932i) q^{87} +(1.12130 + 1.94214i) q^{88} +2.20459 q^{89} +(9.98960 - 17.3025i) q^{90} +3.03712 q^{91} +23.6666 q^{92} -18.5445 q^{94} +11.5879 q^{95} +(6.58682 - 11.4087i) q^{96} +12.2899 q^{97} +(5.11577 + 8.86077i) q^{98} +(1.27122 - 2.20182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 3 q^{3} + 16 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} - 18 q^{11} - 8 q^{13} + 9 q^{14} + 36 q^{15} + 8 q^{16} - 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 3 * q^3 + 16 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 - 18 * q^11 - 8 * q^13 + 9 * q^14 + 36 * q^15 + 8 * q^16 - 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 + q^21 - 4 * q^22 + 44 * q^23 - 30 * q^24 - 13 * q^25 - 9 * q^26 + 36 * q^27 + 5 * q^28 + 24 * q^29 + 22 * q^30 - 42 * q^32 + 12 * q^33 + 7 * q^34 - 24 * q^35 + q^36 + 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 + 36 * q^46 - 36 * q^47 + q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 + q^52 - 6 * q^53 - 14 * q^54 - 28 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 4 * q^59 - 80 * q^60 + 60 * q^61 - 46 * q^63 + 18 * q^64 - 3 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 + 33 * q^76 - 48 * q^77 - 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 - 39 * q^83 - 8 * q^84 - 52 * q^85 + 16 * q^86 + 15 * q^87 + 17 * q^88 + 54 * q^89 - 8 * q^90 + 32 * q^91 + 64 * q^92 + 44 * q^94 - 12 * q^95 + 12 * q^96 + 68 * q^97 - 10 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.30753			1.63167			0.815834	−	0.578286i	$-0.196278\pi$
$2$	2.30753			1.63167			0.815834	+	0.578286i	$0.196278\pi$
$3$	−1.27136	+	2.20206i	−0.734021	+	1.27136i	0.221130	+	0.975244i	$0.429025\pi$
$3$	−1.27136	+	2.20206i	−0.734021	+	1.27136i	−0.955151	+	0.296118i	$0.904308\pi$
$4$	3.32468			1.66234
$5$	1.24923	+	2.16373i	0.558673	+	0.967649i	0.997608	+	0.0691304i	$0.0220225\pi$
$5$	1.24923	+	2.16373i	0.558673	+	0.967649i	−0.438935	+	0.898519i	$0.644644\pi$
$6$	−2.93370	+	5.08132i	−1.19768	+	2.07444i
$7$	−0.800939	+	1.38727i	−0.302727	+	0.524338i	−0.976753	−	0.214370i	$-0.931230\pi$
$7$	−0.800939	+	1.38727i	−0.302727	+	0.524338i	0.674026	+	0.738708i	$0.264564\pi$
$8$	3.05673			1.08072
$9$	−1.73272	−	3.00116i	−0.577574	−	1.00039i
$10$	2.88263	+	4.99286i	0.911568	+	1.57888i
$11$	0.366828	+	0.635365i	0.110603	+	0.191570i	0.916014	−	0.401147i	$-0.131388\pi$
$11$	0.366828	+	0.635365i	0.110603	+	0.191570i	−0.805411	+	0.592717i	$0.798055\pi$
$12$	−4.22687	+	7.32116i	−1.22019	+	2.11344i
$13$	−0.947988	−	1.64196i	−0.262925	−	0.455399i	0.704093	−	0.710108i	$-0.251354\pi$
$13$	−0.947988	−	1.64196i	−0.262925	−	0.455399i	−0.967018	+	0.254709i	$0.918020\pi$
$14$	−1.84819	+	3.20116i	−0.493949	+	0.855545i
$15$	−6.35289			−1.64031
$16$	0.404135			0.101034
$17$	−2.18962	+	3.79253i	−0.531061	+	0.919824i	0.468282	+	0.883579i	$0.344873\pi$
$17$	−2.18962	+	3.79253i	−0.531061	+	0.919824i	−0.999343	+	0.0362453i	$0.988460\pi$
$18$	−3.99830	−	6.92527i	−0.942409	−	1.63230i
$19$	2.31901	−	4.01665i	0.532018	−	0.921482i	−0.467283	−	0.884108i	$-0.654767\pi$
$19$	2.31901	−	4.01665i	0.532018	−	0.921482i	0.999301	−	0.0373747i	$-0.0118995\pi$
$20$	4.15329	+	7.19371i	0.928704	+	1.60856i
$21$	−2.03657	−	3.52744i	−0.444415	−	0.769750i
$22$	0.846466	+	1.46612i	0.180467	+	0.312578i
$23$	7.11846			1.48430			0.742151	−	0.670233i	$-0.233806\pi$
$23$	7.11846			1.48430			0.742151	+	0.670233i	$0.233806\pi$
$24$	−3.88622	+	6.73112i	−0.793270	+	1.37398i
$25$	−0.621150	+	1.07586i	−0.124230	+	0.215173i
$26$	−2.18751	−	3.78887i	−0.429005	−	0.743059i
$27$	1.18350			0.227765
$28$	−2.66287	+	4.61222i	−0.503234	+	0.871628i
$29$	0.128939			0.0239434			0.0119717	−	0.999928i	$-0.496189\pi$
$29$	0.128939			0.0239434			0.0119717	+	0.999928i	$0.496189\pi$
$30$	−14.6595			−2.67644
$31$		0			0
$31$		0			0
$32$	−5.18091			−0.915865
$33$	−1.86549			−0.324740
$34$	−5.05261	+	8.75137i	−0.866515	+	1.50085i
$35$	−4.00223			−0.676500
$36$	−5.76075	−	9.97791i	−0.960125	−	1.66298i
$37$	4.21474	−	7.30014i	0.692899	−	1.20014i	−0.277985	−	0.960585i	$-0.589667\pi$
$37$	4.21474	−	7.30014i	0.692899	−	1.20014i	0.970884	−	0.239550i	$-0.0770000\pi$
$38$	5.35118	−	9.26852i	0.868077	−	1.50355i
$39$	4.82094			0.771969
$40$	3.81856	+	6.61394i	0.603768	+	1.04576i
$41$	3.68699	+	6.38605i	0.575811	+	0.997334i	0.995953	+	0.0898756i	$0.0286470\pi$
$41$	3.68699	+	6.38605i	0.575811	+	0.997334i	−0.420142	+	0.907458i	$0.638020\pi$
$42$	−4.69943	−	8.13966i	−0.725138	−	1.25598i
$43$	0.115246	−	0.199612i	0.0175748	−	0.0304405i	−0.857104	−	0.515143i	$-0.827739\pi$
$43$	0.115246	−	0.199612i	0.0175748	−	0.0304405i	0.874679	+	0.484703i	$0.161072\pi$
$44$	1.21959	+	2.11239i	0.183860	+	0.318454i
$45$	4.32914	−	7.49829i	0.645350	−	1.11778i
$46$	16.4260			2.42189
$47$	−8.03652			−1.17225			−0.586124	−	0.810222i	$-0.699347\pi$
$47$	−8.03652			−1.17225			−0.586124	+	0.810222i	$0.699347\pi$
$48$	−0.513802	+	0.889932i	−0.0741610	+	0.128451i
$49$	2.21699	+	3.83994i	0.316713	+	0.548563i
$50$	−1.43332	+	2.48258i	−0.202702	+	0.351090i
$51$	−5.56760	−	9.64336i	−0.779620	−	1.35034i
$52$	−3.15176	−	5.45900i	−0.437070	−	0.757027i
$53$	2.86712	+	4.96600i	0.393829	+	0.682132i	0.992951	−	0.118526i	$-0.0378168\pi$
$53$	2.86712	+	4.96600i	0.393829	+	0.682132i	−0.599122	+	0.800658i	$0.704483\pi$
$54$	2.73096			0.371636
$55$	−0.916506	+	1.58743i	−0.123582	+	0.214050i
$56$	−2.44826	+	4.24051i	−0.327162	+	0.566662i
$57$	5.89661	+	10.2132i	0.781025	+	1.35278i
$58$	0.297530			0.0390676
$59$	−4.75186	+	8.23046i	−0.618639	+	1.07151i	0.371095	+	0.928595i	$0.378982\pi$
$59$	−4.75186	+	8.23046i	−0.618639	+	1.07151i	−0.989734	+	0.142920i	$0.954351\pi$
$60$	−21.1213			−2.72675
$61$	7.84044			1.00387			0.501933	−	0.864907i	$-0.332623\pi$
$61$	7.84044			1.00387			0.501933	+	0.864907i	$0.332623\pi$
$62$		0			0
$63$	5.55122			0.699388
$64$	−12.7634			−1.59542
$65$	2.36851	−	4.10238i	0.293777	−	0.508837i
$66$	−4.30466			−0.529867
$67$	−2.41329	−	4.17994i	−0.294830	−	0.510661i	0.680115	−	0.733105i	$-0.261930\pi$
$67$	−2.41329	−	4.17994i	−0.294830	−	0.510661i	−0.974945	+	0.222444i	$0.928596\pi$
$68$	−7.27978	+	12.6090i	−0.882804	+	1.52906i
$69$	−9.05014	+	15.6753i	−1.08951	+	1.88709i
$70$	−9.23525			−1.10382
$71$	1.70251	+	2.94883i	0.202051	+	0.349962i	0.949189	−	0.314707i	$-0.101906\pi$
$71$	1.70251	+	2.94883i	0.202051	+	0.349962i	−0.747138	+	0.664668i	$0.768573\pi$
$72$	−5.29647	−	9.17376i	−0.624195	−	1.08114i
$73$	1.34602	+	2.33138i	0.157540	+	0.272867i	0.933981	−	0.357323i	$-0.116310\pi$
$73$	1.34602	+	2.33138i	0.157540	+	0.272867i	−0.776441	+	0.630190i	$0.782977\pi$
$74$	9.72562	−	16.8453i	1.13058	−	1.95822i
$75$	−1.57941	−	2.73562i	−0.182375	−	0.315882i
$76$	7.70998	−	13.3541i	0.884395	−	1.53182i
$77$	−1.17523			−0.133930
$78$	11.1245			1.25960
$79$	2.26397	−	3.92132i	0.254717	−	0.441182i	−0.710102	−	0.704099i	$-0.751351\pi$
$79$	2.26397	−	3.92132i	0.254717	−	0.441182i	0.964819	+	0.262917i	$0.0846844\pi$
$80$	0.504858	+	0.874439i	0.0564448	+	0.0977653i
$81$	3.69351	−	6.39735i	0.410390	−	0.710817i
$82$	8.50783	+	14.7360i	0.939532	+	1.62732i
$83$	1.33517	+	2.31259i	0.146554	+	0.253840i	0.929952	−	0.367681i	$-0.119848\pi$
$83$	1.33517	+	2.31259i	0.146554	+	0.253840i	−0.783397	+	0.621521i	$0.786515\pi$
$84$	−6.77093	−	11.7276i	−0.738769	−	1.27959i
$85$	−10.9414			−1.18676
$86$	0.265933	−	0.460609i	0.0286763	−	0.0496688i
$87$	−0.163928	+	0.283932i	−0.0175749	+	0.0304407i
$88$	1.12130	+	1.94214i	0.119531	+	0.207033i
$89$	2.20459			0.233686			0.116843	−	0.993150i	$-0.462723\pi$
$89$	2.20459			0.233686			0.116843	+	0.993150i	$0.462723\pi$
$90$	9.98960	−	17.3025i	1.05300	−	1.82384i
$91$	3.03712			0.318377
$92$	23.6666			2.46741
$93$		0			0
$94$	−18.5445			−1.91272
$95$	11.5879			1.18890
$96$	6.58682	−	11.4087i	0.672264	−	1.16440i
$97$	12.2899			1.24785			0.623923	−	0.781485i	$-0.285538\pi$
$97$	12.2899			1.24785			0.623923	+	0.781485i	$0.285538\pi$
$98$	5.11577	+	8.86077i	0.516771	+	0.895073i
$99$	1.27122	−	2.20182i	0.127763	−	0.221292i
$100$	−2.06512	+	3.57690i	−0.206512	+	0.357690i
$101$	7.34432			0.730787			0.365394	−	0.930853i	$-0.380934\pi$
$101$	7.34432			0.730787			0.365394	+	0.930853i	$0.380934\pi$
$102$	−12.8474	−	22.2523i	−1.27208	−	2.20331i
$103$	−2.79438	−	4.84000i	−0.275338	−	0.476899i	0.694882	−	0.719123i	$-0.255456\pi$
$103$	−2.79438	−	4.84000i	−0.275338	−	0.476899i	−0.970220	+	0.242224i	$0.922123\pi$
$104$	−2.89775	−	5.01904i	−0.284147	−	0.492158i
$105$	5.08828	−	8.81316i	0.496565	−	0.860076i
$106$	6.61596	+	11.4592i	0.642598	+	1.11301i
$107$	−0.912080	+	1.57977i	−0.0881741	+	0.152722i	−0.906739	−	0.421692i	$-0.861437\pi$
$107$	−0.912080	+	1.57977i	−0.0881741	+	0.152722i	0.818565	+	0.574414i	$0.194770\pi$
$108$	3.93476			0.378622
$109$	11.7653			1.12691			0.563455	−	0.826147i	$-0.309472\pi$
$109$	11.7653			1.12691			0.563455	+	0.826147i	$0.309472\pi$
$110$	−2.11486	+	3.66305i	−0.201644	+	0.349258i
$111$	10.7169	+	18.5622i	1.01720	+	1.76185i
$112$	−0.323688	+	0.560644i	−0.0305856	+	0.0529759i
$113$	−5.52727	−	9.57351i	−0.519962	−	0.900600i	−0.999731	−	0.0232051i	$-0.992613\pi$
$113$	−5.52727	−	9.57351i	−0.519962	−	0.900600i	0.479769	−	0.877395i	$-0.340720\pi$
$114$	13.6066	+	23.5673i	1.27437	+	2.20728i
$115$	8.89259	+	15.4024i	0.829239	+	1.43628i
$116$	0.428681			0.0398020
$117$	−3.28520	+	5.69013i	−0.303717	+	0.526053i
$118$	−10.9650	+	18.9920i	−1.00941	+	1.74836i
$119$	−3.50750	−	6.07518i	−0.321532	−	0.556911i
$120$	−19.4191			−1.77271
$121$	5.23087	−	9.06014i	0.475534	−	0.823649i
$122$	18.0920			1.63797
$123$	−18.7500			−1.69063
$124$		0			0
$125$	9.38846			0.839730
$126$	12.8096			1.14117
$127$	−0.643516	+	1.11460i	−0.0571028	+	0.0989050i	−0.893164	−	0.449732i	$-0.851520\pi$
$127$	−0.643516	+	1.11460i	−0.0571028	+	0.0989050i	0.836061	+	0.548637i	$0.184853\pi$
$128$	−19.0900			−1.68733
$129$	0.293038	+	0.507557i	0.0258006	+	0.0446879i
$130$	5.46540	−	9.46635i	0.479347	−	0.830254i
$131$	4.01018	−	6.94583i	0.350371	−	0.606860i	−0.635944	−	0.771736i	$-0.719389\pi$
$131$	4.01018	−	6.94583i	0.350371	−	0.606860i	0.986314	+	0.164876i	$0.0527223\pi$
$132$	−6.20214			−0.539827
$133$	3.71478	+	6.43418i	0.322112	+	0.557914i
$134$	−5.56873	−	9.64532i	−0.481065	−	0.833229i
$135$	1.47846	+	2.56077i	0.127246	+	0.220396i
$136$	−6.69308	+	11.5928i	−0.573927	+	0.994071i
$137$	−8.23838	−	14.2693i	−0.703852	−	1.21911i	−0.967104	−	0.254381i	$-0.918128\pi$
$137$	−8.23838	−	14.2693i	−0.703852	−	1.21911i	0.263252	−	0.964727i	$-0.415205\pi$
$138$	−20.8834	+	36.1712i	−1.77772	+	3.07910i
$139$	−7.33982			−0.622555			−0.311278	−	0.950319i	$-0.600757\pi$
$139$	−7.33982			−0.622555			−0.311278	+	0.950319i	$0.600757\pi$
$140$	−13.3061			−1.12457
$141$	10.2173	−	17.6969i	0.860454	−	1.49035i
$142$	3.92858	+	6.80451i	0.329679	+	0.571022i
$143$	0.695498	−	1.20464i	0.0581604	−	0.100737i
$144$	−0.700254	−	1.21288i	−0.0583545	−	0.101073i
$145$	0.161074	+	0.278989i	0.0133765	+	0.0231688i
$146$	3.10598	+	5.37972i	0.257053	+	0.445229i
$147$	−11.2744			−0.929897
$148$	14.0127	−	24.2706i	1.15183	−	1.99503i
$149$	3.18096	−	5.50959i	0.260595	−	0.451363i	−0.705805	−	0.708406i	$-0.749415\pi$
$149$	3.18096	−	5.50959i	0.260595	−	0.451363i	0.966400	+	0.257043i	$0.0827480\pi$
$150$	−3.64454	−	6.31252i	−0.297575	−	0.515415i
$151$	5.52473			0.449596			0.224798	−	0.974405i	$-0.427828\pi$
$151$	5.52473			0.449596			0.224798	+	0.974405i	$0.427828\pi$
$152$	7.08861	−	12.2778i	0.574962	−	0.995863i
$153$	15.1760			1.22691
$154$	−2.71187			−0.218529
$155$		0			0
$156$	16.0281			1.28327
$157$	7.99448			0.638029			0.319014	−	0.947750i	$-0.396648\pi$
$157$	7.99448			0.638029			0.319014	+	0.947750i	$0.396648\pi$
$158$	5.22418	−	9.04854i	0.415613	−	0.719863i
$159$	−14.5806			−1.15632
$160$	−6.47215	−	11.2101i	−0.511669	−	0.886236i
$161$	−5.70146	+	9.87521i	−0.449338	+	0.778276i
$162$	8.52288	−	14.7621i	0.669621	−	1.15982i
$163$	−17.0654			−1.33667			−0.668333	−	0.743863i	$-0.732992\pi$
$163$	−17.0654			−1.33667			−0.668333	+	0.743863i	$0.732992\pi$
$164$	12.2581	+	21.2316i	0.957194	+	1.65791i
$165$	−2.33042	−	4.03641i	−0.181423	−	0.314234i
$166$	3.08095	+	5.33636i	0.239128	+	0.414182i
$167$	−12.1861	+	21.1070i	−0.942989	+	1.63331i	−0.183261	+	0.983064i	$0.558665\pi$
$167$	−12.1861	+	21.1070i	−0.942989	+	1.63331i	−0.759728	+	0.650241i	$0.774668\pi$
$168$	−6.22524	−	10.7824i	−0.480288	−	0.831883i
$169$	4.70264	−	8.14521i	0.361741	−	0.626554i
$170$	−25.2475			−1.93639
$171$	−16.0728			−1.22912
$172$	0.383156	−	0.663645i	0.0292153	−	0.0506025i
$173$	−4.48680	−	7.77137i	−0.341125	−	0.590846i	0.643517	−	0.765432i	$-0.277475\pi$
$173$	−4.48680	−	7.77137i	−0.341125	−	0.590846i	−0.984642	+	0.174586i	$0.944141\pi$
$174$	−0.378269	+	0.655180i	−0.0286765	+	0.0496691i
$175$	−0.995006	−	1.72340i	−0.0752154	−	0.130277i
$176$	0.148248	+	0.256774i	0.0111746	+	0.0193550i
$177$	−12.0827	−	20.9278i	−0.908189	−	1.57303i
$178$	5.08714			0.381297
$179$	−5.64526	+	9.77788i	−0.421946	+	0.730833i	−0.996130	−	0.0878940i	$-0.971986\pi$
$179$	−5.64526	+	9.77788i	−0.421946	+	0.730833i	0.574183	+	0.818727i	$0.305320\pi$
$180$	14.3930	−	24.9294i	1.07279	−	1.85813i
$181$	−7.47052	−	12.9393i	−0.555279	−	0.961772i	−0.997882	−	0.0650542i	$-0.979278\pi$
$181$	−7.47052	−	12.9393i	−0.555279	−	0.961772i	0.442602	−	0.896718i	$-0.354055\pi$
$182$	7.00824			0.519485
$183$	−9.96803	+	17.2651i	−0.736858	+	1.27628i
$184$	21.7592			1.60411
$185$	21.0607			1.54841
$186$		0			0
$187$	−3.21286			−0.234947
$188$	−26.7189			−1.94867
$189$	−0.947911	+	1.64183i	−0.0689504	+	0.119426i
$190$	26.7394			1.93988
$191$	−1.13046	−	1.95802i	−0.0817975	−	0.141677i	0.822225	−	0.569163i	$-0.192733\pi$
$191$	−1.13046	−	1.95802i	−0.0817975	−	0.141677i	−0.904022	+	0.427486i	$0.859399\pi$
$192$	16.2269	−	28.1057i	1.17107	−	2.02836i
$193$	−12.8321	+	22.2259i	−0.923677	+	1.59985i	−0.130001	+	0.991514i	$0.541498\pi$
$193$	−12.8321	+	22.2259i	−0.923677	+	1.59985i	−0.793676	+	0.608341i	$0.791835\pi$
$194$	28.3592			2.03607
$195$	6.02246	+	10.4312i	0.431278	+	0.746995i
$196$	7.37079	+	12.7666i	0.526485	+	0.911899i
$197$	−3.09786	−	5.36564i	−0.220713	−	0.382286i	0.734312	−	0.678812i	$-0.237505\pi$
$197$	−3.09786	−	5.36564i	−0.220713	−	0.382286i	−0.955025	+	0.296526i	$0.904172\pi$
$198$	2.93338	−	5.08077i	0.208466	−	0.361074i
$199$	−2.28467	−	3.95716i	−0.161956	−	0.280515i	0.773614	−	0.633657i	$-0.218447\pi$
$199$	−2.28467	−	3.95716i	−0.161956	−	0.280515i	−0.935570	+	0.353141i	$0.885113\pi$
$200$	−1.89869	+	3.28863i	−0.134258	+	0.232541i
$201$	12.2727			0.865647
$202$	16.9472			1.19240
$203$	−0.103272	+	0.178873i	−0.00724829	+	0.0125544i
$204$	−18.5105	−	32.0611i	−1.29599	−	2.24473i
$205$	−9.21179	+	15.9553i	−0.643380	+	1.11437i
$206$	−6.44810	−	11.1684i	−0.449260	−	0.778141i
$207$	−12.3343	−	21.3637i	−0.857295	−	1.48488i
$208$	−0.383115	−	0.663575i	−0.0265643	−	0.0460107i
$209$	3.40272			0.235371
$210$	11.7413	−	20.3366i	0.810230	−	1.40336i
$211$	9.30839	−	16.1226i	0.640816	−	1.10993i	−0.344435	−	0.938810i	$-0.611930\pi$
$211$	9.30839	−	16.1226i	0.640816	−	1.10993i	0.985251	−	0.171115i	$-0.0547371\pi$
$212$	9.53225	+	16.5103i	0.654678	+	1.13394i
$213$	−8.65802			−0.593238
$214$	−2.10465	+	3.64536i	−0.143871	+	0.249192i
$215$	0.575874			0.0392743
$216$	3.61764			0.246149
$217$		0			0
$218$	27.1487			1.83874
$219$	−6.84513			−0.462551
$220$	−3.04709	+	5.27771i	−0.205435	+	0.355823i
$221$	8.30293			0.558516
$222$	24.7296	+	42.8329i	1.65974	+	2.87475i
$223$	3.10748	−	5.38231i	0.208092	−	0.360426i	−0.743021	−	0.669268i	$-0.766608\pi$
$223$	3.10748	−	5.38231i	0.208092	−	0.360426i	0.951113	+	0.308842i	$0.0999413\pi$
$224$	4.14960	−	7.18731i	0.277257	−	0.480223i
$225$	4.30512			0.287008
$226$	−12.7543	−	22.0911i	−0.848405	−	1.46948i
$227$	6.52390	+	11.2997i	0.433006	+	0.749989i	0.997131	−	0.0757009i	$-0.0241194\pi$
$227$	6.52390	+	11.2997i	0.433006	+	0.749989i	−0.564124	+	0.825690i	$0.690786\pi$
$228$	19.6043	+	33.9557i	1.29833	+	2.24877i
$229$	7.63897	−	13.2311i	0.504797	−	0.874334i	−0.495187	−	0.868786i	$-0.664901\pi$
$229$	7.63897	−	13.2311i	0.504797	−	0.874334i	0.999985	−	0.00554817i	$-0.00176605\pi$
$230$	20.5199	+	35.5415i	1.35304	+	2.34354i
$231$	1.49414	−	2.58793i	0.0983073	−	0.170273i
$232$	0.394132			0.0258760
$233$	13.0613			0.855671			0.427836	−	0.903857i	$-0.359276\pi$
$233$	13.0613			0.855671			0.427836	+	0.903857i	$0.359276\pi$
$234$	−7.58069	+	13.1301i	−0.495565	+	0.858344i
$235$	−10.0395	−	17.3889i	−0.654902	−	1.13432i
$236$	−15.7984	+	27.3636i	−1.02839	+	1.78122i
$237$	5.75666	+	9.97082i	0.373935	+	0.647675i
$238$	−8.09366	−	14.0186i	−0.524634	−	0.908693i
$239$	−11.7211	−	20.3016i	−0.758176	−	1.31320i	−0.943780	−	0.330574i	$-0.892758\pi$
$239$	−11.7211	−	20.3016i	−0.758176	−	1.31320i	0.185604	−	0.982625i	$-0.440576\pi$
$240$	−2.56743			−0.165727
$241$	12.3560	−	21.4013i	0.795923	−	1.37858i	−0.126329	−	0.991988i	$-0.540319\pi$
$241$	12.3560	−	21.4013i	0.795923	−	1.37858i	0.922252	−	0.386590i	$-0.126347\pi$
$242$	12.0704	−	20.9065i	0.775914	−	1.34392i
$243$	11.1668	+	19.3415i	0.716353	+	1.24076i
$244$	26.0669			1.66876
$245$	−5.53907	+	9.59394i	−0.353878	+	0.612935i
$246$	−43.2661			−2.75855
$247$	−8.79358			−0.559522
$248$		0			0
$249$	−6.78996			−0.430296
$250$	21.6641			1.37016
$251$	−11.5971	+	20.0867i	−0.732001	+	1.26786i	0.224026	+	0.974583i	$0.428080\pi$
$251$	−11.5971	+	20.0867i	−0.732001	+	1.26786i	−0.956027	+	0.293279i	$0.905253\pi$
$252$	18.4560			1.16262
$253$	2.61125	+	4.52282i	0.164168	+	0.284348i
$254$	−1.48493	+	2.57198i	−0.0931729	+	0.161380i
$255$	13.9104	−	24.0936i	0.871104	−	1.50880i
$256$	−18.5239			−1.15774
$257$	−7.67305	−	13.2901i	−0.478632	−	0.829015i	0.521068	−	0.853515i	$-0.325534\pi$
$257$	−7.67305	−	13.2901i	−0.478632	−	0.829015i	−0.999700	+	0.0245003i	$0.992201\pi$
$258$	0.676194	+	1.17120i	0.0420980	+	0.0729159i
$259$	6.75150	+	11.6939i	0.419518	+	0.726626i
$260$	7.87453	−	13.6391i	0.488358	−	0.845861i
$261$	−0.223416	−	0.386967i	−0.0138291	−	0.0239527i
$262$	9.25359	−	16.0277i	0.571689	−	0.990194i
$263$	6.80588			0.419668			0.209834	−	0.977737i	$-0.432708\pi$
$263$	6.80588			0.419668			0.209834	+	0.977737i	$0.432708\pi$
$264$	−5.70230			−0.350952
$265$	−7.16338	+	12.4073i	−0.440043	+	0.762177i
$266$	8.57195	+	14.8470i	0.525580	+	0.910331i
$267$	−2.80283	+	4.85464i	−0.171530	+	0.297099i
$268$	−8.02341	−	13.8970i	−0.490108	−	0.848892i
$269$	5.25982	+	9.11028i	0.320697	+	0.555464i	0.980632	−	0.195859i	$-0.0627495\pi$
$269$	5.25982	+	9.11028i	0.320697	+	0.555464i	−0.659935	+	0.751323i	$0.729416\pi$
$270$	3.41159	+	5.90905i	0.207623	+	0.359613i
$271$	1.57714			0.0958044			0.0479022	−	0.998852i	$-0.484746\pi$
$271$	1.57714			0.0958044			0.0479022	+	0.998852i	$0.484746\pi$
$272$	−0.884903	+	1.53270i	−0.0536551	+	0.0929334i
$273$	−3.86128	+	6.68794i	−0.233695	+	0.404772i
$274$	−19.0103	−	32.9268i	−1.14845	−	1.98918i
$275$	−0.911421			−0.0549608
$276$	−30.0888	+	52.1154i	−1.81113	+	3.13698i
$277$	−12.1014			−0.727100			−0.363550	−	0.931575i	$-0.618435\pi$
$277$	−12.1014			−0.727100			−0.363550	+	0.931575i	$0.618435\pi$
$278$	−16.9368			−1.01580
$279$		0			0
$280$	−12.2337			−0.731106
$281$	−21.4727			−1.28096			−0.640478	−	0.767976i	$-0.721264\pi$
$281$	−21.4727			−1.28096			−0.640478	+	0.767976i	$0.721264\pi$
$282$	23.5768	−	40.8362i	1.40398	−	2.43176i
$283$	−0.688807			−0.0409453			−0.0204726	−	0.999790i	$-0.506517\pi$
$283$	−0.688807			−0.0409453			−0.0204726	+	0.999790i	$0.506517\pi$
$284$	5.66030	+	9.80392i	0.335877	+	0.581756i
$285$	−14.7324	+	25.5173i	−0.872675	+	1.51152i
$286$	1.60488	−	2.77973i	0.0948985	−	0.164369i
$287$	−11.8122			−0.697253
$288$	8.97709	+	15.5488i	0.528980	+	0.916220i
$289$	−1.08887	−	1.88598i	−0.0640512	−	0.110940i
$290$	0.371684	+	0.643775i	0.0218260	+	0.0378038i
$291$	−15.6249	+	27.0631i	−0.915946	+	1.58647i
$292$	4.47509	+	7.75109i	0.261885	+	0.453598i
$293$	−4.50594	+	7.80452i	−0.263240	+	0.455945i	−0.967101	−	0.254393i	$-0.918124\pi$
$293$	−4.50594	+	7.80452i	−0.263240	+	0.455945i	0.703861	+	0.710338i	$0.251458\pi$
$294$	−26.0160			−1.51728
$295$	−23.7447			−1.38247
$296$	12.8833	−	22.3146i	0.748828	−	1.29701i
$297$	0.434141	+	0.751954i	0.0251914	+	0.0436328i
$298$	7.34016	−	12.7135i	0.425204	−	0.736475i
$299$	−6.74822	−	11.6883i	−0.390259	−	0.675949i
$300$	−5.25104	−	9.09507i	−0.303169	−	0.525104i
$301$	0.184610	+	0.319754i	0.0106407	+	0.0184303i
$302$	12.7485			0.733592
$303$	−9.33729	+	16.1727i	−0.536413	+	0.929095i
$304$	0.937195	−	1.62327i	0.0537518	−	0.0931009i
$305$	9.79451	+	16.9646i	0.560832	+	0.971389i
$306$	35.0191			2.00191
$307$	15.6663	−	27.1349i	0.894124	−	1.54867i	0.0592398	−	0.998244i	$-0.481132\pi$
$307$	15.6663	−	27.1349i	0.894124	−	1.54867i	0.834885	−	0.550425i	$-0.185534\pi$
$308$	−3.90726			−0.222637
$309$	14.2107			0.808416
$310$		0			0
$311$	−17.7139			−1.00447			−0.502233	−	0.864732i	$-0.667488\pi$
$311$	−17.7139			−1.00447			−0.502233	+	0.864732i	$0.667488\pi$
$312$	14.7363			0.834281
$313$	−10.8344	+	18.7656i	−0.612394	+	1.06070i	0.378442	+	0.925625i	$0.376460\pi$
$313$	−10.8344	+	18.7656i	−0.612394	+	1.06070i	−0.990836	+	0.135072i	$0.956873\pi$
$314$	18.4475			1.04105
$315$	6.93475	+	12.0113i	0.390729	+	0.676762i
$316$	7.52698	−	13.0371i	0.423426	−	0.733395i
$317$	−0.508023	+	0.879922i	−0.0285334	+	0.0494213i	−0.879940	−	0.475086i	$-0.842417\pi$
$317$	−0.508023	+	0.879922i	−0.0285334	+	0.0494213i	0.851406	+	0.524507i	$0.175750\pi$
$318$	−33.6451			−1.88672
$319$	0.0472985	+	0.0819234i	0.00264821	+	0.00458683i
$320$	−15.9444	−	27.6165i	−0.891318	−	1.54381i
$321$	−2.31917	−	4.01692i	−0.129443	−	0.224202i
$322$	−13.1563	+	22.7873i	−0.733170	+	1.26989i
$323$	10.1555	+	17.5899i	0.565068	+	0.978726i
$324$	12.2797	−	21.2691i	0.682208	−	1.18162i
$325$	2.35537			0.130652
$326$	−39.3789			−2.18099
$327$	−14.9579	+	25.9079i	−0.827176	+	1.43271i
$328$	11.2701	+	19.5205i	0.622290	+	1.07784i
$329$	6.43677	−	11.1488i	0.354870	−	0.614654i
$330$	−5.37751	−	9.31412i	−0.296022	−	0.512725i
$331$	13.3447	+	23.1137i	0.733492	+	1.27045i	0.955382	+	0.295374i	$0.0954443\pi$
$331$	13.3447	+	23.1137i	0.733492	+	1.27045i	−0.221889	+	0.975072i	$0.571222\pi$
$332$	4.43903	+	7.68862i	0.243623	+	0.421968i
$333$	−29.2119			−1.60080
$334$	−28.1198	+	48.7049i	−1.53864	+	2.66501i
$335$	6.02951	−	10.4434i	0.329427	−	0.570584i
$336$	−0.823049	−	1.42556i	−0.0449010	−	0.0777708i
$337$	−31.9415			−1.73997			−0.869983	−	0.493081i	$-0.835871\pi$
$337$	−31.9415			−1.73997			−0.869983	+	0.493081i	$0.835871\pi$
$338$	10.8515	−	18.7953i	0.590242	−	1.02233i
$339$	28.1086			1.52665
$340$	−36.3765			−1.97279
$341$		0			0
$342$	−37.0885			−2.00552
$343$	−18.3159			−0.988963
$344$	0.352276	−	0.610160i	0.0189934	−	0.0328976i
$345$	−45.2228			−2.43472
$346$	−10.3534	−	17.9326i	−0.556603	−	0.964065i
$347$	1.56066	−	2.70314i	0.0837804	−	0.145112i	−0.821090	−	0.570798i	$-0.806634\pi$
$347$	1.56066	−	2.70314i	0.0837804	−	0.145112i	0.904871	+	0.425686i	$0.139967\pi$
$348$	−0.545009	+	0.943982i	−0.0292155	+	0.0506028i
$349$	−22.0265			−1.17905			−0.589525	−	0.807750i	$-0.700685\pi$
$349$	−22.0265			−1.17905			−0.589525	+	0.807750i	$0.700685\pi$
$350$	−2.29600	−	3.97679i	−0.122727	−	0.212569i
$351$	−1.12194	−	1.94326i	−0.0598849	−	0.103724i
$352$	−1.90051	−	3.29177i	−0.101297	−	0.175452i
$353$	2.46620	−	4.27158i	0.131262	−	0.227353i	−0.792901	−	0.609350i	$-0.791430\pi$
$353$	2.46620	−	4.27158i	0.131262	−	0.227353i	0.924163	+	0.381997i	$0.124764\pi$
$354$	−27.8811	−	48.2914i	−1.48186	−	2.56666i
$355$	−4.25365	+	7.36754i	−0.225760	+	0.391028i
$356$	7.32954			0.388465
$357$	17.8372			0.944046
$358$	−13.0266	+	22.5627i	−0.688476	+	1.19248i
$359$	0.180430	+	0.312514i	0.00952273	+	0.0164938i	0.870747	−	0.491730i	$-0.163635\pi$
$359$	0.180430	+	0.312514i	0.00952273	+	0.0164938i	−0.861225	+	0.508224i	$0.830302\pi$
$360$	13.2330	−	22.9203i	0.697441	−	1.20800i
$361$	−1.25564	−	2.17484i	−0.0660865	−	0.114465i
$362$	−17.2384	−	29.8578i	−0.906032	−	1.56929i
$363$	13.3007	+	23.0374i	0.698104	+	1.20915i
$364$	10.0975			0.529251
$365$	−3.36298	+	5.82486i	−0.176027	+	0.304887i
$366$	−23.0015	+	39.8398i	−1.20231	+	2.08246i
$367$	−14.6935	−	25.4498i	−0.766992	−	1.32847i	−0.939187	−	0.343406i	$-0.888419\pi$
$367$	−14.6935	−	25.4498i	−0.766992	−	1.32847i	0.172195	−	0.985063i	$-0.444914\pi$
$368$	2.87682			0.149965
$369$	12.7771	−	22.1305i	0.665147	−	1.15207i
$370$	48.5981			2.52650
$371$	−9.18555			−0.476890
$372$		0			0
$373$	17.7284			0.917941			0.458971	−	0.888451i	$-0.348218\pi$
$373$	17.7284			0.917941			0.458971	+	0.888451i	$0.348218\pi$
$374$	−7.41376			−0.383356
$375$	−11.9361	+	20.6740i	−0.616379	+	1.06760i
$376$	−24.5655			−1.26687
$377$	−0.122233	−	0.211713i	−0.00629530	−	0.0109038i
$378$	−2.18733	+	3.78857i	−0.112504	+	0.194863i
$379$	1.23021	−	2.13079i	0.0631917	−	0.109451i	−0.832699	−	0.553726i	$-0.813205\pi$
$379$	1.23021	−	2.13079i	0.0631917	−	0.109451i	0.895890	+	0.444275i	$0.146539\pi$
$380$	38.5261			1.97635
$381$	−1.63628	−	2.83413i	−0.0838294	−	0.145197i
$382$	−2.60858	−	4.51819i	−0.133466	−	0.231171i
$383$	−9.55896	−	16.5566i	−0.488440	−	0.846003i	0.511472	−	0.859300i	$-0.329101\pi$
$383$	−9.55896	−	16.5566i	−0.488440	−	0.846003i	−0.999912	+	0.0132974i	$0.995767\pi$
$384$	24.2703	−	42.0374i	1.23854	−	2.14521i
$385$	−1.46813	−	2.54288i	−0.0748229	−	0.129597i
$386$	−29.6105	+	51.2868i	−1.50713	+	2.61043i
$387$	−0.798756			−0.0406031
$388$	40.8599			2.07435
$389$	2.63553	−	4.56487i	0.133627	−	0.231448i	−0.791445	−	0.611240i	$-0.790671\pi$
$389$	2.63553	−	4.56487i	0.133627	−	0.231448i	0.925072	+	0.379792i	$0.124004\pi$
$390$	13.8970	+	24.0703i	0.703702	+	1.21885i
$391$	−15.5867	+	26.9970i	−0.788255	+	1.36530i
$392$	6.77676	+	11.7377i	0.342278	+	0.592843i
$393$	10.1968	+	17.6613i	0.514359	+	0.890896i
$394$	−7.14838	−	12.3814i	−0.360130	−	0.623764i
$395$	11.3129			0.569213
$396$	4.22641	−	7.32036i	0.212385	−	0.367862i
$397$	−8.46275	+	14.6579i	−0.424733	+	0.735660i	−0.996395	−	0.0848295i	$-0.972965\pi$
$397$	−8.46275	+	14.6579i	−0.424733	+	0.735660i	0.571662	+	0.820489i	$0.306299\pi$
$398$	−5.27193	−	9.13124i	−0.264258	−	0.457708i
$399$	−18.8913			−0.945748
$400$	−0.251029	+	0.434794i	−0.0125514	+	0.0217397i
$401$	−38.0397			−1.89961			−0.949805	−	0.312843i	$-0.898719\pi$
$401$	−38.0397			−1.89961			−0.949805	+	0.312843i	$0.898719\pi$
$402$	28.3195			1.41245
$403$		0			0
$404$	24.4175			1.21482
$405$	18.4562			0.917095
$406$	−0.238304	+	0.412754i	−0.0118268	+	0.0204846i
$407$	6.18434			0.306546
$408$	−17.0187	−	29.4772i	−0.842550	−	1.45934i
$409$	0.249342	−	0.431873i	0.0123292	−	0.0213547i	−0.859795	−	0.510639i	$-0.829409\pi$
$409$	0.249342	−	0.431873i	0.0123292	−	0.0213547i	0.872124	+	0.489285i	$0.162742\pi$
$410$	−21.2565	+	36.8173i	−1.04978	+	1.81828i
$411$	41.8958			2.06657
$412$	−9.29040	−	16.0915i	−0.457705	−	0.792769i
$413$	−7.61190	−	13.1842i	−0.374557	−	0.648752i
$414$	−28.4618	−	49.2972i	−1.39882	−	2.42283i
$415$	−3.33588	+	5.77791i	−0.163752	+	0.283627i
$416$	4.91144	+	8.50687i	0.240803	+	0.417084i
$417$	9.33157	−	16.1627i	0.456969	−	0.791493i
$418$	7.85186			0.384047
$419$	13.5100			0.660007			0.330003	−	0.943980i	$-0.392950\pi$
$419$	13.5100			0.660007			0.330003	+	0.943980i	$0.392950\pi$
$420$	16.9169	−	29.3009i	0.825460	−	1.42974i
$421$	15.4576	+	26.7733i	0.753355	+	1.30485i	0.946188	+	0.323618i	$0.104899\pi$
$421$	15.4576	+	26.7733i	0.753355	+	1.30485i	−0.192833	+	0.981232i	$0.561767\pi$
$422$	21.4793	−	37.2033i	1.04560	−	1.81103i
$423$	13.9251	+	24.1189i	0.677060	+	1.17270i
$424$	8.76402	+	15.1797i	0.425618	+	0.737193i
$425$	−2.72016	−	4.71146i	−0.131947	−	0.228539i
$426$	−19.9786			−0.967967
$427$	−6.27971	+	10.8768i	−0.303897	+	0.526364i
$428$	−3.03237	+	5.25223i	−0.146575	+	0.253876i
$429$	1.76846	+	3.06306i	0.0853820	+	0.147886i
$430$	1.32885			0.0640826
$431$	6.02740	−	10.4398i	0.290330	−	0.502865i	−0.683558	−	0.729896i	$-0.739568\pi$
$431$	6.02740	−	10.4398i	0.290330	−	0.502865i	0.973888	+	0.227031i	$0.0729018\pi$
$432$	0.478294			0.0230119
$433$	32.3919			1.55665			0.778327	−	0.627860i	$-0.216069\pi$
$433$	32.3919			1.55665			0.778327	+	0.627860i	$0.216069\pi$
$434$		0			0
$435$	−0.819136			−0.0392745
$436$	39.1158			1.87331
$437$	16.5078	−	28.5924i	0.789675	−	1.36776i
$438$	−15.7953			−0.754730
$439$	−6.18408	−	10.7111i	−0.295150	−	0.511215i	0.679870	−	0.733333i	$-0.262036\pi$
$439$	−6.18408	−	10.7111i	−0.295150	−	0.511215i	−0.975020	+	0.222118i	$0.928703\pi$
$440$	−2.80151	+	4.85236i	−0.133557	+	0.231327i
$441$	7.68287	−	13.3071i	0.365851	−	0.633672i
$442$	19.1592			0.911312
$443$	2.36170	+	4.09059i	0.112208	+	0.194350i	0.916660	−	0.399667i	$-0.130874\pi$
$443$	2.36170	+	4.09059i	0.112208	+	0.194350i	−0.804452	+	0.594017i	$0.797541\pi$
$444$	35.6303	+	61.7135i	1.69094	+	2.92879i
$445$	2.75404	+	4.77013i	0.130554	+	0.226126i
$446$	7.17059	−	12.4198i	0.339537	−	0.588095i
$447$	8.08831	+	14.0094i	0.382564	+	0.662620i
$448$	10.2227	−	17.7062i	0.482976	−	0.836540i
$449$	15.9842			0.754341			0.377170	−	0.926144i	$-0.376897\pi$
$449$	15.9842			0.754341			0.377170	+	0.926144i	$0.376897\pi$
$450$	9.93418			0.468302
$451$	−2.70498	+	4.68517i	−0.127373	+	0.220616i
$452$	−18.3764	−	31.8288i	−0.864353	−	1.49710i
$453$	−7.02394	+	12.1658i	−0.330013	+	0.571600i
$454$	15.0541	+	26.0744i	0.706523	+	1.22373i
$455$	3.79406	+	6.57151i	0.177868	+	0.308077i
$456$	18.0244	+	31.2191i	0.844068	+	1.46197i
$457$	−4.55775			−0.213203			−0.106601	−	0.994302i	$-0.533997\pi$
$457$	−4.55775			−0.213203			−0.106601	+	0.994302i	$0.533997\pi$
$458$	17.6271	−	30.5311i	0.823661	−	1.42662i
$459$	−2.59141	+	4.48846i	−0.120957	+	0.209503i
$460$	29.5650	+	51.2081i	1.37848	+	2.38759i
$461$	16.9910			0.791349			0.395675	−	0.918391i	$-0.370511\pi$
$461$	16.9910			0.791349			0.395675	+	0.918391i	$0.370511\pi$
$462$	3.44777	−	5.97171i	0.160405	−	0.277829i
$463$	−27.4279			−1.27468			−0.637340	−	0.770582i	$-0.719965\pi$
$463$	−27.4279			−1.27468			−0.637340	+	0.770582i	$0.719965\pi$
$464$	0.0521088			0.00241909
$465$		0			0
$466$	30.1392			1.39617
$467$	−22.9105			−1.06017			−0.530086	−	0.847944i	$-0.677840\pi$
$467$	−22.9105			−1.06017			−0.530086	+	0.847944i	$0.677840\pi$
$468$	−10.9222	+	18.9179i	−0.504881	+	0.874479i
$469$	7.73159			0.357012
$470$	−23.1663	−	40.1253i	−1.06858	−	1.85084i
$471$	−10.1639	+	17.6043i	−0.468327	+	0.811165i
$472$	−14.5252	+	25.1583i	−0.668575	+	1.15801i
$473$	0.169102			0.00777531
$474$	13.2836	+	23.0079i	0.610138	+	1.05679i
$475$	2.88091	+	4.98988i	0.132185	+	0.228951i
$476$	−11.6613	−	20.1980i	−0.534496	−	0.925775i
$477$	9.93585	−	17.2094i	0.454931	−	0.787964i
$478$	−27.0468	−	46.8464i	−1.23709	−	2.14270i
$479$	−4.52353	+	7.83498i	−0.206685	+	0.357989i	−0.950668	−	0.310209i	$-0.899601\pi$
$479$	−4.52353	+	7.83498i	−0.206685	+	0.357989i	0.743983	+	0.668198i	$0.232934\pi$
$480$	32.9138			1.50230
$481$	−15.9821			−0.728720
$482$	28.5119	−	49.3841i	1.29868	−	2.24938i
$483$	−14.4972	−	25.1099i	−0.659647	−	1.14254i
$484$	17.3910	−	30.1221i	0.790499	−	1.36918i
$485$	15.3529	+	26.5919i	0.697138	+	1.20748i
$486$	25.7678	+	44.6311i	1.16885	+	2.02451i
$487$	−11.8113	−	20.4578i	−0.535223	−	0.927033i	−0.999153	−	0.0411607i	$-0.986894\pi$
$487$	−11.8113	−	20.4578i	−0.535223	−	0.927033i	0.463930	−	0.885872i	$-0.346439\pi$
$488$	23.9661			1.08490
$489$	21.6963	−	37.5791i	0.981141	−	1.69939i
$490$	−12.7815	+	22.1383i	−0.577411	+	1.00011i
$491$	4.61346	+	7.99074i	0.208202	+	0.360617i	0.951148	−	0.308734i	$-0.0999054\pi$
$491$	4.61346	+	7.99074i	0.208202	+	0.360617i	−0.742946	+	0.669351i	$0.766572\pi$
$492$	−62.3377			−2.81040
$493$	−0.282327	+	0.489005i	−0.0127154	+	0.0220237i
$494$	−20.2914			−0.912955
$495$	6.35220			0.285510
$496$		0			0
$497$	−5.45442			−0.244664
$498$	−15.6680			−0.702101
$499$	14.2070	−	24.6072i	0.635992	−	1.10157i	−0.350313	−	0.936633i	$-0.613925\pi$
$499$	14.2070	−	24.6072i	0.635992	−	1.10157i	0.986304	−	0.164937i	$-0.0527420\pi$
$500$	31.2136			1.39592
$501$	−30.9859	−	53.6692i	−1.38435	−	2.39776i
$502$	−26.7606	+	46.3506i	−1.19438	+	2.06873i
$503$	−9.13903	+	15.8293i	−0.407489	+	0.705792i	−0.994608	−	0.103709i	$-0.966929\pi$
$503$	−9.13903	+	15.8293i	−0.407489	+	0.705792i	0.587118	+	0.809501i	$0.300262\pi$
$504$	16.9686			0.755842
$505$	9.17474	+	15.8911i	0.408271	+	0.707146i
$506$	6.02554	+	10.4365i	0.267868	+	0.463961i
$507$	11.9575	+	20.7110i	0.531052	+	0.919809i
$508$	−2.13949	+	3.70570i	−0.0949243	+	0.164414i
$509$	5.19318	+	8.99485i	0.230184	+	0.398690i	0.957862	−	0.287229i	$-0.0927340\pi$
$509$	5.19318	+	8.99485i	0.230184	+	0.398690i	−0.727678	+	0.685918i	$0.759401\pi$
$510$	32.0987	−	55.5965i	1.42135	−	2.46186i
$511$	−4.31233			−0.190766
$512$	−4.56446			−0.201722
$513$	2.74455	−	4.75370i	0.121175	−	0.209881i
$514$	−17.7058	−	30.6673i	−0.780968	−	1.35268i
$515$	6.98163	−	12.0925i	0.307648	−	0.532861i
$516$	0.974259	+	1.68747i	0.0428894	+	0.0742865i
$517$	−2.94802	−	5.10613i	−0.129654	−	0.224567i
$518$	15.5793	+	26.9841i	0.684514	+	1.18561i
$519$	22.8174			1.00157
$520$	7.23990	−	12.5399i	0.317491	−	0.549910i
$521$	−4.62522	+	8.01111i	−0.202635	+	0.350973i	−0.949376	−	0.314141i	$-0.898284\pi$
$521$	−4.62522	+	8.01111i	−0.202635	+	0.350973i	0.746742	+	0.665114i	$0.231617\pi$
$522$	−0.515537	−	0.892937i	−0.0225645	−	0.0390828i
$523$	6.57516			0.287512			0.143756	−	0.989613i	$-0.454082\pi$
$523$	6.57516			0.287512			0.143756	+	0.989613i	$0.454082\pi$
$524$	13.3326	−	23.0927i	0.582435	−	1.00881i
$525$	5.06005			0.220839
$526$	15.7047			0.684759
$527$		0			0
$528$	−0.753909			−0.0328097
$529$	27.6725			1.20315
$530$	−16.5297	+	28.6303i	−0.718004	+	1.24362i
$531$	32.9346			1.42924
$532$	12.3504	+	21.3916i	0.535460	+	0.927443i
$533$	6.99044	−	12.1078i	0.302790	−	0.524447i
$534$	−6.46760	+	11.2022i	−0.279880	+	0.484767i
$535$	−4.55759			−0.197042
$536$	−7.37678	−	12.7770i	−0.318628	−	0.551881i
$537$	−14.3543	−	24.8624i	−0.619435	−	1.07289i
$538$	12.1372	+	21.0222i	0.523271	+	0.906332i
$539$	−1.62651	+	2.81720i	−0.0700588	+	0.121345i
$540$	4.91541	+	8.51375i	0.211526	+	0.366373i
$541$	1.10164	−	1.90809i	0.0473631	−	0.0820353i	−0.841372	−	0.540457i	$-0.818252\pi$
$541$	1.10164	−	1.90809i	0.0473631	−	0.0820353i	0.888735	+	0.458421i	$0.151585\pi$
$542$	3.63929			0.156321
$543$	37.9909			1.63035
$544$	11.3442	−	19.6488i	0.486380	−	0.842435i
$545$	14.6975	+	25.4569i	0.629574	+	1.09045i
$546$	−8.91001	+	15.4326i	−0.381313	+	0.660454i
$547$	2.43172	+	4.21187i	0.103973	+	0.180086i	0.913318	−	0.407247i	$-0.133511\pi$
$547$	2.43172	+	4.21187i	0.103973	+	0.180086i	−0.809345	+	0.587333i	$0.800178\pi$
$548$	−27.3900	−	47.4408i	−1.17004	−	2.02657i
$549$	−13.5853	−	23.5304i	−0.579807	−	1.00425i
$550$	−2.10313			−0.0896777
$551$	0.299011	−	0.517903i	0.0127383	−	0.0220634i
$552$	−27.6639	+	47.9152i	−1.17745	+	2.03941i
$553$	3.62661	+	6.28147i	0.154219	+	0.267115i
$554$	−27.9242			−1.18639
$555$	−26.7758	+	46.3770i	−1.13657	+	1.96859i
$556$	−24.4025			−1.03490
$557$	−11.0363			−0.467623			−0.233811	−	0.972282i	$-0.575120\pi$
$557$	−11.0363			−0.467623			−0.233811	+	0.972282i	$0.575120\pi$
$558$		0			0
$559$	−0.437007			−0.0184834
$560$	−1.61744			−0.0683494
$561$	4.08471	−	7.07492i	0.172456	−	0.298703i
$562$	−49.5489			−2.09010
$563$	5.59621	+	9.69292i	0.235852	+	0.408508i	0.959520	−	0.281641i	$-0.0908786\pi$
$563$	5.59621	+	9.69292i	0.235852	+	0.408508i	−0.723668	+	0.690148i	$0.757545\pi$
$564$	33.9694	−	58.8366i	1.43037	−	2.47747i
$565$	13.8097	−	23.9190i	0.580976	−	1.00628i
$566$	−1.58944			−0.0668091
$567$	5.91656	+	10.2478i	0.248472	+	0.430366i
$568$	5.20411	+	9.01379i	0.218360	+	0.378210i
$569$	−23.4610	−	40.6356i	−0.983536	−	1.70353i	−0.648270	−	0.761411i	$-0.724507\pi$
$569$	−23.4610	−	40.6356i	−0.983536	−	1.70353i	−0.335266	−	0.942123i	$-0.608826\pi$
$570$	−33.9955	+	58.8819i	−1.42391	+	2.46629i
$571$	−10.2298	−	17.7186i	−0.428105	−	0.741500i	0.568600	−	0.822614i	$-0.307485\pi$
$571$	−10.2298	−	17.7186i	−0.428105	−	0.741500i	−0.996705	+	0.0811145i	$0.974152\pi$
$572$	2.31231	−	4.00503i	0.0966824	−	0.167459i
$573$	5.74892			0.240164
$574$	−27.2570			−1.13769
$575$	−4.42163	+	7.65849i	−0.184395	+	0.319381i
$576$	22.1154	+	38.3050i	0.921474	+	1.59604i
$577$	−1.82417	+	3.15956i	−0.0759413	+	0.131534i	−0.901495	−	0.432789i	$-0.857530\pi$
$577$	−1.82417	+	3.15956i	−0.0759413	+	0.131534i	0.825554	+	0.564323i	$0.190863\pi$
$578$	−2.51260	−	4.35195i	−0.104510	−	0.181017i
$579$	−32.6286	−	56.5143i	−1.35600	−	2.34865i
$580$	0.535521	+	0.927549i	0.0222363	+	0.0385144i
$581$	−4.27758			−0.177464
$582$	−36.0548	+	62.4488i	−1.49452	+	2.58858i
$583$	−2.10348	+	3.64334i	−0.0871173	+	0.150892i
$584$	4.11443	+	7.12641i	0.170256	+	0.294893i
$585$	−16.4159			−0.678713
$586$	−10.3976	+	18.0091i	−0.429520	+	0.743950i
$587$	22.8726			0.944053			0.472027	−	0.881584i	$-0.343523\pi$
$587$	22.8726			0.944053			0.472027	+	0.881584i	$0.343523\pi$
$588$	−37.4838			−1.54580
$589$		0			0
$590$	−54.7914			−2.25573
$591$	15.7540			0.648032
$592$	1.70332	−	2.95024i	0.0700062	−	0.121254i
$593$	−19.4598			−0.799117			−0.399558	−	0.916708i	$-0.630837\pi$
$593$	−19.4598			−0.799117			−0.399558	+	0.916708i	$0.630837\pi$
$594$	1.00179	+	1.73515i	0.0411040	+	0.0711943i
$595$	8.76336	−	15.1786i	0.359263	−	0.622261i
$596$	10.5757	−	18.3176i	0.433197	−	0.750319i
$597$	11.6185			0.475515
$598$	−15.5717	−	26.9710i	−0.636774	−	1.10292i
$599$	−17.5859	−	30.4597i	−0.718541	−	1.24455i	−0.961578	−	0.274533i	$-0.911477\pi$
$599$	−17.5859	−	30.4597i	−0.718541	−	1.24455i	0.243036	−	0.970017i	$-0.421857\pi$
$600$	−4.82784	−	8.36207i	−0.197096	−	0.341380i
$601$	2.94403	−	5.09921i	0.120089	−	0.208001i	−0.799713	−	0.600382i	$-0.795015\pi$
$601$	2.94403	−	5.09921i	0.120089	−	0.208001i	0.919803	+	0.392381i	$0.128349\pi$
$602$	0.425992	+	0.737840i	0.0173621	+	0.0300721i
$603$	−8.36312	+	14.4854i	−0.340573	+	0.589889i
$604$	18.3680			0.747382
$605$	26.1383			1.06267
$606$	−21.5460	+	37.3188i	−0.875248	+	1.51597i
$607$	−19.4424	−	33.6753i	−0.789143	−	1.36684i	−0.926492	−	0.376314i	$-0.877191\pi$
$607$	−19.4424	−	33.6753i	−0.789143	−	1.36684i	0.137349	−	0.990523i	$-0.456142\pi$
$608$	−12.0146	+	20.8099i	−0.487257	+	0.843953i
$609$	−0.262593	−	0.454824i	−0.0106408	−	0.0184304i
$610$	22.6011	+	39.1462i	0.915091	+	1.58498i
$611$	7.61853	+	13.1957i	0.308213	+	0.533840i
$612$	50.4554			2.03954
$613$	−22.8012	+	39.4928i	−0.920931	+	1.59510i	−0.122954	+	0.992412i	$0.539237\pi$
$613$	−22.8012	+	39.4928i	−0.920931	+	1.59510i	−0.797977	+	0.602688i	$0.794096\pi$
$614$	36.1505	−	62.6144i	1.45891	−	2.52691i
$615$	−23.4231	−	40.5699i	−0.944509	−	1.63594i
$616$	−3.59236			−0.144740
$617$	3.31324	−	5.73870i	0.133386	−	0.231031i	−0.791594	−	0.611048i	$-0.790748\pi$
$617$	3.31324	−	5.73870i	0.133386	−	0.231031i	0.924980	+	0.380016i	$0.124082\pi$
$618$	32.7915			1.31907
$619$	−41.5360			−1.66947			−0.834736	−	0.550650i	$-0.814380\pi$
$619$	−41.5360			−1.66947			−0.834736	+	0.550650i	$0.814380\pi$
$620$		0			0
$621$	8.42469			0.338071
$622$	−40.8754			−1.63895
$623$	−1.76574	+	3.05835i	−0.0707429	+	0.122530i
$624$	1.94831			0.0779950
$625$	14.8341	+	25.6934i	0.593364	+	1.02774i
$626$	−25.0006	+	43.3022i	−0.999223	+	1.73071i
$627$	−4.32609	+	7.49300i	−0.172767	+	0.299242i
$628$	26.5791			1.06062
$629$	18.4574	+	31.9691i	0.735943	+	1.27469i
$630$	16.0021	+	27.7165i	0.637540	+	1.10425i
$631$	5.57236	+	9.65160i	0.221832	+	0.384224i	0.955364	−	0.295430i	$-0.0954630\pi$
$631$	5.57236	+	9.65160i	0.221832	+	0.384224i	−0.733532	+	0.679655i	$0.762130\pi$
$632$	6.92036	−	11.9864i	0.275277	−	0.476794i
$633$	23.6687	+	40.9953i	0.940745	+	1.62942i
$634$	−1.17228	+	2.03044i	−0.0465571	+	0.0806392i
$635$	−3.21560			−0.127607
$636$	−48.4758			−1.92219
$637$	4.20336	−	7.28044i	0.166543	−	0.288462i
$638$	0.109143	+	0.189040i	0.00432099	+	0.00748418i
$639$	5.89995	−	10.2190i	0.233398	−	0.404258i
$640$	−23.8478	−	41.3056i	−0.942666	−	1.63275i
$641$	8.77665	+	15.2016i	0.346657	+	0.600427i	0.985653	−	0.168782i	$-0.0539835\pi$
$641$	8.77665	+	15.2016i	0.346657	+	0.600427i	−0.638996	+	0.769210i	$0.720650\pi$
$642$	−5.35154	−	9.26914i	−0.211209	−	0.365824i
$643$	2.19605			0.0866038			0.0433019	−	0.999062i	$-0.486212\pi$
$643$	2.19605			0.0866038			0.0433019	+	0.999062i	$0.486212\pi$
$644$	−18.9555	+	32.8319i	−0.746952	+	1.29376i
$645$	−0.732145	+	1.26811i	−0.0288282	+	0.0499318i
$646$	23.4341	+	40.5891i	0.922003	+	1.59696i
$647$	32.4446			1.27553			0.637764	−	0.770232i	$-0.279860\pi$
$647$	32.4446			1.27553			0.637764	+	0.770232i	$0.279860\pi$
$648$	11.2901	−	19.5550i	0.443516	−	0.768193i
$649$	−6.97247			−0.273693
$650$	5.43508			0.213181
$651$		0			0
$652$	−56.7370			−2.22199
$653$	16.4900			0.645302			0.322651	−	0.946518i	$-0.395426\pi$
$653$	16.4900			0.645302			0.322651	+	0.946518i	$0.395426\pi$
$654$	−34.5158	+	59.7832i	−1.34968	+	2.33771i
$655$	20.0385			0.782970
$656$	1.49004	+	2.58083i	0.0581764	+	0.100764i
$657$	4.66457	−	8.07927i	0.181982	−	0.315202i
$658$	14.8530	−	25.7262i	0.579031	−	1.00291i
$659$	−19.7414			−0.769015			−0.384508	−	0.923122i	$-0.625629\pi$
$659$	−19.7414			−0.769015			−0.384508	+	0.923122i	$0.625629\pi$
$660$	−7.74790	−	13.4198i	−0.301587	−	0.522364i
$661$	−5.89041	−	10.2025i	−0.229110	−	0.396831i	0.728434	−	0.685116i	$-0.240248\pi$
$661$	−5.89041	−	10.2025i	−0.229110	−	0.396831i	−0.957545	+	0.288285i	$0.906915\pi$
$662$	30.7933	+	53.3356i	1.19682	+	2.07295i
$663$	−10.5560	+	18.2836i	−0.409962	+	0.710076i
$664$	4.08127	+	7.06897i	0.158384	+	0.274329i
$665$	−9.28122	+	16.0755i	−0.359910	+	0.623383i
$666$	−67.4072			−2.61198
$667$	0.917847			0.0355392
$668$	−40.5149	+	70.1739i	−1.56757	+	2.71511i
$669$	7.90146	+	13.6857i	0.305488	+	0.529121i
$670$	13.9132	−	24.0984i	0.537516	−	0.931004i
$671$	2.87609	+	4.98154i	0.111030	+	0.192310i
$672$	10.5513	+	18.2754i	0.407024	+	0.704987i
$673$	25.1911	+	43.6322i	0.971044	+	1.68190i	0.692416	+	0.721498i	$0.256546\pi$
$673$	25.1911	+	43.6322i	0.971044	+	1.68190i	0.278628	+	0.960399i	$0.410120\pi$
$674$	−73.7060			−2.83905
$675$	−0.735130	+	1.27328i	−0.0282952	+	0.0490087i
$676$	15.6348	−	27.0802i	0.601337	−	1.04155i
$677$	−1.98998	−	3.44674i	−0.0764810	−	0.132469i	0.825248	−	0.564770i	$-0.191035\pi$
$677$	−1.98998	−	3.44674i	−0.0764810	−	0.132469i	−0.901729	+	0.432301i	$0.857702\pi$
$678$	64.8614			2.49099
$679$	−9.84344	+	17.0493i	−0.377756	+	0.654293i
$680$	−33.4448			−1.28255
$681$	−33.1770			−1.27134
$682$		0			0
$683$	5.23244			0.200214			0.100107	−	0.994977i	$-0.468082\pi$
$683$	5.23244			0.200214			0.100107	+	0.994977i	$0.468082\pi$
$684$	−53.4370			−2.04321
$685$	20.5833	−	35.6512i	0.786446	−	1.36216i
$686$	−42.2643			−1.61366
$687$	19.4238	+	33.6430i	0.741064	+	1.28356i
$688$	0.0465749	−	0.0806701i	0.00177565	−	0.00307552i
$689$	5.43599	−	9.41541i	0.207095	−	0.358699i
$690$	−104.353			−3.97265
$691$	−4.59777	−	7.96356i	−0.174907	−	0.302948i	0.765222	−	0.643767i	$-0.222629\pi$
$691$	−4.59777	−	7.96356i	−0.174907	−	0.302948i	−0.940129	+	0.340818i	$0.889296\pi$
$692$	−14.9172	−	25.8373i	−0.567066	−	0.982187i
$693$	2.03635	+	3.52705i	0.0773544	+	0.133982i
$694$	3.60125	−	6.23756i	0.136702	−	0.236774i
$695$	−9.16912	−	15.8814i	−0.347805	−	0.602415i
$696$	−0.501085	+	0.867904i	−0.0189936	+	0.0328978i
$697$	−32.2924			−1.22316
$698$	−50.8266			−1.92382
$699$	−16.6056	+	28.7617i	−0.628081	+	1.08787i
$700$	−3.30808	−	5.72976i	−0.125034	−	0.216564i
$701$	20.2772	−	35.1211i	0.765858	−	1.32650i	−0.173935	−	0.984757i	$-0.555648\pi$
$701$	20.2772	−	35.1211i	0.765858	−	1.32650i	0.939792	−	0.341747i	$-0.111019\pi$
$702$	−2.58891	−	4.48413i	−0.0977122	−	0.169243i
$703$	−19.5481	−	33.8582i	−0.737269	−	1.27699i
$704$	−4.68197	−	8.10940i	−0.176458	−	0.305635i
$705$	51.0552			1.92285
$706$	5.69081	−	9.85678i	0.214177	−	0.370965i
$707$	−5.88235	+	10.1885i	−0.221229	+	0.383179i
$708$	−40.1710	−	69.5782i	−1.50972	−	2.61491i
$709$	37.2861			1.40031			0.700154	−	0.713992i	$-0.253115\pi$
$709$	37.2861			1.40031			0.700154	+	0.713992i	$0.253115\pi$
$710$	−9.81541	+	17.0008i	−0.368366	+	0.638028i
$711$	−15.6913			−0.588471
$712$	6.73883			0.252548
$713$		0			0
$714$	41.1599			1.54037
$715$	3.47535			0.129971
$716$	−18.7687	+	32.5083i	−0.701418	+	1.21489i
$717$	59.6071			2.22607
$718$	0.416347	+	0.721134i	0.0155379	+	0.0269125i
$719$	−9.28994	+	16.0906i	−0.346456	+	0.600080i	−0.985617	−	0.168993i	$-0.945948\pi$
$719$	−9.28994	+	16.0906i	−0.346456	+	0.600080i	0.639161	+	0.769073i	$0.279282\pi$
$720$	1.74956	−	3.03032i	0.0652022	−	0.112933i
$721$	8.95250			0.333409
$722$	−2.89743	−	5.01850i	−0.107831	−	0.186769i
$723$	31.4180	+	54.4176i	1.16845	+	2.02381i
$724$	−24.8371	−	43.0191i	−0.923063	−	1.59879i
$725$	−0.0800904	+	0.138721i	−0.00297448	+	0.00515196i
$726$	30.6916	+	53.1595i	1.13907	+	1.97293i
$727$	−8.18859	+	14.1830i	−0.303698	+	0.526020i	−0.976971	−	0.213374i	$-0.931555\pi$
$727$	−8.18859	+	14.1830i	−0.303698	+	0.526020i	0.673273	+	0.739394i	$0.264888\pi$
$728$	9.28367			0.344076
$729$	−34.6273			−1.28249
$730$	−7.76017	+	13.4410i	−0.287217	+	0.497474i
$731$	0.504689	+	0.874147i	0.0186666	+	0.0323315i
$732$	−33.1405	+	57.4011i	−1.22491	+	2.12160i
$733$	0.575669	+	0.997088i	0.0212628	+	0.0368283i	0.876461	−	0.481473i	$-0.159898\pi$
$733$	0.575669	+	0.997088i	0.0212628	+	0.0368283i	−0.855198	+	0.518301i	$0.826565\pi$
$734$	−33.9055	−	58.7261i	−1.25148	−	2.16762i
$735$	−14.0843	−	24.3948i	−0.519508	−	0.899814i
$736$	−36.8801			−1.35942
$737$	1.77053	−	3.06664i	0.0652182	−	0.112961i
$738$	29.4834	−	51.0668i	1.08530	−	1.87979i
$739$	−10.3579	−	17.9404i	−0.381022	−	0.659949i	0.610187	−	0.792257i	$-0.291094\pi$
$739$	−10.3579	−	17.9404i	−0.381022	−	0.659949i	−0.991209	+	0.132309i	$0.957761\pi$
$740$	70.0201			2.57399
$741$	11.1798	−	19.3640i	0.410701	−	0.711356i
$742$	−21.1959			−0.778126
$743$	35.2367			1.29271			0.646354	−	0.763038i	$-0.276293\pi$
$743$	35.2367			1.29271			0.646354	+	0.763038i	$0.276293\pi$
$744$		0			0
$745$	15.8950			0.582348
$746$	40.9087			1.49778
$747$	4.62698	−	8.01416i	0.169292	−	0.293223i
$748$	−10.6817			−0.390563
$749$	−1.46104	−	2.53060i	−0.0533853	−	0.0924660i
$750$	−27.5429	+	47.7058i	−1.00573	+	1.74197i
$751$	21.5729	−	37.3654i	0.787207	−	1.36348i	−0.140464	−	0.990086i	$-0.544859\pi$
$751$	21.5729	−	37.3654i	0.787207	−	1.36348i	0.927671	−	0.373398i	$-0.121807\pi$
$752$	−3.24784			−0.118437
$753$	−29.4882	−	51.0750i	−1.07461	−	1.86128i
$754$	−0.282055	−	0.488534i	−0.0102718	−	0.0177913i
$755$	6.90166	+	11.9540i	0.251177	+	0.435052i
$756$	−3.15150	+	5.45856i	−0.114619	+	0.198526i
$757$	−13.6693	−	23.6759i	−0.496819	−	0.860515i	0.503175	−	0.864185i	$-0.332165\pi$
$757$	−13.6693	−	23.6759i	−0.496819	−	0.860515i	−0.999993	+	0.00366955i	$0.998832\pi$
$758$	2.83874	−	4.91685i	0.103108	−	0.178588i
$759$	−13.2794			−0.482011
$760$	35.4212			1.28486
$761$	8.59598	−	14.8887i	0.311604	−	0.539714i	−0.667106	−	0.744963i	$-0.732467\pi$
$761$	8.59598	−	14.8887i	0.311604	−	0.539714i	0.978710	+	0.205249i	$0.0658004\pi$
$762$	−3.77577	−	6.53983i	−0.136782	−	0.236913i
$763$	−9.42328	+	16.3216i	−0.341146	+	0.590882i
$764$	−3.75843	−	6.50979i	−0.135975	−	0.235516i
$765$	18.9583	+	32.8368i	0.685440	+	1.18722i
$766$	−22.0575	−	38.2048i	−0.796972	−	1.38040i
$767$	18.0188			0.650622
$768$	23.5506	−	40.7908i	0.849809	−	1.47191i
$769$	−7.02837	+	12.1735i	−0.253450	+	0.438987i	−0.964473	−	0.264181i	$-0.914899\pi$
$769$	−7.02837	+	12.1735i	−0.253450	+	0.438987i	0.711024	+	0.703168i	$0.248232\pi$
$770$	−3.38775	−	5.86776i	−0.122086	−	0.211459i
$771$	39.0209			1.40530
$772$	−42.6627	+	73.8940i	−1.53546	+	2.65950i
$773$	22.2368			0.799803			0.399902	−	0.916558i	$-0.369044\pi$
$773$	22.2368			0.799803			0.399902	+	0.916558i	$0.369044\pi$
$774$	−1.84315			−0.0662507
$775$		0			0
$776$	37.5668			1.34857
$777$	−34.3344			−1.23174
$778$	6.08156	−	10.5336i	0.218034	−	0.377647i
$779$	34.2007			1.22537
$780$	20.0228	+	34.6804i	0.716930	+	1.24176i
$781$	−1.24906	+	2.16343i	−0.0446948	+	0.0774136i
$782$	−35.9668	+	62.2963i	−1.28617	+	2.22771i
$783$	0.152599			0.00545345
$784$	0.895965	+	1.55186i	0.0319988	+	0.0554235i
$785$	9.98694	+	17.2979i	0.356449	+	0.617388i
$786$	23.5293	+	40.7540i	0.839263	+	1.45365i
$787$	16.0169	−	27.7421i	0.570941	−	0.988899i	−0.425529	−	0.904945i	$-0.639912\pi$
$787$	16.0169	−	27.7421i	0.570941	−	0.988899i	0.996470	−	0.0839540i	$-0.0267549\pi$
$788$	−10.2994	−	17.8390i	−0.366900	−	0.635490i
$789$	−8.65273	+	14.9870i	−0.308045	+	0.533550i
$790$	26.1048			0.928767
$791$	17.7080			0.629625
$792$	3.88579	−	6.73039i	0.138076	−	0.239154i
$793$	−7.43264	−	12.8737i	−0.263941	−	0.457159i
$794$	−19.5280	+	33.8235i	−0.693024	+	1.20035i
$795$	−18.2145	−	31.5484i	−0.646002	−	1.11891i
$796$	−7.59578	−	13.1563i	−0.269225	−	0.466312i
$797$	13.0246	+	22.5593i	0.461356	+	0.799092i	0.999029	−	0.0440614i	$-0.0140297\pi$
$797$	13.0246	+	22.5593i	0.461356	+	0.799092i	−0.537673	+	0.843154i	$0.680696\pi$
$798$	−43.5922			−1.54315
$799$	17.5969	−	30.4788i	0.622535	−	1.07826i
$800$	3.21812	−	5.57395i	0.113778	−	0.197069i
$801$	−3.81994	−	6.61633i	−0.134971	−	0.233776i
$802$	−87.7775			−3.09953
$803$	−0.987519	+	1.71043i	−0.0348488	+	0.0603599i
$804$	40.8027			1.43900
$805$	−28.4897			−1.00413
$806$		0			0
$807$	−26.7486			−0.941594
$808$	22.4496			0.789775
$809$	−4.36471	+	7.55989i	−0.153455	+	0.265792i	−0.932495	−	0.361182i	$-0.882373\pi$
$809$	−4.36471	+	7.55989i	−0.153455	+	0.265792i	0.779040	+	0.626974i	$0.215707\pi$
$810$	42.5881			1.49639
$811$	25.0392	+	43.3692i	0.879245	+	1.52290i	0.852170	+	0.523264i	$0.175286\pi$
$811$	25.0392	+	43.3692i	0.879245	+	1.52290i	0.0270750	+	0.999633i	$0.491381\pi$
$812$	−0.343347	+	0.594695i	−0.0120491	+	0.0208697i
$813$	−2.00511	+	3.47296i	−0.0703225	+	0.121802i
$814$	14.2705			0.500182
$815$	−21.3186	−	36.9249i	−0.746758	−	1.29342i
$816$	−2.25006	−	3.89722i	−0.0787680	−	0.136430i
$817$	−0.534513	−	0.925804i	−0.0187003	−	0.0323898i
$818$	0.575363	−	0.996558i	0.0201171	−	0.0348438i
$819$	−5.26249	−	9.11490i	−0.183886	−	0.318500i
$820$	−30.6263	+	53.0462i	−1.06952	+	1.85246i
$821$	50.7831			1.77234			0.886171	−	0.463359i	$-0.153356\pi$
$821$	50.7831			1.77234			0.886171	+	0.463359i	$0.153356\pi$
$822$	96.6758			3.37195
$823$	−3.16460	+	5.48125i	−0.110311	+	0.191064i	−0.915896	−	0.401416i	$-0.868518\pi$
$823$	−3.16460	+	5.48125i	−0.110311	+	0.191064i	0.805585	+	0.592481i	$0.201851\pi$
$824$	−8.54166	−	14.7946i	−0.297563	−	0.515394i
$825$	1.15875	−	2.00701i	0.0403424	−	0.0698750i
$826$	−17.5647	−	30.4229i	−0.611153	−	1.05855i
$827$	1.84873	+	3.20209i	0.0642865	+	0.111347i	0.896377	−	0.443292i	$-0.146190\pi$
$827$	1.84873	+	3.20209i	0.0642865	+	0.111347i	−0.832091	+	0.554639i	$0.812856\pi$
$828$	−41.0077	−	71.0274i	−1.42511	−	2.46837i
$829$	−26.0416			−0.904461			−0.452230	−	0.891901i	$-0.649372\pi$
$829$	−26.0416			−0.904461			−0.452230	+	0.891901i	$0.649372\pi$
$830$	−7.69763	+	13.3327i	−0.267189	+	0.462784i
$831$	15.3852	−	26.6479i	0.533707	−	0.924407i
$832$	12.0995	+	20.9570i	0.419475	+	0.726553i
$833$	−19.4175			−0.672776
$834$	21.5328	−	37.2960i	0.745621	−	1.29145i
$835$	−60.8930			−2.10729
$836$	11.3130			0.391267
$837$		0			0
$838$	31.1747			1.07691
$839$	7.49300			0.258687			0.129343	−	0.991600i	$-0.458713\pi$
$839$	7.49300			0.258687			0.129343	+	0.991600i	$0.458713\pi$
$840$	15.5535	−	26.9395i	0.536647	−	0.929501i
$841$	−28.9834			−0.999427
$842$	35.6687	+	61.7800i	1.22923	+	2.12908i
$843$	27.2996	−	47.2843i	0.940249	−	1.62856i
$844$	30.9474	−	53.6025i	1.06525	−	1.84507i
$845$	23.4987			0.808380
$846$	32.1325	+	55.6551i	1.10474	+	1.91346i
$847$	8.37922	+	14.5132i	0.287914	+	0.498681i
$848$	1.15870	+	2.00693i	0.0397901	+	0.0689184i
$849$	0.875722	−	1.51680i	0.0300547	−	0.0520563i
$850$	−6.27685	−	10.8718i	−0.215294	−	0.372900i
$851$	30.0025	−	51.9658i	1.02847	−	1.78136i
$852$	−28.7851			−0.986163
$853$	−43.5869			−1.49239			−0.746194	−	0.665728i	$-0.768121\pi$
$853$	−43.5869			−1.49239			−0.746194	+	0.665728i	$0.768121\pi$
$854$	−14.4906	+	25.0985i	−0.495858	+	0.858852i
$855$	−20.0787	−	34.7772i	−0.686675	−	1.18936i
$856$	−2.78799	+	4.82893i	−0.0952914	+	0.165050i
$857$	−19.6114	−	33.9679i	−0.669912	−	1.16032i	−0.977928	−	0.208941i	$-0.932998\pi$
$857$	−19.6114	−	33.9679i	−0.669912	−	1.16032i	0.308016	−	0.951381i	$-0.400335\pi$
$858$	4.08077	+	7.06809i	0.139315	+	0.241301i
$859$	−9.10065	−	15.7628i	−0.310510	−	0.537819i	0.667963	−	0.744195i	$-0.267167\pi$
$859$	−9.10065	−	15.7628i	−0.310510	−	0.537819i	−0.978473	+	0.206375i	$0.933833\pi$
$860$	1.91460			0.0652872
$861$	15.0176	−	26.0113i	0.511799	−	0.886461i
$862$	13.9084	−	24.0900i	0.473721	−	0.820509i
$863$	22.4738	+	38.9258i	0.765018	+	1.32505i	0.940237	+	0.340521i	$0.110603\pi$
$863$	22.4738	+	38.9258i	0.765018	+	1.32505i	−0.175219	+	0.984530i	$0.556063\pi$
$864$	−6.13161			−0.208602
$865$	11.2101	−	19.4164i	0.381155	−	0.660179i
$866$	74.7451			2.53994
$867$	5.53740			0.188060
$868$		0			0
$869$	3.32196			0.112690
$870$	−1.89018			−0.0640830
$871$	−4.57554	+	7.92506i	−0.155036	+	0.268531i
$872$	35.9633			1.21787
$873$	−21.2949	−	36.8839i	−0.720724	−	1.24833i
$874$	38.0922	−	65.9776i	1.28849	−	2.23173i
$875$	−7.51959	+	13.0243i	−0.254208	+	0.440302i
$876$	−22.7579			−0.768917
$877$	21.3255	+	36.9369i	0.720112	+	1.24727i	0.960955	+	0.276706i	$0.0892429\pi$
$877$	21.3255	+	36.9369i	0.720112	+	1.24727i	−0.240843	+	0.970564i	$0.577424\pi$
$878$	−14.2699	−	24.7162i	−0.481587	−	0.834133i
$879$	−11.4574	−	19.8447i	−0.386447	−	0.669346i
$880$	−0.370392	+	0.641538i	−0.0124859	+	0.0216263i
$881$	−4.45826	−	7.72193i	−0.150203	−	0.260159i	0.781099	−	0.624407i	$-0.214659\pi$
$881$	−4.45826	−	7.72193i	−0.150203	−	0.260159i	−0.931302	+	0.364248i	$0.881326\pi$
$882$	17.7284	−	30.7065i	0.596947	−	1.03394i
$883$	−47.0683			−1.58398			−0.791988	−	0.610537i	$-0.790954\pi$
$883$	−47.0683			−1.58398			−0.791988	+	0.610537i	$0.790954\pi$
$884$	27.6046			0.928443
$885$	30.1880	−	52.2872i	1.01476	−	1.75762i
$886$	5.44969	+	9.43914i	0.183086	+	0.317114i
$887$	−1.57828	+	2.73367i	−0.0529936	+	0.0917876i	−0.891305	−	0.453404i	$-0.850210\pi$
$887$	−1.57828	+	2.73367i	−0.0529936	+	0.0917876i	0.838312	+	0.545191i	$0.183543\pi$
$888$	32.7588	+	56.7398i	1.09931	+	1.90406i
$889$	−1.03083	−	1.78546i	−0.0345731	−	0.0598823i
$890$	6.35501	+	11.0072i	0.213020	+	0.368962i
$891$	5.41954			0.181561
$892$	10.3314	−	17.8944i	0.345920	−	0.599150i
$893$	−18.6368	+	32.2799i	−0.623657	+	1.08021i
$894$	18.6640	+	32.3270i	0.624217	+	1.08118i
$895$	−28.2089			−0.942920
$896$	15.2899	−	26.4829i	0.510800	−	0.884732i
$897$	34.3177			1.14583
$898$	36.8840			1.23083
$899$		0			0
$900$	14.3131			0.477105
$901$	−25.1116			−0.836589
$902$	−6.24182	+	10.8112i	−0.207830	+	0.359972i
$903$	−0.938824			−0.0312421
$904$	−16.8954	−	29.2637i	−0.561932	−	0.973295i
$905$	18.6648	−	32.3284i	0.620439	−	1.07463i
$906$	−16.2079	+	28.0729i	−0.538472	+	0.932661i
$907$	26.9632			0.895297			0.447649	−	0.894210i	$-0.352262\pi$
$907$	26.9632			0.895297			0.447649	+	0.894210i	$0.352262\pi$
$908$	21.6899	+	37.5680i	0.719804	+	1.24674i
$909$	−12.7257	−	22.0415i	−0.422084	−	0.731071i
$910$	8.75490	+	15.1639i	0.290222	+	0.502680i
$911$	2.53901	−	4.39769i	0.0841212	−	0.145702i	−0.820895	−	0.571079i	$-0.806525\pi$
$911$	2.53901	−	4.39769i	0.0841212	−	0.145702i	0.905016	+	0.425377i	$0.139858\pi$
$912$	2.38303	+	4.12753i	0.0789100	+	0.136676i
$913$	−0.979560	+	1.69665i	−0.0324187	+	0.0561508i
$914$	−10.5171			−0.347876
$915$	−49.8095			−1.64665
$916$	25.3971	−	43.9891i	0.839144	−	1.45344i
$917$	6.42382	+	11.1264i	0.212133	+	0.367425i
$918$	−5.97976	+	10.3572i	−0.197361	+	0.341840i
$919$	24.6385	+	42.6751i	0.812749	+	1.40772i	0.910933	+	0.412554i	$0.135363\pi$
$919$	24.6385	+	42.6751i	0.812749	+	1.40772i	−0.0981848	+	0.995168i	$0.531304\pi$
$920$	27.1823	+	47.0811i	0.896174	+	1.55222i
$921$	39.8351	+	68.9965i	1.31261	+	2.27351i
$922$	39.2072			1.29122
$923$	3.22791	−	5.59091i	0.106248	−	0.184027i
$924$	4.96754	−	8.60403i	0.163420	−	0.283052i
$925$	5.23597	+	9.06896i	0.172158	+	0.298186i
$926$	−63.2905			−2.07986
$927$	−9.68376	+	16.7728i	−0.318056	+	0.550890i
$928$	−0.668022			−0.0219289
$929$	39.9606			1.31107			0.655533	−	0.755167i	$-0.272444\pi$
$929$	39.9606			1.31107			0.655533	+	0.755167i	$0.272444\pi$
$930$		0			0
$931$	20.5649			0.673989
$932$	43.4245			1.42242
$933$	22.5208	−	39.0072i	0.737299	−	1.27704i
$934$	−52.8666			−1.72985
$935$	−4.01360	−	6.95176i	−0.131259	−	0.227347i
$936$	−10.0420	+	17.3932i	−0.328232	+	0.568515i
$937$	−22.5446	+	39.0485i	−0.736502	+	1.27566i	0.217560	+	0.976047i	$0.430190\pi$
$937$	−22.5446	+	39.0485i	−0.736502	+	1.27566i	−0.954061	+	0.299611i	$0.903143\pi$
$938$	17.8409			0.582525
$939$	−27.5488	−	47.7159i	−0.899020	−	1.55715i
$940$	−33.3780	−	57.8124i	−1.08867	−	1.88563i
$941$	25.0962	+	43.4678i	0.818112	+	1.41701i	0.907072	+	0.420976i	$0.138312\pi$
$941$	25.0962	+	43.4678i	0.818112	+	1.41701i	−0.0889605	+	0.996035i	$0.528354\pi$
$942$	−23.4534	+	40.6225i	−0.764153	+	1.32355i
$943$	26.2457	+	45.4589i	0.854678	+	1.48034i
$944$	−1.92039	+	3.32622i	−0.0625035	+	0.108259i
$945$	−4.73663			−0.154083
$946$	0.390207			0.0126867
$947$	15.1630	−	26.2630i	0.492730	−	0.853434i	−0.507234	−	0.861808i	$-0.669332\pi$
$947$	15.1630	−	26.2630i	0.492730	−	0.853434i	0.999965	+	0.00837391i	$0.00266553\pi$
$948$	19.1390	+	33.1498i	0.621607	+	1.07666i
$949$	2.55203	−	4.42024i	0.0828423	−	0.143487i
$950$	6.64777	+	11.5143i	0.215682	+	0.373573i
$951$	−1.29176	−	2.23740i	−0.0418883	−	0.0725526i
$952$	−10.7215	−	18.5702i	−0.347486	−	0.601864i
$953$	35.4775			1.14923			0.574614	−	0.818425i	$-0.305152\pi$
$953$	35.4775			1.14923			0.574614	+	0.818425i	$0.305152\pi$
$954$	22.9272	−	39.7111i	0.742297	−	1.28570i
$955$	2.82442	−	4.89204i	0.0913961	−	0.158303i
$956$	−38.9689	−	67.4962i	−1.26035	−	2.18298i
$957$	−0.240534			−0.00777536
$958$	−10.4382	+	18.0794i	−0.337242	+	0.584120i
$959$	26.3938			0.852299
$960$	81.0843			2.61698
$961$		0			0
$962$	−36.8791			−1.18903
$963$	6.32153			0.203708
$964$	41.0799	−	71.1524i	1.32309	−	2.29167i
$965$	−64.1211			−2.06413
$966$	−33.4527	−	57.9418i	−1.07632	−	1.86425i
$967$	−17.7222	+	30.6957i	−0.569906	+	0.987107i	0.426668	+	0.904408i	$0.359687\pi$
$967$	−17.7222	+	30.6957i	−0.569906	+	0.987107i	−0.996575	+	0.0826987i	$0.973646\pi$
$968$	15.9894	−	27.6944i	0.513918	−	0.890133i
$969$	−51.6453			−1.65909
$970$	35.4271	+	61.3616i	1.13750	+	1.97020i
$971$	20.0486	+	34.7252i	0.643391	+	1.11439i	0.984671	+	0.174424i	$0.0558063\pi$
$971$	20.0486	+	34.7252i	0.643391	+	1.11439i	−0.341280	+	0.939962i	$0.610860\pi$
$972$	37.1261	+	64.3044i	1.19082	+	2.06256i
$973$	5.87875	−	10.1823i	0.188464	−	0.326429i
$974$	−27.2550	−	47.2070i	−0.873305	−	1.51261i
$975$	−2.99453	+	5.18667i	−0.0959016	+	0.166106i
$976$	3.16860			0.101424
$977$	−38.6708			−1.23719			−0.618595	−	0.785710i	$-0.712298\pi$
$977$	−38.6708			−1.23719			−0.618595	+	0.785710i	$0.712298\pi$
$978$	50.0648	−	86.7148i	1.60090	−	2.77283i
$979$	0.808705	+	1.40072i	0.0258463	+	0.0447671i
$980$	−18.4156	+	31.8968i	−0.588265	+	1.01891i
$981$	−20.3860	−	35.3096i	−0.650874	−	1.12735i
$982$	10.6457	+	18.4389i	0.339717	+	0.588407i
$983$	−10.7898	−	18.6885i	−0.344141	−	0.596070i	0.641056	−	0.767494i	$-0.278497\pi$
$983$	−10.7898	−	18.6885i	−0.344141	−	0.596070i	−0.985197	+	0.171424i	$0.945163\pi$
$984$	−57.3137			−1.82710
$985$	7.73987	−	13.4058i	0.246613	−	0.427146i
$986$	−0.651478	+	1.12839i	−0.0207473	+	0.0359354i
$987$	16.3669	+	28.3483i	0.520965	+	0.902338i
$988$	−29.2359			−0.930116
$989$	0.820373	−	1.42093i	0.0260864	−	0.0451829i
$990$	14.6579			0.465858
$991$	−46.8764			−1.48908			−0.744538	−	0.667580i	$-0.767330\pi$
$991$	−46.8764			−1.48908			−0.744538	+	0.667580i	$0.767330\pi$
$992$		0			0
$993$	−67.8639			−2.15360
$994$	−12.5862			−0.399211
$995$	5.70814	−	9.88680i	0.180960	−	0.313432i
$996$	−22.5744			−0.715299
$997$	−22.2695	−	38.5718i	−0.705281	−	1.22158i	−0.966590	−	0.256327i	$-0.917488\pi$
$997$	−22.2695	−	38.5718i	−0.705281	−	1.22158i	0.261309	−	0.965255i	$-0.415846\pi$
$998$	32.7830	−	56.7818i	1.03773	−	1.79740i
$999$	4.98814	−	8.63971i	0.157818	−	0.273348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.i.439.8		16
31.2	even	5		961.2.g.n.547.2		16
31.3	odd	30		961.2.g.t.448.2		16
31.4	even	5		961.2.g.l.235.1		16
31.5	even	3		961.2.a.j.1.8		8
31.6	odd	6		961.2.c.j.521.8		16
31.7	even	15		961.2.g.j.338.1		16
31.8	even	5		961.2.g.j.816.1		16
31.9	even	15		961.2.d.n.374.1		16
31.10	even	15		961.2.d.q.531.4		16
31.11	odd	30		961.2.d.o.388.1		16
31.12	odd	30		961.2.g.s.844.2		16
31.13	odd	30		961.2.d.p.628.4		16
31.14	even	15		961.2.g.l.732.1		16
31.15	odd	10		961.2.g.s.846.2		16
31.16	even	5		961.2.g.m.846.2		16
31.17	odd	30		31.2.g.a.19.1	yes	16
31.18	even	15		961.2.d.q.628.4		16
31.19	even	15		961.2.g.m.844.2		16
31.20	even	15		961.2.d.n.388.1		16
31.21	odd	30		961.2.d.p.531.4		16
31.22	odd	30		961.2.d.o.374.1		16
31.23	odd	10		961.2.g.k.816.1		16
31.24	odd	30		961.2.g.k.338.1		16
31.25	even	3	inner	961.2.c.i.521.8		16
31.26	odd	6		961.2.a.i.1.8		8
31.27	odd	10		31.2.g.a.18.1	✓	16
31.28	even	15		961.2.g.n.448.2		16
31.29	odd	10		961.2.g.t.547.2		16
31.30	odd	2		961.2.c.j.439.8		16
93.5	odd	6		8649.2.a.be.1.1		8
93.17	even	30		279.2.y.c.19.2		16
93.26	even	6		8649.2.a.bf.1.1		8
93.89	even	10		279.2.y.c.235.2		16
124.27	even	10		496.2.bg.c.49.2		16
124.79	even	30		496.2.bg.c.81.2		16
155.17	even	60		775.2.ck.a.174.4		32
155.27	even	20		775.2.ck.a.49.1		32
155.48	even	60		775.2.ck.a.174.1		32
155.58	even	20		775.2.ck.a.49.4		32
155.79	odd	30		775.2.bl.a.701.2		16
155.89	odd	10		775.2.bl.a.576.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.1	✓	16	31.27	odd	10
31.2.g.a.19.1	yes	16	31.17	odd	30
279.2.y.c.19.2		16	93.17	even	30
279.2.y.c.235.2		16	93.89	even	10
496.2.bg.c.49.2		16	124.27	even	10
496.2.bg.c.81.2		16	124.79	even	30
775.2.bl.a.576.2		16	155.89	odd	10
775.2.bl.a.701.2		16	155.79	odd	30
775.2.ck.a.49.1		32	155.27	even	20
775.2.ck.a.49.4		32	155.58	even	20
775.2.ck.a.174.1		32	155.48	even	60
775.2.ck.a.174.4		32	155.17	even	60
961.2.a.i.1.8		8	31.26	odd	6
961.2.a.j.1.8		8	31.5	even	3
961.2.c.i.439.8		16	1.1	even	1	trivial
961.2.c.i.521.8		16	31.25	even	3	inner
961.2.c.j.439.8		16	31.30	odd	2
961.2.c.j.521.8		16	31.6	odd	6
961.2.d.n.374.1		16	31.9	even	15
961.2.d.n.388.1		16	31.20	even	15
961.2.d.o.374.1		16	31.22	odd	30
961.2.d.o.388.1		16	31.11	odd	30
961.2.d.p.531.4		16	31.21	odd	30
961.2.d.p.628.4		16	31.13	odd	30
961.2.d.q.531.4		16	31.10	even	15
961.2.d.q.628.4		16	31.18	even	15
961.2.g.j.338.1		16	31.7	even	15
961.2.g.j.816.1		16	31.8	even	5
961.2.g.k.338.1		16	31.24	odd	30
961.2.g.k.816.1		16	31.23	odd	10
961.2.g.l.235.1		16	31.4	even	5
961.2.g.l.732.1		16	31.14	even	15
961.2.g.m.844.2		16	31.19	even	15
961.2.g.m.846.2		16	31.16	even	5
961.2.g.n.448.2		16	31.28	even	15
961.2.g.n.547.2		16	31.2	even	5
961.2.g.s.844.2		16	31.12	odd	30
961.2.g.s.846.2		16	31.15	odd	10
961.2.g.t.448.2		16	31.3	odd	30
961.2.g.t.547.2		16	31.29	odd	10
8649.2.a.be.1.1		8	93.5	odd	6
8649.2.a.bf.1.1		8	93.26	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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.30753 q^{2} +(-1.27136 + 2.20206i) q^{3} +3.32468 q^{4} +(1.24923 + 2.16373i) q^{5} +(-2.93370 + 5.08132i) q^{6} +(-0.800939 + 1.38727i) q^{7} +3.05673 q^{8} +(-1.73272 - 3.00116i) q^{9} +(2.88263 + 4.99286i) q^{10} +(0.366828 + 0.635365i) q^{11} +(-4.22687 + 7.32116i) q^{12} +(-0.947988 - 1.64196i) q^{13} +(-1.84819 + 3.20116i) q^{14} -6.35289 q^{15} +0.404135 q^{16} +(-2.18962 + 3.79253i) q^{17} +(-3.99830 - 6.92527i) q^{18} +(2.31901 - 4.01665i) q^{19} +(4.15329 + 7.19371i) q^{20} +(-2.03657 - 3.52744i) q^{21} +(0.846466 + 1.46612i) q^{22} +7.11846 q^{23} +(-3.88622 + 6.73112i) q^{24} +(-0.621150 + 1.07586i) q^{25} +(-2.18751 - 3.78887i) q^{26} +1.18350 q^{27} +(-2.66287 + 4.61222i) q^{28} +0.128939 q^{29} -14.6595 q^{30} -5.18091 q^{32} -1.86549 q^{33} +(-5.05261 + 8.75137i) q^{34} -4.00223 q^{35} +(-5.76075 - 9.97791i) q^{36} +(4.21474 - 7.30014i) q^{37} +(5.35118 - 9.26852i) q^{38} +4.82094 q^{39} +(3.81856 + 6.61394i) q^{40} +(3.68699 + 6.38605i) q^{41} +(-4.69943 - 8.13966i) q^{42} +(0.115246 - 0.199612i) q^{43} +(1.21959 + 2.11239i) q^{44} +(4.32914 - 7.49829i) q^{45} +16.4260 q^{46} -8.03652 q^{47} +(-0.513802 + 0.889932i) q^{48} +(2.21699 + 3.83994i) q^{49} +(-1.43332 + 2.48258i) q^{50} +(-5.56760 - 9.64336i) q^{51} +(-3.15176 - 5.45900i) q^{52} +(2.86712 + 4.96600i) q^{53} +2.73096 q^{54} +(-0.916506 + 1.58743i) q^{55} +(-2.44826 + 4.24051i) q^{56} +(5.89661 + 10.2132i) q^{57} +0.297530 q^{58} +(-4.75186 + 8.23046i) q^{59} -21.1213 q^{60} +7.84044 q^{61} +5.55122 q^{63} -12.7634 q^{64} +(2.36851 - 4.10238i) q^{65} -4.30466 q^{66} +(-2.41329 - 4.17994i) q^{67} +(-7.27978 + 12.6090i) q^{68} +(-9.05014 + 15.6753i) q^{69} -9.23525 q^{70} +(1.70251 + 2.94883i) q^{71} +(-5.29647 - 9.17376i) q^{72} +(1.34602 + 2.33138i) q^{73} +(9.72562 - 16.8453i) q^{74} +(-1.57941 - 2.73562i) q^{75} +(7.70998 - 13.3541i) q^{76} -1.17523 q^{77} +11.1245 q^{78} +(2.26397 - 3.92132i) q^{79} +(0.504858 + 0.874439i) q^{80} +(3.69351 - 6.39735i) q^{81} +(8.50783 + 14.7360i) q^{82} +(1.33517 + 2.31259i) q^{83} +(-6.77093 - 11.7276i) q^{84} -10.9414 q^{85} +(0.265933 - 0.460609i) q^{86} +(-0.163928 + 0.283932i) q^{87} +(1.12130 + 1.94214i) q^{88} +2.20459 q^{89} +(9.98960 - 17.3025i) q^{90} +3.03712 q^{91} +23.6666 q^{92} -18.5445 q^{94} +11.5879 q^{95} +(6.58682 - 11.4087i) q^{96} +12.2899 q^{97} +(5.11577 + 8.86077i) q^{98} +(1.27122 - 2.20182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 3 q^{3} + 16 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} - 18 q^{11} - 8 q^{13} + 9 q^{14} + 36 q^{15} + 8 q^{16} - 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 3 * q^3 + 16 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 - 18 * q^11 - 8 * q^13 + 9 * q^14 + 36 * q^15 + 8 * q^16 - 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 + q^21 - 4 * q^22 + 44 * q^23 - 30 * q^24 - 13 * q^25 - 9 * q^26 + 36 * q^27 + 5 * q^28 + 24 * q^29 + 22 * q^30 - 42 * q^32 + 12 * q^33 + 7 * q^34 - 24 * q^35 + q^36 + 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 + 36 * q^46 - 36 * q^47 + q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 + q^52 - 6 * q^53 - 14 * q^54 - 28 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 4 * q^59 - 80 * q^60 + 60 * q^61 - 46 * q^63 + 18 * q^64 - 3 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 + 33 * q^76 - 48 * q^77 - 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 - 39 * q^83 - 8 * q^84 - 52 * q^85 + 16 * q^86 + 15 * q^87 + 17 * q^88 + 54 * q^89 - 8 * q^90 + 32 * q^91 + 64 * q^92 + 44 * q^94 - 12 * q^95 + 12 * q^96 + 68 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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