LMFDB - Embedded newform 980.2.x.j.667.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,4,0,0,0,0,0,16,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.4
Character	$\chi$	$=$	980.667
Dual form			980.2.x.j.263.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.939280 + 1.05724i) q^{2} +(0.815107 - 3.04202i) q^{3} +(-0.235506 - 1.98609i) q^{4} +(0.727838 - 2.11430i) q^{5} +(2.45053 + 3.71907i) q^{6} +(2.32097 + 1.61650i) q^{8} +(-5.99142 - 3.45915i) q^{9} +(1.55167 + 2.75542i) q^{10} +(-3.44275 + 1.98767i) q^{11} +(-6.23368 - 0.902458i) q^{12} +(-2.52606 + 2.52606i) q^{13} +(-5.83847 - 3.93748i) q^{15} +(-3.88907 + 0.935470i) q^{16} +(-0.277420 + 1.03535i) q^{17} +(9.28476 - 3.08525i) q^{18} +(-0.658126 + 1.13991i) q^{19} +(-4.37059 - 0.947619i) q^{20} +(1.13226 - 5.50679i) q^{22} +(-5.02084 + 1.34533i) q^{23} +(6.80928 - 5.74282i) q^{24} +(-3.94050 - 3.07773i) q^{25} +(-0.297970 - 5.04332i) q^{26} +(-8.72570 + 8.72570i) q^{27} -4.50936i q^{29} +(9.64681 - 2.47426i) q^{30} +(-2.23010 + 1.28755i) q^{31} +(2.66391 - 4.99035i) q^{32} +(3.24033 + 12.0931i) q^{33} +(-0.834032 - 1.26578i) q^{34} +(-5.45915 + 12.7141i) q^{36} +(7.29473 - 1.95462i) q^{37} +(-0.586989 - 1.76649i) q^{38} +(5.62531 + 9.74333i) q^{39} +(5.10706 - 3.73067i) q^{40} +11.3180 q^{41} +(-1.77452 - 1.77452i) q^{43} +(4.75847 + 6.36949i) q^{44} +(-11.6744 + 10.1499i) q^{45} +(3.29364 - 6.57186i) q^{46} +(-1.76949 - 6.60383i) q^{47} +(-0.324292 + 12.5932i) q^{48} +(6.95513 - 1.27520i) q^{50} +(2.92342 + 1.68784i) q^{51} +(5.61187 + 4.42207i) q^{52} +(-8.08454 - 2.16624i) q^{53} +(-1.02927 - 17.4210i) q^{54} +(1.69676 + 8.72570i) q^{55} +(2.93118 + 2.93118i) q^{57} +(4.76746 + 4.23555i) q^{58} +(-4.17259 - 7.22714i) q^{59} +(-6.44517 + 12.5230i) q^{60} +(0.673601 - 1.16671i) q^{61} +(0.733444 - 3.56712i) q^{62} +(2.77382 + 7.50373i) q^{64} +(3.50228 + 7.17940i) q^{65} +(-15.8288 - 7.93298i) q^{66} +(-5.32697 - 1.42736i) q^{67} +(2.12162 + 0.307150i) q^{68} +16.3701i q^{69} +3.47330i q^{71} +(-8.31418 - 17.7137i) q^{72} +(2.33220 + 0.624911i) q^{73} +(-4.78530 + 9.54820i) q^{74} +(-12.5745 + 9.47841i) q^{75} +(2.41895 + 1.03864i) q^{76} +(-15.5848 - 3.20442i) q^{78} +(1.72570 - 2.98900i) q^{79} +(-0.852754 + 8.90353i) q^{80} +(9.05394 + 15.6819i) q^{81} +(-10.6307 + 11.9658i) q^{82} +(-8.37751 - 8.37751i) q^{83} +(1.98711 + 1.34011i) q^{85} +(3.54285 - 0.209319i) q^{86} +(-13.7176 - 3.67561i) q^{87} +(-11.2036 - 0.951889i) q^{88} +(8.15730 + 4.70962i) q^{89} +(0.234670 - 21.8763i) q^{90} +(3.85438 + 9.65498i) q^{92} +(2.09898 + 7.83352i) q^{93} +(8.64387 + 4.33207i) q^{94} +(1.93109 + 2.22114i) q^{95} +(-13.0094 - 12.1714i) q^{96} +(-9.04418 - 9.04418i) q^{97} +27.5026 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 16 q^{8} - 8 q^{16} + 40 q^{18} - 72 q^{22} - 32 q^{25} + 36 q^{30} - 16 q^{32} - 176 q^{36} + 48 q^{37} + 56 q^{50} - 16 q^{53} - 32 q^{57} - 36 q^{58} + 80 q^{60} - 64 q^{65} - 56 q^{72}+ \cdots - 32 q^{93}+O(q^{100}) $ 64 * q + 4 * q^2 + 16 * q^8 - 8 * q^16 + 40 * q^18 - 72 * q^22 - 32 * q^25 + 36 * q^30 - 16 * q^32 - 176 * q^36 + 48 * q^37 + 56 * q^50 - 16 * q^53 - 32 * q^57 - 36 * q^58 + 80 * q^60 - 64 * q^65 - 56 * q^72 + 56 * q^78 - 56 * q^86 - 88 * q^88 + 272 * q^92 - 32 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.939280	+	1.05724i	−0.664171	+	0.747580i
$2$	−0.939280	+	1.05724i	−0.664171	+	0.747580i
$3$	0.815107	−	3.04202i	0.470602	−	1.75631i	−0.167011	−	0.985955i	$-0.553412\pi$
$3$	0.815107	−	3.04202i	0.470602	−	1.75631i	0.637613	−	0.770357i	$-0.279922\pi$
$4$	−0.235506	−	1.98609i	−0.117753	−	0.993043i
$5$	0.727838	−	2.11430i	0.325499	−	0.945542i
$5$	0.727838	−	2.11430i	0.325499	−	0.945542i
$6$	2.45053	+	3.71907i	1.00042	+	1.51830i
$7$		0			0
$7$		0			0
$8$	2.32097	+	1.61650i	0.820588	+	0.571521i
$9$	−5.99142	−	3.45915i	−1.99714	−	1.15305i
$10$	1.55167	+	2.75542i	0.490682	+	0.871339i
$11$	−3.44275	+	1.98767i	−1.03803	+	0.599306i	−0.919274	−	0.393618i	$-0.871223\pi$
$11$	−3.44275	+	1.98767i	−1.03803	+	0.599306i	−0.118754	+	0.992924i	$0.537890\pi$
$12$	−6.23368	−	0.902458i	−1.79951	−	0.260517i
$13$	−2.52606	+	2.52606i	−0.700602	+	0.700602i	−0.964540	−	0.263937i	$-0.914979\pi$
$13$	−2.52606	+	2.52606i	−0.700602	+	0.700602i	0.263937	+	0.964540i	$0.414979\pi$
$14$		0			0
$15$	−5.83847	−	3.93748i	−1.50749	−	1.01665i
$16$	−3.88907	+	0.935470i	−0.972268	+	0.233868i
$17$	−0.277420	+	1.03535i	−0.0672843	+	0.251108i	−0.991373	−	0.131069i	$-0.958159\pi$
$17$	−0.277420	+	1.03535i	−0.0672843	+	0.251108i	0.924089	+	0.382177i	$0.124826\pi$
$18$	9.28476	−	3.08525i	2.18844	−	0.727200i
$19$	−0.658126	+	1.13991i	−0.150984	+	0.261513i	−0.931590	−	0.363512i	$-0.881578\pi$
$19$	−0.658126	+	1.13991i	−0.150984	+	0.261513i	0.780605	+	0.625024i	$0.214911\pi$
$20$	−4.37059	−	0.947619i	−0.977293	−	0.211894i
$21$		0			0
$22$	1.13226	−	5.50679i	0.241399	−	1.17405i
$23$	−5.02084	+	1.34533i	−1.04692	+	0.280521i	−0.740977	−	0.671530i	$-0.765637\pi$
$23$	−5.02084	+	1.34533i	−1.04692	+	0.280521i	−0.305940	+	0.952051i	$0.598971\pi$
$24$	6.80928	−	5.74282i	1.38994	−	1.17225i
$25$	−3.94050	−	3.07773i	−0.788101	−	0.615546i
$26$	−0.297970	−	5.04332i	−0.0584366	−	0.989077i
$27$	−8.72570	+	8.72570i	−1.67926	+	1.67926i
$28$		0			0
$29$		−	4.50936i		−	0.837366i	−0.908132	−	0.418683i	$-0.862492\pi$
$29$		−	4.50936i		−	0.837366i	0.908132	−	0.418683i	$-0.137508\pi$
$30$	9.64681	−	2.47426i	1.76126	−	0.451736i
$31$	−2.23010	+	1.28755i	−0.400539	+	0.231251i	−0.686716	−	0.726925i	$-0.740949\pi$
$31$	−2.23010	+	1.28755i	−0.400539	+	0.231251i	0.286178	+	0.958177i	$0.407615\pi$
$32$	2.66391	−	4.99035i	0.470918	−	0.882177i
$33$	3.24033	+	12.0931i	0.564069	+	2.10513i
$34$	−0.834032	−	1.26578i	−0.143035	−	0.217079i
$35$		0			0
$36$	−5.45915	+	12.7141i	−0.909858	+	2.11902i
$37$	7.29473	−	1.95462i	1.19925	−	0.321337i	0.396712	−	0.917943i	$-0.370151\pi$
$37$	7.29473	−	1.95462i	1.19925	−	0.321337i	0.802534	+	0.596606i	$0.203485\pi$
$38$	−0.586989	−	1.76649i	−0.0952222	−	0.286562i
$39$	5.62531	+	9.74333i	0.900771	+	1.56018i
$40$	5.10706	−	3.73067i	0.807498	−	0.589871i
$41$	11.3180			1.76757			0.883784	−	0.467894i	$-0.154987\pi$
$41$	11.3180			1.76757			0.883784	+	0.467894i	$0.154987\pi$
$42$		0			0
$43$	−1.77452	−	1.77452i	−0.270611	−	0.270611i	0.558735	−	0.829346i	$-0.311287\pi$
$43$	−1.77452	−	1.77452i	−0.270611	−	0.270611i	−0.829346	+	0.558735i	$0.811287\pi$
$44$	4.75847	+	6.36949i	0.717367	+	0.960236i
$45$	−11.6744	+	10.1499i	−1.74032	+	1.51306i
$46$	3.29364	−	6.57186i	0.485620	−	0.968968i
$47$	−1.76949	−	6.60383i	−0.258107	−	0.963268i	−0.966336	−	0.257285i	$-0.917172\pi$
$47$	−1.76949	−	6.60383i	−0.258107	−	0.963268i	0.708229	−	0.705983i	$-0.249495\pi$
$48$	−0.324292	+	12.5932i	−0.0468075	+	1.81766i
$49$		0			0
$50$	6.95513	−	1.27520i	0.983604	−	0.180340i
$51$	2.92342	+	1.68784i	0.409360	+	0.236344i
$52$	5.61187	+	4.42207i	0.778226	+	0.613230i
$53$	−8.08454	−	2.16624i	−1.11050	−	0.297557i	−0.343465	−	0.939166i	$-0.611601\pi$
$53$	−8.08454	−	2.16624i	−1.11050	−	0.297557i	−0.767032	+	0.641609i	$0.778267\pi$
$54$	−1.02927	−	17.4210i	−0.140066	−	2.37070i
$55$	1.69676	+	8.72570i	0.228792	+	1.17657i
$56$		0			0
$57$	2.93118	+	2.93118i	0.388244	+	0.388244i
$58$	4.76746	+	4.23555i	0.625999	+	0.556155i
$59$	−4.17259	−	7.22714i	−0.543225	−	0.940893i	−0.998716	−	0.0506532i	$-0.983870\pi$
$59$	−4.17259	−	7.22714i	−0.543225	−	0.940893i	0.455491	−	0.890240i	$-0.349464\pi$
$60$	−6.44517	+	12.5230i	−0.832068	+	1.61671i
$61$	0.673601	−	1.16671i	0.0862458	−	0.149382i	−0.819676	−	0.572828i	$-0.805846\pi$
$61$	0.673601	−	1.16671i	0.0862458	−	0.149382i	0.905921	+	0.423446i	$0.139180\pi$
$62$	0.733444	−	3.56712i	0.0931475	−	0.453025i
$63$		0			0
$64$	2.77382	+	7.50373i	0.346728	+	0.937966i
$65$	3.50228	+	7.17940i	0.434404	+	0.890495i
$66$	−15.8288	−	7.93298i	−1.94840	−	0.976483i
$67$	−5.32697	−	1.42736i	−0.650793	−	0.174379i	−0.0817054	−	0.996657i	$-0.526037\pi$
$67$	−5.32697	−	1.42736i	−0.650793	−	0.174379i	−0.569087	+	0.822277i	$0.692703\pi$
$68$	2.12162	+	0.307150i	0.257284	+	0.0372474i
$69$			16.3701i			1.97073i
$70$		0			0
$71$			3.47330i			0.412205i	0.978530	+	0.206102i	$0.0660780\pi$
$71$			3.47330i			0.412205i	−0.978530	+	0.206102i	$0.933922\pi$
$72$	−8.31418	−	17.7137i	−0.979836	−	2.08758i
$73$	2.33220	+	0.624911i	0.272963	+	0.0731403i	0.392704	−	0.919665i	$-0.371540\pi$
$73$	2.33220	+	0.624911i	0.272963	+	0.0731403i	−0.119741	+	0.992805i	$0.538206\pi$
$74$	−4.78530	+	9.54820i	−0.556280	+	1.10996i
$75$	−12.5745	+	9.47841i	−1.45197	+	1.09447i
$76$	2.41895	+	1.03864i	0.277472	+	0.119140i
$77$		0			0
$78$	−15.5848	−	3.20442i	−1.76463	−	0.362829i
$79$	1.72570	−	2.98900i	0.194157	−	0.336289i	−0.752467	−	0.658630i	$-0.771136\pi$
$79$	1.72570	−	2.98900i	0.194157	−	0.336289i	0.946624	+	0.322341i	$0.104470\pi$
$80$	−0.852754	+	8.90353i	−0.0953408	+	0.995445i
$81$	9.05394	+	15.6819i	1.00599	+	1.74243i
$82$	−10.6307	+	11.9658i	−1.17397	+	1.32140i
$83$	−8.37751	−	8.37751i	−0.919551	−	0.919551i	0.0774458	−	0.996997i	$-0.475324\pi$
$83$	−8.37751	−	8.37751i	−0.919551	−	0.919551i	−0.996997	+	0.0774458i	$0.975324\pi$
$84$		0			0
$85$	1.98711	+	1.34011i	0.215533	+	0.145356i
$86$	3.54285	−	0.209319i	0.382036	−	0.0225714i
$87$	−13.7176	−	3.67561i	−1.47068	−	0.394066i
$88$	−11.2036	−	0.951889i	−1.19431	−	0.101472i
$89$	8.15730	+	4.70962i	0.864672	+	0.499219i	0.865574	−	0.500781i	$-0.166954\pi$
$89$	8.15730	+	4.70962i	0.864672	+	0.499219i	−0.000902138		1.00000i	$0.500287\pi$
$90$	0.234670	−	21.8763i	0.0247364	−	2.30596i
$91$		0			0
$92$	3.85438	+	9.65498i	0.401846	+	1.00660i
$93$	2.09898	+	7.83352i	0.217655	+	0.812298i
$94$	8.64387	+	4.33207i	0.891547	+	0.446819i
$95$	1.93109	+	2.22114i	0.198126	+	0.227884i
$96$	−13.0094	−	12.1714i	−1.32776	−	1.24223i
$97$	−9.04418	−	9.04418i	−0.918298	−	0.918298i	0.0786079	−	0.996906i	$-0.474952\pi$
$97$	−9.04418	−	9.04418i	−0.918298	−	0.918298i	−0.996906	+	0.0786079i	$0.974952\pi$
$98$		0			0
$99$	27.5026			2.76411
$100$	−5.18463	+	8.55100i	−0.518463	+	0.855100i
$101$	−5.13644	−	8.89658i	−0.511095	−	0.885242i	−0.999917	−	0.0128590i	$-0.995907\pi$
$101$	−5.13644	−	8.89658i	−0.511095	−	0.885242i	0.488822	−	0.872383i	$-0.337427\pi$
$102$	−4.53035	+	1.50540i	−0.448572	+	0.149057i
$103$	4.03745	−	1.08183i	0.397821	−	0.106596i	−0.0543611	−	0.998521i	$-0.517312\pi$
$103$	4.03745	−	1.08183i	0.397821	−	0.106596i	0.452183	+	0.891925i	$0.350646\pi$
$104$	−9.94629	+	1.77953i	−0.975314	+	0.174497i
$105$		0			0
$106$	9.88388	−	6.51257i	0.960007	−	0.632557i
$107$	−4.11801	−	15.3686i	−0.398104	−	1.48574i	−0.816429	−	0.577446i	$-0.804050\pi$
$107$	−4.11801	−	15.3686i	−0.398104	−	1.48574i	0.418326	−	0.908297i	$-0.362617\pi$
$108$	19.3849	+	15.2750i	1.86532	+	1.46984i
$109$	2.58551	−	1.49274i	0.247647	−	0.142979i	−0.371040	−	0.928617i	$-0.620999\pi$
$109$	2.58551	−	1.49274i	0.247647	−	0.142979i	0.618686	+	0.785638i	$0.287665\pi$
$110$	−10.8189	−	6.40199i	−1.03154	−	0.610405i
$111$		−	23.7839i		−	2.25747i
$112$		0			0
$113$	−0.407307	+	0.407307i	−0.0383162	+	0.0383162i	−0.726005	−	0.687689i	$-0.758625\pi$
$113$	−0.407307	+	0.407307i	−0.0383162	+	0.0383162i	0.687689	+	0.726005i	$0.258625\pi$
$114$	−5.85215	+	0.345757i	−0.548104	+	0.0323831i
$115$	−0.809931	+	11.5947i	−0.0755265	+	1.08121i
$116$	−8.95597	+	1.06198i	−0.831541	+	0.0986024i
$117$	23.8727	−	6.39666i	2.20703	−	0.591371i
$118$	11.5600	+	2.37688i	1.06419	+	0.218810i
$119$		0			0
$120$	−7.18598	−	18.5767i	−0.655987	−	1.69581i
$121$	2.40168	−	4.15983i	0.218334	−	0.378166i
$122$	0.600792	+	1.80803i	0.0543932	+	0.163691i
$123$	9.22535	−	34.4295i	0.831822	−	3.10440i
$124$	3.08239	+	4.12595i	0.276807	+	0.370522i
$125$	−9.37529	+	6.09130i	−0.838551	+	0.544823i
$126$		0			0
$127$	−10.3756	+	10.3756i	−0.920687	+	0.920687i	−0.997078	−	0.0763907i	$-0.975660\pi$
$127$	−10.3756	+	10.3756i	−0.920687	+	0.920687i	0.0763907	+	0.997078i	$0.475660\pi$
$128$	−10.5386	−	4.11551i	−0.931492	−	0.363763i
$129$	−6.84453	+	3.95169i	−0.602627	+	0.347927i
$130$	−10.8800	−	3.04072i	−0.954235	−	0.266689i
$131$	8.53900	+	4.92999i	0.746056	+	0.430736i	0.824267	−	0.566201i	$-0.191588\pi$
$131$	8.53900	+	4.92999i	0.746056	+	0.430736i	−0.0782112	+	0.996937i	$0.524921\pi$
$132$	23.2548	−	9.28357i	2.02407	−	0.808031i
$133$		0			0
$134$	6.51257	−	4.29119i	0.562600	−	0.370702i
$135$	12.0978	+	24.7996i	1.04121	+	2.13441i
$136$	−2.31753	+	1.95456i	−0.198726	+	0.167602i
$137$	4.17809	−	15.5929i	0.356958	−	1.33219i	−0.521044	−	0.853530i	$-0.674457\pi$
$137$	4.17809	−	15.5929i	0.356958	−	1.33219i	0.878002	−	0.478657i	$-0.158876\pi$
$138$	−17.3071	−	15.3761i	−1.47328	−	1.30890i
$139$	9.10621			0.772379			0.386189	−	0.922420i	$-0.373791\pi$
$139$	9.10621			0.772379			0.386189	+	0.922420i	$0.373791\pi$
$140$		0			0
$141$	−21.5313			−1.81326
$142$	−3.67210	−	3.26240i	−0.308156	−	0.273774i
$143$	3.67561	−	13.7176i	0.307370	−	1.14712i
$144$	26.5370	+	7.84808i	2.21142	+	0.654007i
$145$	−9.53412	−	3.28208i	−0.791765	−	0.272562i
$146$	−2.85127	+	1.87872i	−0.235973	+	0.155484i
$147$		0			0
$148$	−5.59999	−	14.0276i	−0.460316	−	1.15306i
$149$	−1.70973	−	0.987112i	−0.140066	−	0.0808674i	0.428329	−	0.903623i	$-0.359102\pi$
$149$	−1.70973	−	0.987112i	−0.140066	−	0.0808674i	−0.568396	+	0.822755i	$0.692436\pi$
$150$	1.78999	−	22.1971i	0.146152	−	1.81238i
$151$	−7.47376	+	4.31498i	−0.608206	+	0.351148i	−0.772263	−	0.635303i	$-0.780875\pi$
$151$	−7.47376	+	4.31498i	−0.608206	+	0.351148i	0.164057	+	0.986451i	$0.447542\pi$
$152$	−3.37016	+	1.58183i	−0.273356	+	0.128303i
$153$	5.24355	−	5.24355i	0.423916	−	0.423916i
$154$		0			0
$155$	1.09911	+	5.65223i	0.0882827	+	0.453998i
$156$	18.0263	−	13.4670i	1.44326	−	1.07822i
$157$	−4.10320	+	15.3134i	−0.327471	+	1.22214i	0.584333	+	0.811514i	$0.301356\pi$
$157$	−4.10320	+	15.3134i	−0.327471	+	1.22214i	−0.911804	+	0.410625i	$0.865311\pi$
$158$	1.53917	+	4.63199i	0.122450	+	0.368501i
$159$	−13.1795	+	22.8276i	−1.04520	+	1.81035i
$160$	−8.61218	−	9.26447i	−0.680852	−	0.732421i
$161$		0			0
$162$	−25.0837	−	5.15751i	−1.97076	−	0.405212i
$163$	6.72849	−	1.80289i	0.527016	−	0.141213i	0.0145060	−	0.999895i	$-0.495382\pi$
$163$	6.72849	−	1.80289i	0.527016	−	0.141213i	0.512510	+	0.858681i	$0.328716\pi$
$164$	−2.66545	−	22.4784i	−0.208136	−	1.75527i
$165$	27.9268	+	1.95078i	2.17410	+	0.151868i
$166$	16.7258	−	0.988197i	1.29818	−	0.0766989i
$167$	−11.9207	+	11.9207i	−0.922449	+	0.922449i	−0.997202	−	0.0747528i	$-0.976183\pi$
$167$	−11.9207	+	11.9207i	−0.922449	+	0.922449i	0.0747528	+	0.997202i	$0.476183\pi$
$168$		0			0
$169$			0.238064i			0.0183127i
$170$	−3.28327	+	0.842110i	−0.251816	+	0.0645869i
$171$	7.88621	−	4.55310i	0.603073	−	0.348185i
$172$	−3.10643	+	3.94225i	−0.236863	+	0.300594i
$173$	−0.0573054	−	0.213867i	−0.00435685	−	0.0162600i	0.963713	−	0.266940i	$-0.0860125\pi$
$173$	−0.0573054	−	0.213867i	−0.00435685	−	0.0162600i	−0.968070	+	0.250680i	$0.919346\pi$
$174$	16.7706	−	11.0503i	1.27138	−	0.837721i
$175$		0			0
$176$	11.5297	−	10.9508i	0.869083	−	0.825447i
$177$	−25.3862	+	6.80222i	−1.90814	+	0.511286i
$178$	−12.6412	+	4.20056i	−0.947496	+	0.314845i
$179$	−10.2023	−	17.6708i	−0.762553	−	1.32078i	−0.941531	−	0.336927i	$-0.890612\pi$
$179$	−10.2023	−	17.6708i	−0.762553	−	1.32078i	0.178978	−	0.983853i	$-0.442721\pi$
$180$	22.9080	+	20.7961i	1.70746	+	1.55005i
$181$	13.1697			0.978898			0.489449	−	0.872032i	$-0.337198\pi$
$181$	13.1697			0.978898			0.489449	+	0.872032i	$0.337198\pi$
$182$		0			0
$183$	−3.00010	−	3.00010i	−0.221774	−	0.221774i
$184$	−13.8280	−	4.99374i	−1.01941	−	0.368143i
$185$	1.17674	−	16.8459i	0.0865158	−	1.23853i
$186$	−10.2534	−	5.13874i	−0.751818	−	0.376791i
$187$	−1.10284	−	4.11586i	−0.0806477	−	0.300981i
$188$	−12.6991	+	5.06960i	−0.926174	+	0.369739i
$189$		0			0
$190$	−4.16211	−	0.0446475i	−0.301951	−	0.00323907i
$191$	−10.4817	−	6.05163i	−0.758431	−	0.437880i	0.0703012	−	0.997526i	$-0.477604\pi$
$191$	−10.4817	−	6.05163i	−0.758431	−	0.437880i	−0.828732	+	0.559646i	$0.810937\pi$
$192$	25.0875	−	2.32169i	1.81053	−	0.167554i
$193$	−0.678188	−	0.181720i	−0.0488170	−	0.0130805i	0.234328	−	0.972158i	$-0.424711\pi$
$193$	−0.678188	−	0.181720i	−0.0488170	−	0.0130805i	−0.283145	+	0.959077i	$0.591378\pi$
$194$	18.0569	−	1.06684i	1.29641	−	0.0765944i
$195$	24.6946	−	4.80202i	1.76842	−	0.343880i
$196$		0			0
$197$	−1.16924	−	1.16924i	−0.0833051	−	0.0833051i	0.664226	−	0.747531i	$-0.268761\pi$
$197$	−1.16924	−	1.16924i	−0.0833051	−	0.0833051i	−0.747531	+	0.664226i	$0.768761\pi$
$198$	−25.8326	+	29.0768i	−1.83584	+	2.06640i
$199$	8.72570	+	15.1133i	0.618548	+	1.07136i	0.989751	+	0.142805i	$0.0456122\pi$
$199$	8.72570	+	15.1133i	0.618548	+	1.07136i	−0.371203	+	0.928552i	$0.621054\pi$
$200$	−4.17063	−	13.5132i	−0.294908	−	0.955526i
$201$	−8.68410	+	15.0413i	−0.612529	+	1.06093i
$202$	14.2304	+	2.92593i	1.00124	+	0.205868i
$203$		0			0
$204$	2.66370	−	6.20365i	0.186497	−	0.434343i
$205$	8.23764	−	23.9295i	0.575342	−	1.67131i
$206$	−2.64854	+	5.28469i	−0.184533	+	0.368202i
$207$	34.7356	+	9.30738i	2.41429	+	0.646907i
$208$	7.46097	−	12.1871i	0.517325	−	0.845022i
$209$		−	5.23255i		−	0.361943i
$210$		0			0
$211$			6.32503i			0.435433i	0.976012	+	0.217717i	$0.0698608\pi$
$211$			6.32503i			0.435433i	−0.976012	+	0.217717i	$0.930139\pi$
$212$	−2.39839	+	16.5667i	−0.164722	+	1.13781i
$213$	10.5658	+	2.83111i	0.723960	+	0.193984i
$214$	20.1163	+	10.0817i	1.37512	+	0.689173i
$215$	−5.04341	+	2.46029i	−0.343958	+	0.167791i
$216$	−34.3572	+	6.14697i	−2.33771	+	0.418248i
$217$		0			0
$218$	−0.850329	+	4.13560i	−0.0575916	+	0.280098i
$219$	3.80199	−	6.58523i	0.256914	−	0.444989i
$220$	16.9304	−	5.42487i	1.14145	−	0.365745i
$221$	−1.91456	−	3.31612i	−0.128788	−	0.223067i
$222$	25.1453	+	22.3398i	1.68764	+	1.49935i
$223$	−1.13429	−	1.13429i	−0.0759578	−	0.0759578i	0.668107	−	0.744065i	$-0.267105\pi$
$223$	−1.13429	−	1.13429i	−0.0759578	−	0.0759578i	−0.744065	+	0.668107i	$0.767105\pi$
$224$		0			0
$225$	12.9629	+	32.0707i	0.864191	+	2.13805i
$226$	−0.0480453	−	0.813196i	−0.00319592	−	0.0540930i
$227$	4.84005	+	1.29689i	0.321246	+	0.0860775i	0.415838	−	0.909439i	$-0.363488\pi$
$227$	4.84005	+	1.29689i	0.321246	+	0.0860775i	−0.0945927	+	0.995516i	$0.530155\pi$
$228$	5.13126	−	6.51188i	0.339826	−	0.431260i
$229$	8.93604	+	5.15923i	0.590510	+	0.340931i	0.765299	−	0.643675i	$-0.222591\pi$
$229$	8.93604	+	5.15923i	0.590510	+	0.340931i	−0.174789	+	0.984606i	$0.555924\pi$
$230$	−11.4976	−	11.7470i	−0.758131	−	0.774573i
$231$		0			0
$232$	7.28940	−	10.4661i	0.478572	−	0.687132i
$233$	−3.30639	−	12.3396i	−0.216609	−	0.808395i	−0.985594	−	0.169129i	$-0.945905\pi$
$233$	−3.30639	−	12.3396i	−0.216609	−	0.808395i	0.768985	−	0.639267i	$-0.220762\pi$
$234$	−15.6603	+	31.2473i	−1.02375	+	2.04270i
$235$	−15.2504	−	1.06529i	−0.994824	−	0.0694919i
$236$	−13.3710	+	9.98916i	−0.870381	+	0.650239i
$237$	−7.68598	−	7.68598i	−0.499258	−	0.499258i
$238$		0			0
$239$	−19.1256			−1.23713			−0.618565	−	0.785733i	$-0.712286\pi$
$239$	−19.1256			−1.23713			−0.618565	+	0.785733i	$0.712286\pi$
$240$	26.3896	+	9.85143i	1.70344	+	0.635907i
$241$	7.07911	+	12.2614i	0.456006	+	0.789825i	0.998745	−	0.0500757i	$-0.0159463\pi$
$241$	7.07911	+	12.2614i	0.456006	+	0.789825i	−0.542740	+	0.839901i	$0.682613\pi$
$242$	2.14208	+	6.44639i	0.137698	+	0.414389i
$243$	19.3260	−	5.17838i	1.23976	−	0.332193i
$244$	−2.47583	−	1.06306i	−0.158499	−	0.0680556i
$245$		0			0
$246$	27.7350	+	42.0923i	1.76832	+	2.68371i
$247$	−1.21701	−	4.54193i	−0.0774363	−	0.288996i
$248$	−7.25734	−	0.616604i	−0.460842	−	0.0391544i
$249$	−32.3131	+	18.6560i	−2.04776	+	1.18227i
$250$	2.36606	−	15.6334i	0.149643	−	0.988740i
$251$			8.70910i			0.549714i	0.961485	+	0.274857i	$0.0886305\pi$
$251$			8.70910i			0.549714i	−0.961485	+	0.274857i	$0.911370\pi$
$252$		0			0
$253$	14.6114	−	14.6114i	0.918611	−	0.918611i
$254$	−1.22389	−	20.7151i	−0.0767937	−	1.29978i
$255$	5.69636	−	4.95250i	0.356720	−	0.310138i
$256$	14.2498	−	7.27623i	0.890612	−	0.454764i
$257$	−5.76635	+	1.54509i	−0.359695	+	0.0963799i	−0.434141	−	0.900845i	$-0.642948\pi$
$257$	−5.76635	+	1.54509i	−0.359695	+	0.0963799i	0.0744458	+	0.997225i	$0.476281\pi$
$258$	2.25105	−	10.9480i	0.140144	−	0.681596i
$259$		0			0
$260$	13.4341	−	8.64661i	0.833147	−	0.536240i
$261$	−15.5985	+	27.0174i	−0.965524	+	1.67234i
$262$	−13.2327	+	4.39711i	−0.817518	+	0.271655i
$263$	−4.09029	+	15.2652i	−0.252218	+	0.941292i	0.717398	+	0.696663i	$0.245333\pi$
$263$	−4.09029	+	15.2652i	−0.252218	+	0.941292i	−0.969617	+	0.244629i	$0.921334\pi$
$264$	−12.0278	+	33.3057i	−0.740260	+	2.04982i
$265$	−10.4643	+	15.5164i	−0.642818	+	0.953167i
$266$		0			0
$267$	20.9758	−	20.9758i	1.28370	−	1.28370i
$268$	−1.58032	+	10.9160i	−0.0965334	+	0.666799i
$269$	−6.92467	+	3.99796i	−0.422205	+	0.243760i	−0.696020	−	0.718022i	$-0.745048\pi$
$269$	−6.92467	+	3.99796i	−0.422205	+	0.243760i	0.273815	+	0.961782i	$0.411714\pi$
$270$	−37.5823	−	10.5035i	−2.28719	−	0.639222i
$271$	26.0319	+	15.0295i	1.58133	+	0.912980i	0.994666	+	0.103148i	$0.0328915\pi$
$271$	26.0319	+	15.0295i	1.58133	+	0.912980i	0.586662	+	0.809832i	$0.300442\pi$
$272$	0.110372	−	4.28606i	0.00669229	−	0.259880i
$273$		0			0
$274$	12.5610	+	19.0633i	0.758835	+	1.15166i
$275$	19.6837	+	2.76343i	1.18697	+	0.166641i
$276$	32.5124	−	3.85525i	1.95702	−	0.232059i
$277$	−0.639600	+	2.38702i	−0.0384299	+	0.143422i	−0.982475	−	0.186394i	$-0.940320\pi$
$277$	−0.639600	+	2.38702i	−0.0384299	+	0.143422i	0.944045	+	0.329816i	$0.106987\pi$
$278$	−8.55328	+	9.62743i	−0.512992	+	0.577415i
$279$	17.8153			1.06657
$280$		0			0
$281$	−2.85110			−0.170082			−0.0850411	−	0.996377i	$-0.527102\pi$
$281$	−2.85110			−0.170082			−0.0850411	+	0.996377i	$0.527102\pi$
$282$	20.2239	−	22.7637i	1.20432	−	1.35556i
$283$	−2.23944	+	8.35771i	−0.133121	+	0.496814i	−0.999999	−	0.00170684i	$-0.999457\pi$
$283$	−2.23944	+	8.35771i	−0.133121	+	0.496814i	0.866878	+	0.498521i	$0.166123\pi$
$284$	6.89827	−	0.817982i	0.409337	−	0.0485383i
$285$	8.33080	−	4.06396i	0.493474	−	0.240728i
$286$	11.0503	+	16.7706i	0.653418	+	0.991667i
$287$		0			0
$288$	−33.2230	+	20.6844i	−1.95768	+	1.21884i
$289$	13.7275	+	7.92555i	0.807497	+	0.466209i
$290$	12.4251	−	6.99704i	0.729630	−	0.410880i
$291$	−34.8846	+	20.1406i	−2.04497	+	1.18066i
$292$	0.691880	−	4.77912i	0.0404892	−	0.279677i
$293$	16.5266	−	16.5266i	0.965497	−	0.965497i	−0.0339277	−	0.999424i	$-0.510802\pi$
$293$	16.5266	−	16.5266i	0.965497	−	0.965497i	0.999424	+	0.0339277i	$0.0108016\pi$
$294$		0			0
$295$	−18.3173	+	3.56191i	−1.06647	+	0.207382i
$296$	20.0905	+	7.25535i	1.16774	+	0.421709i
$297$	12.6966	−	47.3842i	0.736729	−	2.74951i
$298$	2.64953	−	0.880416i	0.153483	−	0.0510011i
$299$	9.28454	−	16.0813i	0.536939	−	0.930006i
$300$	21.7863	+	22.7417i	1.25783	+	1.31299i
$301$		0			0
$302$	2.45799	−	11.9545i	0.141442	−	0.687905i
$303$	−31.2503	+	8.37350i	−1.79528	+	0.481045i
$304$	1.49315	−	5.04884i	0.0856380	−	0.289571i
$305$	−1.97650	−	2.27337i	−0.113174	−	0.130173i
$306$	0.618521	+	10.4688i	0.0353585	+	0.598464i
$307$	15.0259	−	15.0259i	0.857575	−	0.857575i	−0.133477	−	0.991052i	$-0.542614\pi$
$307$	15.0259	−	15.0259i	0.857575	−	0.857575i	0.991052	+	0.133477i	$0.0426143\pi$
$308$		0			0
$309$		−	13.1638i		−	0.748863i
$310$	−7.00813	−	4.14701i	−0.398035	−	0.235534i
$311$	24.3986	−	14.0866i	1.38352	−	0.798776i	0.390945	−	0.920414i	$-0.372148\pi$
$311$	24.3986	−	14.0866i	1.38352	−	0.798776i	0.992574	+	0.121638i	$0.0388148\pi$
$312$	−2.69394	+	31.7073i	−0.152514	+	1.79507i
$313$	−6.64347	−	24.7938i	−0.375511	−	1.40143i	−0.852597	−	0.522570i	$-0.824973\pi$
$313$	−6.64347	−	24.7938i	−0.375511	−	1.40143i	0.477085	−	0.878857i	$-0.341693\pi$
$314$	−12.3358	−	18.7216i	−0.696150	−	1.05652i
$315$		0			0
$316$	−6.34283	−	2.72346i	−0.356812	−	0.153207i
$317$	25.4060	−	6.80753i	1.42695	−	0.382349i	0.539003	−	0.842304i	$-0.318801\pi$
$317$	25.4060	−	6.80753i	1.42695	−	0.382349i	0.887942	+	0.459955i	$0.152134\pi$
$318$	−11.7550	−	35.3754i	−0.659185	−	1.98375i
$319$	8.96312	+	15.5246i	0.501838	+	0.869209i
$320$	17.8840	−	0.403191i	0.999746	−	0.0225390i
$321$	−50.1083			−2.79678
$322$		0			0
$323$	−0.997621	−	0.997621i	−0.0555091	−	0.0555091i
$324$	29.0133	−	21.6751i	1.61185	−	1.20417i
$325$	17.7285	−	2.17941i	0.983398	−	0.120892i
$326$	−4.41385	+	8.80704i	−0.244460	+	0.487777i
$327$	−2.43349	−	9.08191i	−0.134572	−	0.502231i
$328$	26.2687	+	18.2955i	1.45044	+	1.01020i
$329$		0			0
$330$	−28.2935	+	27.6929i	−1.55751	+	1.52445i
$331$	−14.8975	−	8.60110i	−0.818843	−	0.472759i	0.0311741	−	0.999514i	$-0.490075\pi$
$331$	−14.8975	−	8.60110i	−0.818843	−	0.472759i	−0.850017	+	0.526755i	$0.823409\pi$
$332$	−14.6655	+	18.6114i	−0.804874	+	1.02143i
$333$	−50.4671	−	13.5226i	−2.76558	−	0.741034i
$334$	−1.40614	−	23.7998i	−0.0769407	−	1.30227i
$335$	−6.89503	+	10.2239i	−0.376715	+	0.558592i
$336$		0			0
$337$	−12.9038	−	12.9038i	−0.702913	−	0.702913i	0.262121	−	0.965035i	$-0.415578\pi$
$337$	−12.9038	−	12.9038i	−0.702913	−	0.702913i	−0.965035	+	0.262121i	$0.915578\pi$
$338$	−0.251691	−	0.223609i	−0.0136902	−	0.0121627i
$339$	0.907038	+	1.57104i	0.0492635	+	0.0853270i
$340$	2.19360	−	4.26218i	0.118965	−	0.231149i
$341$	5.11846	−	8.86543i	0.277180	−	0.480090i
$342$	−2.59364	+	12.6142i	−0.140248	+	0.682100i
$343$		0			0
$344$	−1.25009	−	6.98711i	−0.0674002	−	0.376720i
$345$	34.6112	+	11.9148i	1.86340	+	0.641469i
$346$	0.279934	+	0.140295i	0.0150493	+	0.00754232i
$347$	18.2417	+	4.88784i	0.979264	+	0.262393i	0.712735	−	0.701434i	$-0.247456\pi$
$347$	18.2417	+	4.88784i	0.979264	+	0.262393i	0.266529	+	0.963827i	$0.414123\pi$
$348$	−4.06951	+	28.1099i	−0.218148	+	1.50685i
$349$		−	22.9263i		−	1.22721i	−0.789611	−	0.613607i	$-0.789718\pi$
$349$		−	22.9263i		−	1.22721i	0.789611	−	0.613607i	$-0.210282\pi$
$350$		0			0
$351$		−	44.0832i		−	2.35299i
$352$	0.747983	+	22.4755i	0.0398676	+	1.19795i
$353$	−28.9021	−	7.74430i	−1.53830	−	0.412188i	−0.612587	−	0.790403i	$-0.709871\pi$
$353$	−28.9021	−	7.74430i	−1.53830	−	0.412188i	−0.925718	+	0.378215i	$0.876538\pi$
$354$	16.6532	−	33.2285i	0.885108	−	1.76607i
$355$	7.34358	+	2.52800i	0.389757	+	0.134172i
$356$	7.43261	−	17.3102i	0.393928	−	0.917441i
$357$		0			0
$358$	28.2651	+	5.81164i	1.49385	+	0.307155i
$359$	4.27518	−	7.40483i	0.225635	−	0.390812i	−0.730875	−	0.682512i	$-0.760888\pi$
$359$	4.27518	−	7.40483i	0.225635	−	0.390812i	0.956510	+	0.291700i	$0.0942209\pi$
$360$	−43.5035	+	4.68592i	−2.29283	+	0.246970i
$361$	8.63374	+	14.9541i	0.454407	+	0.787057i
$362$	−12.3701	+	13.9235i	−0.650156	+	0.731805i
$363$	−10.6967	−	10.6967i	−0.561429	−	0.561429i
$364$		0			0
$365$	3.01871	−	4.47613i	0.158007	−	0.234291i
$366$	5.98976	−	0.353887i	0.313090	−	0.0184980i
$367$	5.06713	+	1.35773i	0.264502	+	0.0708731i	0.388633	−	0.921393i	$-0.372948\pi$
$367$	5.06713	+	1.35773i	0.264502	+	0.0708731i	−0.124131	+	0.992266i	$0.539614\pi$
$368$	18.2679	−	9.92893i	0.952280	−	0.517581i
$369$	−67.8106	−	39.1505i	−3.53008	−	2.03809i
$370$	16.7048	+	17.0671i	0.868442	+	0.887276i
$371$		0			0
$372$	15.0637	−	6.01360i	0.781017	−	0.311791i
$373$	−0.799311	−	2.98307i	−0.0413867	−	0.154457i	0.942140	−	0.335219i	$-0.108810\pi$
$373$	−0.799311	−	2.98307i	−0.0413867	−	0.154457i	−0.983527	+	0.180762i	$0.942144\pi$
$374$	5.38732	+	2.69998i	0.278572	+	0.139612i
$375$	10.8880	+	33.4849i	0.562254	+	1.72915i
$376$	6.56819	−	18.1877i	0.338728	−	0.937959i
$377$	11.3909	+	11.3909i	0.586661	+	0.586661i
$378$		0			0
$379$	17.0070			0.873589			0.436794	−	0.899561i	$-0.356114\pi$
$379$	17.0070			0.873589			0.436794	+	0.899561i	$0.356114\pi$
$380$	3.95659	−	4.35841i	0.202969	−	0.223582i
$381$	23.1056	+	40.0201i	1.18374	+	2.05029i
$382$	16.2433	−	5.39751i	0.831079	−	0.276161i
$383$	−26.3270	+	7.05430i	−1.34525	+	0.360458i	−0.858379	−	0.513017i	$-0.828528\pi$
$383$	−26.3270	+	7.05430i	−1.34525	+	0.360458i	−0.486869	+	0.873475i	$0.661861\pi$
$384$	−21.1096	+	28.7041i	−1.07724	+	1.46480i
$385$		0			0
$386$	0.829130	−	0.546320i	0.0422016	−	0.0278070i
$387$	4.49355	+	16.7702i	0.228420	+	0.852475i
$388$	−15.8326	+	20.0925i	−0.803777	+	1.02004i
$389$	10.9526	−	6.32350i	0.555320	−	0.320614i	−0.195945	−	0.980615i	$-0.562777\pi$
$389$	10.9526	−	6.32350i	0.555320	−	0.320614i	0.751265	+	0.660001i	$0.229444\pi$
$390$	−18.1183	+	30.6185i	−0.917454	+	1.55043i
$391$		−	5.57153i		−	0.281764i
$392$		0			0
$393$	21.9573	−	21.9573i	1.10760	−	1.10760i
$394$	2.33441	−	0.137922i	0.117606	−	0.00694841i
$395$	−5.06361	−	5.82416i	−0.254778	−	0.293045i
$396$	−6.47702	−	54.6225i	−0.325483	−	2.74488i
$397$	−11.7173	+	3.13965i	−0.588076	+	0.157574i	−0.540574	−	0.841297i	$-0.681793\pi$
$397$	−11.7173	+	3.13965i	−0.588076	+	0.157574i	−0.0475022	+	0.998871i	$0.515126\pi$
$398$	−24.1743	−	4.97053i	−1.21175	−	0.249150i
$399$		0			0
$400$	18.2040	+	8.28330i	0.910202	+	0.414165i
$401$	7.12839	−	12.3467i	0.355975	−	0.616566i	−0.631310	−	0.775531i	$-0.717482\pi$
$401$	7.12839	−	12.3467i	0.355975	−	0.616566i	0.987284	+	0.158965i	$0.0508156\pi$
$402$	−7.74544	−	23.3092i	−0.386307	−	1.16255i
$403$	2.38094	−	8.88580i	0.118603	−	0.442633i
$404$	−16.4597	+	12.2966i	−0.818901	+	0.611779i
$405$	39.7459	−	7.72884i	1.97499	−	0.384049i
$406$		0			0
$407$	−21.2288	+	21.2288i	−1.05227	+	1.05227i
$408$	4.05678	+	8.64314i	0.200840	+	0.427899i
$409$	25.8941	−	14.9499i	1.28038	−	0.739227i	0.303461	−	0.952844i	$-0.401858\pi$
$409$	25.8941	−	14.9499i	1.28038	−	0.739227i	0.976918	+	0.213617i	$0.0685243\pi$
$410$	17.5618	+	31.1857i	0.867314	+	1.54015i
$411$	−44.0282	−	25.4197i	−2.17175	−	1.25386i
$412$	−3.09945	−	7.76394i	−0.152699	−	0.382502i
$413$		0			0
$414$	−42.4666	+	27.9816i	−2.08712	+	1.37522i
$415$	−23.8100	+	11.6151i	−1.16879	+	0.570161i
$416$	5.87670	+	19.3351i	0.288129	+	0.947982i
$417$	7.42253	−	27.7013i	0.363483	−	1.35654i
$418$	5.53205	+	4.91483i	0.270582	+	0.240392i
$419$	−37.6505			−1.83935			−0.919674	−	0.392684i	$-0.871547\pi$
$419$	−37.6505			−1.83935			−0.919674	+	0.392684i	$0.871547\pi$
$420$		0			0
$421$	−8.37171			−0.408012			−0.204006	−	0.978970i	$-0.565396\pi$
$421$	−8.37171			−0.408012			−0.204006	+	0.978970i	$0.565396\pi$
$422$	−6.68706	−	5.94097i	−0.325521	−	0.289202i
$423$	−12.2419	+	45.6872i	−0.595219	+	2.22139i
$424$	−15.2622	−	18.0965i	−0.741200	−	0.878843i
$425$	4.27969	−	3.22596i	0.207596	−	0.156482i
$426$	−12.9174	+	8.51141i	−0.625852	+	0.412379i
$427$		0			0
$428$	−29.5536	+	11.7981i	−1.42853	+	0.570285i
$429$	−38.7331	−	22.3626i	−1.87005	−	1.07967i
$430$	2.13606	−	7.64299i	0.103010	−	0.368578i
$431$	−4.31232	+	2.48972i	−0.207717	+	0.119925i	−0.600250	−	0.799812i	$-0.704932\pi$
$431$	−4.31232	+	2.48972i	−0.207717	+	0.119925i	0.392533	+	0.919738i	$0.371599\pi$
$432$	25.7722	−	42.0975i	1.23997	−	2.02542i
$433$	−2.70541	+	2.70541i	−0.130014	+	0.130014i	−0.769119	−	0.639106i	$-0.779305\pi$
$433$	−2.70541	+	2.70541i	−0.130014	+	0.130014i	0.639106	+	0.769119i	$0.279305\pi$
$434$		0			0
$435$	−17.7555	+	26.3277i	−0.851310	+	1.26232i
$436$	−3.57362	−	4.78349i	−0.171145	−	0.229087i
$437$	1.77079	−	6.60868i	0.0847084	−	0.316136i
$438$	3.39103	+	10.2050i	0.162030	+	0.487613i
$439$	18.7676	−	32.5065i	0.895731	−	1.55145i	0.0628330	−	0.998024i	$-0.479986\pi$
$439$	18.7676	−	32.5065i	0.895731	−	1.55145i	0.832898	−	0.553427i	$-0.186680\pi$
$440$	−10.1670	+	22.9949i	−0.484692	+	1.09624i
$441$		0			0
$442$	5.30425	+	1.09062i	0.252297	+	0.0518754i
$443$	−12.2588	+	3.28474i	−0.582433	+	0.156063i	−0.537993	−	0.842950i	$-0.680817\pi$
$443$	−12.2588	+	3.28474i	−0.582433	+	0.156063i	−0.0444406	+	0.999012i	$0.514151\pi$
$444$	−47.2370	+	5.60126i	−2.24177	+	0.265824i
$445$	15.8947	−	13.8191i	0.753482	−	0.655089i
$446$	2.26463	−	0.133799i	0.107234	−	0.00633557i
$447$	−4.39643	+	4.39643i	−0.207944	+	0.207944i
$448$		0			0
$449$		−	25.1638i		−	1.18755i	−0.804630	−	0.593777i	$-0.797636\pi$
$449$		−	25.1638i		−	1.18755i	0.804630	−	0.593777i	$-0.202364\pi$
$450$	−46.0822	−	16.4186i	−2.17234	−	0.773979i
$451$	−38.9649	+	22.4964i	−1.83479	+	1.05931i
$452$	0.904870	+	0.713024i	0.0425615	+	0.0335378i
$453$	7.03434	+	26.2525i	0.330502	+	1.23345i
$454$	−5.91729	+	3.89895i	−0.277712	+	0.182987i
$455$		0			0
$456$	2.06492	+	11.5414i	0.0966987	+	0.540478i
$457$	−26.2723	+	7.03963i	−1.22896	+	0.329300i	−0.814176	−	0.580618i	$-0.802811\pi$
$457$	−26.2723	+	7.03963i	−1.22896	+	0.329300i	−0.414788	+	0.909918i	$0.636144\pi$
$458$	−13.8480	+	4.60157i	−0.647074	+	0.215017i
$459$	−6.61343	−	11.4548i	−0.308689	−	0.534664i
$460$	23.2189	−	1.12203i	1.08258	−	0.0523151i
$461$	20.0052			0.931737			0.465868	−	0.884854i	$-0.345742\pi$
$461$	20.0052			0.931737			0.465868	+	0.884854i	$0.345742\pi$
$462$		0			0
$463$	10.1515	+	10.1515i	0.471781	+	0.471781i	0.902491	−	0.430710i	$-0.141737\pi$
$463$	10.1515	+	10.1515i	0.471781	+	0.471781i	−0.430710	+	0.902491i	$0.641737\pi$
$464$	4.21837	+	17.5372i	0.195833	+	0.814145i
$465$	18.0901	+	1.26366i	0.838908	+	0.0586006i
$466$	16.1515	+	8.09471i	0.748206	+	0.374980i
$467$	−1.07000	−	3.99329i	−0.0495137	−	0.184787i	0.936740	−	0.350026i	$-0.113827\pi$
$467$	−1.07000	−	3.99329i	−0.0495137	−	0.184787i	−0.986254	+	0.165239i	$0.947161\pi$
$468$	−18.3265	−	45.9067i	−0.847141	−	2.12204i
$469$		0			0
$470$	15.4506	−	15.1227i	0.712684	−	0.697557i
$471$	43.2390	+	24.9640i	1.99235	+	1.15028i
$472$	1.99824	−	23.5190i	0.0919764	−	1.08255i
$473$	9.63636	+	2.58206i	0.443080	+	0.118723i
$474$	15.3452	−	0.906625i	0.704828	−	0.0416427i
$475$	6.10167	−	2.46627i	0.279964	−	0.113160i
$476$		0			0
$477$	40.9445	+	40.9445i	1.87472	+	1.87472i
$478$	17.9643	−	20.2203i	0.821667	−	0.924855i
$479$	4.66449	+	8.07913i	0.213126	+	0.369145i	0.952691	−	0.303940i	$-0.0983022\pi$
$479$	4.66449	+	8.07913i	0.213126	+	0.369145i	−0.739565	+	0.673085i	$0.764969\pi$
$480$	−35.2026	+	18.6469i	−1.60677	+	0.851110i
$481$	−13.4894	+	23.3644i	−0.615065	+	1.06532i
$482$	−19.6125	−	4.03256i	−0.893324	−	0.183678i
$483$		0			0
$484$	−8.82738	−	3.79027i	−0.401245	−	0.172285i
$485$	−25.7048	+	12.5394i	−1.16719	+	0.569384i
$486$	−12.6777	+	25.2961i	−0.575073	+	1.14745i
$487$	−28.0071	−	7.50448i	−1.26912	−	0.340061i	−0.439429	−	0.898278i	$-0.644819\pi$
$487$	−28.0071	−	7.50448i	−1.26912	−	0.340061i	−0.829695	+	0.558217i	$0.811486\pi$
$488$	3.44940	−	1.61903i	0.156147	−	0.0732898i
$489$		−	21.9378i		−	0.992060i
$490$		0			0
$491$		−	28.1818i		−	1.27183i	−0.771760	−	0.635914i	$-0.780623\pi$
$491$		−	28.1818i		−	1.27183i	0.771760	−	0.635914i	$-0.219377\pi$
$492$	−70.5525	−	10.2140i	−3.18075	−	0.460482i
$493$	4.66874	+	1.25099i	0.210270	+	0.0563416i
$494$	5.94502	+	2.97948i	0.267479	+	0.134053i
$495$	20.0174	−	58.1486i	0.899716	−	2.61359i
$496$	7.46858	−	7.09358i	0.335349	−	0.318511i
$497$		0			0
$498$	10.6272	−	51.6859i	0.476218	−	2.31610i
$499$	15.5368	−	26.9104i	0.695521	−	1.20468i	−0.274484	−	0.961592i	$-0.588507\pi$
$499$	15.5368	−	26.9104i	0.695521	−	1.20468i	0.970005	−	0.243085i	$-0.0781595\pi$
$500$	14.3058	+	17.1856i	0.639774	+	0.768563i
$501$	26.5463	+	45.9796i	1.18600	+	2.05422i
$502$	−9.20760	−	8.18029i	−0.410955	−	0.365104i
$503$	28.6110	+	28.6110i	1.27570	+	1.27570i	0.943049	+	0.332654i	$0.107944\pi$
$503$	28.6110	+	28.6110i	1.27570	+	1.27570i	0.332654	+	0.943049i	$0.392056\pi$
$504$		0			0
$505$	−22.5485	+	4.38469i	−1.00340	+	0.195116i
$506$	1.72354	+	29.1719i	0.0766206	+	1.29685i
$507$	0.724197	+	0.194048i	0.0321627	+	0.00861798i
$508$	23.0504	+	18.1633i	1.02270	+	0.805868i
$509$	10.6109	+	6.12618i	0.470318	+	0.271538i	0.716373	−	0.697718i	$-0.245801\pi$
$509$	10.6109	+	6.12618i	0.470318	+	0.271538i	−0.246055	+	0.969256i	$0.579134\pi$
$510$	−0.114504	+	10.6742i	−0.00507030	+	0.472661i
$511$		0			0
$512$	−5.69184	+	21.8998i	−0.251546	+	0.967845i
$513$	−4.20388	−	15.6891i	−0.185606	−	0.692690i
$514$	3.78269	−	7.54767i	0.166847	−	0.332914i
$515$	0.651297	−	9.32376i	0.0286996	−	0.410854i
$516$	9.46033	+	12.6632i	0.416468	+	0.557465i
$517$	19.2182	+	19.2182i	0.845214	+	0.845214i
$518$		0			0
$519$	−0.697297			−0.0306080
$520$	−3.47685	+	22.3246i	−0.152470	+	0.979000i
$521$	−17.7836	−	30.8021i	−0.779115	−	1.34947i	−0.932453	−	0.361292i	$-0.882336\pi$
$521$	−17.7836	−	30.8021i	−0.779115	−	1.34947i	0.153338	−	0.988174i	$-0.450998\pi$
$522$	−13.9125	−	41.8683i	−0.608933	−	1.83252i
$523$	11.0942	−	2.97269i	0.485118	−	0.129987i	−0.00796695	−	0.999968i	$-0.502536\pi$
$523$	11.0942	−	2.97269i	0.485118	−	0.129987i	0.493085	+	0.869981i	$0.335869\pi$
$524$	7.78040	−	18.1202i	0.339889	−	0.791586i
$525$		0			0
$526$	−12.2970	−	18.6627i	−0.536175	−	0.813733i
$527$	−0.714386	−	2.66612i	−0.0311191	−	0.116138i
$528$	−23.9146	−	43.9996i	−1.04075	−	1.91484i
$529$	3.48031	−	2.00936i	0.151318	−	0.0873633i
$530$	−6.57564	−	25.6376i	−0.285628	−	1.11362i
$531$			57.7344i			2.50546i
$532$		0			0
$533$	−28.5898	+	28.5898i	−1.23836	+	1.23836i
$534$	2.47427	+	41.8786i	0.107072	+	1.81227i
$535$	−35.4911	−	2.47918i	−1.53441	−	0.107184i
$536$	−10.0564	−	11.9239i	−0.434371	−	0.515035i
$537$	−62.0710	+	16.6319i	−2.67856	+	0.717718i
$538$	2.27741	−	11.0762i	0.0981860	−	0.477530i
$539$		0			0
$540$	46.4050	−	29.8678i	1.99695	−	1.28530i
$541$	−6.42555	+	11.1294i	−0.276256	+	0.478489i	−0.970451	−	0.241297i	$-0.922427\pi$
$541$	−6.42555	+	11.1294i	−0.276256	+	0.478489i	0.694195	+	0.719787i	$0.255760\pi$
$542$	−40.3411	+	13.4050i	−1.73280	+	0.575795i
$543$	10.7347	−	40.0626i	0.460672	−	1.71925i
$544$	4.42771	+	4.14250i	0.189837	+	0.177608i
$545$	−1.27427	−	6.55300i	−0.0545838	−	0.280700i
$546$		0			0
$547$	1.19674	−	1.19674i	0.0511688	−	0.0511688i	−0.681059	−	0.732228i	$-0.738480\pi$
$547$	1.19674	−	1.19674i	0.0511688	−	0.0511688i	0.732228	+	0.681059i	$0.238480\pi$
$548$	−31.9527	−	4.62584i	−1.36495	−	0.197606i
$549$	−8.07165	+	4.66017i	−0.344490	+	0.198891i
$550$	−21.4101	+	18.2147i	−0.912929	+	0.776678i
$551$	5.14025	+	2.96772i	0.218982	+	0.126429i
$552$	−26.4623	+	37.9945i	−1.12631	+	1.61715i
$553$		0			0
$554$	−1.92289	−	2.91829i	−0.0816956	−	0.123986i
$555$	−50.2863	−	17.3109i	−2.13454	−	0.734805i
$556$	−2.14457	−	18.0857i	−0.0909499	−	0.767005i
$557$	−4.30105	+	16.0517i	−0.182241	+	0.680133i	0.812963	+	0.582315i	$0.197853\pi$
$557$	−4.30105	+	16.0517i	−0.182241	+	0.680133i	−0.995204	+	0.0978181i	$0.968814\pi$
$558$	−16.7336	+	18.8350i	−0.708388	+	0.797350i
$559$	8.96505			0.379181
$560$		0			0
$561$	−13.4195			−0.566570
$562$	2.67798	−	3.01429i	0.112964	−	0.127150i
$563$	9.63625	−	35.9630i	0.406119	−	1.51566i	−0.395862	−	0.918310i	$-0.629554\pi$
$563$	9.63625	−	35.9630i	0.406119	−	1.51566i	0.801982	−	0.597349i	$-0.203779\pi$
$564$	5.07076	+	42.7631i	0.213517	+	1.80065i
$565$	0.564715	+	1.15762i	0.0237577	+	0.0487015i
$566$	−6.73263	−	10.2179i	−0.282993	−	0.429488i
$567$		0			0
$568$	−5.61460	+	8.06143i	−0.235583	+	0.338250i
$569$	−14.2519	−	8.22834i	−0.597471	−	0.344950i	0.170575	−	0.985345i	$-0.445437\pi$
$569$	−14.2519	−	8.22834i	−0.597471	−	0.344950i	−0.768046	+	0.640395i	$0.778771\pi$
$570$	−3.52839	+	12.6248i	−0.147788	+	0.528796i
$571$	38.7542	−	22.3748i	1.62181	−	0.936355i	0.635380	−	0.772199i	$-0.280843\pi$
$571$	38.7542	−	22.3748i	1.62181	−	0.936355i	0.986434	−	0.164156i	$-0.0524900\pi$
$572$	−28.1099	−	4.06951i	−1.17533	−	0.170155i
$573$	−26.9529	+	26.9529i	−1.12597	+	1.12597i
$574$		0			0
$575$	23.9252	+	10.1515i	0.997749	+	0.423347i
$576$	9.33734	−	54.5530i	0.389056	−	2.27304i
$577$	−3.54445	+	13.2280i	−0.147557	+	0.550691i	0.852071	+	0.523426i	$0.175346\pi$
$577$	−3.54445	+	13.2280i	−0.147557	+	0.550691i	−0.999628	+	0.0272648i	$0.991320\pi$
$578$	−21.2731	+	7.06888i	−0.884845	+	0.294027i
$579$	−1.10559	+	1.91494i	−0.0459468	+	0.0795822i
$580$	−4.27315	+	19.7085i	−0.177433	+	0.818352i
$581$		0			0
$582$	11.4729	−	55.7990i	0.475569	−	2.31294i
$583$	32.1388	−	8.61157i	1.33105	−	0.356655i
$584$	4.40280	+	5.22041i	0.182189	+	0.216022i
$585$	3.85099	−	55.1296i	0.159219	−	2.27933i
$586$	1.94945	+	32.9957i	0.0805312	+	1.36304i
$587$	24.5126	−	24.5126i	1.01175	−	1.01175i	0.0118150	−	0.999930i	$-0.496239\pi$
$587$	24.5126	−	24.5126i	1.01175	−	1.01175i	0.999930	−	0.0118150i	$-0.00376091\pi$
$588$		0			0
$589$		−	3.38948i		−	0.139661i
$590$	13.4393	−	22.7114i	0.553286	−	0.935012i
$591$	−4.50992	+	2.60380i	−0.185513	+	0.107106i
$592$	−26.5413	+	14.4257i	−1.09084	+	0.592891i
$593$	−11.8464	−	44.2116i	−0.486475	−	1.81555i	−0.573323	−	0.819329i	$-0.694346\pi$
$593$	−11.8464	−	44.2116i	−0.486475	−	1.81555i	0.0868479	−	0.996222i	$-0.472321\pi$
$594$	38.1708	+	57.9303i	1.56617	+	2.37691i
$595$		0			0
$596$	−1.55784	+	3.62814i	−0.0638115	+	0.148614i
$597$	53.0875	−	14.2248i	2.17273	−	0.582180i
$598$	8.28098	+	24.9208i	0.338635	+	1.01909i
$599$	−15.6035	−	27.0260i	−0.637540	−	1.10425i	−0.985971	−	0.166918i	$-0.946619\pi$
$599$	−15.6035	−	27.0260i	−0.637540	−	1.10425i	0.348430	−	0.937335i	$-0.386715\pi$
$600$	−44.5069	+	1.67246i	−1.81699	+	0.0682780i
$601$	−3.84939			−0.157020			−0.0785099	−	0.996913i	$-0.525016\pi$
$601$	−3.84939			−0.157020			−0.0785099	+	0.996913i	$0.525016\pi$
$602$		0			0
$603$	26.9786	+	26.9786i	1.09866	+	1.09866i
$604$	10.3300	+	13.8273i	0.420323	+	0.562626i
$605$	−7.04708	−	8.10554i	−0.286504	−	0.329537i
$606$	20.5000	−	40.9041i	0.832756	−	1.66162i
$607$	−1.49094	−	5.56425i	−0.0605152	−	0.225846i	0.929045	−	0.369967i	$-0.120631\pi$
$607$	−1.49094	−	5.56425i	−0.0605152	−	0.225846i	−0.989560	+	0.144121i	$0.953964\pi$
$608$	3.93534	+	6.32089i	0.159599	+	0.256346i
$609$		0			0
$610$	4.25998	+	0.0456974i	0.172482	+	0.00185023i
$611$	21.1515	+	12.2118i	0.855698	+	0.494038i
$612$	−11.6490	−	9.17926i	−0.470884	−	0.371049i
$613$	−19.6676	−	5.26991i	−0.794366	−	0.212850i	−0.161257	−	0.986912i	$-0.551555\pi$
$613$	−19.6676	−	5.26991i	−0.794366	−	0.212850i	−0.633109	+	0.774063i	$0.718222\pi$
$614$	1.77243	+	29.9995i	0.0715296	+	1.21068i
$615$	−66.0796	−	44.5642i	−2.66459	−	1.79700i
$616$		0			0
$617$	−5.54965	−	5.54965i	−0.223420	−	0.223420i	0.586517	−	0.809937i	$-0.300499\pi$
$617$	−5.54965	−	5.54965i	−0.223420	−	0.223420i	−0.809937	+	0.586517i	$0.800499\pi$
$618$	13.9173	+	12.3645i	0.559835	+	0.497373i
$619$	2.52112	+	4.36671i	0.101332	+	0.175513i	0.912234	−	0.409670i	$-0.134356\pi$
$619$	2.52112	+	4.36671i	0.101332	+	0.175513i	−0.810901	+	0.585183i	$0.801023\pi$
$620$	10.9670	−	3.51406i	0.440444	−	0.141128i
$621$	32.0714	−	55.5492i	1.28698	−	2.22911i
$622$	−8.02430	+	39.0264i	−0.321745	+	1.56482i
$623$		0			0
$624$	−30.9919	−	32.6302i	−1.24067	−	1.30625i
$625$	6.05513	+	24.2556i	0.242205	+	0.970225i
$626$	32.4530	+	16.2646i	1.29708	+	0.650063i
$627$	−15.9175	−	4.26509i	−0.635685	−	0.170331i
$628$	31.3800	+	4.54292i	1.25220	+	0.181282i
$629$			8.09482i			0.322762i
$630$		0			0
$631$			22.4036i			0.891874i	0.895064	+	0.445937i	$0.147130\pi$
$631$			22.4036i			0.891874i	−0.895064	+	0.445937i	$0.852870\pi$
$632$	8.83705	−	4.14779i	0.351519	−	0.164990i
$633$	19.2409	+	5.15558i	0.764756	+	0.204916i
$634$	−16.6662	+	33.2544i	−0.661900	+	1.32070i
$635$	14.3854	+	29.4889i	0.570866	+	1.17023i
$636$	48.4414	+	20.7996i	1.92083	+	0.824759i
$637$		0			0
$638$	−24.8321	−	5.10577i	−0.983111	−	0.202139i
$639$	12.0146	−	20.8100i	0.475292	−	0.823230i
$640$	−16.3718	+	19.2864i	−0.647153	+	0.762360i
$641$	21.5598	+	37.3426i	0.851559	+	1.47494i	0.879801	+	0.475343i	$0.157676\pi$
$641$	21.5598	+	37.3426i	0.851559	+	1.47494i	−0.0282413	+	0.999601i	$0.508991\pi$
$642$	47.0658	−	52.9765i	1.85754	−	2.09081i
$643$	1.10922	+	1.10922i	0.0437432	+	0.0437432i	0.728640	−	0.684897i	$-0.240153\pi$
$643$	1.10922	+	1.10922i	0.0437432	+	0.0437432i	−0.684897	+	0.728640i	$0.740153\pi$
$644$		0			0
$645$	3.37334	+	17.3476i	0.132825	+	0.683060i
$646$	1.99177	−	0.117678i	0.0783651	−	0.00462997i
$647$	32.5679	+	8.72654i	1.28038	+	0.343076i	0.833997	−	0.551769i	$-0.186047\pi$
$647$	32.5679	+	8.72654i	1.28038	+	0.343076i	0.446378	+	0.894844i	$0.352714\pi$
$648$	−4.33590	+	51.0329i	−0.170330	+	2.00476i
$649$	28.7304	+	16.5875i	1.12777	+	0.651116i
$650$	−14.3478	+	20.7903i	−0.562769	+	0.815462i
$651$		0			0
$652$	−5.16530	−	12.9388i	−0.202289	−	0.506721i
$653$	9.95952	+	37.1694i	0.389746	+	1.45455i	0.830547	+	0.556948i	$0.188028\pi$
$653$	9.95952	+	37.1694i	0.389746	+	1.45455i	−0.440801	+	0.897605i	$0.645306\pi$
$654$	11.8875	+	5.95768i	0.464837	+	0.232964i
$655$	16.6385	−	14.4657i	0.650119	−	0.565223i
$656$	−44.0164	+	10.5876i	−1.71855	+	0.413377i
$657$	−11.8115	−	11.8115i	−0.460811	−	0.460811i
$658$		0			0
$659$	−12.4757			−0.485985			−0.242993	−	0.970028i	$-0.578129\pi$
$659$	−12.4757			−0.485985			−0.242993	+	0.970028i	$0.578129\pi$
$660$	−2.70251	−	55.9244i	−0.105195	−	2.17686i
$661$	−3.31297	−	5.73823i	−0.128859	−	0.223191i	0.794376	−	0.607427i	$-0.207798\pi$
$661$	−3.31297	−	5.73823i	−0.128859	−	0.223191i	−0.923235	+	0.384236i	$0.874465\pi$
$662$	23.0864	−	7.67141i	0.897278	−	0.298158i
$663$	−11.6483	+	3.12115i	−0.452382	+	0.121215i
$664$	−5.90168	−	32.9862i	−0.229030	−	1.28011i
$665$		0			0
$666$	61.6993	−	40.6542i	2.39080	−	1.57532i
$667$	6.06657	+	22.6407i	0.234898	+	0.876653i
$668$	26.4829	+	20.8681i	1.02465	+	0.807411i
$669$	−4.37511	+	2.52597i	−0.169151	+	0.0976596i
$670$	−4.33275	−	16.8928i	−0.167389	−	0.652626i
$671$			5.35559i			0.206750i
$672$		0			0
$673$	−27.7823	+	27.7823i	−1.07093	+	1.07093i	−0.0736433	+	0.997285i	$0.523463\pi$
$673$	−27.7823	+	27.7823i	−1.07093	+	1.07093i	−0.997285	+	0.0736433i	$0.976537\pi$
$674$	25.7626	−	1.52211i	0.992339	−	0.0586294i
$675$	61.2390	−	7.52828i	2.35709	−	0.289764i
$676$	0.472817	−	0.0560656i	0.0181853	−	0.00215637i
$677$	17.0379	−	4.56530i	0.654821	−	0.175459i	0.0839136	−	0.996473i	$-0.473258\pi$
$677$	17.0379	−	4.56530i	0.654821	−	0.175459i	0.570908	+	0.821014i	$0.306591\pi$
$678$	−2.51292	−	0.516687i	−0.0965082	−	0.0198433i
$679$		0			0
$680$	2.44573	+	6.32254i	0.0937896	+	0.242458i
$681$	7.89032	−	13.6664i	0.302358	−	0.523699i
$682$	4.56521	+	13.7386i	0.174811	+	0.526076i
$683$	1.40860	−	5.25698i	0.0538987	−	0.201153i	−0.933726	−	0.357989i	$-0.883463\pi$
$683$	1.40860	−	5.25698i	0.0538987	−	0.201153i	0.987625	+	0.156836i	$0.0501293\pi$
$684$	−10.9001	−	14.5904i	−0.416776	−	0.557878i
$685$	−29.9269	−	20.1828i	−1.14345	−	0.771145i
$686$		0			0
$687$	22.9783	−	22.9783i	0.876677	−	0.876677i
$688$	8.56123	+	5.24121i	0.326394	+	0.199819i
$689$	25.8941	−	14.9499i	0.986485	−	0.569547i
$690$	−45.1064	+	25.4010i	−1.71717	+	0.966999i
$691$	−32.0466	−	18.5021i	−1.21911	−	0.703854i	−0.254384	−	0.967103i	$-0.581873\pi$
$691$	−32.0466	−	18.5021i	−1.21911	−	0.703854i	−0.964728	+	0.263249i	$0.915206\pi$
$692$	−0.411262	+	0.164180i	−0.0156338	+	0.00624120i
$693$		0			0
$694$	−22.3016	+	14.6947i	−0.846559	+	0.557805i
$695$	6.62785	−	19.2532i	0.251409	−	0.730317i
$696$	−25.8964	−	30.7055i	−0.981601	−	1.16389i
$697$	−3.13983	+	11.7180i	−0.118930	+	0.443851i
$698$	24.2385	+	21.5342i	0.917442	+	0.815081i
$699$	−40.2324			−1.52173
$700$		0			0
$701$	−29.4765			−1.11331			−0.556656	−	0.830743i	$-0.687916\pi$
$701$	−29.4765			−1.11331			−0.556656	+	0.830743i	$0.687916\pi$
$702$	46.6065	+	41.4065i	1.75905	+	1.56279i
$703$	−2.57277	+	9.60170i	−0.0970338	+	0.362135i
$704$	−24.4645	−	20.3200i	−0.922041	−	0.765838i
$705$	−15.6713	+	45.5236i	−0.590216	+	1.71452i
$706$	35.3348	−	23.2824i	1.32984	−	0.876244i
$707$		0			0
$708$	19.4884	+	48.8172i	0.732419	+	1.83466i
$709$	15.6918	+	9.05966i	0.589318	+	0.340243i	0.764828	−	0.644235i	$-0.222824\pi$
$709$	15.6918	+	9.05966i	0.589318	+	0.340243i	−0.175510	+	0.984478i	$0.556157\pi$
$710$	−9.57038	+	5.38942i	−0.359170	+	0.202261i
$711$	−20.6788	+	11.9389i	−0.775515	+	0.447744i
$712$	11.3197	+	24.1172i	0.424225	+	0.903830i
$713$	9.46481	−	9.46481i	0.354460	−	0.354460i
$714$		0			0
$715$	−26.3277	−	17.7555i	−0.984602	−	0.664017i
$716$	−32.6931	+	24.4242i	−1.22180	+	0.912773i
$717$	−15.5894	+	58.1804i	−0.582197	+	2.17279i
$718$	3.81308	+	11.4751i	0.142303	+	0.428247i
$719$	−4.66449	+	8.07913i	−0.173956	+	0.301301i	−0.939799	−	0.341726i	$-0.888988\pi$
$719$	−4.66449	+	8.07913i	−0.173956	+	0.301301i	0.765843	+	0.643027i	$0.222322\pi$
$720$	35.9078	−	50.3949i	1.33820	−	1.87811i
$721$		0			0
$722$	−23.9195	−	4.91814i	−0.890193	−	0.183034i
$723$	43.0696	−	11.5405i	1.60178	−	0.429195i
$724$	−3.10155	−	26.1562i	−0.115268	−	0.972088i
$725$	−13.8786	+	17.7691i	−0.515438	+	0.659929i
$726$	21.3561	−	1.26176i	0.792598	−	0.0468283i
$727$	11.9373	−	11.9373i	0.442729	−	0.442729i	−0.450199	−	0.892928i	$-0.648647\pi$
$727$	11.9373	−	11.9373i	0.442729	−	0.442729i	0.892928	+	0.450199i	$0.148647\pi$
$728$		0			0
$729$		−	8.68729i		−	0.321751i
$730$	1.89692	+	7.39584i	0.0702082	+	0.273732i
$731$	2.32952	−	1.34495i	0.0861605	−	0.0497448i
$732$	−5.25192	+	6.66501i	−0.194117	+	0.246346i
$733$	−11.7409	−	43.8178i	−0.433662	−	1.61845i	−0.744249	−	0.667903i	$-0.767192\pi$
$733$	−11.7409	−	43.8178i	−0.433662	−	1.61845i	0.310587	−	0.950545i	$-0.399474\pi$
$734$	−6.19490	+	4.08187i	−0.228658	+	0.150665i
$735$		0			0
$736$	−6.66142	+	28.6396i	−0.245543	+	1.05567i
$737$	21.1765	−	5.67423i	0.780047	−	0.209013i
$738$	105.085	−	34.9187i	3.86822	−	1.28538i
$739$	11.9877	+	20.7633i	0.440975	+	0.763792i	0.997762	−	0.0668636i	$-0.0212992\pi$
$739$	11.9877	+	20.7633i	0.440975	+	0.763792i	−0.556787	+	0.830656i	$0.687966\pi$
$740$	−33.7345	+	1.63019i	−1.24010	+	0.0599271i
$741$	−14.8087			−0.544009
$742$		0			0
$743$	26.3785	+	26.3785i	0.967733	+	0.967733i	0.999495	−	0.0317628i	$-0.0101121\pi$
$743$	26.3785	+	26.3785i	0.967733	+	0.967733i	−0.0317628	+	0.999495i	$0.510112\pi$
$744$	−7.79123	+	21.5744i	−0.285640	+	0.790956i
$745$	−3.33145	+	2.89642i	−0.122055	+	0.106116i
$746$	3.90459	+	1.95687i	0.142957	+	0.0716463i
$747$	21.2141	+	79.1721i	0.776184	+	2.89676i
$748$	−7.91472	+	3.15964i	−0.289391	+	0.115528i
$749$		0			0
$750$	−45.6284	−	19.9405i	−1.66611	−	0.728123i
$751$	−45.3197	−	26.1653i	−1.65374	−	0.954786i	−0.975516	−	0.219930i	$-0.929417\pi$
$751$	−45.3197	−	26.1653i	−1.65374	−	0.954786i	−0.678223	−	0.734857i	$-0.737249\pi$
$752$	13.0594	+	24.0275i	0.476226	+	0.876192i
$753$	26.4933	+	7.09885i	0.965468	+	0.258696i
$754$	−22.7421	+	1.34365i	−0.828219	+	0.0489329i
$755$	3.68346	+	18.9424i	0.134055	+	0.689383i
$756$		0			0
$757$	23.8139	+	23.8139i	0.865530	+	0.865530i	0.991974	−	0.126444i	$-0.0403563\pi$
$757$	23.8139	+	23.8139i	0.865530	+	0.865530i	−0.126444	+	0.991974i	$0.540356\pi$
$758$	−15.9743	+	17.9804i	−0.580212	+	0.653078i
$759$	−32.5383	−	56.3581i	−1.18107	−	2.04567i
$760$	0.891529	+	8.27683i	0.0323391	+	0.300232i
$761$	−9.43544	+	16.3427i	−0.342034	+	0.592421i	−0.984810	−	0.173633i	$-0.944449\pi$
$761$	−9.43544	+	16.3427i	−0.342034	+	0.592421i	0.642776	+	0.766054i	$0.277783\pi$
$762$	−64.0134	−	13.1619i	−2.31896	−	0.476807i
$763$		0			0
$764$	−9.55054	+	22.2428i	−0.345526	+	0.804716i
$765$	−7.26997	−	14.9029i	−0.262846	−	0.538815i
$766$	17.2704	−	34.4599i	0.624004	−	1.24509i
$767$	28.7964	+	7.71597i	1.03978	+	0.278607i
$768$	−10.5193	−	49.2791i	−0.379583	−	1.77821i
$769$			12.2463i			0.441614i	0.975318	+	0.220807i	$0.0708691\pi$
$769$			12.2463i			0.441614i	−0.975318	+	0.220807i	$0.929131\pi$
$770$		0			0
$771$			18.8008i			0.677093i
$772$	−0.201194	+	1.38974i	−0.00724113	+	0.0500177i
$773$	−4.15790	−	1.11411i	−0.149549	−	0.0400716i	0.183268	−	0.983063i	$-0.441332\pi$
$773$	−4.15790	−	1.11411i	−0.149549	−	0.0400716i	−0.332817	+	0.942991i	$0.607999\pi$
$774$	−21.9508	−	11.0011i	−0.789004	−	0.395427i
$775$	12.7505	+	1.79006i	0.458011	+	0.0643010i
$776$	−6.37133	−	35.6113i	−0.228718	−	1.27837i
$777$		0			0
$778$	−3.60213	+	17.5191i	−0.129143	+	0.628089i
$779$	−7.44864	+	12.9014i	−0.266875	+	0.462242i
$780$	−15.3529	−	47.9147i	−0.549724	−	1.71562i
$781$	−6.90378	−	11.9577i	−0.247037	−	0.427880i
$782$	5.89043	+	5.23322i	0.210641	+	0.187140i
$783$	39.3473	+	39.3473i	1.40616	+	1.40616i
$784$		0			0
$785$	29.3905	+	19.8210i	1.04899	+	0.707443i
$786$	2.59005	+	43.8382i	0.0923841	+	1.56366i
$787$	4.08160	+	1.09366i	0.145493	+	0.0389848i	0.330831	−	0.943690i	$-0.392671\pi$
$787$	4.08160	+	1.09366i	0.145493	+	0.0389848i	−0.185337	+	0.982675i	$0.559338\pi$
$788$	−2.04685	+	2.59758i	−0.0729161	+	0.0925350i
$789$	43.1030	+	24.8855i	1.53451	+	0.885948i
$790$	10.9137	+	0.117072i	0.388291	+	0.00416525i
$791$		0			0
$792$	63.8327	+	44.4581i	2.26820	+	1.57975i
$793$	1.24563	+	4.64874i	0.0442334	+	0.165081i
$794$	7.68650	−	15.3370i	0.272784	−	0.544290i
$795$	38.6718	+	44.4802i	1.37155	+	1.57755i
$796$	27.9615	−	20.8893i	0.991067	−	0.740400i
$797$	35.3989	+	35.3989i	1.25389	+	1.25389i	0.953960	+	0.299933i	$0.0969644\pi$
$797$	35.3989	+	35.3989i	1.25389	+	1.25389i	0.299933	+	0.953960i	$0.403036\pi$
$798$		0			0
$799$	7.32815			0.259251
$800$	−25.8561	+	11.4657i	−0.914152	+	0.405372i
$801$	−32.5825	−	56.4346i	−1.15125	−	1.99402i
$802$	6.35788	+	19.1334i	0.224505	+	0.675625i
$803$	−9.27129	+	2.48424i	−0.327177	+	0.0876668i
$804$	31.9185	+	13.7050i	1.12568	+	0.483340i
$805$		0			0
$806$	7.15804	+	10.8635i	0.252131	+	0.382650i
$807$	6.51753	+	24.3238i	0.229428	+	0.856237i
$808$	2.45982	−	28.9518i	0.0865362	−	1.01852i
$809$	−25.0379	+	14.4556i	−0.880284	+	0.508232i	−0.870752	−	0.491722i	$-0.836368\pi$
$809$	−25.0379	+	14.4556i	−0.880284	+	0.508232i	−0.00953207	+	0.999955i	$0.503034\pi$
$810$	−29.1613	+	49.2805i	−1.02463	+	1.73154i
$811$			23.9566i			0.841229i	0.907240	+	0.420614i	$0.138185\pi$
$811$			23.9566i			0.841229i	−0.907240	+	0.420614i	$0.861815\pi$
$812$		0			0
$813$	66.9390	−	66.9390i	2.34765	−	2.34765i
$814$	−2.50411	−	42.3837i	−0.0877691	−	1.48555i
$815$	1.08540	−	15.5382i	0.0380199	−	0.544281i
$816$	−12.9483	−	3.82935i	−0.453281	−	0.134054i
$817$	3.19064	−	0.854928i	0.111626	−	0.0299102i
$818$	−8.51612	+	41.4184i	−0.297759	+	1.44816i
$819$		0			0
$820$	−49.4661	−	10.7251i	−1.72743	−	0.374537i
$821$	−17.8387	+	30.8975i	−0.622574	+	1.07833i	0.366430	+	0.930445i	$0.380580\pi$
$821$	−17.8387	+	30.8975i	−0.622574	+	1.07833i	−0.989005	+	0.147885i	$0.952754\pi$
$822$	68.2295	−	22.6721i	2.37978	−	0.790780i
$823$	−3.41164	+	12.7324i	−0.118922	+	0.443824i	−0.999550	−	0.0299839i	$-0.990454\pi$
$823$	−3.41164	+	12.7324i	−0.118922	+	0.443824i	0.880628	+	0.473808i	$0.157121\pi$
$824$	11.1196	+	4.01565i	0.387369	+	0.139892i
$825$	24.4507	−	57.6257i	0.851265	−	2.00627i
$826$		0			0
$827$	−6.42266	+	6.42266i	−0.223338	+	0.223338i	−0.809902	−	0.586565i	$-0.800480\pi$
$827$	−6.42266	+	6.42266i	−0.223338	+	0.223338i	0.586565	+	0.809902i	$0.300480\pi$
$828$	10.3048	−	71.1798i	0.358117	−	2.47367i
$829$	−16.2271	+	9.36870i	−0.563589	+	0.325388i	−0.754585	−	0.656202i	$-0.772162\pi$
$829$	−16.2271	+	9.36870i	−0.563589	+	0.325388i	0.190996	+	0.981591i	$0.438828\pi$
$830$	10.0844	−	36.0827i	0.350033	−	1.25245i
$831$	6.74002	+	3.89135i	0.233809	+	0.134990i
$832$	−25.9617	−	11.9480i	−0.900059	−	0.414223i
$833$		0			0
$834$	22.3150	+	33.8666i	0.772706	+	1.17271i
$835$	16.5275	+	33.8802i	0.571958	+	1.17247i
$836$	−10.3923	+	1.23230i	−0.359425	+	0.0426199i
$837$	8.22443	−	30.6940i	0.284278	−	1.06094i
$838$	35.3644	−	39.8056i	1.22164	−	1.37506i
$839$	50.3921			1.73973			0.869864	−	0.493291i	$-0.164206\pi$
$839$	50.3921			1.73973			0.869864	+	0.493291i	$0.164206\pi$
$840$		0			0
$841$	8.66571			0.298818
$842$	7.86338	−	8.85090i	0.270990	−	0.305022i
$843$	−2.32395	+	8.67309i	−0.0800410	+	0.298717i
$844$	12.5621	−	1.48958i	0.432404	−	0.0512735i
$845$	0.503339	+	0.173272i	0.0173154	+	0.00596075i
$846$	−36.8038	−	55.8557i	−1.26534	−	1.92036i
$847$		0			0
$848$	33.4678	+	0.861844i	1.14929	+	0.0295958i
$849$	23.5989	+	13.6249i	0.809914	+	0.467604i
$850$	−0.609221	+	7.55474i	−0.0208961	+	0.259125i
$851$	−33.9960	+	19.6276i	−1.16537	+	0.672826i
$852$	3.13451	−	21.6514i	0.107386	−	0.741765i
$853$	−12.0652	+	12.0652i	−0.413104	+	0.413104i	−0.882818	−	0.469714i	$-0.844357\pi$
$853$	−12.0652	+	12.0652i	−0.413104	+	0.413104i	0.469714	+	0.882818i	$0.344357\pi$
$854$		0			0
$855$	−3.88673	−	19.9877i	−0.132923	−	0.683565i
$856$	15.2857	−	42.3270i	0.522454	−	1.44671i
$857$	−5.32241	+	19.8635i	−0.181810	+	0.678525i	0.813481	+	0.581592i	$0.197570\pi$
$857$	−5.32241	+	19.8635i	−0.181810	+	0.678525i	−0.995291	+	0.0969329i	$0.969097\pi$
$858$	60.0237	−	19.9454i	2.04918	−	0.680925i
$859$	21.8383	−	37.8250i	0.745112	−	1.29057i	−0.205030	−	0.978756i	$-0.565729\pi$
$859$	21.8383	−	37.8250i	0.745112	−	1.29057i	0.950142	−	0.311816i	$-0.100937\pi$
$860$	6.07410	+	9.43723i	0.207125	+	0.321807i
$861$		0			0
$862$	1.41825	−	6.89769i	0.0483057	−	0.234936i
$863$	−24.6545	+	6.60616i	−0.839250	+	0.224876i	−0.652745	−	0.757578i	$-0.726383\pi$
$863$	−24.6545	+	6.60616i	−0.839250	+	0.224876i	−0.186505	+	0.982454i	$0.559716\pi$
$864$	20.2997	+	66.7888i	0.690611	+	2.27220i
$865$	−0.493887	−	0.0344997i	−0.0167927	−	0.00117302i
$866$	−0.319125	−	5.40139i	−0.0108443	−	0.183547i
$867$	35.2990	−	35.2990i	1.19882	−	1.19882i
$868$		0			0
$869$			13.7205i			0.465437i
$870$	−11.1573	−	43.5009i	−0.378269	−	1.47482i
$871$	17.0618	−	9.85064i	0.578117	−	0.333776i
$872$	8.41391	+	0.714869i	0.284931	+	0.0242085i
$873$	22.9023	+	85.4726i	0.775126	+	2.89281i
$874$	5.32368	+	8.07955i	0.180076	+	0.273295i
$875$		0			0
$876$	−13.9742	−	6.00021i	−0.472145	−	0.202728i
$877$	−49.9561	+	13.3857i	−1.68690	+	0.452002i	−0.969586	−	0.244751i	$-0.921294\pi$
$877$	−49.9561	+	13.3857i	−1.68690	+	0.452002i	−0.717310	+	0.696754i	$0.754627\pi$
$878$	16.7391	+	50.3746i	0.564916	+	1.70006i
$879$	−36.8034	−	63.7454i	−1.24135	−	2.15008i
$880$	−14.7615	−	32.3476i	−0.497609	−	1.09044i
$881$	29.9298			1.00836			0.504181	−	0.863598i	$-0.331795\pi$
$881$	29.9298			1.00836			0.504181	+	0.863598i	$0.331795\pi$
$882$		0			0
$883$	−22.0057	−	22.0057i	−0.740550	−	0.740550i	0.232134	−	0.972684i	$-0.425429\pi$
$883$	−22.0057	−	22.0057i	−0.740550	−	0.740550i	−0.972684	+	0.232134i	$0.925429\pi$
$884$	−6.13521	+	4.58346i	−0.206350	+	0.154158i
$885$	−4.09515	+	58.6249i	−0.137657	+	1.97065i
$886$	8.04170	−	16.0458i	0.270166	−	0.539068i
$887$	12.4757	+	46.5601i	0.418894	+	1.56333i	0.776905	+	0.629618i	$0.216788\pi$
$887$	12.4757	+	46.5601i	0.418894	+	1.56333i	−0.358011	+	0.933717i	$0.616545\pi$
$888$	38.4469	−	55.2019i	1.29019	−	1.85245i
$889$		0			0
$890$	−0.319503	+	29.7845i	−0.0107098	+	0.998380i
$891$	−62.3408	−	35.9925i	−2.08850	−	1.20579i
$892$	−1.98567	+	2.51993i	−0.0664851	+	0.0843736i
$893$	8.69230	+	2.32910i	0.290877	+	0.0779402i
$894$	−0.518595	−	8.77755i	−0.0173444	−	0.293565i
$895$	−44.7870	+	8.70910i	−1.49706	+	0.291113i
$896$		0			0
$897$	−41.3518	−	41.3518i	−1.38070	−	1.38070i
$898$	26.6041	+	23.6359i	0.887792	+	0.788739i
$899$	5.80603	+	10.0563i	0.193642	+	0.335398i
$900$	60.6424	−	33.2982i	2.02141	−	1.10994i
$901$	4.48563	−	7.76933i	0.149438	−	0.258834i
$902$	12.8149	−	62.3256i	0.426689	−	2.07522i
$903$		0			0
$904$	−1.60376	+	0.286935i	−0.0533404	+	0.00954330i
$905$	9.58543	−	27.8447i	0.318630	−	0.925589i
$906$	−34.3624	−	17.2215i	−1.14161	−	0.572145i
$907$	7.78619	+	2.08630i	0.258536	+	0.0692745i	0.385759	−	0.922600i	$-0.373940\pi$
$907$	7.78619	+	2.08630i	0.258536	+	0.0692745i	−0.127223	+	0.991874i	$0.540606\pi$
$908$	1.43587	−	9.91819i	0.0476510	−	0.329147i
$909$			71.0708i			2.35727i
$910$		0			0
$911$		−	15.9014i		−	0.526836i	−0.964682	−	0.263418i	$-0.915150\pi$
$911$		−	15.9014i		−	0.526836i	0.964682	−	0.263418i	$-0.0848498\pi$
$912$	−14.1416	−	8.65754i	−0.468275	−	0.286680i
$913$	45.4934	+	12.1899i	1.50561	+	0.403427i
$914$	17.2344	−	34.3882i	0.570065	−	1.13746i
$915$	−8.52670	+	4.15952i	−0.281884	+	0.137509i
$916$	8.14218	−	18.9628i	0.269025	−	0.626548i
$917$		0			0
$918$	18.3223	+	3.76729i	0.604727	+	0.124339i
$919$	−22.6796	+	39.2823i	−0.748132	+	1.29580i	0.200585	+	0.979676i	$0.435716\pi$
$919$	−22.6796	+	39.2823i	−0.748132	+	1.29580i	−0.948717	+	0.316127i	$0.897618\pi$
$920$	−20.6228	+	25.6018i	−0.679912	+	0.844065i
$921$	−33.4614	−	57.9569i	−1.10259	−	1.90975i
$922$	−18.7905	+	21.1503i	−0.618833	+	0.696548i
$923$	−8.77375	−	8.77375i	−0.288792	−	0.288792i
$924$		0			0
$925$	−34.7607	−	14.7490i	−1.14292	−	0.484946i
$926$	−20.2677	+	1.19746i	−0.666038	+	0.0393508i
$927$	−27.9322	−	7.48442i	−0.917415	−	0.245821i
$928$	−22.5032	−	12.0125i	−0.738705	−	0.394331i
$929$	33.4187	+	19.2943i	1.09643	+	0.633025i	0.935281	−	0.353905i	$-0.115146\pi$
$929$	33.4187	+	19.2943i	1.09643	+	0.633025i	0.161150	+	0.986930i	$0.448480\pi$
$930$	−18.3277	+	17.9386i	−0.600988	+	0.588231i
$931$		0			0
$932$	−23.7289	+	9.47283i	−0.777265	+	0.310293i
$933$	−22.9641	−	85.7032i	−0.751811	−	2.80580i
$934$	5.22689	+	2.61957i	0.171029	+	0.0857151i
$935$	−9.50483	−	0.663945i	−0.310841	−	0.0217133i
$936$	65.7480	+	23.7438i	2.14904	+	0.776090i
$937$	−15.2293	−	15.2293i	−0.497519	−	0.497519i	0.413146	−	0.910665i	$-0.364430\pi$
$937$	−15.2293	−	15.2293i	−0.497519	−	0.497519i	−0.910665	+	0.413146i	$0.864430\pi$
$938$		0			0
$939$	−80.8383			−2.63806
$940$	1.47579	+	30.5394i	0.0481351	+	0.996086i
$941$	−23.7077	−	41.0629i	−0.772848	−	1.33861i	−0.935996	−	0.352010i	$-0.885498\pi$
$941$	−23.7077	−	41.0629i	−0.772848	−	1.33861i	0.163148	−	0.986602i	$-0.447835\pi$
$942$	−67.0065	+	22.2657i	−2.18319	+	0.725456i
$943$	−56.8256	+	15.2264i	−1.85050	+	0.495839i
$944$	22.9883	+	24.2035i	0.748205	+	0.787758i
$945$		0			0
$946$	−11.7811	+	7.76266i	−0.383036	+	0.252386i
$947$	9.12616	+	34.0593i	0.296560	+	1.10678i	0.939970	+	0.341257i	$0.110853\pi$
$947$	9.12616	+	34.0593i	0.296560	+	1.10678i	−0.643410	+	0.765522i	$0.722481\pi$
$948$	−13.4549	+	17.0751i	−0.436996	+	0.554574i
$949$	−7.46983	+	4.31271i	−0.242481	+	0.139996i
$950$	−3.12374	+	8.76745i	−0.101348	+	0.284454i
$951$		−	82.8346i		−	2.68610i
$952$		0			0
$953$	34.4409	−	34.4409i	1.11565	−	1.11565i	0.123279	−	0.992372i	$-0.460659\pi$
$953$	34.4409	−	34.4409i	1.11565	−	1.11565i	0.992372	−	0.123279i	$-0.0393409\pi$
$954$	−81.7464	+	4.82974i	−2.64664	+	0.156369i
$955$	−20.4239	+	17.7569i	−0.660903	+	0.574599i
$956$	4.50419	+	37.9850i	0.145676	+	1.22852i
$957$	54.5320	−	14.6118i	1.76277	−	0.472332i
$958$	−12.9228	−	2.65709i	−0.417518	−	0.0858467i
$959$		0			0
$960$	13.3509	−	54.7321i	0.430897	−	1.76647i
$961$	−12.1844	+	21.1040i	−0.393046	+	0.680775i
$962$	−12.0314	−	36.2072i	−0.387907	−	1.16737i
$963$	−28.4896	+	106.325i	−0.918065	+	3.42627i
$964$	22.6850	−	16.9474i	0.730634	−	0.545838i
$965$	−0.877821	+	1.30163i	−0.0282581	+	0.0419009i
$966$		0			0
$967$	28.3737	−	28.3737i	0.912437	−	0.912437i	−0.0840261	−	0.996464i	$-0.526778\pi$
$967$	28.3737	−	28.3737i	0.912437	−	0.912437i	0.996464	+	0.0840261i	$0.0267779\pi$
$968$	12.2986	−	5.77252i	0.395292	−	0.185536i
$969$	−3.84795	+	2.22162i	−0.123614	+	0.0713686i
$970$	10.8869	−	38.9541i	0.349556	−	1.25074i
$971$	−6.28643	−	3.62947i	−0.201741	−	0.116475i	0.395726	−	0.918369i	$-0.370493\pi$
$971$	−6.28643	−	3.62947i	−0.201741	−	0.116475i	−0.597467	+	0.801893i	$0.703826\pi$
$972$	−14.8361	−	37.1635i	−0.475867	−	1.19202i
$973$		0			0
$974$	34.2406	−	22.5614i	1.09714	−	0.722913i
$975$	7.82079	−	55.7068i	0.250466	−	1.78405i
$976$	−1.52826	+	5.16756i	−0.0489184	+	0.165410i
$977$	3.08533	−	11.5146i	0.0987084	−	0.368385i	−0.898847	−	0.438262i	$-0.855594\pi$
$977$	3.08533	−	11.5146i	0.0987084	−	0.368385i	0.997556	+	0.0698774i	$0.0222608\pi$
$978$	23.1934	+	20.6057i	0.741644	+	0.658897i
$979$	−37.4447			−1.19674
$980$		0			0
$981$	−20.6545			−0.659446
$982$	29.7949	+	26.4706i	0.950794	+	0.844712i
$983$	4.89406	−	18.2649i	0.156096	−	0.582560i	−0.842913	−	0.538050i	$-0.819161\pi$
$983$	4.89406	−	18.2649i	0.156096	−	0.582560i	0.999009	−	0.0445091i	$-0.0141724\pi$
$984$	77.0672	−	64.9970i	2.45681	−	2.07203i
$985$	−3.32315	+	1.62111i	−0.105884	+	0.0516528i
$986$	−5.70785	+	3.76095i	−0.181775	+	0.119773i
$987$		0			0
$988$	−8.73406	+	3.48673i	−0.277867	+	0.110928i
$989$	11.2969	+	6.52224i	0.359219	+	0.207395i
$990$	42.6750	+	75.7810i	1.35630	+	2.40848i
$991$	19.1208	−	11.0394i	0.607392	−	0.350678i	−0.164552	−	0.986368i	$-0.552618\pi$
$991$	19.1208	−	11.0394i	0.607392	−	0.350678i	0.771944	+	0.635690i	$0.219284\pi$
$992$	0.484520	+	14.5589i	0.0153835	+	0.462246i
$993$	−38.3078	+	38.3078i	−1.21566	+	1.21566i
$994$		0			0
$995$	38.3050	−	7.44864i	1.21435	−	0.236138i
$996$	44.6623	+	59.7830i	1.41518	+	1.89430i
$997$	−7.72606	+	28.8340i	−0.244687	+	0.913183i	0.728854	+	0.684669i	$0.240053\pi$
$997$	−7.72606	+	28.8340i	−0.244687	+	0.913183i	−0.973541	+	0.228514i	$0.926613\pi$
$998$	13.8574	+	41.7025i	0.438648	+	1.32007i
$999$	−46.5962	+	80.7070i	−1.47424	+	2.55346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.j.667.4		64
4.3	odd	2	inner	980.2.x.j.667.1		64
5.3	odd	4	inner	980.2.x.j.863.14		64
7.2	even	3		980.2.k.i.687.16	yes	32
7.3	odd	6	inner	980.2.x.j.67.8		64
7.4	even	3	inner	980.2.x.j.67.7		64
7.5	odd	6		980.2.k.i.687.15	yes	32
7.6	odd	2	inner	980.2.x.j.667.3		64
20.3	even	4	inner	980.2.x.j.863.7		64
28.3	even	6	inner	980.2.x.j.67.13		64
28.11	odd	6	inner	980.2.x.j.67.14		64
28.19	even	6		980.2.k.i.687.12	yes	32
28.23	odd	6		980.2.k.i.687.11	✓	32
28.27	even	2	inner	980.2.x.j.667.2		64
35.3	even	12	inner	980.2.x.j.263.2		64
35.13	even	4	inner	980.2.x.j.863.13		64
35.18	odd	12	inner	980.2.x.j.263.1		64
35.23	odd	12		980.2.k.i.883.11	yes	32
35.33	even	12		980.2.k.i.883.12	yes	32
140.3	odd	12	inner	980.2.x.j.263.3		64
140.23	even	12		980.2.k.i.883.16	yes	32
140.83	odd	4	inner	980.2.x.j.863.8		64
140.103	odd	12		980.2.k.i.883.15	yes	32
140.123	even	12	inner	980.2.x.j.263.4		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.i.687.11	✓	32	28.23	odd	6
980.2.k.i.687.12	yes	32	28.19	even	6
980.2.k.i.687.15	yes	32	7.5	odd	6
980.2.k.i.687.16	yes	32	7.2	even	3
980.2.k.i.883.11	yes	32	35.23	odd	12
980.2.k.i.883.12	yes	32	35.33	even	12
980.2.k.i.883.15	yes	32	140.103	odd	12
980.2.k.i.883.16	yes	32	140.23	even	12
980.2.x.j.67.7		64	7.4	even	3	inner
980.2.x.j.67.8		64	7.3	odd	6	inner
980.2.x.j.67.13		64	28.3	even	6	inner
980.2.x.j.67.14		64	28.11	odd	6	inner
980.2.x.j.263.1		64	35.18	odd	12	inner
980.2.x.j.263.2		64	35.3	even	12	inner
980.2.x.j.263.3		64	140.3	odd	12	inner
980.2.x.j.263.4		64	140.123	even	12	inner
980.2.x.j.667.1		64	4.3	odd	2	inner
980.2.x.j.667.2		64	28.27	even	2	inner
980.2.x.j.667.3		64	7.6	odd	2	inner
980.2.x.j.667.4		64	1.1	even	1	trivial
980.2.x.j.863.7		64	20.3	even	4	inner
980.2.x.j.863.8		64	140.83	odd	4	inner
980.2.x.j.863.13		64	35.13	even	4	inner
980.2.x.j.863.14		64	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.939280 + 1.05724i) q^{2} +(0.815107 - 3.04202i) q^{3} +(-0.235506 - 1.98609i) q^{4} +(0.727838 - 2.11430i) q^{5} +(2.45053 + 3.71907i) q^{6} +(2.32097 + 1.61650i) q^{8} +(-5.99142 - 3.45915i) q^{9} +(1.55167 + 2.75542i) q^{10} +(-3.44275 + 1.98767i) q^{11} +(-6.23368 - 0.902458i) q^{12} +(-2.52606 + 2.52606i) q^{13} +(-5.83847 - 3.93748i) q^{15} +(-3.88907 + 0.935470i) q^{16} +(-0.277420 + 1.03535i) q^{17} +(9.28476 - 3.08525i) q^{18} +(-0.658126 + 1.13991i) q^{19} +(-4.37059 - 0.947619i) q^{20} +(1.13226 - 5.50679i) q^{22} +(-5.02084 + 1.34533i) q^{23} +(6.80928 - 5.74282i) q^{24} +(-3.94050 - 3.07773i) q^{25} +(-0.297970 - 5.04332i) q^{26} +(-8.72570 + 8.72570i) q^{27} -4.50936i q^{29} +(9.64681 - 2.47426i) q^{30} +(-2.23010 + 1.28755i) q^{31} +(2.66391 - 4.99035i) q^{32} +(3.24033 + 12.0931i) q^{33} +(-0.834032 - 1.26578i) q^{34} +(-5.45915 + 12.7141i) q^{36} +(7.29473 - 1.95462i) q^{37} +(-0.586989 - 1.76649i) q^{38} +(5.62531 + 9.74333i) q^{39} +(5.10706 - 3.73067i) q^{40} +11.3180 q^{41} +(-1.77452 - 1.77452i) q^{43} +(4.75847 + 6.36949i) q^{44} +(-11.6744 + 10.1499i) q^{45} +(3.29364 - 6.57186i) q^{46} +(-1.76949 - 6.60383i) q^{47} +(-0.324292 + 12.5932i) q^{48} +(6.95513 - 1.27520i) q^{50} +(2.92342 + 1.68784i) q^{51} +(5.61187 + 4.42207i) q^{52} +(-8.08454 - 2.16624i) q^{53} +(-1.02927 - 17.4210i) q^{54} +(1.69676 + 8.72570i) q^{55} +(2.93118 + 2.93118i) q^{57} +(4.76746 + 4.23555i) q^{58} +(-4.17259 - 7.22714i) q^{59} +(-6.44517 + 12.5230i) q^{60} +(0.673601 - 1.16671i) q^{61} +(0.733444 - 3.56712i) q^{62} +(2.77382 + 7.50373i) q^{64} +(3.50228 + 7.17940i) q^{65} +(-15.8288 - 7.93298i) q^{66} +(-5.32697 - 1.42736i) q^{67} +(2.12162 + 0.307150i) q^{68} +16.3701i q^{69} +3.47330i q^{71} +(-8.31418 - 17.7137i) q^{72} +(2.33220 + 0.624911i) q^{73} +(-4.78530 + 9.54820i) q^{74} +(-12.5745 + 9.47841i) q^{75} +(2.41895 + 1.03864i) q^{76} +(-15.5848 - 3.20442i) q^{78} +(1.72570 - 2.98900i) q^{79} +(-0.852754 + 8.90353i) q^{80} +(9.05394 + 15.6819i) q^{81} +(-10.6307 + 11.9658i) q^{82} +(-8.37751 - 8.37751i) q^{83} +(1.98711 + 1.34011i) q^{85} +(3.54285 - 0.209319i) q^{86} +(-13.7176 - 3.67561i) q^{87} +(-11.2036 - 0.951889i) q^{88} +(8.15730 + 4.70962i) q^{89} +(0.234670 - 21.8763i) q^{90} +(3.85438 + 9.65498i) q^{92} +(2.09898 + 7.83352i) q^{93} +(8.64387 + 4.33207i) q^{94} +(1.93109 + 2.22114i) q^{95} +(-13.0094 - 12.1714i) q^{96} +(-9.04418 - 9.04418i) q^{97} +27.5026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 16 q^{8} - 8 q^{16} + 40 q^{18} - 72 q^{22} - 32 q^{25} + 36 q^{30} - 16 q^{32} - 176 q^{36} + 48 q^{37} + 56 q^{50} - 16 q^{53} - 32 q^{57} - 36 q^{58} + 80 q^{60} - 64 q^{65} - 56 q^{72}+ \cdots - 32 q^{93}+O(q^{100}) \) 64 * q + 4 * q^2 + 16 * q^8 - 8 * q^16 + 40 * q^18 - 72 * q^22 - 32 * q^25 + 36 * q^30 - 16 * q^32 - 176 * q^36 + 48 * q^37 + 56 * q^50 - 16 * q^53 - 32 * q^57 - 36 * q^58 + 80 * q^60 - 64 * q^65 - 56 * q^72 + 56 * q^78 - 56 * q^86 - 88 * q^88 + 272 * q^92 - 32 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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