LMFDB - Embedded newform 195.2.o.a.161.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(86,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.86"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.o (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.11
Character	$\chi$	$=$	195.161
Dual form			195.2.o.a.86.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.260415 + 0.260415i) q^{2} +(1.18585 + 1.26244i) q^{3} -1.86437i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.0199472 + 0.637571i) q^{6} +(2.54331 + 2.54331i) q^{7} +(1.00634 - 1.00634i) q^{8} +(-0.187534 + 2.99413i) q^{9} -0.368282i q^{10} +(0.348374 - 0.348374i) q^{11} +(2.35366 - 2.21086i) q^{12} +(-0.339913 - 3.58949i) q^{13} +1.32463i q^{14} +(0.0541629 - 1.73120i) q^{15} -3.20461 q^{16} +5.28437 q^{17} +(-0.828552 + 0.730879i) q^{18} +(-3.44898 + 3.44898i) q^{19} +(-1.31831 + 1.31831i) q^{20} +(-0.194812 + 6.22677i) q^{21} +0.181443 q^{22} -9.38135 q^{23} +(2.46381 + 0.0770834i) q^{24} +1.00000i q^{25} +(0.846238 - 1.02327i) q^{26} +(-4.00231 + 3.31383i) q^{27} +(4.74167 - 4.74167i) q^{28} -6.80884i q^{29} +(0.464935 - 0.436726i) q^{30} +(-2.96376 + 2.96376i) q^{31} +(-2.84720 - 2.84720i) q^{32} +(0.852920 + 0.0266847i) q^{33} +(1.37613 + 1.37613i) q^{34} -3.59678i q^{35} +(5.58217 + 0.349633i) q^{36} +(1.76399 + 1.76399i) q^{37} -1.79633 q^{38} +(4.12845 - 4.68571i) q^{39} -1.42318 q^{40} +(-2.21539 - 2.21539i) q^{41} +(-1.67227 + 1.57081i) q^{42} -5.41717i q^{43} +(-0.649497 - 0.649497i) q^{44} +(2.24978 - 1.98456i) q^{45} +(-2.44304 - 2.44304i) q^{46} +(-2.47000 + 2.47000i) q^{47} +(-3.80017 - 4.04564i) q^{48} +5.93686i q^{49} +(-0.260415 + 0.260415i) q^{50} +(6.26646 + 6.67123i) q^{51} +(-6.69214 + 0.633724i) q^{52} -6.94843i q^{53} +(-1.90523 - 0.179291i) q^{54} -0.492675 q^{55} +5.11886 q^{56} +(-8.44410 - 0.264184i) q^{57} +(1.77312 - 1.77312i) q^{58} +(-0.248775 + 0.248775i) q^{59} +(-3.22760 - 0.100980i) q^{60} -3.60093 q^{61} -1.54361 q^{62} +(-8.09197 + 7.13805i) q^{63} +4.92631i q^{64} +(-2.29780 + 2.77851i) q^{65} +(0.215164 + 0.229062i) q^{66} +(-1.34019 + 1.34019i) q^{67} -9.85202i q^{68} +(-11.1248 - 11.8434i) q^{69} +(0.936655 - 0.936655i) q^{70} +(11.6961 + 11.6961i) q^{71} +(2.82439 + 3.20183i) q^{72} +(6.48532 + 6.48532i) q^{73} +0.918735i q^{74} +(-1.26244 + 1.18585i) q^{75} +(6.43016 + 6.43016i) q^{76} +1.77204 q^{77} +(2.29534 - 0.145118i) q^{78} +2.66096 q^{79} +(2.26600 + 2.26600i) q^{80} +(-8.92966 - 1.12300i) q^{81} -1.15384i q^{82} +(7.35570 + 7.35570i) q^{83} +(11.6090 + 0.363202i) q^{84} +(-3.73662 - 3.73662i) q^{85} +(1.41071 - 1.41071i) q^{86} +(8.59579 - 8.07424i) q^{87} -0.701163i q^{88} +(-2.54802 + 2.54802i) q^{89} +(1.10268 + 0.0690654i) q^{90} +(8.26469 - 9.99370i) q^{91} +17.4903i q^{92} +(-7.25614 - 0.227017i) q^{93} -1.28645 q^{94} +4.87759 q^{95} +(0.218090 - 6.97078i) q^{96} +(10.4901 - 10.4901i) q^{97} +(-1.54604 + 1.54604i) q^{98} +(0.977745 + 1.10841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} - 16 q^{7} + 4 q^{15} - 64 q^{16} + 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} - 24 q^{27} + 32 q^{28} + 32 q^{31} - 4 q^{33} - 16 q^{34} + 32 q^{37} - 8 q^{39} + 8 q^{42} - 8 q^{45} - 40 q^{46}+ \cdots - 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 - 16 * q^7 + 4 * q^15 - 64 * q^16 + 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 - 24 * q^27 + 32 * q^28 + 32 * q^31 - 4 * q^33 - 16 * q^34 + 32 * q^37 - 8 * q^39 + 8 * q^42 - 8 * q^45 - 40 * q^46 + 8 * q^48 - 32 * q^54 + 8 * q^55 - 36 * q^57 + 24 * q^58 + 16 * q^60 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 + 132 * q^72 - 64 * q^73 + 16 * q^76 - 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 24 * q^85 + 16 * q^87 + 8 * q^91 - 108 * q^93 - 32 * q^94 - 76 * q^96 + 24 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	0.260415	+	0.260415i	0.184141	+	0.184141i	0.793157	−	0.609017i	$-0.208436\pi$
$2$	0.260415	+	0.260415i	0.184141	+	0.184141i	−0.609017	+	0.793157i	$0.708436\pi$
$3$	1.18585	+	1.26244i	0.684649	+	0.728873i
$3$	1.18585	+	1.26244i	0.684649	+	0.728873i
$4$		−	1.86437i		−	0.932184i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−0.0199472	+	0.637571i	−0.00814341	+	0.260287i
$7$	2.54331	+	2.54331i	0.961281	+	0.961281i	0.999278	−	0.0379967i	$-0.0120976\pi$
$7$	2.54331	+	2.54331i	0.961281	+	0.961281i	−0.0379967	+	0.999278i	$0.512098\pi$
$8$	1.00634	−	1.00634i	0.355794	−	0.355794i
$9$	−0.187534	+	2.99413i	−0.0625113	+	0.998044i
$10$		−	0.368282i		−	0.116461i
$11$	0.348374	−	0.348374i	0.105039	−	0.105039i	−0.652634	−	0.757673i	$-0.726336\pi$
$11$	0.348374	−	0.348374i	0.105039	−	0.105039i	0.757673	+	0.652634i	$0.226336\pi$
$12$	2.35366	−	2.21086i	0.679444	−	0.638219i
$13$	−0.339913	−	3.58949i	−0.0942750	−	0.995546i
$13$	−0.339913	−	3.58949i	−0.0942750	−	0.995546i
$14$			1.32463i			0.354022i
$15$	0.0541629	−	1.73120i	0.0139848	−	0.446995i
$16$	−3.20461			−0.801152
$17$	5.28437			1.28165			0.640824	−	0.767688i	$-0.278593\pi$
$17$	5.28437			1.28165			0.640824	+	0.767688i	$0.278593\pi$
$18$	−0.828552	+	0.730879i	−0.195292	+	0.172270i
$19$	−3.44898	+	3.44898i	−0.791249	+	0.791249i	−0.981697	−	0.190448i	$-0.939006\pi$
$19$	−3.44898	+	3.44898i	−0.791249	+	0.791249i	0.190448	+	0.981697i	$0.439006\pi$
$20$	−1.31831	+	1.31831i	−0.294783	+	0.294783i
$21$	−0.194812	+	6.22677i	−0.0425115	+	1.35879i
$22$	0.181443			0.0386838
$23$	−9.38135			−1.95615			−0.978073	−	0.208262i	$-0.933219\pi$
$23$	−9.38135			−1.95615			−0.978073	+	0.208262i	$0.933219\pi$
$24$	2.46381	+	0.0770834i	0.502923	+	0.0157346i
$25$			1.00000i			0.200000i
$26$	0.846238	−	1.02327i	0.165961	−	0.200681i
$27$	−4.00231	+	3.31383i	−0.770246	+	0.637747i
$28$	4.74167	−	4.74167i	0.896091	−	0.896091i
$29$		−	6.80884i		−	1.26437i	−0.774817	−	0.632185i	$-0.782158\pi$
$29$		−	6.80884i		−	1.26437i	0.774817	−	0.632185i	$-0.217842\pi$
$30$	0.464935	−	0.436726i	0.0848852	−	0.0797349i
$31$	−2.96376	+	2.96376i	−0.532306	+	0.532306i	−0.921258	−	0.388952i	$-0.872837\pi$
$31$	−2.96376	+	2.96376i	−0.532306	+	0.532306i	0.388952	+	0.921258i	$0.372837\pi$
$32$	−2.84720	−	2.84720i	−0.503319	−	0.503319i
$33$	0.852920	+	0.0266847i	0.148474	+	0.00464521i
$34$	1.37613	+	1.37613i	0.236004	+	0.236004i
$35$		−	3.59678i		−	0.607968i
$36$	5.58217	+	0.349633i	0.930361	+	0.0582721i
$37$	1.76399	+	1.76399i	0.289998	+	0.289998i	0.837079	−	0.547082i	$-0.184261\pi$
$37$	1.76399	+	1.76399i	0.289998	+	0.289998i	−0.547082	+	0.837079i	$0.684261\pi$
$38$	−1.79633			−0.291403
$39$	4.12845	−	4.68571i	0.661081	−	0.750314i
$40$	−1.42318			−0.225024
$41$	−2.21539	−	2.21539i	−0.345986	−	0.345986i	0.512626	−	0.858612i	$-0.328673\pi$
$41$	−2.21539	−	2.21539i	−0.345986	−	0.345986i	−0.858612	+	0.512626i	$0.828673\pi$
$42$	−1.67227	+	1.57081i	−0.258037	+	0.242381i
$43$		−	5.41717i		−	0.826110i	−0.910706	−	0.413055i	$-0.864462\pi$
$43$		−	5.41717i		−	0.826110i	0.910706	−	0.413055i	$-0.135538\pi$
$44$	−0.649497	−	0.649497i	−0.0979153	−	0.0979153i
$45$	2.24978	−	1.98456i	0.335377	−	0.295841i
$46$	−2.44304	−	2.44304i	−0.360207	−	0.360207i
$47$	−2.47000	+	2.47000i	−0.360286	+	0.360286i	−0.863918	−	0.503632i	$-0.831997\pi$
$47$	−2.47000	+	2.47000i	−0.360286	+	0.360286i	0.503632	+	0.863918i	$0.331997\pi$
$48$	−3.80017	−	4.04564i	−0.548508	−	0.583938i
$49$			5.93686i			0.848123i
$50$	−0.260415	+	0.260415i	−0.0368282	+	0.0368282i
$51$	6.26646	+	6.67123i	0.877480	+	0.934159i
$52$	−6.69214	+	0.633724i	−0.928032	+	0.0878817i
$53$		−	6.94843i		−	0.954441i	−0.878784	−	0.477220i	$-0.841644\pi$
$53$		−	6.94843i		−	0.954441i	0.878784	−	0.477220i	$-0.158356\pi$
$54$	−1.90523	−	0.179291i	−0.259269	−	0.0243984i
$55$	−0.492675			−0.0664322
$56$	5.11886			0.684036
$57$	−8.44410	−	0.264184i	−1.11845	−	0.0349921i
$58$	1.77312	−	1.77312i	0.232822	−	0.232822i
$59$	−0.248775	+	0.248775i	−0.0323877	+	0.0323877i	−0.723115	−	0.690727i	$-0.757290\pi$
$59$	−0.248775	+	0.248775i	−0.0323877	+	0.0323877i	0.690727	+	0.723115i	$0.257290\pi$
$60$	−3.22760	−	0.100980i	−0.416682	−	0.0130364i
$61$	−3.60093			−0.461052			−0.230526	−	0.973066i	$-0.574045\pi$
$61$	−3.60093			−0.461052			−0.230526	+	0.973066i	$0.574045\pi$
$62$	−1.54361			−0.196039
$63$	−8.09197	+	7.13805i	−1.01949	+	0.899310i
$64$			4.92631i			0.615789i
$65$	−2.29780	+	2.77851i	−0.285007	+	0.344632i
$66$	0.215164	+	0.229062i	0.0264848	+	0.0281956i
$67$	−1.34019	+	1.34019i	−0.163731	+	0.163731i	−0.784217	−	0.620486i	$-0.786935\pi$
$67$	−1.34019	+	1.34019i	−0.163731	+	0.163731i	0.620486	+	0.784217i	$0.286935\pi$
$68$		−	9.85202i		−	1.19473i
$69$	−11.1248	−	11.8434i	−1.33927	−	1.42578i
$70$	0.936655	−	0.936655i	0.111952	−	0.111952i
$71$	11.6961	+	11.6961i	1.38807	+	1.38807i	0.829361	+	0.558713i	$0.188705\pi$
$71$	11.6961	+	11.6961i	1.38807	+	1.38807i	0.558713	+	0.829361i	$0.311295\pi$
$72$	2.82439	+	3.20183i	0.332857	+	0.377339i
$73$	6.48532	+	6.48532i	0.759050	+	0.759050i	0.976149	−	0.217100i	$-0.0696597\pi$
$73$	6.48532	+	6.48532i	0.759050	+	0.759050i	−0.217100	+	0.976149i	$0.569660\pi$
$74$			0.918735i			0.106801i
$75$	−1.26244	+	1.18585i	−0.145775	+	0.136930i
$76$	6.43016	+	6.43016i	0.737590	+	0.737590i
$77$	1.77204			0.201943
$78$	2.29534	−	0.145118i	0.259896	−	0.0164314i
$79$	2.66096			0.299382			0.149691	−	0.988733i	$-0.452172\pi$
$79$	2.66096			0.299382			0.149691	+	0.988733i	$0.452172\pi$
$80$	2.26600	+	2.26600i	0.253346	+	0.253346i
$81$	−8.92966	−	1.12300i	−0.992185	−	0.124778i
$82$		−	1.15384i		−	0.127420i
$83$	7.35570	+	7.35570i	0.807393	+	0.807393i	0.984239	−	0.176846i	$-0.0565894\pi$
$83$	7.35570	+	7.35570i	0.807393	+	0.807393i	−0.176846	+	0.984239i	$0.556589\pi$
$84$	11.6090	+	0.363202i	1.26664	+	0.0396286i
$85$	−3.73662	−	3.73662i	−0.405293	−	0.405293i
$86$	1.41071	−	1.41071i	0.152121	−	0.152121i
$87$	8.59579	−	8.07424i	0.921565	−	0.865650i
$88$		−	0.701163i		−	0.0747442i
$89$	−2.54802	+	2.54802i	−0.270090	+	0.270090i	−0.829136	−	0.559046i	$-0.811167\pi$
$89$	−2.54802	+	2.54802i	−0.270090	+	0.270090i	0.559046	+	0.829136i	$0.311167\pi$
$90$	1.10268	+	0.0690654i	0.116233	+	0.00728013i
$91$	8.26469	−	9.99370i	0.866375	−	1.04762i
$92$			17.4903i			1.82349i
$93$	−7.25614	−	0.227017i	−0.752426	−	0.0235406i
$94$	−1.28645			−0.132687
$95$	4.87759			0.500430
$96$	0.218090	−	6.97078i	0.0222587	−	0.711452i
$97$	10.4901	−	10.4901i	1.06511	−	1.06511i	0.0673840	−	0.997727i	$-0.478535\pi$
$97$	10.4901	−	10.4901i	1.06511	−	1.06511i	0.997727	−	0.0673840i	$-0.0214653\pi$
$98$	−1.54604	+	1.54604i	−0.156174	+	0.156174i
$99$	0.977745	+	1.10841i	0.0982670	+	0.111399i
$100$	1.86437			0.186437
$101$	2.56854			0.255579			0.127790	−	0.991801i	$-0.459212\pi$
$101$	2.56854			0.255579			0.127790	+	0.991801i	$0.459212\pi$
$102$	−0.105409	+	3.36916i	−0.0104370	+	0.333597i
$103$		−	15.2419i		−	1.50183i	−0.660400	−	0.750914i	$-0.729613\pi$
$103$		−	15.2419i		−	1.50183i	0.660400	−	0.750914i	$-0.270387\pi$
$104$	−3.95431	−	3.27017i	−0.387752	−	0.320667i
$105$	4.54074	−	4.26524i	0.443131	−	0.416244i
$106$	1.80947	−	1.80947i	0.175752	−	0.175752i
$107$		−	8.85806i		−	0.856341i	−0.903698	−	0.428171i	$-0.859158\pi$
$107$		−	8.85806i		−	0.856341i	0.903698	−	0.428171i	$-0.140842\pi$
$108$	6.17820	+	7.46179i	0.594498	+	0.718011i
$109$	−7.99281	+	7.99281i	−0.765573	+	0.765573i	−0.977324	−	0.211751i	$-0.932083\pi$
$109$	−7.99281	+	7.99281i	−0.765573	+	0.765573i	0.211751	+	0.977324i	$0.432083\pi$
$110$	−0.128300	−	0.128300i	−0.0122329	−	0.0122329i
$111$	−0.135118	+	4.31875i	−0.0128248	+	0.409918i
$112$	−8.15031	−	8.15031i	−0.770132	−	0.770132i
$113$			11.4219i			1.07448i	0.843430	+	0.537239i	$0.180533\pi$
$113$			11.4219i			1.07448i	−0.843430	+	0.537239i	$0.819467\pi$
$114$	−2.13017	−	2.26776i	−0.199509	−	0.212396i
$115$	6.63361	+	6.63361i	0.618588	+	0.618588i
$116$	−12.6942			−1.17863
$117$	10.8112	−	0.344594i	0.999492	−	0.0318577i
$118$	−0.129569			−0.0119278
$119$	13.4398	+	13.4398i	1.23202	+	1.23202i
$120$	−1.68767	−	1.79668i	−0.154062	−	0.164014i
$121$			10.7573i			0.977934i
$122$	−0.937735	−	0.937735i	−0.0848986	−	0.0848986i
$123$	0.169694	−	5.42392i	0.0153008	−	0.489058i
$124$	5.52553	+	5.52553i	0.496207	+	0.496207i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−3.96612	−	0.248413i	−0.353330	−	0.0221304i
$127$			2.64759i			0.234936i	0.993077	+	0.117468i	$0.0374777\pi$
$127$			2.64759i			0.234936i	−0.993077	+	0.117468i	$0.962522\pi$
$128$	−6.97729	+	6.97729i	−0.616711	+	0.616711i
$129$	6.83887	−	6.42393i	0.602129	−	0.565595i
$130$	−1.32194	+	0.125184i	−0.115942	+	0.0109794i
$131$			5.12086i			0.447412i	0.974657	+	0.223706i	$0.0718155\pi$
$131$			5.12086i			0.447412i	−0.974657	+	0.223706i	$0.928184\pi$
$132$	0.0497501	−	1.59016i	0.00433019	−	0.138405i
$133$	−17.5436			−1.52123
$134$	−0.698012			−0.0602991
$135$	5.17330	+	0.486831i	0.445246	+	0.0418997i
$136$	5.31786	−	5.31786i	0.456003	−	0.456003i
$137$	8.25322	−	8.25322i	0.705120	−	0.705120i	−0.260385	−	0.965505i	$-0.583849\pi$
$137$	8.25322	−	8.25322i	0.705120	−	0.705120i	0.965505	+	0.260385i	$0.0838494\pi$
$138$	0.187132	−	5.98127i	0.0159297	−	0.509160i
$139$	−0.517263			−0.0438737			−0.0219369	−	0.999759i	$-0.506983\pi$
$139$	−0.517263			−0.0438737			−0.0219369	+	0.999759i	$0.506983\pi$
$140$	−6.70573			−0.566738
$141$	−6.04728	−	0.189197i	−0.509273	−	0.0159332i
$142$			6.09168i			0.511202i
$143$	−1.36890	−	1.13207i	−0.114473	−	0.0946682i
$144$	0.600973	−	9.59502i	0.0500811	−	0.799585i
$145$	−4.81458	+	4.81458i	−0.399829	+	0.399829i
$146$			3.37774i			0.279544i
$147$	−7.49496	+	7.04021i	−0.618174	+	0.580666i
$148$	3.28872	−	3.28872i	0.270331	−	0.270331i
$149$	0.824702	+	0.824702i	0.0675622	+	0.0675622i	0.740080	−	0.672518i	$-0.234787\pi$
$149$	0.824702	+	0.824702i	0.0675622	+	0.0675622i	−0.672518	+	0.740080i	$0.734787\pi$
$150$	−0.637571	−	0.0199472i	−0.0520574	−	0.00162868i
$151$	−6.80265	−	6.80265i	−0.553591	−	0.553591i	0.373884	−	0.927475i	$-0.378026\pi$
$151$	−6.80265	−	6.80265i	−0.553591	−	0.553591i	−0.927475	+	0.373884i	$0.878026\pi$
$152$			6.94167i			0.563044i
$153$	−0.991000	+	15.8221i	−0.0801176	+	1.27914i
$154$	0.461466	+	0.461466i	0.0371860	+	0.0371860i
$155$	4.19138			0.336660
$156$	−8.73589	−	7.69696i	−0.699431	−	0.616250i
$157$	8.40663			0.670922			0.335461	−	0.942054i	$-0.391108\pi$
$157$	8.40663			0.670922			0.335461	+	0.942054i	$0.391108\pi$
$158$	0.692954	+	0.692954i	0.0551284	+	0.0551284i
$159$	8.77202	−	8.23978i	0.695666	−	0.653457i
$160$			4.02655i			0.318327i
$161$	−23.8597	−	23.8597i	−1.88041	−	1.88041i
$162$	−2.03297	−	2.61786i	−0.159725	−	0.205679i
$163$	6.91500	+	6.91500i	0.541625	+	0.541625i	0.924005	−	0.382380i	$-0.124896\pi$
$163$	6.91500	+	6.91500i	0.541625	+	0.541625i	−0.382380	+	0.924005i	$0.624896\pi$
$164$	−4.13030	+	4.13030i	−0.322522	+	0.322522i
$165$	−0.584237	−	0.621975i	−0.0454828	−	0.0484207i
$166$			3.83106i			0.297348i
$167$	2.11987	−	2.11987i	0.164040	−	0.164040i	−0.620314	−	0.784354i	$-0.712995\pi$
$167$	2.11987	−	2.11987i	0.164040	−	0.164040i	0.784354	+	0.620314i	$0.212995\pi$
$168$	6.07018	+	6.46228i	0.468325	+	0.498576i
$169$	−12.7689	+	2.44023i	−0.982224	+	0.187710i
$170$		−	1.94614i		−	0.149262i
$171$	−9.67989	−	10.9735i	−0.740240	−	0.839164i
$172$	−10.0996			−0.770087
$173$	21.2987			1.61931			0.809655	−	0.586906i	$-0.199654\pi$
$173$	21.2987			1.61931			0.809655	+	0.586906i	$0.199654\pi$
$174$	4.34112	+	0.135817i	0.329099	+	0.0102963i
$175$	−2.54331	+	2.54331i	−0.192256	+	0.192256i
$176$	−1.11640	+	1.11640i	−0.0841518	+	0.0841518i
$177$	−0.609074	−	0.0190556i	−0.0457808	−	0.00143231i
$178$	−1.32708			−0.0994692
$179$	−2.77071			−0.207093			−0.103546	−	0.994625i	$-0.533019\pi$
$179$	−2.77071			−0.207093			−0.103546	+	0.994625i	$0.533019\pi$
$180$	−3.69996	−	4.19442i	−0.275779	−	0.312633i
$181$		−	20.1030i		−	1.49425i	−0.664686	−	0.747123i	$-0.731435\pi$
$181$		−	20.1030i		−	1.49425i	0.664686	−	0.747123i	$-0.268565\pi$
$182$	4.75475	−	0.450260i	0.352446	−	0.0333755i
$183$	−4.27015	−	4.54598i	−0.315659	−	0.336048i
$184$	−9.44081	+	9.44081i	−0.695985	+	0.695985i
$185$		−	2.49465i		−	0.183411i
$186$	−1.83049	−	1.94872i	−0.134218	−	0.142887i
$187$	1.84094	−	1.84094i	0.134623	−	0.134623i
$188$	4.60499	+	4.60499i	0.335853	+	0.335853i
$189$	−18.6072	−	1.75102i	−1.35348	−	0.127368i
$190$	1.27020	+	1.27020i	0.0921497	+	0.0921497i
$191$			13.9497i			1.00937i	0.863304	+	0.504684i	$0.168391\pi$
$191$			13.9497i			1.00937i	−0.863304	+	0.504684i	$0.831609\pi$
$192$	−6.21919	+	5.84185i	−0.448832	+	0.421599i
$193$	−0.516880	−	0.516880i	−0.0372058	−	0.0372058i	0.688259	−	0.725465i	$-0.258375\pi$
$193$	−0.516880	−	0.516880i	−0.0372058	−	0.0372058i	−0.725465	+	0.688259i	$0.758375\pi$
$194$	5.46356			0.392261
$195$	−6.23255	+	0.394042i	−0.446322	+	0.0282179i
$196$	11.0685			0.790607
$197$	−3.72469	−	3.72469i	−0.265373	−	0.265373i	0.561859	−	0.827233i	$-0.310086\pi$
$197$	−3.72469	−	3.72469i	−0.265373	−	0.265373i	−0.827233	+	0.561859i	$0.810086\pi$
$198$	−0.0340268	+	0.543265i	−0.00241818	+	0.0386081i
$199$		−	14.3661i		−	1.01839i	−0.860652	−	0.509193i	$-0.829944\pi$
$199$		−	14.3661i		−	1.01839i	0.860652	−	0.509193i	$-0.170056\pi$
$200$	1.00634	+	1.00634i	0.0711588	+	0.0711588i
$201$	−3.28119	−	0.102656i	−0.231437	−	0.00724080i
$202$	0.668886	+	0.668886i	0.0470626	+	0.0470626i
$203$	17.3170	−	17.3170i	1.21542	−	1.21542i
$204$	12.4376	−	11.6830i	0.870808	−	0.817973i
$205$			3.13303i			0.218820i
$206$	3.96921	−	3.96921i	0.276548	−	0.276548i
$207$	1.75932	−	28.0890i	0.122281	−	1.95232i
$208$	1.08929	+	11.5029i	0.0755286	+	0.797584i
$209$			2.40306i			0.166223i
$210$	2.29321	+	0.0717458i	0.158246	+	0.00495093i
$211$	9.49226			0.653474			0.326737	−	0.945115i	$-0.394051\pi$
$211$	9.49226			0.653474			0.326737	+	0.945115i	$0.394051\pi$
$212$	−12.9544			−0.889715
$213$	−0.895898	+	28.6355i	−0.0613859	+	1.96207i
$214$	2.30677	−	2.30677i	0.157687	−	0.157687i
$215$	−3.83051	+	3.83051i	−0.261239	+	0.261239i
$216$	−0.692846	+	7.36251i	−0.0471422	+	0.500956i
$217$	−15.0755			−1.02339
$218$	−4.16289			−0.281947
$219$	−0.496762	+	15.8780i	−0.0335681	+	1.07293i
$220$			0.918527i			0.0619271i
$221$	−1.79623	−	18.9682i	−0.120827	−	1.27594i
$222$	−1.15985	+	1.08948i	−0.0778442	+	0.0731211i
$223$	4.69628	−	4.69628i	0.314486	−	0.314486i	−0.532159	−	0.846645i	$-0.678619\pi$
$223$	4.69628	−	4.69628i	0.314486	−	0.314486i	0.846645	+	0.532159i	$0.178619\pi$
$224$		−	14.4826i		−	0.967662i
$225$	−2.99413	−	0.187534i	−0.199609	−	0.0125023i
$226$	−2.97442	+	2.97442i	−0.197855	+	0.197855i
$227$	7.76531	+	7.76531i	0.515402	+	0.515402i	0.916177	−	0.400775i	$-0.131259\pi$
$227$	7.76531	+	7.76531i	0.515402	+	0.515402i	−0.400775	+	0.916177i	$0.631259\pi$
$228$	−0.492537	+	15.7429i	−0.0326191	+	1.04260i
$229$	−5.52070	−	5.52070i	−0.364818	−	0.364818i	0.500765	−	0.865583i	$-0.333052\pi$
$229$	−5.52070	−	5.52070i	−0.364818	−	0.364818i	−0.865583	+	0.500765i	$0.833052\pi$
$230$			3.45498i			0.227815i
$231$	2.10137	+	2.23711i	0.138260	+	0.147191i
$232$	−6.85200	−	6.85200i	−0.449856	−	0.449856i
$233$	−9.73604			−0.637829			−0.318915	−	0.947783i	$-0.603318\pi$
$233$	−9.73604			−0.637829			−0.318915	+	0.947783i	$0.603318\pi$
$234$	2.90512	+	2.72565i	0.189914	+	0.178181i
$235$	3.49311			0.227865
$236$	0.463808	+	0.463808i	0.0301913	+	0.0301913i
$237$	3.15550	+	3.35932i	0.204971	+	0.218211i
$238$			6.99984i			0.453732i
$239$	−16.1376	−	16.1376i	−1.04385	−	1.04385i	−0.998993	−	0.0448582i	$-0.985716\pi$
$239$	−16.1376	−	16.1376i	−1.04385	−	1.04385i	−0.0448582	−	0.998993i	$-0.514284\pi$
$240$	−0.173571	+	5.54783i	−0.0112039	+	0.358111i
$241$	−6.35964	−	6.35964i	−0.409660	−	0.409660i	0.471960	−	0.881620i	$-0.343547\pi$
$241$	−6.35964	−	6.35964i	−0.409660	−	0.409660i	−0.881620	+	0.471960i	$0.843547\pi$
$242$	−2.80135	+	2.80135i	−0.180078	+	0.180078i
$243$	−9.17148	−	12.6049i	−0.588351	−	0.808606i
$244$			6.71346i			0.429786i
$245$	4.19799	−	4.19799i	0.268200	−	0.268200i
$246$	1.45666	−	1.36828i	0.0928731	−	0.0872381i
$247$	13.5524	+	11.2077i	0.862320	+	0.713130i
$248$			5.96508i			0.378783i
$249$	−0.563431	+	18.0089i	−0.0357060	+	1.14127i
$250$	0.368282			0.0232922
$251$	4.33610			0.273692			0.136846	−	0.990592i	$-0.456303\pi$
$251$	4.33610			0.273692			0.136846	+	0.990592i	$0.456303\pi$
$252$	13.3080	+	15.0864i	0.838323	+	0.950354i
$253$	−3.26821	+	3.26821i	−0.205471	+	0.205471i
$254$	−0.689471	+	0.689471i	−0.0432612	+	0.0432612i
$255$	0.286217	−	9.14833i	0.0179236	−	0.572890i
$256$	6.21864			0.388665
$257$	−4.95572			−0.309129			−0.154565	−	0.987983i	$-0.549398\pi$
$257$	−4.95572			−0.309129			−0.154565	+	0.987983i	$0.549398\pi$
$258$	3.45383	+	0.108057i	0.215026	+	0.00672736i
$259$			8.97273i			0.557538i
$260$	5.18017	+	4.28395i	0.321260	+	0.265679i
$261$	20.3866	+	1.27689i	1.26190	+	0.0790375i
$262$	−1.33355	+	1.33355i	−0.0823868	+	0.0823868i
$263$			21.5950i			1.33160i	0.746129	+	0.665801i	$0.231910\pi$
$263$			21.5950i			1.33160i	−0.746129	+	0.665801i	$0.768090\pi$
$264$	0.885180	−	0.831472i	0.0544790	−	0.0511736i
$265$	−4.91329	+	4.91329i	−0.301821	+	0.301821i
$266$	−4.56862	−	4.56862i	−0.280120	−	0.280120i
$267$	−6.23830	−	0.195173i	−0.381778	−	0.0119444i
$268$	2.49862	+	2.49862i	0.152627	+	0.152627i
$269$		−	4.12228i		−	0.251340i	−0.992072	−	0.125670i	$-0.959892\pi$
$269$		−	4.12228i		−	0.251340i	0.992072	−	0.125670i	$-0.0401080\pi$
$270$	1.22042	+	1.47398i	0.0742726	+	0.0897035i
$271$	−2.86523	−	2.86523i	−0.174050	−	0.174050i	0.614706	−	0.788756i	$-0.289275\pi$
$271$	−2.86523	−	2.86523i	−0.174050	−	0.174050i	−0.788756	+	0.614706i	$0.789275\pi$
$272$	−16.9343			−1.02680
$273$	22.4172	−	1.41728i	1.35675	−	0.0857779i
$274$	4.29852			0.259683
$275$	0.348374	+	0.348374i	0.0210077	+	0.0210077i
$276$	−22.0805	+	20.7408i	−1.32909	+	1.24845i
$277$		−	13.8782i		−	0.833857i	−0.908939	−	0.416929i	$-0.863106\pi$
$277$		−	13.8782i		−	0.833857i	0.908939	−	0.416929i	$-0.136894\pi$
$278$	−0.134703	−	0.134703i	−0.00807894	−	0.00807894i
$279$	−8.31807	−	9.42968i	−0.497990	−	0.564540i
$280$	−3.61958	−	3.61958i	−0.216311	−	0.216311i
$281$	−14.6864	+	14.6864i	−0.876116	+	0.876116i	−0.993130	−	0.117015i	$-0.962668\pi$
$281$	−14.6864	+	14.6864i	−0.876116	+	0.876116i	0.117015	+	0.993130i	$0.462668\pi$
$282$	−1.52553	−	1.62407i	−0.0908439	−	0.0967119i
$283$		−	7.59425i		−	0.451431i	−0.974193	−	0.225716i	$-0.927528\pi$
$283$		−	7.59425i		−	0.451431i	0.974193	−	0.225716i	$-0.0724720\pi$
$284$	21.8059	−	21.8059i	1.29394	−	1.29394i
$285$	5.78407	+	6.15769i	0.342619	+	0.364750i
$286$	−0.0616749	−	0.651289i	−0.00364692	−	0.0385115i
$287$		−	11.2688i		−	0.665179i
$288$	9.05885	−	7.99095i	0.533798	−	0.470871i
$289$	10.9246			0.642623
$290$	−2.50757			−0.147250
$291$	25.6829	+	0.803522i	1.50556	+	0.0471033i
$292$	12.0910	−	12.0910i	0.707574	−	0.707574i
$293$	15.8408	−	15.8408i	0.925429	−	0.925429i	−0.0719771	−	0.997406i	$-0.522931\pi$
$293$	15.8408	−	15.8408i	0.925429	−	0.925429i	0.997406	+	0.0719771i	$0.0229308\pi$
$294$	−3.78517	−	0.118424i	−0.220756	−	0.00690662i
$295$	0.351821			0.0204838
$296$	3.55033			0.206359
$297$	−0.239849	+	2.54875i	−0.0139175	+	0.147894i
$298$			0.429529i			0.0248819i
$299$	3.18885	+	33.6743i	0.184416	+	1.94743i
$300$	2.21086	+	2.35366i	0.127644	+	0.135889i
$301$	13.7775	−	13.7775i	0.794124	−	0.794124i
$302$		−	3.54302i		−	0.203878i
$303$	3.04590	+	3.24264i	0.174982	+	0.186285i
$304$	11.0526	−	11.0526i	0.633911	−	0.633911i
$305$	2.54624	+	2.54624i	0.145797	+	0.145797i
$306$	−4.37838	+	3.86224i	−0.250295	+	0.220789i
$307$	19.6820	+	19.6820i	1.12331	+	1.12331i	0.991240	+	0.132074i	$0.0421636\pi$
$307$	19.6820	+	19.6820i	1.12331	+	1.12331i	0.132074	+	0.991240i	$0.457836\pi$
$308$		−	3.30374i		−	0.188248i
$309$	19.2421	−	18.0746i	1.09464	−	1.02823i
$310$	1.09150	+	1.09150i	0.0619929	+	0.0619929i
$311$	15.5168			0.879877			0.439938	−	0.898028i	$-0.355000\pi$
$311$	15.5168			0.879877			0.439938	+	0.898028i	$0.355000\pi$
$312$	−0.560791	−	8.87003i	−0.0317486	−	0.502166i
$313$	−3.72939			−0.210797			−0.105399	−	0.994430i	$-0.533612\pi$
$313$	−3.72939			−0.210797			−0.105399	+	0.994430i	$0.533612\pi$
$314$	2.18921	+	2.18921i	0.123544	+	0.123544i
$315$	10.7693	+	0.674520i	0.606779	+	0.0380049i
$316$		−	4.96102i		−	0.279079i
$317$	−18.4547	−	18.4547i	−1.03652	−	1.03652i	−0.999307	−	0.0372111i	$-0.988153\pi$
$317$	−18.4547	−	18.4547i	−1.03652	−	1.03652i	−0.0372111	−	0.999307i	$-0.511847\pi$
$318$	4.43012	+	0.138602i	0.248429	+	0.00777241i
$319$	−2.37202	−	2.37202i	−0.132808	−	0.132808i
$320$	3.48343	−	3.48343i	0.194729	−	0.194729i
$321$	11.1828	−	10.5043i	0.624164	−	0.586293i
$322$		−	12.4268i		−	0.692519i
$323$	−18.2257	+	18.2257i	−1.01410	+	1.01410i
$324$	−2.09369	+	16.6482i	−0.116316	+	0.924899i
$325$	3.58949	−	0.339913i	0.199109	−	0.0188550i
$326$			3.60154i			0.199471i
$327$	−19.5687	−	0.612233i	−1.08215	−	0.0338566i
$328$	−4.45886			−0.246199
$329$	−12.5639			−0.692673
$330$	0.00982748	−	0.314115i	0.000540985	−	0.0172915i
$331$	−15.0140	+	15.0140i	−0.825244	+	0.825244i	−0.986855	−	0.161611i	$-0.948331\pi$
$331$	−15.0140	+	15.0140i	−0.825244	+	0.825244i	0.161611	+	0.986855i	$0.448331\pi$
$332$	13.7137	−	13.7137i	0.752639	−	0.752639i
$333$	−5.61242	+	4.95080i	−0.307559	+	0.271302i
$334$	1.10409			0.0604131
$335$	1.89532			0.103552
$336$	0.624297	−	19.9543i	0.0340582	−	1.08860i
$337$			18.0210i			0.981666i	0.871254	+	0.490833i	$0.163308\pi$
$337$			18.0210i			0.981666i	−0.871254	+	0.490833i	$0.836692\pi$
$338$	−3.96068	−	2.68974i	−0.215433	−	0.146303i
$339$	−14.4195	+	13.5446i	−0.783158	+	0.735641i
$340$	−6.96643	+	6.96643i	−0.377808	+	0.377808i
$341$			2.06499i			0.111825i
$342$	0.336873	−	5.37844i	0.0182160	−	0.290833i
$343$	2.70390	−	2.70390i	0.145997	−	0.145997i
$344$	−5.45150	−	5.45150i	−0.293925	−	0.293925i
$345$	−0.508121	+	16.2410i	−0.0273563	+	0.874387i
$346$	5.54649	+	5.54649i	0.298181	+	0.298181i
$347$			12.1453i			0.651991i	0.945371	+	0.325996i	$0.105700\pi$
$347$			12.1453i			0.651991i	−0.945371	+	0.325996i	$0.894300\pi$
$348$	−15.0534	−	16.0257i	−0.806945	−	0.859069i
$349$	22.2952	+	22.2952i	1.19343	+	1.19343i	0.976097	+	0.217337i	$0.0697371\pi$
$349$	22.2952	+	22.2952i	1.19343	+	1.19343i	0.217337	+	0.976097i	$0.430263\pi$
$350$	−1.32463			−0.0708045
$351$	13.2554	+	13.2399i	0.707522	+	0.706692i
$352$	−1.98378			−0.105736
$353$	−7.05913	−	7.05913i	−0.375720	−	0.375720i	0.493836	−	0.869555i	$-0.335594\pi$
$353$	−7.05913	−	7.05913i	−0.375720	−	0.375720i	−0.869555	+	0.493836i	$0.835594\pi$
$354$	−0.153649	−	0.163574i	−0.00816637	−	0.00869386i
$355$		−	16.5408i		−	0.877895i
$356$	4.75045	+	4.75045i	0.251774	+	0.251774i
$357$	−1.02946	+	32.9046i	−0.0544848	+	1.74149i
$358$	−0.721534	−	0.721534i	−0.0381343	−	0.0381343i
$359$	−17.9957	+	17.9957i	−0.949776	+	0.949776i	−0.998798	−	0.0490218i	$-0.984390\pi$
$359$	−17.9957	+	17.9957i	−0.949776	+	0.949776i	0.0490218	+	0.998798i	$0.484390\pi$
$360$	0.266894	−	4.26118i	0.0140666	−	0.224584i
$361$		−	4.79088i		−	0.252151i
$362$	5.23512	−	5.23512i	0.275152	−	0.275152i
$363$	−13.5805	+	12.7565i	−0.712789	+	0.669541i
$364$	−18.6319	−	15.4084i	−0.976579	−	0.807621i
$365$		−	9.17163i		−	0.480065i
$366$	0.0718286	−	2.29585i	0.00375454	−	0.120006i
$367$	17.4749			0.912181			0.456090	−	0.889933i	$-0.349249\pi$
$367$	17.4749			0.912181			0.456090	+	0.889933i	$0.349249\pi$
$368$	30.0635			1.56717
$369$	7.04863	−	6.21771i	0.366937	−	0.323681i
$370$	0.649644	−	0.649644i	0.0337734	−	0.0337734i
$371$	17.6720	−	17.6720i	0.917486	−	0.917486i
$372$	−0.423244	+	13.5281i	−0.0219442	+	0.701400i
$373$	12.9747			0.671805			0.335903	−	0.941897i	$-0.390959\pi$
$373$	12.9747			0.671805			0.335903	+	0.941897i	$0.390959\pi$
$374$	0.958813			0.0495790
$375$	1.73120	+	0.0541629i	0.0893990	+	0.00279696i
$376$			4.97131i			0.256376i
$377$	−24.4403	+	2.31442i	−1.25874	+	0.119199i
$378$	−4.38960	−	5.30159i	−0.225777	−	0.272684i
$379$	−4.51436	+	4.51436i	−0.231887	+	0.231887i	−0.813480	−	0.581593i	$-0.802430\pi$
$379$	−4.51436	+	4.51436i	−0.231887	+	0.231887i	0.581593	+	0.813480i	$0.302430\pi$
$380$		−	9.09362i		−	0.466493i
$381$	−3.34244	+	3.13964i	−0.171238	+	0.160848i
$382$	−3.63271	+	3.63271i	−0.185866	+	0.185866i
$383$	−24.9851	−	24.9851i	−1.27668	−	1.27668i	−0.942516	−	0.334161i	$-0.891547\pi$
$383$	−24.9851	−	24.9851i	−1.27668	−	1.27668i	−0.334161	−	0.942516i	$-0.608453\pi$
$384$	−17.0824	−	0.534446i	−0.871734	−	0.0272733i
$385$	−1.25302	−	1.25302i	−0.0638600	−	0.0638600i
$386$		−	0.269206i		−	0.0137022i
$387$	16.2197	+	1.01590i	0.824494	+	0.0516412i
$388$	−19.5575	−	19.5575i	−0.992880	−	0.992880i
$389$	−5.36318			−0.271924			−0.135962	−	0.990714i	$-0.543413\pi$
$389$	−5.36318			−0.271924			−0.135962	+	0.990714i	$0.543413\pi$
$390$	−1.72566	−	1.52043i	−0.0873823	−	0.0769901i
$391$	−49.5745			−2.50709
$392$	5.97449	+	5.97449i	0.301757	+	0.301757i
$393$	−6.46481	+	6.07256i	−0.326106	+	0.306320i
$394$		−	1.93993i		−	0.0977322i
$395$	−1.88159	−	1.88159i	−0.0946729	−	0.0946729i
$396$	2.06648	−	1.82288i	0.103845	−	0.0916030i
$397$	−2.52951	−	2.52951i	−0.126952	−	0.126952i	0.640776	−	0.767728i	$-0.278613\pi$
$397$	−2.52951	−	2.52951i	−0.126952	−	0.126952i	−0.767728	+	0.640776i	$0.778613\pi$
$398$	3.74114	−	3.74114i	0.187527	−	0.187527i
$399$	−20.8041	−	22.1479i	−1.04151	−	1.10878i
$400$		−	3.20461i		−	0.160230i
$401$	−11.1604	+	11.1604i	−0.557326	+	0.557326i	−0.928545	−	0.371219i	$-0.878940\pi$
$401$	−11.1604	+	11.1604i	−0.557326	+	0.557326i	0.371219	+	0.928545i	$0.378940\pi$
$402$	−0.827736	−	0.881202i	−0.0412837	−	0.0439504i
$403$	11.6458	+	9.63096i	0.580119	+	0.479752i
$404$		−	4.78871i		−	0.238247i
$405$	5.52014	+	7.10831i	0.274298	+	0.353215i
$406$	9.01920			0.447615
$407$	1.22905			0.0609219
$408$	13.0197	+	0.407337i	0.644570	+	0.0201662i
$409$	−12.4909	+	12.4909i	−0.617634	+	0.617634i	−0.944924	−	0.327290i	$-0.893865\pi$
$409$	−12.4909	+	12.4909i	−0.617634	+	0.617634i	0.327290	+	0.944924i	$0.393865\pi$
$410$	−0.815887	+	0.815887i	−0.0402938	+	0.0402938i
$411$	20.2063	+	0.632179i	0.996703	+	0.0311831i
$412$	−28.4165			−1.39998
$413$	−1.26542			−0.0622674
$414$	7.77294	−	6.85663i	0.382019	−	0.336985i
$415$		−	10.4025i		−	0.510640i
$416$	−9.25221	+	11.1878i	−0.453627	+	0.548528i
$417$	−0.613395	−	0.653016i	−0.0300381	−	0.0319784i
$418$	−0.625793	+	0.625793i	−0.0306085	+	0.0306085i
$419$			6.25022i			0.305343i	0.988277	+	0.152672i	$0.0487877\pi$
$419$			6.25022i			0.305343i	−0.988277	+	0.152672i	$0.951212\pi$
$420$	−7.95197	−	8.46562i	−0.388016	−	0.413080i
$421$	−24.9169	+	24.9169i	−1.21438	+	1.21438i	−0.244803	+	0.969573i	$0.578723\pi$
$421$	−24.9169	+	24.9169i	−1.21438	+	1.21438i	−0.969573	+	0.244803i	$0.921277\pi$
$422$	2.47192	+	2.47192i	0.120331	+	0.120331i
$423$	−6.93229	−	7.85871i	−0.337060	−	0.382104i
$424$	−6.99247	−	6.99247i	−0.339585	−	0.339585i
$425$			5.28437i			0.256330i
$426$	−7.69041	+	7.22380i	−0.372602	+	0.349994i
$427$	−9.15829	−	9.15829i	−0.443201	−	0.443201i
$428$	−16.5147			−0.798268
$429$	−0.194134	−	3.07062i	−0.00937290	−	0.148251i
$430$	−1.99504			−0.0962095
$431$	3.03234	+	3.03234i	0.146063	+	0.146063i	0.776357	−	0.630294i	$-0.217066\pi$
$431$	3.03234	+	3.03234i	0.146063	+	0.146063i	−0.630294	+	0.776357i	$0.717066\pi$
$432$	12.8258	−	10.6195i	0.617084	−	0.510932i
$433$			30.0237i			1.44285i	0.692493	+	0.721424i	$0.256512\pi$
$433$			30.0237i			1.44285i	−0.692493	+	0.721424i	$0.743488\pi$
$434$	−3.92588	−	3.92588i	−0.188448	−	0.188448i
$435$	−11.7875	−	0.368787i	−0.565167	−	0.0176820i
$436$	14.9016	+	14.9016i	0.713655	+	0.713655i
$437$	32.3560	−	32.3560i	1.54780	−	1.54780i
$438$	−4.26422	+	4.00549i	−0.203752	+	0.191390i
$439$		−	13.8417i		−	0.660629i	−0.943871	−	0.330314i	$-0.892845\pi$
$439$		−	13.8417i		−	0.660629i	0.943871	−	0.330314i	$-0.107155\pi$
$440$	−0.495797	+	0.495797i	−0.0236362	+	0.0236362i
$441$	−17.7757	−	1.11336i	−0.846464	−	0.0530173i
$442$	4.47184	−	5.40736i	0.212704	−	0.257202i
$443$		−	5.89439i		−	0.280051i	−0.990148	−	0.140026i	$-0.955282\pi$
$443$		−	5.89439i		−	0.280051i	0.990148	−	0.140026i	$-0.0447185\pi$
$444$	8.05175	+	0.251909i	0.382119	+	0.0119551i
$445$	3.60345			0.170820
$446$	2.44596			0.115819
$447$	−0.0631704	+	2.01911i	−0.00298786	+	0.0955006i
$448$	−12.5291	+	12.5291i	−0.591946	+	0.591946i
$449$	15.1945	−	15.1945i	0.717073	−	0.717073i	−0.250932	−	0.968005i	$-0.580737\pi$
$449$	15.1945	−	15.1945i	0.717073	−	0.717073i	0.968005	+	0.250932i	$0.0807369\pi$
$450$	−0.730879	−	0.828552i	−0.0344540	−	0.0390583i
$451$	−1.54357			−0.0726837
$452$	21.2946			1.00161
$453$	0.521068	−	16.6549i	0.0244819	−	0.782514i
$454$			4.04440i			0.189813i
$455$	−12.9106	+	1.22260i	−0.605260	+	0.0573161i
$456$	−8.76348	+	8.23176i	−0.410387	+	0.385487i
$457$	5.58713	−	5.58713i	0.261355	−	0.261355i	−0.564250	−	0.825604i	$-0.690834\pi$
$457$	5.58713	−	5.58713i	0.261355	−	0.261355i	0.825604	+	0.564250i	$0.190834\pi$
$458$		−	2.87534i		−	0.134356i
$459$	−21.1497	+	17.5115i	−0.987184	+	0.817368i
$460$	12.3675	−	12.3675i	0.576638	−	0.576638i
$461$	−14.7907	−	14.7907i	−0.688870	−	0.688870i	0.273113	−	0.961982i	$-0.411947\pi$
$461$	−14.7907	−	14.7907i	−0.688870	−	0.688870i	−0.961982	+	0.273113i	$0.911947\pi$
$462$	−0.0353473	+	1.12980i	−0.00164451	+	0.0525632i
$463$	8.79012	+	8.79012i	0.408512	+	0.408512i	0.881219	−	0.472708i	$-0.156723\pi$
$463$	8.79012	+	8.79012i	0.408512	+	0.408512i	−0.472708	+	0.881219i	$0.656723\pi$
$464$			21.8197i			1.01295i
$465$	4.97034	+	5.29139i	0.230494	+	0.245382i
$466$	−2.53541	−	2.53541i	−0.117450	−	0.117450i
$467$	9.31080			0.430853			0.215426	−	0.976520i	$-0.430886\pi$
$467$	9.31080			0.430853			0.215426	+	0.976520i	$0.430886\pi$
$468$	−0.642450	−	20.1560i	−0.0296972	−	0.931711i
$469$	−6.81706			−0.314783
$470$	0.909655	+	0.909655i	0.0419593	+	0.0419593i
$471$	9.96897	+	10.6129i	0.459346	+	0.489017i
$472$			0.500703i			0.0230467i
$473$	−1.88720	−	1.88720i	−0.0867734	−	0.0867734i
$474$	−0.0530788	+	1.69655i	−0.00243799	+	0.0779253i
$475$	−3.44898	−	3.44898i	−0.158250	−	0.158250i
$476$	25.0567	−	25.0567i	1.14847	−	1.14847i
$477$	20.8045	+	1.30307i	0.952574	+	0.0596634i
$478$		−	8.40491i		−	0.384432i
$479$	21.2367	−	21.2367i	0.970331	−	0.970331i	−0.0292411	−	0.999572i	$-0.509309\pi$
$479$	21.2367	−	21.2367i	0.970331	−	0.970331i	0.999572	+	0.0292411i	$0.00930906\pi$
$480$	−5.08330	+	4.77487i	−0.232020	+	0.217942i
$481$	5.73221	−	6.93142i	0.261366	−	0.316045i
$482$		−	3.31229i		−	0.150870i
$483$	1.82760	−	58.4155i	0.0831588	−	2.65800i
$484$	20.0555			0.911614
$485$	−14.8353			−0.673635
$486$	0.894116	−	5.67089i	0.0405579	−	0.257237i
$487$	−11.9347	+	11.9347i	−0.540814	+	0.540814i	−0.923768	−	0.382954i	$-0.874907\pi$
$487$	−11.9347	+	11.9347i	−0.540814	+	0.540814i	0.382954	+	0.923768i	$0.374907\pi$
$488$	−3.62375	+	3.62375i	−0.164040	+	0.164040i
$489$	−0.529675	+	16.9299i	−0.0239527	+	0.765599i
$490$	2.18644			0.0987732
$491$	−8.47582			−0.382508			−0.191254	−	0.981541i	$-0.561255\pi$
$491$	−8.47582			−0.382508			−0.191254	+	0.981541i	$0.561255\pi$
$492$	−10.1122	−	0.316372i	−0.455892	−	0.0142632i
$493$		−	35.9805i		−	1.62048i
$494$	0.610596	+	6.44790i	0.0274720	+	0.290105i
$495$	0.0923933	−	1.47513i	0.00415277	−	0.0663023i
$496$	9.49767	−	9.49767i	0.426458	−	0.426458i
$497$			59.4937i			2.66866i
$498$	−4.83650	+	4.54305i	−0.216729	+	0.203579i
$499$	25.0163	−	25.0163i	1.11988	−	1.11988i	0.128124	−	0.991758i	$-0.459104\pi$
$499$	25.0163	−	25.0163i	1.11988	−	1.11988i	0.991758	−	0.128124i	$-0.0408957\pi$
$500$	−1.31831	−	1.31831i	−0.0589565	−	0.0589565i
$501$	5.19005	+	0.162377i	0.231875	+	0.00725449i
$502$	1.12918	+	1.12918i	0.0503979	+	0.0503979i
$503$			20.4948i			0.913820i	0.889513	+	0.456910i	$0.151044\pi$
$503$			20.4948i			0.913820i	−0.889513	+	0.456910i	$0.848956\pi$
$504$	−0.959960	+	15.3265i	−0.0427600	+	0.682699i
$505$	−1.81623	−	1.81623i	−0.0808213	−	0.0808213i
$506$	−1.70218			−0.0756712
$507$	−18.2226	−	13.2263i	−0.809296	−	0.587401i
$508$	4.93608			0.219003
$509$	25.6979	+	25.6979i	1.13904	+	1.13904i	0.988623	+	0.150415i	$0.0480609\pi$
$509$	25.6979	+	25.6979i	1.13904	+	1.13904i	0.150415	+	0.988623i	$0.451939\pi$
$510$	2.45689	−	2.30782i	0.108793	−	0.102192i
$511$			32.9884i			1.45932i
$512$	15.5740	+	15.5740i	0.688280	+	0.688280i
$513$	2.37456	−	25.2332i	0.104839	−	1.11407i
$514$	−1.29054	−	1.29054i	−0.0569234	−	0.0569234i
$515$	−10.7776	+	10.7776i	−0.474920	+	0.474920i
$516$	−11.9766	−	12.7502i	−0.527239	−	0.561295i
$517$			1.72096i			0.0756879i
$518$	−2.33663	+	2.33663i	−0.102666	+	0.102666i
$519$	25.2570	+	26.8884i	1.10866	+	1.18027i
$520$	0.483757	+	5.10848i	0.0212141	+	0.224022i
$521$			5.36438i			0.235018i	0.993072	+	0.117509i	$0.0374909\pi$
$521$			5.36438i			0.235018i	−0.993072	+	0.117509i	$0.962509\pi$
$522$	4.97644	+	5.64148i	0.217813	+	0.246921i
$523$	−18.4316			−0.805960			−0.402980	−	0.915209i	$-0.632026\pi$
$523$	−18.4316			−0.805960			−0.402980	+	0.915209i	$0.632026\pi$
$524$	9.54718			0.417070
$525$	−6.22677	−	0.194812i	−0.271758	−	0.00850231i
$526$	−5.62365	+	5.62365i	−0.245203	+	0.245203i
$527$	−15.6616	+	15.6616i	−0.682230	+	0.682230i
$528$	−2.73327	−	0.0855139i	−0.118950	−	0.00372152i
$529$	65.0097			2.82651
$530$	−2.55898			−0.111155
$531$	−0.698211	−	0.791519i	−0.0302998	−	0.0343490i
$532$			32.7078i			1.41806i
$533$	−7.19908	+	8.70516i	−0.311827	+	0.377062i
$534$	−1.57372	−	1.67537i	−0.0681015	−	0.0725004i
$535$	−6.26360	+	6.26360i	−0.270799	+	0.270799i
$536$			2.69738i			0.116509i
$537$	−3.28564	−	3.49787i	−0.141786	−	0.150944i
$538$	1.07350	−	1.07350i	0.0462820	−	0.0462820i
$539$	2.06824	+	2.06824i	0.0890856	+	0.0890856i
$540$	0.907632	−	9.64493i	0.0390582	−	0.415052i
$541$	−19.8497	−	19.8497i	−0.853407	−	0.853407i	0.137144	−	0.990551i	$-0.456208\pi$
$541$	−19.8497	−	19.8497i	−0.853407	−	0.853407i	−0.990551	+	0.137144i	$0.956208\pi$
$542$		−	1.49229i		−	0.0640995i
$543$	25.3790	−	23.8391i	1.08912	−	1.02303i
$544$	−15.0457	−	15.0457i	−0.645078	−	0.645078i
$545$	11.3035			0.484191
$546$	6.20684	+	5.46867i	0.265628	+	0.234038i
$547$	−9.53713			−0.407778			−0.203889	−	0.978994i	$-0.565358\pi$
$547$	−9.53713			−0.407778			−0.203889	+	0.978994i	$0.565358\pi$
$548$	−15.3870	−	15.3870i	−0.657302	−	0.657302i
$549$	0.675297	−	10.7817i	0.0288210	−	0.460150i
$550$			0.181443i			0.00773676i
$551$	23.4835	+	23.4835i	1.00043	+	1.00043i
$552$	−23.1138	−	0.723146i	−0.983791	−	0.0307791i
$553$	6.76766	+	6.76766i	0.287790	+	0.287790i
$554$	3.61407	−	3.61407i	0.153547	−	0.153547i
$555$	3.14936	−	2.95828i	0.133683	−	0.125572i
$556$			0.964369i			0.0408984i
$557$	−13.2999	+	13.2999i	−0.563537	+	0.563537i	−0.930310	−	0.366773i	$-0.880462\pi$
$557$	−13.2999	+	13.2999i	−0.563537	+	0.563537i	0.366773	+	0.930310i	$0.380462\pi$
$558$	0.289479	−	4.62177i	0.0122546	−	0.195655i
$559$	−19.4449	+	1.84137i	−0.822431	+	0.0778815i
$560$			11.5263i			0.487074i
$561$	4.50715	+	0.141012i	0.190292	+	0.00595352i
$562$	−7.64909			−0.322657
$563$	−21.9634			−0.925647			−0.462823	−	0.886451i	$-0.653164\pi$
$563$	−21.9634			−0.925647			−0.462823	+	0.886451i	$0.653164\pi$
$564$	−0.352732	+	11.2744i	−0.0148527	+	0.474736i
$565$	8.07648	−	8.07648i	0.339780	−	0.339780i
$566$	1.97765	−	1.97765i	0.0831270	−	0.0831270i
$567$	−19.8548	−	25.5671i	−0.833821	−	1.07372i
$568$	23.5405			0.987737
$569$	−18.1666			−0.761585			−0.380792	−	0.924661i	$-0.624349\pi$
$569$	−18.1666			−0.761585			−0.380792	+	0.924661i	$0.624349\pi$
$570$	−0.0972943	+	3.10981i	−0.00407521	+	0.130256i
$571$			29.6650i			1.24144i	0.784032	+	0.620720i	$0.213160\pi$
$571$			29.6650i			1.24144i	−0.784032	+	0.620720i	$0.786840\pi$
$572$	−2.11059	+	2.55214i	−0.0882482	+	0.106710i
$573$	−17.6108	+	16.5422i	−0.735700	+	0.691062i
$574$	2.93457	−	2.93457i	0.122487	−	0.122487i
$575$		−	9.38135i		−	0.391229i
$576$	−14.7500	−	0.923850i	−0.614584	−	0.0384938i
$577$	11.2277	−	11.2277i	0.467414	−	0.467414i	−0.433662	−	0.901076i	$-0.642779\pi$
$577$	11.2277	−	11.2277i	0.467414	−	0.467414i	0.901076	+	0.433662i	$0.142779\pi$
$578$	2.84492	+	2.84492i	0.118333	+	0.118333i
$579$	0.0395919	−	1.26547i	0.00164538	−	0.0525913i
$580$	8.97615	+	8.97615i	0.372714	+	0.372714i
$581$			37.4156i			1.55226i
$582$	6.47895	+	6.89745i	0.268561	+	0.285908i
$583$	−2.42065	−	2.42065i	−0.100253	−	0.100253i
$584$	13.0529			0.540131
$585$	−7.88831	−	7.40098i	−0.326142	−	0.305993i
$586$	8.25035			0.340819
$587$	9.11946	+	9.11946i	0.376400	+	0.376400i	0.869802	−	0.493401i	$-0.164247\pi$
$587$	9.11946	+	9.11946i	0.376400	+	0.376400i	−0.493401	+	0.869802i	$0.664247\pi$
$588$	13.1255	+	13.9734i	0.541288	+	0.576252i
$589$		−	20.4438i		−	0.842374i
$590$	0.0916193	+	0.0916193i	0.00377191	+	0.00377191i
$591$	0.285304	−	9.11914i	0.0117358	−	0.375111i
$592$	−5.65288	−	5.65288i	−0.232332	−	0.232332i
$593$	−6.63125	+	6.63125i	−0.272313	+	0.272313i	−0.830031	−	0.557718i	$-0.811677\pi$
$593$	−6.63125	+	6.63125i	−0.272313	+	0.272313i	0.557718	+	0.830031i	$0.311677\pi$
$594$	−0.726192	+	0.601272i	−0.0297960	+	0.0246705i
$595$		−	19.0068i		−	0.779201i
$596$	1.53755	−	1.53755i	0.0629804	−	0.0629804i
$597$	18.1364	−	17.0360i	0.742274	−	0.697237i
$598$	−7.93885	+	9.59969i	−0.324644	+	0.392561i
$599$		−	39.9553i		−	1.63253i	−0.577679	−	0.816264i	$-0.696041\pi$
$599$		−	39.9553i		−	1.63253i	0.577679	−	0.816264i	$-0.303959\pi$
$600$	−0.0770834	+	2.46381i	−0.00314692	+	0.100585i
$601$	20.6271			0.841398			0.420699	−	0.907200i	$-0.361785\pi$
$601$	20.6271			0.841398			0.420699	+	0.907200i	$0.361785\pi$
$602$	7.17574			0.292461
$603$	−3.76139	−	4.26405i	−0.153176	−	0.173646i
$604$	−12.6826	+	12.6826i	−0.516049	+	0.516049i
$605$	7.60654	−	7.60654i	0.309250	−	0.309250i
$606$	−0.0512353	+	1.63763i	−0.00208129	+	0.0665241i
$607$	1.59959			0.0649252			0.0324626	−	0.999473i	$-0.489665\pi$
$607$	1.59959			0.0649252			0.0324626	+	0.999473i	$0.489665\pi$
$608$	19.6399			0.796502
$609$	42.3971	+	1.32645i	1.71802	+	0.0537503i
$610$			1.32616i			0.0536946i
$611$	9.70563	+	8.02646i	0.392648	+	0.324716i
$612$	29.4983	+	1.84759i	1.19240	+	0.0746843i
$613$	10.4572	−	10.4572i	0.422362	−	0.422362i	−0.463654	−	0.886016i	$-0.653462\pi$
$613$	10.4572	−	10.4572i	0.422362	−	0.422362i	0.886016	+	0.463654i	$0.153462\pi$
$614$			10.2510i			0.413696i
$615$	−3.95528	+	3.71530i	−0.159492	+	0.149815i
$616$	1.78328	−	1.78328i	0.0718502	−	0.0718502i
$617$	−7.17003	−	7.17003i	−0.288654	−	0.288654i	0.547894	−	0.836548i	$-0.315430\pi$
$617$	−7.17003	−	7.17003i	−0.288654	−	0.288654i	−0.836548	+	0.547894i	$0.815430\pi$
$618$	9.71779	+	0.304033i	0.390907	+	0.0122300i
$619$	−34.7195	−	34.7195i	−1.39550	−	1.39550i	−0.812411	−	0.583085i	$-0.801846\pi$
$619$	−34.7195	−	34.7195i	−1.39550	−	1.39550i	−0.583085	−	0.812411i	$-0.698154\pi$
$620$		−	7.81428i		−	0.313829i
$621$	37.5471	−	31.0882i	1.50671	−	1.24753i
$622$	4.04080	+	4.04080i	0.162021	+	0.162021i
$623$	−12.9608			−0.519265
$624$	−13.2301	+	15.0159i	−0.529626	+	0.601116i
$625$	−1.00000			−0.0400000
$626$	−0.971187	−	0.971187i	−0.0388164	−	0.0388164i
$627$	−3.03374	+	2.84967i	−0.121156	+	0.113805i
$628$		−	15.6730i		−	0.625423i
$629$	9.32156	+	9.32156i	0.371675	+	0.371675i
$630$	2.62882	+	2.98012i	0.104734	+	0.118731i
$631$	15.2658	+	15.2658i	0.607723	+	0.607723i	0.942351	−	0.334627i	$-0.108610\pi$
$631$	15.2658	+	15.2658i	0.607723	+	0.607723i	−0.334627	+	0.942351i	$0.608610\pi$
$632$	2.67783	−	2.67783i	0.106518	−	0.106518i
$633$	11.2564	+	11.9835i	0.447400	+	0.476300i
$634$		−	9.61174i		−	0.381731i
$635$	1.87213	−	1.87213i	0.0742932	−	0.0742932i
$636$	−15.3620	−	16.3543i	−0.609142	−	0.648489i
$637$	21.3103	−	2.01802i	0.844345	−	0.0799568i
$638$		−	1.23542i		−	0.0489106i
$639$	−37.2132	+	32.8263i	−1.47213	+	1.29859i
$640$	9.86737			0.390042
$641$	25.8774			1.02210			0.511048	−	0.859552i	$-0.329258\pi$
$641$	25.8774			1.02210			0.511048	+	0.859552i	$0.329258\pi$
$642$	5.64764	+	0.176694i	0.222895	+	0.00697354i
$643$	−5.93694	+	5.93694i	−0.234130	+	0.234130i	−0.814414	−	0.580284i	$-0.802942\pi$
$643$	−5.93694	+	5.93694i	−0.234130	+	0.234130i	0.580284	+	0.814414i	$0.302942\pi$
$644$	−44.4832	+	44.4832i	−1.75289	+	1.75289i
$645$	−9.37822	−	0.293409i	−0.369267	−	0.0115530i
$646$	−9.49246			−0.373476
$647$	−8.94367			−0.351612			−0.175806	−	0.984425i	$-0.556253\pi$
$647$	−8.94367			−0.351612			−0.175806	+	0.984425i	$0.556253\pi$
$648$	−10.1164	+	7.85614i	−0.397409	+	0.308618i
$649$			0.173333i			0.00680392i
$650$	1.02327	+	0.846238i	0.0401361	+	0.0331922i
$651$	−17.8772	−	19.0320i	−0.700664	−	0.745922i
$652$	12.8921	−	12.8921i	0.504894	−	0.504894i
$653$			29.3417i			1.14823i	0.818775	+	0.574115i	$0.194654\pi$
$653$			29.3417i			1.14823i	−0.818775	+	0.574115i	$0.805346\pi$
$654$	−4.93655	−	5.25542i	−0.193034	−	0.205503i
$655$	3.62100	−	3.62100i	0.141484	−	0.141484i
$656$	7.09945	+	7.09945i	0.277187	+	0.277187i
$657$	−20.6341	+	18.2017i	−0.805014	+	0.710116i
$658$	−3.27183	−	3.27183i	−0.127549	−	0.127549i
$659$		−	20.2846i		−	0.790175i	−0.918644	−	0.395087i	$-0.870714\pi$
$659$		−	20.2846i		−	0.790175i	0.918644	−	0.395087i	$-0.129286\pi$
$660$	−1.15959	+	1.08923i	−0.0451370	+	0.0423983i
$661$	−13.3192	−	13.3192i	−0.518055	−	0.518055i	0.398927	−	0.916983i	$-0.369383\pi$
$661$	−13.3192	−	13.3192i	−0.518055	−	0.518055i	−0.916983	+	0.398927i	$0.869383\pi$
$662$	−7.81973			−0.303922
$663$	21.8163	−	24.7610i	0.847274	−	0.961639i
$664$	14.8046			0.574531
$665$	12.4052	+	12.4052i	0.481054	+	0.481054i
$666$	−2.75082	−	0.172294i	−0.106592	−	0.00667626i
$667$			63.8761i			2.47329i
$668$	−3.95221	−	3.95221i	−0.152916	−	0.152916i
$669$	11.4979	+	0.359725i	0.444533	+	0.0139078i
$670$	0.493569	+	0.493569i	0.0190682	+	0.0190682i
$671$	−1.25447	+	1.25447i	−0.0484283	+	0.0484283i
$672$	18.2835	−	17.1742i	0.705303	−	0.662509i
$673$			26.5074i			1.02179i	0.859644	+	0.510893i	$0.170685\pi$
$673$			26.5074i			1.02179i	−0.859644	+	0.510893i	$0.829315\pi$
$674$	−4.69293	+	4.69293i	−0.180765	+	0.180765i
$675$	−3.31383	−	4.00231i	−0.127549	−	0.154049i
$676$	4.54949	+	23.8060i	0.174981	+	0.915614i
$677$		−	24.4044i		−	0.937939i	−0.883214	−	0.468970i	$-0.844625\pi$
$677$		−	24.4044i		−	0.937939i	0.883214	−	0.468970i	$-0.155375\pi$
$678$	−7.28225	−	0.227834i	−0.279673	−	0.00874993i
$679$	53.3593			2.04774
$680$	−7.52060			−0.288402
$681$	−0.594807	+	19.0117i	−0.0227930	+	0.728532i
$682$	−0.537753	+	0.537753i	−0.0205916	+	0.0205916i
$683$	24.2961	−	24.2961i	0.929666	−	0.929666i	−0.0680180	−	0.997684i	$-0.521668\pi$
$683$	24.2961	−	24.2961i	0.929666	−	0.929666i	0.997684	+	0.0680180i	$0.0216675\pi$
$684$	−20.4586	+	18.0469i	−0.782256	+	0.690040i
$685$	−11.6718			−0.445957
$686$	1.40827			0.0537679
$687$	0.422874	−	13.5163i	0.0161337	−	0.515679i
$688$			17.3599i			0.661839i
$689$	−24.9414	+	2.36187i	−0.950190	+	0.0899799i
$690$	−4.36172	+	4.09708i	−0.166048	+	0.155973i
$691$	−20.5928	+	20.5928i	−0.783388	+	0.783388i	−0.980401	−	0.197013i	$-0.936876\pi$
$691$	−20.5928	+	20.5928i	−0.783388	+	0.783388i	0.197013	+	0.980401i	$0.436876\pi$
$692$		−	39.7086i		−	1.50950i
$693$	−0.332319	+	5.30574i	−0.0126237	+	0.201548i
$694$	−3.16280	+	3.16280i	−0.120058	+	0.120058i
$695$	0.365760	+	0.365760i	0.0138741	+	0.0138741i
$696$	0.524849	−	16.7757i	0.0198943	−	0.635881i
$697$	−11.7069	−	11.7069i	−0.443432	−	0.443432i
$698$			11.6120i			0.439520i
$699$	−11.5455	−	12.2912i	−0.436689	−	0.464897i
$700$	4.74167	+	4.74167i	0.179218	+	0.179218i
$701$	−20.2981			−0.766648			−0.383324	−	0.923614i	$-0.625221\pi$
$701$	−20.2981			−0.766648			−0.383324	+	0.923614i	$0.625221\pi$
$702$	0.00405037	+	6.89976i	0.000152871	+	0.260415i
$703$	−12.1679			−0.458921
$704$	1.71620	+	1.71620i	0.0646816	+	0.0646816i
$705$	4.14229	+	4.40985i	0.156008	+	0.166085i
$706$		−	3.67660i		−	0.138371i
$707$	6.53260	+	6.53260i	0.245684	+	0.245684i
$708$	−0.0355267	+	1.13554i	−0.00133518	+	0.0426761i
$709$	−24.9325	−	24.9325i	−0.936361	−	0.936361i	0.0617322	−	0.998093i	$-0.480338\pi$
$709$	−24.9325	−	24.9325i	−0.936361	−	0.936361i	−0.998093	+	0.0617322i	$0.980338\pi$
$710$	4.30747	−	4.30747i	0.161656	−	0.161656i
$711$	−0.499021	+	7.96728i	−0.0187148	+	0.298796i
$712$			5.12834i			0.192193i
$713$	27.8040	−	27.8040i	1.04127	−	1.04127i
$714$	−8.83691	+	8.30074i	−0.330713	+	0.310647i
$715$	0.167467	+	1.76845i	0.00626290	+	0.0661364i
$716$			5.16563i			0.193049i
$717$	1.23610	−	39.5094i	0.0461631	−	1.47551i
$718$	−9.37268			−0.349785
$719$	−44.3697			−1.65471			−0.827355	−	0.561679i	$-0.810156\pi$
$719$	−44.3697			−1.65471			−0.827355	+	0.561679i	$0.810156\pi$
$720$	−7.20965	+	6.35975i	−0.268688	+	0.237014i
$721$	38.7649	−	38.7649i	1.44368	−	1.44368i
$722$	1.24761	−	1.24761i	0.0464314	−	0.0464314i
$723$	0.487135	−	15.5703i	0.0181168	−	0.579064i
$724$	−37.4794			−1.39291
$725$	6.80884			0.252874
$726$	−6.85852	−	0.214578i	−0.254544	−	0.00796372i
$727$		−	19.3095i		−	0.716150i	−0.933693	−	0.358075i	$-0.883433\pi$
$727$		−	19.3095i		−	0.716150i	0.933693	−	0.358075i	$-0.116567\pi$
$728$	−1.73997	−	18.3741i	−0.0644875	−	0.680990i
$729$	5.03704	−	26.5260i	0.186557	−	0.982444i
$730$	2.38843	−	2.38843i	0.0883996	−	0.0883996i
$731$		−	28.6263i		−	1.05878i
$732$	−8.47538	+	7.96114i	−0.313259	+	0.294252i
$733$	−8.23013	+	8.23013i	−0.303987	+	0.303987i	−0.842571	−	0.538585i	$-0.818959\pi$
$733$	−8.23013	+	8.23013i	−0.303987	+	0.303987i	0.538585	+	0.842571i	$0.318959\pi$
$734$	4.55071	+	4.55071i	0.167970	+	0.167970i
$735$	10.2779	+	0.321558i	0.379107	+	0.0118608i
$736$	26.7106	+	26.7106i	0.984565	+	0.984565i
$737$			0.933777i			0.0343961i
$738$	3.45475	+	0.216384i	0.127171	+	0.00796521i
$739$	−11.8446	−	11.8446i	−0.435710	−	0.435710i	0.454855	−	0.890565i	$-0.349691\pi$
$739$	−11.8446	−	11.8446i	−0.435710	−	0.435710i	−0.890565	+	0.454855i	$0.849691\pi$
$740$	−4.65095			−0.170972
$741$	1.92197	+	30.3998i	0.0706055	+	1.11677i
$742$	9.20411			0.337893
$743$	−7.55046	−	7.55046i	−0.276999	−	0.276999i	0.554911	−	0.831910i	$-0.312752\pi$
$743$	−7.55046	−	7.55046i	−0.276999	−	0.276999i	−0.831910	+	0.554911i	$0.812752\pi$
$744$	−7.53058	+	7.07367i	−0.276085	+	0.259333i
$745$		−	1.16630i		−	0.0427301i
$746$	3.37880	+	3.37880i	0.123707	+	0.123707i
$747$	−23.4034	+	20.6445i	−0.856285	+	0.755342i
$748$	−3.43218	−	3.43218i	−0.125493	−	0.125493i
$749$	22.5288	−	22.5288i	0.823185	−	0.823185i
$750$	0.436726	+	0.464935i	0.0159470	+	0.0169770i
$751$			0.869234i			0.0317188i	0.999874	+	0.0158594i	$0.00504841\pi$
$751$			0.869234i			0.0317188i	−0.999874	+	0.0158594i	$0.994952\pi$
$752$	7.91537	−	7.91537i	0.288644	−	0.288644i
$753$	5.14195	+	5.47409i	0.187383	+	0.199487i
$754$	−6.96732	−	5.76190i	−0.253735	−	0.209836i
$755$			9.62039i			0.350122i
$756$	−3.26456	+	34.6907i	−0.118731	+	1.26169i
$757$	−32.3586			−1.17609			−0.588046	−	0.808828i	$-0.700103\pi$
$757$	−32.3586			−1.17609			−0.588046	+	0.808828i	$0.700103\pi$
$758$	−2.35121			−0.0853998
$759$	−8.00154	−	0.250338i	−0.290438	−	0.00908670i
$760$	4.90850	−	4.90850i	0.178050	−	0.178050i
$761$	30.6519	−	30.6519i	1.11113	−	1.11113i	0.118133	−	0.992998i	$-0.462309\pi$
$761$	30.6519	−	30.6519i	1.11113	−	1.11113i	0.992998	−	0.118133i	$-0.0376908\pi$
$762$	−1.68803	−	0.0528120i	−0.0611507	−	0.00191318i
$763$	−40.6564			−1.47186
$764$	26.0074			0.940916
$765$	11.8887	−	10.4872i	0.429836	−	0.379165i
$766$		−	13.0129i		−	0.470177i
$767$	0.977538	+	0.808414i	0.0352968	+	0.0291901i
$768$	7.37436	+	7.85069i	0.266099	+	0.283287i
$769$	−10.9540	+	10.9540i	−0.395013	+	0.395013i	−0.876470	−	0.481457i	$-0.840108\pi$
$769$	−10.9540	+	10.9540i	−0.395013	+	0.395013i	0.481457	+	0.876470i	$0.340108\pi$
$770$		−	0.652612i		−	0.0235185i
$771$	−5.87673	−	6.25633i	−0.211645	−	0.225316i
$772$	−0.963655	+	0.963655i	−0.0346827	+	0.0346827i
$773$	27.0891	+	27.0891i	0.974326	+	0.974326i	0.999679	−	0.0253530i	$-0.00807098\pi$
$773$	27.0891	+	27.0891i	0.974326	+	0.974326i	−0.0253530	+	0.999679i	$0.508071\pi$
$774$	3.95929	+	4.48841i	0.142314	+	0.161332i
$775$	−2.96376	−	2.96376i	−0.106461	−	0.106461i
$776$		−	21.1132i		−	0.757921i
$777$	−11.3276	+	10.6403i	−0.406375	+	0.381718i
$778$	−1.39665	−	1.39665i	−0.0500723	−	0.0500723i
$779$	15.2816			0.547522
$780$	0.734639	+	11.6198i	0.0263043	+	0.416055i
$781$	8.14924			0.291603
$782$	−12.9099	−	12.9099i	−0.461658	−	0.461658i
$783$	22.5634	+	27.2511i	0.806349	+	0.973876i
$784$		−	19.0253i		−	0.679475i
$785$	−5.94438	−	5.94438i	−0.212164	−	0.212164i
$786$	−3.26491	−	0.102147i	−0.116456	−	0.00364346i
$787$	−36.5342	−	36.5342i	−1.30230	−	1.30230i	−0.926836	−	0.375468i	$-0.877482\pi$
$787$	−36.5342	−	36.5342i	−1.30230	−	1.30230i	−0.375468	−	0.926836i	$-0.622518\pi$
$788$	−6.94420	+	6.94420i	−0.247377	+	0.247377i
$789$	−27.2625	+	25.6083i	−0.970569	+	0.911681i
$790$		−	0.979985i		−	0.0348663i
$791$	−29.0494	+	29.0494i	−1.03288	+	1.03288i
$792$	2.09938	+	0.131492i	0.0745980	+	0.00467236i
$793$	1.22401	+	12.9255i	0.0434657	+	0.458999i
$794$		−	1.31744i		−	0.0467543i
$795$	−12.0292	−	0.376347i	−0.426630	−	0.0133477i
$796$	−26.7837			−0.949324
$797$	29.5724			1.04751			0.523754	−	0.851870i	$-0.324531\pi$
$797$	29.5724			1.04751			0.523754	+	0.851870i	$0.324531\pi$
$798$	0.349947	−	11.1853i	0.0123880	−	0.395956i
$799$	−13.0524	+	13.0524i	−0.461760	+	0.461760i
$800$	2.84720	−	2.84720i	0.100664	−	0.100664i
$801$	−7.15128	−	8.10696i	−0.252678	−	0.286445i
$802$	−5.81269			−0.205253
$803$	4.51863			0.159459
$804$	−0.191389	+	6.11734i	−0.00674976	+	0.215742i
$805$			33.7427i			1.18927i
$806$	0.524694	+	5.54078i	0.0184815	+	0.195166i
$807$	5.20415	−	4.88840i	0.183195	−	0.172080i
$808$	2.58482	−	2.58482i	0.0909337	−	0.0909337i
$809$		−	53.6701i		−	1.88694i	−0.331455	−	0.943471i	$-0.607540\pi$
$809$		−	53.6701i		−	1.88694i	0.331455	−	0.943471i	$-0.392460\pi$
$810$	−0.413582	+	3.28863i	−0.0145318	+	0.115551i
$811$	22.4475	−	22.4475i	0.788238	−	0.788238i	−0.192967	−	0.981205i	$-0.561811\pi$
$811$	22.4475	−	22.4475i	0.788238	−	0.788238i	0.981205	+	0.192967i	$0.0618110\pi$
$812$	−32.2853	−	32.2853i	−1.13299	−	1.13299i
$813$	0.219470	−	7.01491i	0.00769717	−	0.246024i
$814$	0.320063	+	0.320063i	0.0112182	+	0.0112182i
$815$		−	9.77929i		−	0.342554i
$816$	−20.0815	−	21.3787i	−0.702994	−	0.748403i
$817$	18.6837	+	18.6837i	0.653659	+	0.653659i
$818$	−6.50562			−0.227464
$819$	28.3726	+	26.6197i	0.991417	+	0.930169i
$820$	5.84113			0.203981
$821$	−33.6801	−	33.6801i	−1.17544	−	1.17544i	−0.980892	−	0.194553i	$-0.937674\pi$
$821$	−33.6801	−	33.6801i	−1.17544	−	1.17544i	−0.194553	−	0.980892i	$-0.562326\pi$
$822$	5.09738	+	5.42664i	0.177792	+	0.189276i
$823$			43.9680i			1.53263i	0.642467	+	0.766313i	$0.277911\pi$
$823$			43.9680i			1.53263i	−0.642467	+	0.766313i	$0.722089\pi$
$824$	−15.3385	−	15.3385i	−0.534342	−	0.534342i
$825$	−0.0266847	+	0.852920i	−0.000929042	+	0.0296949i
$826$	−0.329535	−	0.329535i	−0.0114660	−	0.0114660i
$827$	−30.1945	+	30.1945i	−1.04996	+	1.04996i	−0.0512796	+	0.998684i	$0.516330\pi$
$827$	−30.1945	+	30.1945i	−1.04996	+	1.04996i	−0.998684	+	0.0512796i	$0.983670\pi$
$828$	−52.3682	−	3.28002i	−1.81992	−	0.113989i
$829$			34.9574i			1.21412i	0.794656	+	0.607060i	$0.207651\pi$
$829$			34.9574i			1.21412i	−0.794656	+	0.607060i	$0.792349\pi$
$830$	2.70897	−	2.70897i	0.0940297	−	0.0940297i
$831$	17.5204	−	16.4574i	0.607776	−	0.570900i
$832$	17.6829	−	1.67452i	0.613046	−	0.0580535i
$833$			31.3726i			1.08700i
$834$	0.0103180	−	0.329792i	0.000357282	−	0.0114198i
$835$	−2.99795			−0.103748
$836$	4.48020			0.154951
$837$	2.04049	−	21.6833i	0.0705298	−	0.749483i
$838$	−1.62765	+	1.62765i	−0.0562262	+	0.0562262i
$839$	3.70208	−	3.70208i	0.127810	−	0.127810i	−0.640308	−	0.768118i	$-0.721193\pi$
$839$	3.70208	−	3.70208i	0.127810	−	0.127810i	0.768118	+	0.640308i	$0.221193\pi$
$840$	0.277252	−	8.86179i	0.00956611	−	0.305761i
$841$	−17.3603			−0.598632
$842$	−12.9775			−0.447233
$843$	−35.9565	−	1.12495i	−1.23841	−	0.0387452i
$844$		−	17.6971i		−	0.609158i
$845$	10.7545	+	7.30348i	0.369966	+	0.251247i
$846$	0.241253	−	3.85179i	0.00829444	−	0.132427i
$847$	−27.3591	+	27.3591i	−0.940069	+	0.940069i
$848$			22.2670i			0.764652i
$849$	9.58732	−	9.00562i	0.329036	−	0.309072i
$850$	−1.37613	+	1.37613i	−0.0472008	+	0.0472008i
$851$	−16.5486	−	16.5486i	−0.567278	−	0.567278i
$852$	53.3871	+	1.67028i	1.82901	+	0.0572230i
$853$	19.6790	+	19.6790i	0.673797	+	0.673797i	0.958589	−	0.284792i	$-0.0919245\pi$
$853$	19.6790	+	19.6790i	0.673797	+	0.673797i	−0.284792	+	0.958589i	$0.591925\pi$
$854$		−	4.76990i		−	0.163223i
$855$	−0.914714	+	14.6042i	−0.0312826	+	0.499451i
$856$	−8.91420	−	8.91420i	−0.304681	−	0.304681i
$857$	−13.8696			−0.473777			−0.236889	−	0.971537i	$-0.576128\pi$
$857$	−13.8696			−0.473777			−0.236889	+	0.971537i	$0.576128\pi$
$858$	0.749079	−	0.850190i	0.0255731	−	0.0290250i
$859$	47.5429			1.62214			0.811072	−	0.584946i	$-0.198884\pi$
$859$	47.5429			1.62214			0.811072	+	0.584946i	$0.198884\pi$
$860$	7.14149	+	7.14149i	0.243523	+	0.243523i
$861$	14.2263	−	13.3631i	0.484831	−	0.455414i
$862$			1.57933i			0.0537922i
$863$	−18.8498	−	18.8498i	−0.641654	−	0.641654i	0.309308	−	0.950962i	$-0.399903\pi$
$863$	−18.8498	−	18.8498i	−0.641654	−	0.641654i	−0.950962	+	0.309308i	$0.899903\pi$
$864$	20.8305	+	1.96025i	0.708670	+	0.0666890i
$865$	−15.0605	−	15.0605i	−0.512071	−	0.512071i
$866$	−7.81862	+	7.81862i	−0.265687	+	0.265687i
$867$	12.9549	+	13.7917i	0.439972	+	0.468391i
$868$			28.1063i			0.953990i
$869$	0.927010	−	0.927010i	0.0314466	−	0.0314466i
$870$	−2.97360	−	3.16567i	−0.100814	−	0.107326i
$871$	5.26617	+	4.35507i	0.178437	+	0.147566i
$872$			16.0869i			0.544773i
$873$	29.4416	+	33.3761i	0.996447	+	1.12961i
$874$	16.8520			0.570026
$875$	3.59678			0.121594
$876$	29.6024	+	0.926148i	1.00017	+	0.0312916i
$877$	37.6363	−	37.6363i	1.27089	−	1.27089i	0.325265	−	0.945623i	$-0.394546\pi$
$877$	37.6363	−	37.6363i	1.27089	−	1.27089i	0.945623	−	0.325265i	$-0.105454\pi$
$878$	3.60458	−	3.60458i	0.121649	−	0.121649i
$879$	38.7829	+	1.21337i	1.30811	+	0.0409260i
$880$	1.57883			0.0532223
$881$	−48.6517			−1.63912			−0.819559	−	0.572995i	$-0.805781\pi$
$881$	−48.6517			−1.63912			−0.819559	+	0.572995i	$0.805781\pi$
$882$	−4.33913	−	4.91900i	−0.146106	−	0.165631i
$883$		−	27.2665i		−	0.917592i	−0.888542	−	0.458796i	$-0.848281\pi$
$883$		−	27.2665i		−	0.917592i	0.888542	−	0.458796i	$-0.151719\pi$
$884$	−35.3638	+	3.34883i	−1.18941	+	0.112633i
$885$	0.417206	+	0.444154i	0.0140242	+	0.0149301i
$886$	1.53499	−	1.53499i	0.0515689	−	0.0515689i
$887$			32.1996i			1.08116i	0.841294	+	0.540578i	$0.181794\pi$
$887$			32.1996i			1.08116i	−0.841294	+	0.540578i	$0.818206\pi$
$888$	4.21015	+	4.48210i	0.141283	+	0.150409i
$889$	−6.73364	+	6.73364i	−0.225839	+	0.225839i
$890$	0.938391	+	0.938391i	0.0314549	+	0.0314549i
$891$	−3.50208	+	2.71963i	−0.117324	+	0.0911111i
$892$	−8.75559	−	8.75559i	−0.293159	−	0.293159i
$893$		−	17.0379i		−	0.570153i
$894$	−0.542256	+	0.509355i	−0.0181358	+	0.0170354i
$895$	1.95919	+	1.95919i	0.0654885	+	0.0654885i
$896$	−35.4908			−1.18566
$897$	−38.7304	+	43.9583i	−1.29317	+	1.46772i
$898$	7.91374			0.264085
$899$	20.1797	+	20.1797i	0.673032	+	0.673032i
$900$	−0.349633	+	5.58217i	−0.0116544	+	0.186072i
$901$		−	36.7181i		−	1.22326i
$902$	−0.401967	−	0.401967i	−0.0133840	−	0.0133840i
$903$	33.7314	+	1.05533i	1.12251	+	0.0351192i
$904$	11.4943	+	11.4943i	0.382293	+	0.382293i
$905$	−14.2150	+	14.2150i	−0.472522	+	0.472522i
$906$	4.47286	−	4.20147i	0.148601	−	0.139585i
$907$		−	52.9829i		−	1.75927i	−0.475651	−	0.879634i	$-0.657787\pi$
$907$		−	52.9829i		−	1.75927i	0.475651	−	0.879634i	$-0.342213\pi$
$908$	14.4774	−	14.4774i	0.480449	−	0.480449i
$909$	−0.481689	+	7.69056i	−0.0159766	+	0.255080i
$910$	−3.68050	−	3.04374i	−0.122007	−	0.100899i
$911$		−	16.3239i		−	0.540835i	−0.962743	−	0.270417i	$-0.912838\pi$
$911$		−	16.3239i		−	0.540835i	0.962743	−	0.270417i	$-0.0871617\pi$
$912$	27.0600	+	0.846607i	0.896047	+	0.0280340i
$913$	5.12506			0.169615
$914$	2.90994			0.0962522
$915$	−0.195037	+	6.23395i	−0.00644772	+	0.206088i
$916$	−10.2926	+	10.2926i	−0.340078	+	0.340078i
$917$	−13.0239	+	13.0239i	−0.430089	+	0.430089i
$918$	−10.0680	−	0.947440i	−0.332292	−	0.0312702i
$919$	46.3976			1.53051			0.765257	−	0.643725i	$-0.222612\pi$
$919$	46.3976			1.53051			0.765257	+	0.643725i	$0.222612\pi$
$920$	13.3513			0.440180
$921$	−1.50760	+	48.1874i	−0.0496772	+	1.58783i
$922$		−	7.70340i		−	0.253698i
$923$	38.0075	−	45.9588i	1.25103	−	1.51275i
$924$	4.17079	−	3.91773i	0.137209	−	0.128884i
$925$	−1.76399	+	1.76399i	−0.0579995	+	0.0579995i
$926$			4.57815i			0.150447i
$927$	45.6363	+	2.85837i	1.49889	+	0.0938813i
$928$	−19.3861	+	19.3861i	−0.636382	+	0.636382i
$929$	−20.0595	−	20.0595i	−0.658131	−	0.658131i	0.296807	−	0.954938i	$-0.404078\pi$
$929$	−20.0595	−	20.0595i	−0.658131	−	0.658131i	−0.954938	+	0.296807i	$0.904078\pi$
$930$	−0.0836064	+	2.67230i	−0.00274156	+	0.0876283i
$931$	−20.4761	−	20.4761i	−0.671077	−	0.671077i
$932$			18.1516i			0.594575i
$933$	18.4005	+	19.5891i	0.602407	+	0.641318i
$934$	2.42467	+	2.42467i	0.0793376	+	0.0793376i
$935$	−2.60348			−0.0851428
$936$	10.5329	−	11.2265i	0.344279	−	0.366948i
$937$	−23.7901			−0.777188			−0.388594	−	0.921409i	$-0.627039\pi$
$937$	−23.7901			−0.777188			−0.388594	+	0.921409i	$0.627039\pi$
$938$	−1.77526	−	1.77526i	−0.0579644	−	0.0579644i
$939$	−4.42248	−	4.70815i	−0.144322	−	0.153645i
$940$		−	6.51244i		−	0.212412i
$941$	31.8370	+	31.8370i	1.03786	+	1.03786i	0.999255	+	0.0386033i	$0.0122909\pi$
$941$	31.8370	+	31.8370i	1.03786	+	1.03786i	0.0386033	+	0.999255i	$0.487709\pi$
$942$	−0.167689	+	5.35982i	−0.00546359	+	0.174632i
$943$	20.7833	+	20.7833i	0.676798	+	0.676798i
$944$	0.797226	−	0.797226i	0.0259475	−	0.0259475i
$945$	11.9191	+	14.3955i	0.387730	+	0.468284i
$946$		−	0.982907i		−	0.0319571i
$947$	37.4100	−	37.4100i	1.21566	−	1.21566i	0.246523	−	0.969137i	$-0.420712\pi$
$947$	37.4100	−	37.4100i	1.21566	−	1.21566i	0.969137	−	0.246523i	$-0.0792881\pi$
$948$	6.26301	−	5.88301i	0.203413	−	0.191071i
$949$	21.0746	−	25.4835i	0.684109	−	0.827228i
$950$		−	1.79633i		−	0.0582806i
$951$	1.41359	−	45.1825i	0.0458388	−	1.46514i
$952$	27.0500			0.876694
$953$	17.7294			0.574311			0.287156	−	0.957884i	$-0.407290\pi$
$953$	17.7294			0.574311			0.287156	+	0.957884i	$0.407290\pi$
$954$	5.07847	+	5.75714i	0.164421	+	0.186394i
$955$	9.86395	−	9.86395i	0.319190	−	0.319190i
$956$	−30.0863	+	30.0863i	−0.973062	+	0.973062i
$957$	0.181692	−	5.80740i	0.00587326	−	0.187727i
$958$	11.0607			0.357355
$959$	41.9810			1.35564
$960$	8.52844	+	0.266823i	0.275254	+	0.00861168i
$961$			13.4323i			0.433300i
$962$	3.29779	−	0.312290i	0.106325	−	0.0100686i
$963$	26.5222	+	1.66119i	0.854666	+	0.0535310i
$964$	−11.8567	+	11.8567i	−0.381879	+	0.381879i
$965$			0.730979i			0.0235310i
$966$	15.6882	−	14.7363i	0.504759	−	0.474133i
$967$	−1.98285	+	1.98285i	−0.0637640	+	0.0637640i	−0.738270	−	0.674506i	$-0.764357\pi$
$967$	−1.98285	+	1.98285i	−0.0637640	+	0.0637640i	0.674506	+	0.738270i	$0.264357\pi$
$968$	10.8254	+	10.8254i	0.347943	+	0.347943i
$969$	−44.6218	−	1.39605i	−1.43346	−	0.0448476i
$970$	−3.86332	−	3.86332i	−0.124044	−	0.124044i
$971$		−	45.7568i		−	1.46841i	−0.678930	−	0.734203i	$-0.737556\pi$
$971$		−	45.7568i		−	1.46841i	0.678930	−	0.734203i	$-0.262444\pi$
$972$	−23.5002	+	17.0990i	−0.753770	+	0.548451i
$973$	−1.31556	−	1.31556i	−0.0421750	−	0.0421750i
$974$	−6.21595			−0.199172
$975$	4.68571	+	4.12845i	0.150063	+	0.132216i
$976$	11.5396			0.369373
$977$	−4.54207	−	4.54207i	−0.145314	−	0.145314i	0.630707	−	0.776021i	$-0.282765\pi$
$977$	−4.54207	−	4.54207i	−0.145314	−	0.145314i	−0.776021	+	0.630707i	$0.782765\pi$
$978$	−4.54674	+	4.27087i	−0.145389	+	0.136567i
$979$			1.77533i			0.0567397i
$980$	−7.82661	−	7.82661i	−0.250012	−	0.250012i
$981$	−22.4326	−	25.4305i	−0.716218	−	0.811932i
$982$	−2.20723	−	2.20723i	−0.0704354	−	0.0704354i
$983$	−22.8720	+	22.8720i	−0.729505	+	0.729505i	−0.970521	−	0.241016i	$-0.922519\pi$
$983$	−22.8720	+	22.8720i	−0.729505	+	0.729505i	0.241016	+	0.970521i	$0.422519\pi$
$984$	−5.28752	−	5.62906i	−0.168560	−	0.179448i
$985$			5.26751i			0.167837i
$986$	9.36984	−	9.36984i	0.298396	−	0.298396i
$987$	−14.8989	−	15.8613i	−0.474238	−	0.504870i
$988$	20.8953	−	25.2667i	0.664769	−	0.803842i
$989$			50.8203i			1.61599i
$990$	0.408207	−	0.360086i	0.0129737	−	0.0114443i
$991$	−13.1807			−0.418700			−0.209350	−	0.977841i	$-0.567135\pi$
$991$	−13.1807			−0.418700			−0.209350	+	0.977841i	$0.567135\pi$
$992$	16.8768			0.535840
$993$	−36.7586	−	1.15004i	−1.16650	−	0.0364954i
$994$	−15.4930	+	15.4930i	−0.491409	+	0.491409i
$995$	−10.1584	+	10.1584i	−0.322042	+	0.322042i
$996$	33.5752	+	1.05044i	1.06387	+	0.0332846i
$997$	9.27082			0.293610			0.146805	−	0.989165i	$-0.453101\pi$
$997$	9.27082			0.293610			0.146805	+	0.989165i	$0.453101\pi$
$998$	13.0292			0.412432
$999$	−12.9056	−	1.21447i	−0.408314	−	0.0384242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.o.a.161.11	yes	40
3.2	odd	2	inner	195.2.o.a.161.10	yes	40
5.2	odd	4		975.2.n.r.824.10		40
5.3	odd	4		975.2.n.q.824.11		40
5.4	even	2		975.2.o.p.551.10		40
13.8	odd	4	inner	195.2.o.a.86.10	✓	40
15.2	even	4		975.2.n.r.824.11		40
15.8	even	4		975.2.n.q.824.10		40
15.14	odd	2		975.2.o.p.551.11		40
39.8	even	4	inner	195.2.o.a.86.11	yes	40
65.8	even	4		975.2.n.r.749.11		40
65.34	odd	4		975.2.o.p.476.11		40
65.47	even	4		975.2.n.q.749.10		40
195.8	odd	4		975.2.n.r.749.10		40
195.47	odd	4		975.2.n.q.749.11		40
195.164	even	4		975.2.o.p.476.10		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.10	✓	40	13.8	odd	4	inner
195.2.o.a.86.11	yes	40	39.8	even	4	inner
195.2.o.a.161.10	yes	40	3.2	odd	2	inner
195.2.o.a.161.11	yes	40	1.1	even	1	trivial
975.2.n.q.749.10		40	65.47	even	4
975.2.n.q.749.11		40	195.47	odd	4
975.2.n.q.824.10		40	15.8	even	4
975.2.n.q.824.11		40	5.3	odd	4
975.2.n.r.749.10		40	195.8	odd	4
975.2.n.r.749.11		40	65.8	even	4
975.2.n.r.824.10		40	5.2	odd	4
975.2.n.r.824.11		40	15.2	even	4
975.2.o.p.476.10		40	195.164	even	4
975.2.o.p.476.11		40	65.34	odd	4
975.2.o.p.551.10		40	5.4	even	2
975.2.o.p.551.11		40	15.14	odd	2

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.260415 + 0.260415i) q^{2} +(1.18585 + 1.26244i) q^{3} -1.86437i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.0199472 + 0.637571i) q^{6} +(2.54331 + 2.54331i) q^{7} +(1.00634 - 1.00634i) q^{8} +(-0.187534 + 2.99413i) q^{9} -0.368282i q^{10} +(0.348374 - 0.348374i) q^{11} +(2.35366 - 2.21086i) q^{12} +(-0.339913 - 3.58949i) q^{13} +1.32463i q^{14} +(0.0541629 - 1.73120i) q^{15} -3.20461 q^{16} +5.28437 q^{17} +(-0.828552 + 0.730879i) q^{18} +(-3.44898 + 3.44898i) q^{19} +(-1.31831 + 1.31831i) q^{20} +(-0.194812 + 6.22677i) q^{21} +0.181443 q^{22} -9.38135 q^{23} +(2.46381 + 0.0770834i) q^{24} +1.00000i q^{25} +(0.846238 - 1.02327i) q^{26} +(-4.00231 + 3.31383i) q^{27} +(4.74167 - 4.74167i) q^{28} -6.80884i q^{29} +(0.464935 - 0.436726i) q^{30} +(-2.96376 + 2.96376i) q^{31} +(-2.84720 - 2.84720i) q^{32} +(0.852920 + 0.0266847i) q^{33} +(1.37613 + 1.37613i) q^{34} -3.59678i q^{35} +(5.58217 + 0.349633i) q^{36} +(1.76399 + 1.76399i) q^{37} -1.79633 q^{38} +(4.12845 - 4.68571i) q^{39} -1.42318 q^{40} +(-2.21539 - 2.21539i) q^{41} +(-1.67227 + 1.57081i) q^{42} -5.41717i q^{43} +(-0.649497 - 0.649497i) q^{44} +(2.24978 - 1.98456i) q^{45} +(-2.44304 - 2.44304i) q^{46} +(-2.47000 + 2.47000i) q^{47} +(-3.80017 - 4.04564i) q^{48} +5.93686i q^{49} +(-0.260415 + 0.260415i) q^{50} +(6.26646 + 6.67123i) q^{51} +(-6.69214 + 0.633724i) q^{52} -6.94843i q^{53} +(-1.90523 - 0.179291i) q^{54} -0.492675 q^{55} +5.11886 q^{56} +(-8.44410 - 0.264184i) q^{57} +(1.77312 - 1.77312i) q^{58} +(-0.248775 + 0.248775i) q^{59} +(-3.22760 - 0.100980i) q^{60} -3.60093 q^{61} -1.54361 q^{62} +(-8.09197 + 7.13805i) q^{63} +4.92631i q^{64} +(-2.29780 + 2.77851i) q^{65} +(0.215164 + 0.229062i) q^{66} +(-1.34019 + 1.34019i) q^{67} -9.85202i q^{68} +(-11.1248 - 11.8434i) q^{69} +(0.936655 - 0.936655i) q^{70} +(11.6961 + 11.6961i) q^{71} +(2.82439 + 3.20183i) q^{72} +(6.48532 + 6.48532i) q^{73} +0.918735i q^{74} +(-1.26244 + 1.18585i) q^{75} +(6.43016 + 6.43016i) q^{76} +1.77204 q^{77} +(2.29534 - 0.145118i) q^{78} +2.66096 q^{79} +(2.26600 + 2.26600i) q^{80} +(-8.92966 - 1.12300i) q^{81} -1.15384i q^{82} +(7.35570 + 7.35570i) q^{83} +(11.6090 + 0.363202i) q^{84} +(-3.73662 - 3.73662i) q^{85} +(1.41071 - 1.41071i) q^{86} +(8.59579 - 8.07424i) q^{87} -0.701163i q^{88} +(-2.54802 + 2.54802i) q^{89} +(1.10268 + 0.0690654i) q^{90} +(8.26469 - 9.99370i) q^{91} +17.4903i q^{92} +(-7.25614 - 0.227017i) q^{93} -1.28645 q^{94} +4.87759 q^{95} +(0.218090 - 6.97078i) q^{96} +(10.4901 - 10.4901i) q^{97} +(-1.54604 + 1.54604i) q^{98} +(0.977745 + 1.10841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} - 16 q^{7} + 4 q^{15} - 64 q^{16} + 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} - 24 q^{27} + 32 q^{28} + 32 q^{31} - 4 q^{33} - 16 q^{34} + 32 q^{37} - 8 q^{39} + 8 q^{42} - 8 q^{45} - 40 q^{46}+ \cdots - 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 - 16 * q^7 + 4 * q^15 - 64 * q^16 + 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 - 24 * q^27 + 32 * q^28 + 32 * q^31 - 4 * q^33 - 16 * q^34 + 32 * q^37 - 8 * q^39 + 8 * q^42 - 8 * q^45 - 40 * q^46 + 8 * q^48 - 32 * q^54 + 8 * q^55 - 36 * q^57 + 24 * q^58 + 16 * q^60 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 + 132 * q^72 - 64 * q^73 + 16 * q^76 - 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 24 * q^85 + 16 * q^87 + 8 * q^91 - 108 * q^93 - 32 * q^94 - 76 * q^96 + 24 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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