LMFDB - Embedded newform 242.2.c.f.27.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [242,2,Mod(3,242)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("242.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(242, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	242.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.93237972891$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			27.1
Root			$-1.40126 + 1.01807i$ of defining polynomial
Character	$\chi$	$=$	242.27
Dual form			242.2.c.f.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.592242 - 0.430289i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.535233 + 1.64728i) q^{5} +(0.226216 - 0.696222i) q^{6} +(-3.82831 + 2.78143i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.761449 - 2.34350i) q^{9} -1.73205 q^{10} +0.732051 q^{12} +(0.927051 + 2.85317i) q^{13} +(-3.82831 - 2.78143i) q^{14} +(1.02579 - 0.745282i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.60570 + 4.94183i) q^{17} +(1.99350 - 1.44836i) q^{18} +(-1.02579 - 0.745282i) q^{19} +(-0.535233 - 1.64728i) q^{20} +3.46410 q^{21} -1.26795 q^{23} +(0.226216 + 0.696222i) q^{24} +(1.61803 + 1.17557i) q^{25} +(-2.42705 + 1.76336i) q^{26} +(-1.23607 + 3.80423i) q^{27} +(1.46228 - 4.50045i) q^{28} +(2.42705 - 1.76336i) q^{29} +(1.02579 + 0.745282i) q^{30} +(0.0606144 + 0.186552i) q^{31} +1.00000 q^{32} -5.19615 q^{34} +(-2.53275 - 7.79500i) q^{35} +(1.99350 + 1.44836i) q^{36} +(5.82181 - 4.22979i) q^{37} +(0.391818 - 1.20589i) q^{38} +(0.678648 - 2.08867i) q^{39} +(1.40126 - 1.01807i) q^{40} +(0.650326 + 0.472490i) q^{41} +(1.07047 + 3.29456i) q^{42} +4.26795 q^{45} +(-0.391818 - 1.20589i) q^{46} +(6.63083 + 4.81758i) q^{47} +(-0.592242 + 0.430289i) q^{48} +(4.75648 - 14.6390i) q^{49} +(-0.618034 + 1.90211i) q^{50} +(3.07738 - 2.23585i) q^{51} +(-2.42705 - 1.76336i) q^{52} +(3.45980 + 10.6482i) q^{53} -4.00000 q^{54} +4.73205 q^{56} +(0.286831 + 0.882774i) q^{57} +(2.42705 + 1.76336i) q^{58} +(-7.65662 + 5.56286i) q^{59} +(-0.391818 + 1.20589i) q^{60} +(0.783636 - 2.41178i) q^{61} +(-0.158691 + 0.115296i) q^{62} +(9.43334 + 6.85373i) q^{63} +(0.309017 + 0.951057i) q^{64} -5.19615 q^{65} -10.1962 q^{67} +(-1.60570 - 4.94183i) q^{68} +(0.750932 + 0.545584i) q^{69} +(6.63083 - 4.81758i) q^{70} +(-2.92457 + 9.00090i) q^{71} +(-0.761449 + 2.34350i) q^{72} +(0.750932 - 0.545584i) q^{73} +(5.82181 + 4.22979i) q^{74} +(-0.452432 - 1.39244i) q^{75} +1.26795 q^{76} +2.19615 q^{78} +(-1.46228 - 4.50045i) q^{79} +(1.40126 + 1.01807i) q^{80} +(-3.61153 + 2.62393i) q^{81} +(-0.248403 + 0.764504i) q^{82} +(2.53275 - 7.79500i) q^{83} +(-2.80252 + 2.03615i) q^{84} +(-7.28115 - 5.29007i) q^{85} -2.19615 q^{87} +6.46410 q^{89} +(1.31887 + 4.05906i) q^{90} +(-11.4849 - 8.34429i) q^{91} +(1.02579 - 0.745282i) q^{92} +(0.0443728 - 0.136566i) q^{93} +(-2.53275 + 7.79500i) q^{94} +(1.77672 - 1.29087i) q^{95} +(-0.592242 - 0.430289i) q^{96} +(-0.309017 - 0.951057i) q^{97} +15.3923 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} - 6 q^{7} - 2 q^{8} - 2 q^{9} - 8 q^{12} - 6 q^{13} - 6 q^{14} + 6 q^{15} - 2 q^{16} - 2 q^{18} - 6 q^{19} - 24 q^{23} + 2 q^{24} + 4 q^{25} - 6 q^{26} + 8 q^{27}+ \cdots + 40 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 - 6 * q^7 - 2 * q^8 - 2 * q^9 - 8 * q^12 - 6 * q^13 - 6 * q^14 + 6 * q^15 - 2 * q^16 - 2 * q^18 - 6 * q^19 - 24 * q^23 + 2 * q^24 + 4 * q^25 - 6 * q^26 + 8 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 10 * q^31 + 8 * q^32 + 6 * q^35 - 2 * q^36 + 4 * q^37 - 6 * q^38 + 6 * q^39 + 12 * q^41 + 48 * q^45 + 6 * q^46 + 6 * q^47 + 2 * q^48 - 10 * q^49 + 4 * q^50 + 18 * q^51 - 6 * q^52 - 12 * q^53 - 32 * q^54 + 24 * q^56 + 12 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 - 12 * q^61 + 10 * q^62 + 6 * q^63 - 2 * q^64 - 40 * q^67 - 12 * q^69 + 6 * q^70 + 12 * q^71 - 2 * q^72 - 12 * q^73 + 4 * q^74 - 4 * q^75 + 24 * q^76 - 24 * q^78 + 6 * q^79 - 2 * q^81 + 12 * q^82 - 6 * q^83 - 18 * q^85 + 24 * q^87 + 24 * q^89 - 12 * q^90 - 18 * q^91 + 6 * q^92 - 28 * q^93 + 6 * q^94 - 6 * q^95 + 2 * q^96 + 2 * q^97 + 40 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.592242	−	0.430289i	−0.341931	−	0.248427i	0.403545	−	0.914960i	$-0.367778\pi$
$3$	−0.592242	−	0.430289i	−0.341931	−	0.248427i	−0.745476	+	0.666532i	$0.767778\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.535233	+	1.64728i	−0.239364	+	0.736685i	0.757149	+	0.653242i	$0.226592\pi$
$5$	−0.535233	+	1.64728i	−0.239364	+	0.736685i	−0.996513	+	0.0834430i	$0.973408\pi$
$6$	0.226216	−	0.696222i	0.0923524	−	0.284231i
$7$	−3.82831	+	2.78143i	−1.44696	+	1.05128i	−0.460436	+	0.887693i	$0.652307\pi$
$7$	−3.82831	+	2.78143i	−1.44696	+	1.05128i	−0.986529	+	0.163589i	$0.947693\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.761449	−	2.34350i	−0.253816	−	0.781167i
$10$	−1.73205			−0.547723
$11$		0			0
$11$		0			0
$12$	0.732051			0.211325
$13$	0.927051	+	2.85317i	0.257118	+	0.791327i	0.993405	+	0.114658i	$0.0365772\pi$
$13$	0.927051	+	2.85317i	0.257118	+	0.791327i	−0.736287	+	0.676669i	$0.763423\pi$
$14$	−3.82831	−	2.78143i	−1.02316	−	0.743368i
$15$	1.02579	−	0.745282i	0.264858	−	0.192431i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.60570	+	4.94183i	−0.389439	+	1.19857i	0.543769	+	0.839235i	$0.316997\pi$
$17$	−1.60570	+	4.94183i	−0.389439	+	1.19857i	−0.933208	+	0.359336i	$0.883003\pi$
$18$	1.99350	−	1.44836i	0.469872	−	0.341382i
$19$	−1.02579	−	0.745282i	−0.235333	−	0.170979i	0.463869	−	0.885904i	$-0.346461\pi$
$19$	−1.02579	−	0.745282i	−0.235333	−	0.170979i	−0.699202	+	0.714925i	$0.746461\pi$
$20$	−0.535233	−	1.64728i	−0.119682	−	0.368343i
$21$	3.46410			0.755929
$22$		0			0
$23$	−1.26795			−0.264386			−0.132193	−	0.991224i	$-0.542202\pi$
$23$	−1.26795			−0.264386			−0.132193	+	0.991224i	$0.542202\pi$
$24$	0.226216	+	0.696222i	0.0461762	+	0.142116i
$25$	1.61803	+	1.17557i	0.323607	+	0.235114i
$26$	−2.42705	+	1.76336i	−0.475984	+	0.345823i
$27$	−1.23607	+	3.80423i	−0.237881	+	0.732124i
$28$	1.46228	−	4.50045i	0.276346	−	0.850505i
$29$	2.42705	−	1.76336i	0.450692	−	0.327447i	−0.339177	−	0.940723i	$-0.610149\pi$
$29$	2.42705	−	1.76336i	0.450692	−	0.327447i	0.789869	+	0.613276i	$0.210149\pi$
$30$	1.02579	+	0.745282i	0.187283	+	0.136069i
$31$	0.0606144	+	0.186552i	0.0108867	+	0.0335057i	0.956352	−	0.292216i	$-0.0943927\pi$
$31$	0.0606144	+	0.186552i	0.0108867	+	0.0335057i	−0.945466	+	0.325722i	$0.894393\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−5.19615			−0.891133
$35$	−2.53275	−	7.79500i	−0.428113	−	1.31760i
$36$	1.99350	+	1.44836i	0.332250	+	0.241394i
$37$	5.82181	−	4.22979i	0.957100	−	0.695374i	0.00462428	−	0.999989i	$-0.498528\pi$
$37$	5.82181	−	4.22979i	0.957100	−	0.695374i	0.952475	+	0.304616i	$0.0985280\pi$
$38$	0.391818	−	1.20589i	0.0635612	−	0.195621i
$39$	0.678648	−	2.08867i	0.108671	−	0.334454i
$40$	1.40126	−	1.01807i	0.221558	−	0.160972i
$41$	0.650326	+	0.472490i	0.101564	+	0.0737905i	0.637408	−	0.770526i	$-0.280007\pi$
$41$	0.650326	+	0.472490i	0.101564	+	0.0737905i	−0.535844	+	0.844317i	$0.680007\pi$
$42$	1.07047	+	3.29456i	0.165177	+	0.508361i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	4.26795			0.636228
$46$	−0.391818	−	1.20589i	−0.0577704	−	0.177799i
$47$	6.63083	+	4.81758i	0.967205	+	0.702716i	0.954813	−	0.297207i	$-0.0960552\pi$
$47$	6.63083	+	4.81758i	0.967205	+	0.702716i	0.0123925	+	0.999923i	$0.496055\pi$
$48$	−0.592242	+	0.430289i	−0.0854827	+	0.0621068i
$49$	4.75648	−	14.6390i	0.679498	−	2.09128i
$50$	−0.618034	+	1.90211i	−0.0874032	+	0.268999i
$51$	3.07738	−	2.23585i	0.430919	−	0.313081i
$52$	−2.42705	−	1.76336i	−0.336571	−	0.244533i
$53$	3.45980	+	10.6482i	0.475240	+	1.46264i	0.845633	+	0.533764i	$0.179223\pi$
$53$	3.45980	+	10.6482i	0.475240	+	1.46264i	−0.370393	+	0.928875i	$0.620777\pi$
$54$	−4.00000			−0.544331
$55$		0			0
$56$	4.73205			0.632347
$57$	0.286831	+	0.882774i	0.0379916	+	0.116926i
$58$	2.42705	+	1.76336i	0.318687	+	0.231540i
$59$	−7.65662	+	5.56286i	−0.996807	+	0.724223i	−0.961401	−	0.275150i	$-0.911272\pi$
$59$	−7.65662	+	5.56286i	−0.996807	+	0.724223i	−0.0354057	+	0.999373i	$0.511272\pi$
$60$	−0.391818	+	1.20589i	−0.0505835	+	0.155680i
$61$	0.783636	−	2.41178i	0.100334	−	0.308797i	−0.888273	−	0.459316i	$-0.848094\pi$
$61$	0.783636	−	2.41178i	0.100334	−	0.308797i	0.988607	+	0.150519i	$0.0480945\pi$
$62$	−0.158691	+	0.115296i	−0.0201537	+	0.0146425i
$63$	9.43334	+	6.85373i	1.18849	+	0.863488i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−5.19615			−0.644503
$66$		0			0
$67$	−10.1962			−1.24566			−0.622829	−	0.782358i	$-0.714017\pi$
$67$	−10.1962			−1.24566			−0.622829	+	0.782358i	$0.714017\pi$
$68$	−1.60570	−	4.94183i	−0.194720	−	0.599285i
$69$	0.750932	+	0.545584i	0.0904016	+	0.0656806i
$70$	6.63083	−	4.81758i	0.792535	−	0.575811i
$71$	−2.92457	+	9.00090i	−0.347082	+	1.06821i	0.613377	+	0.789790i	$0.289811\pi$
$71$	−2.92457	+	9.00090i	−0.347082	+	1.06821i	−0.960460	+	0.278420i	$0.910189\pi$
$72$	−0.761449	+	2.34350i	−0.0897377	+	0.276184i
$73$	0.750932	−	0.545584i	0.0878900	−	0.0638558i	−0.542972	−	0.839750i	$-0.682701\pi$
$73$	0.750932	−	0.545584i	0.0878900	−	0.0638558i	0.630862	+	0.775895i	$0.282701\pi$
$74$	5.82181	+	4.22979i	0.676772	+	0.491703i
$75$	−0.452432	−	1.39244i	−0.0522424	−	0.160786i
$76$	1.26795			0.145444
$77$		0			0
$78$	2.19615			0.248665
$79$	−1.46228	−	4.50045i	−0.164520	−	0.506340i	0.834481	−	0.551037i	$-0.185768\pi$
$79$	−1.46228	−	4.50045i	−0.164520	−	0.506340i	−0.999001	+	0.0446971i	$0.985768\pi$
$80$	1.40126	+	1.01807i	0.156665	+	0.113824i
$81$	−3.61153	+	2.62393i	−0.401282	+	0.291548i
$82$	−0.248403	+	0.764504i	−0.0274315	+	0.0844254i
$83$	2.53275	−	7.79500i	0.278005	−	0.855613i	−0.710403	−	0.703795i	$-0.751487\pi$
$83$	2.53275	−	7.79500i	0.278005	−	0.855613i	0.988409	−	0.151818i	$-0.0485127\pi$
$84$	−2.80252	+	2.03615i	−0.305780	+	0.222162i
$85$	−7.28115	−	5.29007i	−0.789752	−	0.573788i
$86$		0			0
$87$	−2.19615			−0.235452
$88$		0			0
$89$	6.46410			0.685193			0.342597	−	0.939483i	$-0.388694\pi$
$89$	6.46410			0.685193			0.342597	+	0.939483i	$0.388694\pi$
$90$	1.31887	+	4.05906i	0.139021	+	0.427863i
$91$	−11.4849	−	8.34429i	−1.20395	−	0.874719i
$92$	1.02579	−	0.745282i	0.106946	−	0.0777010i
$93$	0.0443728	−	0.136566i	0.00460125	−	0.0141612i
$94$	−2.53275	+	7.79500i	−0.261233	+	0.803993i
$95$	1.77672	−	1.29087i	0.182288	−	0.132440i
$96$	−0.592242	−	0.430289i	−0.0604454	−	0.0439162i
$97$	−0.309017	−	0.951057i	−0.0313759	−	0.0965652i	0.934142	−	0.356901i	$-0.116167\pi$
$97$	−0.309017	−	0.951057i	−0.0313759	−	0.0965652i	−0.965518	+	0.260336i	$0.916167\pi$
$98$	15.3923			1.55486
$99$		0			0
$100$	−2.00000			−0.200000
$101$	5.06550	+	15.5900i	0.504036	+	1.55126i	0.802385	+	0.596807i	$0.203564\pi$
$101$	5.06550	+	15.5900i	0.504036	+	1.55126i	−0.298349	+	0.954457i	$0.596436\pi$
$102$	3.07738	+	2.23585i	0.304706	+	0.221382i
$103$	6.78952	−	4.93287i	0.668991	−	0.486050i	−0.200696	−	0.979654i	$-0.564320\pi$
$103$	6.78952	−	4.93287i	0.668991	−	0.486050i	0.869687	+	0.493603i	$0.164320\pi$
$104$	0.927051	−	2.85317i	0.0909048	−	0.279776i
$105$	−1.85410	+	5.70634i	−0.180942	+	0.556882i
$106$	−9.05788	+	6.58093i	−0.879779	+	0.639197i
$107$	−10.1843	−	7.39931i	−0.984551	−	0.715318i	−0.0258300	−	0.999666i	$-0.508223\pi$
$107$	−10.1843	−	7.39931i	−0.984551	−	0.715318i	−0.958721	+	0.284348i	$0.908223\pi$
$108$	−1.23607	−	3.80423i	−0.118941	−	0.366062i
$109$	−2.07180			−0.198442			−0.0992211	−	0.995065i	$-0.531635\pi$
$109$	−2.07180			−0.198442			−0.0992211	+	0.995065i	$0.531635\pi$
$110$		0			0
$111$	−5.26795			−0.500012
$112$	1.46228	+	4.50045i	0.138173	+	0.425252i
$113$	−8.78302	−	6.38124i	−0.826237	−	0.600296i	0.0922554	−	0.995735i	$-0.470592\pi$
$113$	−8.78302	−	6.38124i	−0.826237	−	0.600296i	−0.918492	+	0.395439i	$0.870592\pi$
$114$	−0.750932	+	0.545584i	−0.0703312	+	0.0510986i
$115$	0.678648	−	2.08867i	0.0632843	−	0.194769i
$116$	−0.927051	+	2.85317i	−0.0860745	+	0.264910i
$117$	5.98050	−	4.34509i	0.552897	−	0.401704i
$118$	−7.65662	−	5.56286i	−0.704849	−	0.512103i
$119$	−7.59825	−	23.3850i	−0.696531	−	2.14370i
$120$	−1.26795			−0.115747
$121$		0			0
$122$	2.53590			0.229589
$123$	−0.181843	−	0.559656i	−0.0163963	−	0.0504625i
$124$	−0.158691	−	0.115296i	−0.0142508	−	0.0103538i
$125$	−9.80881	+	7.12652i	−0.877327	+	0.637415i
$126$	−3.60322	+	11.0896i	−0.321000	+	0.987937i
$127$	4.28187	−	13.1782i	0.379954	−	1.16938i	−0.560121	−	0.828411i	$-0.689245\pi$
$127$	4.28187	−	13.1782i	0.379954	−	1.16938i	0.940075	−	0.340968i	$-0.110755\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$		0			0
$130$	−1.60570	−	4.94183i	−0.140829	−	0.433428i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	6.00000			0.520266
$134$	−3.15078	−	9.69712i	−0.272186	−	0.837703i
$135$	−5.60503	−	4.07230i	−0.482405	−	0.350487i
$136$	4.20378	−	3.05422i	0.360471	−	0.261897i
$137$	−2.92457	+	9.00090i	−0.249863	+	0.768998i	0.744936	+	0.667136i	$0.232480\pi$
$137$	−2.92457	+	9.00090i	−0.249863	+	0.768998i	−0.994799	+	0.101862i	$0.967520\pi$
$138$	−0.286831	+	0.882774i	−0.0244166	+	0.0751467i
$139$	−16.3390	+	11.8710i	−1.38586	+	1.00689i	−0.389553	+	0.921004i	$0.627371\pi$
$139$	−16.3390	+	11.8710i	−1.38586	+	1.00689i	−0.996305	+	0.0858811i	$0.972629\pi$
$140$	6.63083	+	4.81758i	0.560407	+	0.407160i
$141$	−1.85410	−	5.70634i	−0.156144	−	0.480560i
$142$	−9.46410			−0.794210
$143$		0			0
$144$	−2.46410			−0.205342
$145$	1.60570	+	4.94183i	0.133346	+	0.410397i
$146$	0.750932	+	0.545584i	0.0621476	+	0.0451529i
$147$	−9.11596	+	6.62313i	−0.751872	+	0.546267i
$148$	−2.22373	+	6.84395i	−0.182790	+	0.562569i
$149$	−4.63525	+	14.2658i	−0.379735	+	1.16870i	0.560493	+	0.828159i	$0.310612\pi$
$149$	−4.63525	+	14.2658i	−0.379735	+	1.16870i	−0.940228	+	0.340545i	$0.889388\pi$
$150$	1.18448	−	0.860577i	0.0967126	−	0.0702658i
$151$	3.55345	+	2.58173i	0.289176	+	0.210098i	0.722910	−	0.690943i	$-0.242804\pi$
$151$	3.55345	+	2.58173i	0.289176	+	0.210098i	−0.433734	+	0.901041i	$0.642804\pi$
$152$	0.391818	+	1.20589i	0.0317806	+	0.0978107i
$153$	12.8038			1.03513
$154$		0			0
$155$	−0.339746			−0.0272891
$156$	0.678648	+	2.08867i	0.0543354	+	0.167227i
$157$	−3.23607	−	2.35114i	−0.258266	−	0.187641i	0.451116	−	0.892465i	$-0.351026\pi$
$157$	−3.23607	−	2.35114i	−0.258266	−	0.187641i	−0.709382	+	0.704824i	$0.751026\pi$
$158$	3.82831	−	2.78143i	0.304564	−	0.221279i
$159$	2.53275	−	7.79500i	0.200860	−	0.618184i
$160$	−0.535233	+	1.64728i	−0.0423139	+	0.130229i
$161$	4.85410	−	3.52671i	0.382557	−	0.277944i
$162$	−3.61153	−	2.62393i	−0.283749	−	0.206156i
$163$	6.85899	+	21.1098i	0.537237	+	1.65345i	0.738764	+	0.673964i	$0.235410\pi$
$163$	6.85899	+	21.1098i	0.537237	+	1.65345i	−0.201527	+	0.979483i	$0.564590\pi$
$164$	−0.803848			−0.0627700
$165$		0			0
$166$	8.19615			0.636145
$167$	5.06550	+	15.5900i	0.391980	+	1.20639i	0.931288	+	0.364283i	$0.118686\pi$
$167$	5.06550	+	15.5900i	0.391980	+	1.20639i	−0.539308	+	0.842108i	$0.681314\pi$
$168$	−2.80252	−	2.03615i	−0.216219	−	0.157092i
$169$	3.23607	−	2.35114i	0.248928	−	0.180857i
$170$	2.78115	−	8.55951i	0.213305	−	0.656484i
$171$	−0.965479	+	2.97144i	−0.0738320	+	0.227232i
$172$		0			0
$173$	3.55345	+	2.58173i	0.270164	+	0.196285i	0.714616	−	0.699517i	$-0.246602\pi$
$173$	3.55345	+	2.58173i	0.270164	+	0.196285i	−0.444452	+	0.895803i	$0.646602\pi$
$174$	−0.678648	−	2.08867i	−0.0514482	−	0.158341i
$175$	−9.46410			−0.715419
$176$		0			0
$177$	6.92820			0.520756
$178$	1.99752	+	6.14773i	0.149720	+	0.460792i
$179$	11.2101	+	8.14459i	0.837880	+	0.608755i	0.921778	−	0.387719i	$-0.126737\pi$
$179$	11.2101	+	8.14459i	0.837880	+	0.608755i	−0.0838978	+	0.996474i	$0.526737\pi$
$180$	−3.45284	+	2.50864i	−0.257360	+	0.186983i
$181$	2.22373	−	6.84395i	0.165289	−	0.508707i	−0.833769	−	0.552114i	$-0.813821\pi$
$181$	2.22373	−	6.84395i	0.165289	−	0.508707i	0.999057	+	0.0434073i	$0.0138213\pi$
$182$	4.38685	−	13.5013i	0.325175	−	1.00079i
$183$	−1.50186	+	1.09117i	−0.111021	+	0.0806615i
$184$	1.02579	+	0.745282i	0.0756224	+	0.0549429i
$185$	3.85162	+	11.8541i	0.283177	+	0.871528i
$186$	0.143594			0.0105288
$187$		0			0
$188$	−8.19615			−0.597766
$189$	−5.84914	−	18.0018i	−0.425462	−	1.30944i
$190$	1.77672	+	1.29087i	0.128897	+	0.0936493i
$191$	17.3648	−	12.6163i	1.25647	−	0.912882i	0.257895	−	0.966173i	$-0.416971\pi$
$191$	17.3648	−	12.6163i	1.25647	−	0.912882i	0.998579	+	0.0532907i	$0.0169710\pi$
$192$	0.226216	−	0.696222i	0.0163257	−	0.0502455i
$193$	3.17297	−	9.76540i	0.228395	−	0.702929i	−0.769534	−	0.638606i	$-0.779511\pi$
$193$	3.17297	−	9.76540i	0.228395	−	0.702929i	0.997929	−	0.0643227i	$-0.0204887\pi$
$194$	0.809017	−	0.587785i	0.0580840	−	0.0422005i
$195$	3.07738	+	2.23585i	0.220376	+	0.160112i
$196$	4.75648	+	14.6390i	0.339749	+	1.04564i
$197$	−13.3923			−0.954162			−0.477081	−	0.878859i	$-0.658305\pi$
$197$	−13.3923			−0.954162			−0.477081	+	0.878859i	$0.658305\pi$
$198$		0			0
$199$	−0.392305			−0.0278098			−0.0139049	−	0.999903i	$-0.504426\pi$
$199$	−0.392305			−0.0278098			−0.0139049	+	0.999903i	$0.504426\pi$
$200$	−0.618034	−	1.90211i	−0.0437016	−	0.134500i
$201$	6.03859	+	4.38729i	0.425929	+	0.309455i
$202$	−13.2617	+	9.63516i	−0.933087	+	0.677927i
$203$	−4.38685	+	13.5013i	−0.307897	+	0.947609i
$204$	−1.17545	+	3.61767i	−0.0822982	+	0.253288i
$205$	−1.12640	+	0.818376i	−0.0786711	+	0.0571579i
$206$	6.78952	+	4.93287i	0.473048	+	0.343690i
$207$	0.965479	+	2.97144i	0.0671054	+	0.206529i
$208$	3.00000			0.208013
$209$		0			0
$210$	−6.00000			−0.414039
$211$	−7.99007	−	24.5909i	−0.550059	−	1.69291i	−0.708647	−	0.705563i	$-0.750694\pi$
$211$	−7.99007	−	24.5909i	−0.550059	−	1.69291i	0.158588	−	0.987345i	$-0.449306\pi$
$212$	−9.05788	−	6.58093i	−0.622098	−	0.451980i
$213$	5.60503	−	4.07230i	0.384051	−	0.279029i
$214$	3.89005	−	11.9723i	0.265918	−	0.818412i
$215$		0			0
$216$	3.23607	−	2.35114i	0.220187	−	0.159975i
$217$	−0.750932	−	0.545584i	−0.0509766	−	0.0370367i
$218$	−0.640220	−	1.97040i	−0.0433612	−	0.133452i
$219$	−0.679492			−0.0459158
$220$		0			0
$221$	−15.5885			−1.04859
$222$	−1.62789	−	5.01012i	−0.109257	−	0.336257i
$223$	16.4977	+	11.9863i	1.10477	+	0.802662i	0.981832	−	0.189753i	$-0.0607686\pi$
$223$	16.4977	+	11.9863i	1.10477	+	0.802662i	0.122937	+	0.992414i	$0.460769\pi$
$224$	−3.82831	+	2.78143i	−0.255790	+	0.185842i
$225$	1.52290	−	4.68700i	0.101527	−	0.312467i
$226$	3.35481	−	10.3251i	0.223159	−	0.686813i
$227$	13.2617	−	9.63516i	0.880207	−	0.639508i	−0.0530994	−	0.998589i	$-0.516910\pi$
$227$	13.2617	−	9.63516i	0.880207	−	0.639508i	0.933306	+	0.359082i	$0.116910\pi$
$228$	−0.750932	−	0.545584i	−0.0497317	−	0.0361322i
$229$	−4.07784	−	12.5503i	−0.269471	−	0.829346i	−0.990630	−	0.136576i	$-0.956390\pi$
$229$	−4.07784	−	12.5503i	−0.269471	−	0.829346i	0.721159	−	0.692770i	$-0.243610\pi$
$230$	2.19615			0.144810
$231$		0			0
$232$	−3.00000			−0.196960
$233$	−2.10250	−	6.47084i	−0.137740	−	0.423919i	0.858266	−	0.513204i	$-0.171542\pi$
$233$	−2.10250	−	6.47084i	−0.137740	−	0.423919i	−0.996006	+	0.0892853i	$0.971542\pi$
$234$	5.98050	+	4.34509i	0.390958	+	0.284047i
$235$	−11.4849	+	8.34429i	−0.749194	+	0.544321i
$236$	2.92457	−	9.00090i	0.190373	−	0.585908i
$237$	−1.07047	+	3.29456i	−0.0695343	+	0.214004i
$238$	19.8925	−	14.4527i	1.28944	−	0.936832i
$239$	11.4849	+	8.34429i	0.742898	+	0.539747i	0.893617	−	0.448829i	$-0.148159\pi$
$239$	11.4849	+	8.34429i	0.742898	+	0.539747i	−0.150719	+	0.988577i	$0.548159\pi$
$240$	−0.391818	−	1.20589i	−0.0252917	−	0.0778400i
$241$	26.7846			1.72535			0.862674	−	0.505760i	$-0.168788\pi$
$241$	26.7846			1.72535			0.862674	+	0.505760i	$0.168788\pi$
$242$		0			0
$243$	15.2679			0.979439
$244$	0.783636	+	2.41178i	0.0501671	+	0.154399i
$245$	21.5686	+	15.6705i	1.37797	+	1.00115i
$246$	0.476072	−	0.345887i	0.0303532	−	0.0220529i
$247$	1.17545	−	3.61767i	0.0747923	−	0.230187i
$248$	0.0606144	−	0.186552i	0.00384902	−	0.0118461i
$249$	−4.85410	+	3.52671i	−0.307616	+	0.223496i
$250$	−9.80881	−	7.12652i	−0.620364	−	0.450721i
$251$	2.81958	+	8.67778i	0.177970	+	0.547736i	0.999757	−	0.0220593i	$-0.00702228\pi$
$251$	2.81958	+	8.67778i	0.177970	+	0.547736i	−0.821786	+	0.569796i	$0.807022\pi$
$252$	−11.6603			−0.734527
$253$		0			0
$254$	13.8564			0.869428
$255$	2.03595	+	6.26600i	0.127496	+	0.392392i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	15.6887	−	11.3985i	0.978634	−	0.711020i	0.0212315	−	0.999775i	$-0.493241\pi$
$257$	15.6887	−	11.3985i	0.978634	−	0.711020i	0.957403	+	0.288755i	$0.0932413\pi$
$258$		0			0
$259$	−10.5228	+	32.3859i	−0.653856	+	2.01236i
$260$	4.20378	−	3.05422i	0.260707	−	0.189415i
$261$	−5.98050	−	4.34509i	−0.370184	−	0.268954i
$262$		0			0
$263$	9.80385			0.604531			0.302266	−	0.953224i	$-0.402257\pi$
$263$	9.80385			0.604531			0.302266	+	0.953224i	$0.402257\pi$
$264$		0			0
$265$	−19.3923			−1.19126
$266$	1.85410	+	5.70634i	0.113682	+	0.349878i
$267$	−3.82831	−	2.78143i	−0.234289	−	0.170221i
$268$	8.24886	−	5.99315i	0.503879	−	0.366090i
$269$	2.96300	−	9.11916i	0.180657	−	0.556005i	−0.819189	−	0.573523i	$-0.805576\pi$
$269$	2.96300	−	9.11916i	0.180657	−	0.556005i	0.999847	+	0.0175177i	$0.00557633\pi$
$270$	2.14093	−	6.58911i	0.130293	−	0.401001i
$271$	13.2617	−	9.63516i	0.805588	−	0.585294i	−0.106960	−	0.994263i	$-0.534112\pi$
$271$	13.2617	−	9.63516i	0.805588	−	0.585294i	0.912548	+	0.408969i	$0.134112\pi$
$272$	4.20378	+	3.05422i	0.254891	+	0.185189i
$273$	3.21140	+	9.88367i	0.194363	+	0.598187i
$274$	−9.46410			−0.571747
$275$		0			0
$276$	−0.928203			−0.0558713
$277$	−2.57118	−	7.91327i	−0.154487	−	0.475463i	0.843621	−	0.536938i	$-0.180419\pi$
$277$	−2.57118	−	7.91327i	−0.154487	−	0.475463i	−0.998109	+	0.0614759i	$0.980419\pi$
$278$	−16.3390	−	11.8710i	−0.979950	−	0.711975i
$279$	0.391030	−	0.284100i	0.0234103	−	0.0170086i
$280$	−2.53275	+	7.79500i	−0.151361	+	0.465841i
$281$	5.56231	−	17.1190i	0.331819	−	1.02123i	−0.636448	−	0.771319i	$-0.719597\pi$
$281$	5.56231	−	17.1190i	0.331819	−	1.02123i	0.968268	−	0.249916i	$-0.0804029\pi$
$282$	4.85410	−	3.52671i	0.289058	−	0.210013i
$283$	−5.60503	−	4.07230i	−0.333185	−	0.242073i	0.408596	−	0.912715i	$-0.366018\pi$
$283$	−5.60503	−	4.07230i	−0.333185	−	0.242073i	−0.741781	+	0.670642i	$0.766018\pi$
$284$	−2.92457	−	9.00090i	−0.173541	−	0.534105i
$285$	−1.60770			−0.0952316
$286$		0			0
$287$	−3.80385			−0.224534
$288$	−0.761449	−	2.34350i	−0.0448688	−	0.138092i
$289$	−8.09017	−	5.87785i	−0.475892	−	0.345756i
$290$	−4.20378	+	3.05422i	−0.246854	+	0.179350i
$291$	−0.226216	+	0.696222i	−0.0132610	+	0.0408132i
$292$	−0.286831	+	0.882774i	−0.0167855	+	0.0516604i
$293$	−19.2422	+	13.9802i	−1.12414	+	0.816735i	−0.984831	−	0.173515i	$-0.944488\pi$
$293$	−19.2422	+	13.9802i	−1.12414	+	0.816735i	−0.139307	+	0.990249i	$0.544488\pi$
$294$	−9.11596	−	6.62313i	−0.531654	−	0.386269i
$295$	−5.06550	−	15.5900i	−0.294925	−	0.907685i
$296$	−7.19615			−0.418268
$297$		0			0
$298$	−15.0000			−0.868927
$299$	−1.17545	−	3.61767i	−0.0679782	−	0.209215i
$300$	1.18448	+	0.860577i	0.0683862	+	0.0496855i
$301$		0			0
$302$	−1.35730	+	4.17733i	−0.0781037	+	0.240378i
$303$	3.70820	−	11.4127i	0.213031	−	0.655641i
$304$	−1.02579	+	0.745282i	−0.0588332	+	0.0427448i
$305$	3.55345	+	2.58173i	0.203470	+	0.147830i
$306$	3.95661	+	12.1772i	0.226184	+	0.696123i
$307$	25.2679			1.44212			0.721059	−	0.692874i	$-0.243656\pi$
$307$	25.2679			1.44212			0.721059	+	0.692874i	$0.243656\pi$
$308$		0			0
$309$	−6.14359			−0.349497
$310$	−0.104987	−	0.323118i	−0.00596288	−	0.0183518i
$311$	−7.10690	−	5.16346i	−0.402995	−	0.292793i	0.367765	−	0.929919i	$-0.380123\pi$
$311$	−7.10690	−	5.16346i	−0.402995	−	0.292793i	−0.770760	+	0.637126i	$0.780123\pi$
$312$	−1.77672	+	1.29087i	−0.100587	+	0.0730809i
$313$	−9.82198	+	30.2290i	−0.555171	+	1.70864i	0.140319	+	0.990106i	$0.455187\pi$
$313$	−9.82198	+	30.2290i	−0.555171	+	1.70864i	−0.695490	+	0.718535i	$0.744813\pi$
$314$	1.23607	−	3.80423i	0.0697554	−	0.214685i
$315$	−16.3390	+	11.8710i	−0.920600	+	0.668855i
$316$	3.82831	+	2.78143i	0.215359	+	0.156468i
$317$	−2.42776	−	7.47189i	−0.136357	−	0.419663i	0.859442	−	0.511234i	$-0.170811\pi$
$317$	−2.42776	−	7.47189i	−0.136357	−	0.419663i	−0.995799	+	0.0915706i	$0.970811\pi$
$318$	8.19615			0.459617
$319$		0			0
$320$	−1.73205			−0.0968246
$321$	2.84771	+	8.76436i	0.158944	+	0.489179i
$322$	4.85410	+	3.52671i	0.270509	+	0.196536i
$323$	5.33017	−	3.87260i	0.296579	−	0.215477i
$324$	1.37948	−	4.24561i	0.0766380	−	0.235867i
$325$	−1.85410	+	5.70634i	−0.102847	+	0.316531i
$326$	−17.9571	+	13.0466i	−0.994550	+	0.722583i
$327$	1.22700	+	0.891471i	0.0678535	+	0.0492984i
$328$	−0.248403	−	0.764504i	−0.0137157	−	0.0422127i
$329$	−38.7846			−2.13826
$330$		0			0
$331$	28.7846			1.58215			0.791073	−	0.611722i	$-0.209523\pi$
$331$	28.7846			1.58215			0.791073	+	0.611722i	$0.209523\pi$
$332$	2.53275	+	7.79500i	0.139003	+	0.427806i
$333$	−14.3455	−	10.4226i	−0.786130	−	0.571157i
$334$	−13.2617	+	9.63516i	−0.725645	+	0.527212i
$335$	5.45732	−	16.7959i	0.298165	−	0.917658i
$336$	1.07047	−	3.29456i	0.0583987	−	0.179733i
$337$	−2.15219	+	1.56366i	−0.117237	+	0.0851779i	−0.644859	−	0.764302i	$-0.723084\pi$
$337$	−2.15219	+	1.56366i	−0.117237	+	0.0851779i	0.527622	+	0.849479i	$0.323084\pi$
$338$	3.23607	+	2.35114i	0.176019	+	0.127885i
$339$	2.45589	+	7.55847i	0.133386	+	0.410520i
$340$	9.00000			0.488094
$341$		0			0
$342$	−3.12436			−0.168946
$343$	12.2719	+	37.7691i	0.662622	+	2.03934i
$344$		0			0
$345$	−1.30065	+	0.944980i	−0.0700248	+	0.0508760i
$346$	−1.35730	+	4.17733i	−0.0729687	+	0.224575i
$347$	−8.77370	+	27.0027i	−0.470997	+	1.44958i	0.380284	+	0.924870i	$0.375826\pi$
$347$	−8.77370	+	27.0027i	−0.470997	+	1.44958i	−0.851281	+	0.524710i	$0.824174\pi$
$348$	1.77672	−	1.29087i	0.0952424	−	0.0691977i
$349$	17.7403	+	12.8891i	0.949616	+	0.689936i	0.950716	−	0.310063i	$-0.100350\pi$
$349$	17.7403	+	12.8891i	0.949616	+	0.689936i	−0.00110009	+	0.999999i	$0.500350\pi$
$350$	−2.92457	−	9.00090i	−0.156325	−	0.481118i
$351$	−12.0000			−0.640513
$352$		0			0
$353$	21.9282			1.16712			0.583560	−	0.812070i	$-0.301659\pi$
$353$	21.9282			1.16712			0.583560	+	0.812070i	$0.301659\pi$
$354$	2.14093	+	6.58911i	0.113789	+	0.350207i
$355$	−13.2617	−	9.63516i	−0.703855	−	0.511381i
$356$	−5.22957	+	3.79950i	−0.277167	+	0.201373i
$357$	−5.56231	+	17.1190i	−0.294388	+	0.906034i
$358$	−4.28187	+	13.1782i	−0.226304	+	0.696491i
$359$	5.33017	−	3.87260i	0.281316	−	0.204388i	−0.438175	−	0.898890i	$-0.644375\pi$
$359$	5.33017	−	3.87260i	0.281316	−	0.204388i	0.719491	+	0.694502i	$0.244375\pi$
$360$	−3.45284	−	2.50864i	−0.181981	−	0.132217i
$361$	−5.37452	−	16.5411i	−0.282869	−	0.870582i
$362$	7.19615			0.378221
$363$		0			0
$364$	14.1962			0.744081
$365$	0.496805	+	1.52901i	0.0260040	+	0.0800320i
$366$	−1.50186	−	1.09117i	−0.0785037	−	0.0570363i
$367$	−6.94821	+	5.04817i	−0.362693	+	0.263512i	−0.754175	−	0.656674i	$-0.771963\pi$
$367$	−6.94821	+	5.04817i	−0.362693	+	0.263512i	0.391481	+	0.920186i	$0.371963\pi$
$368$	−0.391818	+	1.20589i	−0.0204249	+	0.0628614i
$369$	0.612089	−	1.88382i	0.0318641	−	0.0980676i
$370$	−10.0837	+	7.32622i	−0.524225	+	0.380872i
$371$	−42.8623	−	31.1413i	−2.22530	−	1.61678i
$372$	0.0443728	+	0.136566i	0.00230062	+	0.00708060i
$373$	−11.3205			−0.586154			−0.293077	−	0.956089i	$-0.594679\pi$
$373$	−11.3205			−0.586154			−0.293077	+	0.956089i	$0.594679\pi$
$374$		0			0
$375$	8.87564			0.458336
$376$	−2.53275	−	7.79500i	−0.130617	−	0.401997i
$377$	7.28115	+	5.29007i	0.374998	+	0.272452i
$378$	15.3132	−	11.1257i	0.787628	−	0.572245i
$379$	1.11484	−	3.43112i	0.0572654	−	0.176245i	−0.918332	−	0.395810i	$-0.870464\pi$
$379$	1.11484	−	3.43112i	0.0572654	−	0.176245i	0.975598	+	0.219565i	$0.0704639\pi$
$380$	−0.678648	+	2.08867i	−0.0348139	+	0.107146i
$381$	−8.20634	+	5.96225i	−0.420424	+	0.305456i
$382$	17.3648	+	12.6163i	0.888462	+	0.645505i
$383$	−0.209975	−	0.646235i	−0.0107292	−	0.0330211i	0.945549	−	0.325481i	$-0.105526\pi$
$383$	−0.209975	−	0.646235i	−0.0107292	−	0.0330211i	−0.956278	+	0.292460i	$0.905526\pi$
$384$	0.732051			0.0373573
$385$		0			0
$386$	10.2679			0.522625
$387$		0			0
$388$	0.809017	+	0.587785i	0.0410716	+	0.0298403i
$389$	−26.4227	+	19.1972i	−1.33968	+	0.973337i	−0.340229	+	0.940343i	$0.610504\pi$
$389$	−26.4227	+	19.1972i	−1.33968	+	0.973337i	−0.999456	+	0.0329947i	$0.989496\pi$
$390$	−1.17545	+	3.61767i	−0.0595214	+	0.183188i
$391$	2.03595	−	6.26600i	0.102962	−	0.316885i
$392$	−12.4526	+	9.04737i	−0.628953	+	0.456961i
$393$		0			0
$394$	−4.13845	−	12.7368i	−0.208492	−	0.641673i
$395$	8.19615			0.412393
$396$		0			0
$397$	5.58846			0.280477			0.140238	−	0.990118i	$-0.455213\pi$
$397$	5.58846			0.280477			0.140238	+	0.990118i	$0.455213\pi$
$398$	−0.121229	−	0.373104i	−0.00607665	−	0.0187020i
$399$	−3.55345	−	2.58173i	−0.177895	−	0.129248i
$400$	1.61803	−	1.17557i	0.0809017	−	0.0587785i
$401$	−2.28435	+	7.03050i	−0.114075	+	0.351086i	−0.991753	−	0.128164i	$-0.959092\pi$
$401$	−2.28435	+	7.03050i	−0.114075	+	0.351086i	0.877678	+	0.479251i	$0.159092\pi$
$402$	−2.30653	+	7.09878i	−0.115039	+	0.354055i
$403$	−0.476072	+	0.345887i	−0.0237148	+	0.0172298i
$404$	−13.2617	−	9.63516i	−0.659792	−	0.479367i
$405$	−2.38934	−	7.35362i	−0.118727	−	0.365404i
$406$	−14.1962			−0.704543
$407$		0			0
$408$	−3.80385			−0.188319
$409$	−0.822064	−	2.53005i	−0.0406484	−	0.125103i	0.928673	−	0.370899i	$-0.120951\pi$
$409$	−0.822064	−	2.53005i	−0.0406484	−	0.125103i	−0.969321	+	0.245796i	$0.920951\pi$
$410$	−1.12640	−	0.818376i	−0.0556288	−	0.0404167i
$411$	5.60503	−	4.07230i	0.276476	−	0.200872i
$412$	−2.59336	+	7.98156i	−0.127766	+	0.393223i
$413$	13.8392	−	42.5927i	0.680983	−	2.09585i
$414$	−2.52766	+	1.83645i	−0.124228	+	0.0902566i
$415$	11.4849	+	8.34429i	0.563773	+	0.409605i
$416$	0.927051	+	2.85317i	0.0454524	+	0.139888i
$417$	14.7846			0.724005
$418$		0			0
$419$	−39.3731			−1.92350			−0.961750	−	0.273928i	$-0.911677\pi$
$419$	−39.3731			−1.92350			−0.961750	+	0.273928i	$0.911677\pi$
$420$	−1.85410	−	5.70634i	−0.0904709	−	0.278441i
$421$	−6.13919	−	4.46038i	−0.299206	−	0.217386i	0.428045	−	0.903757i	$-0.359202\pi$
$421$	−6.13919	−	4.46038i	−0.299206	−	0.217386i	−0.727251	+	0.686372i	$0.759202\pi$
$422$	20.9183	−	15.1980i	1.01829	−	0.739828i
$423$	6.24095	−	19.2077i	0.303446	−	0.933909i
$424$	3.45980	−	10.6482i	0.168023	−	0.517121i
$425$	−8.40755	+	6.10844i	−0.407826	+	0.296303i
$426$	5.60503	+	4.07230i	0.271565	+	0.197303i
$427$	3.70820	+	11.4127i	0.179453	+	0.552298i
$428$	12.5885			0.608486
$429$		0			0
$430$		0			0
$431$	5.06550	+	15.5900i	0.243997	+	0.750944i	0.995800	+	0.0915568i	$0.0291843\pi$
$431$	5.06550	+	15.5900i	0.243997	+	0.750944i	−0.751803	+	0.659387i	$0.770816\pi$
$432$	3.23607	+	2.35114i	0.155695	+	0.113119i
$433$	−25.7143	+	18.6825i	−1.23575	+	0.897825i	−0.997308	−	0.0733318i	$-0.976637\pi$
$433$	−25.7143	+	18.6825i	−1.23575	+	0.897825i	−0.238442	+	0.971157i	$0.576637\pi$
$434$	0.286831	−	0.882774i	0.0137683	−	0.0423745i
$435$	1.17545	−	3.61767i	0.0563587	−	0.173454i
$436$	1.67612	−	1.21777i	0.0802715	−	0.0583207i
$437$	1.30065	+	0.944980i	0.0622187	+	0.0452045i
$438$	−0.209975	−	0.646235i	−0.0100330	−	0.0308783i
$439$	−21.1244			−1.00821			−0.504105	−	0.863642i	$-0.668178\pi$
$439$	−21.1244			−1.00821			−0.504105	+	0.863642i	$0.668178\pi$
$440$		0			0
$441$	−37.9282			−1.80610
$442$	−4.81710	−	14.8255i	−0.229126	−	0.705177i
$443$	−13.8114	−	10.0346i	−0.656198	−	0.476756i	0.209179	−	0.977877i	$-0.432921\pi$
$443$	−13.8114	−	10.0346i	−0.656198	−	0.476756i	−0.865377	+	0.501122i	$0.832921\pi$
$444$	4.26186	−	3.09642i	0.202259	−	0.146950i
$445$	−3.45980	+	10.6482i	−0.164010	+	0.504772i
$446$	−6.30157	+	19.3942i	−0.298388	+	0.918344i
$447$	8.88362	−	6.45433i	0.420181	−	0.305279i
$448$	−3.82831	−	2.78143i	−0.180871	−	0.131410i
$449$	−3.06798	−	9.44228i	−0.144787	−	0.445609i	0.852196	−	0.523222i	$-0.175270\pi$
$449$	−3.06798	−	9.44228i	−0.144787	−	0.445609i	−0.996984	+	0.0776131i	$0.975270\pi$
$450$	4.92820			0.232318
$451$		0			0
$452$	10.8564			0.510642
$453$	−0.993610	−	3.05802i	−0.0466839	−	0.143678i
$454$	13.2617	+	9.63516i	0.622400	+	0.452200i
$455$	19.8925	−	14.4527i	0.932574	−	0.677555i
$456$	0.286831	−	0.882774i	0.0134321	−	0.0413397i
$457$	−1.60570	+	4.94183i	−0.0751115	+	0.231169i	−0.981562	−	0.191142i	$-0.938781\pi$
$457$	−1.60570	+	4.94183i	−0.0751115	+	0.231169i	0.906451	+	0.422311i	$0.138781\pi$
$458$	10.6759	−	7.75650i	0.498853	−	0.362438i
$459$	−16.8151	−	12.2169i	−0.784862	−	0.570235i
$460$	0.678648	+	2.08867i	0.0316421	+	0.0973845i
$461$	33.0000			1.53696			0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000			1.53696			0.768482	+	0.639872i	$0.221013\pi$
$462$		0			0
$463$	28.7846			1.33773			0.668867	−	0.743382i	$-0.266780\pi$
$463$	28.7846			1.33773			0.668867	+	0.743382i	$0.266780\pi$
$464$	−0.927051	−	2.85317i	−0.0430373	−	0.132455i
$465$	0.201212	+	0.146189i	0.00933097	+	0.00677935i
$466$	5.50443	−	3.99920i	0.254988	−	0.185259i
$467$	6.63277	−	20.4136i	0.306928	−	0.944628i	−0.672023	−	0.740531i	$-0.734574\pi$
$467$	6.63277	−	20.4136i	0.306928	−	0.944628i	0.978951	−	0.204097i	$-0.0654258\pi$
$468$	−2.28435	+	7.03050i	−0.105594	+	0.324985i
$469$	39.0340	−	28.3599i	1.80242	−	1.30954i
$470$	−11.4849	−	8.34429i	−0.529760	−	0.384893i
$471$	0.904865	+	2.78489i	0.0416940	+	0.128321i
$472$	9.46410			0.435621
$473$		0			0
$474$	−3.46410			−0.159111
$475$	−0.783636	−	2.41178i	−0.0359557	−	0.110660i
$476$	19.8925	+	14.4527i	0.911770	+	0.662440i
$477$	22.3195	−	16.2161i	1.02194	−	0.742484i
$478$	−4.38685	+	13.5013i	−0.200650	+	0.617537i
$479$	−2.71459	+	8.35466i	−0.124033	+	0.381734i	−0.993724	−	0.111863i	$-0.964318\pi$
$479$	−2.71459	+	8.35466i	−0.124033	+	0.381734i	0.869691	+	0.493597i	$0.164318\pi$
$480$	1.02579	−	0.745282i	0.0468208	−	0.0340173i
$481$	17.4654	+	12.6894i	0.796355	+	0.578586i
$482$	8.27690	+	25.4737i	0.377002	+	1.16029i
$483$	−4.39230			−0.199857
$484$		0			0
$485$	1.73205			0.0786484
$486$	4.71806	+	14.5207i	0.214015	+	0.658672i
$487$	10.5017	+	7.62990i	0.475876	+	0.345744i	0.799727	−	0.600364i	$-0.204978\pi$
$487$	10.5017	+	7.62990i	0.475876	+	0.345744i	−0.323851	+	0.946108i	$0.604978\pi$
$488$	−2.05158	+	1.49056i	−0.0928709	+	0.0674746i
$489$	5.02113	−	15.4534i	0.227063	−	0.698829i
$490$	−8.23847	+	25.3554i	−0.372176	+	1.14544i
$491$	26.9994	−	19.6162i	1.21846	−	0.885267i	0.222493	−	0.974934i	$-0.428581\pi$
$491$	26.9994	−	19.6162i	1.21846	−	0.885267i	0.995972	+	0.0896677i	$0.0285805\pi$
$492$	0.476072	+	0.345887i	0.0214630	+	0.0155938i
$493$	4.81710	+	14.8255i	0.216951	+	0.667707i
$494$	3.80385			0.171143
$495$		0			0
$496$	0.196152			0.00880750
$497$	−13.8392	−	42.5927i	−0.620773	−	1.91054i
$498$	−4.85410	−	3.52671i	−0.217518	−	0.158036i
$499$	−12.9443	+	9.40456i	−0.579465	+	0.421006i	−0.838531	−	0.544853i	$-0.816585\pi$
$499$	−12.9443	+	9.40456i	−0.579465	+	0.421006i	0.259066	+	0.965860i	$0.416585\pi$
$500$	3.74663	−	11.5309i	0.167554	−	0.515680i
$501$	3.70820	−	11.4127i	0.165670	−	0.509881i
$502$	−7.38176	+	5.36316i	−0.329464	+	0.239370i
$503$	11.4849	+	8.34429i	0.512088	+	0.372053i	0.813615	−	0.581404i	$-0.197496\pi$
$503$	11.4849	+	8.34429i	0.512088	+	0.372053i	−0.301527	+	0.953458i	$0.597496\pi$
$504$	−3.60322	−	11.0896i	−0.160500	−	0.493968i
$505$	−28.3923			−1.26344
$506$		0			0
$507$	−2.92820			−0.130046
$508$	4.28187	+	13.1782i	0.189977	+	0.584689i
$509$	−10.4591	−	7.59901i	−0.463593	−	0.336820i	0.331346	−	0.943509i	$-0.392497\pi$
$509$	−10.4591	−	7.59901i	−0.463593	−	0.336820i	−0.794939	+	0.606689i	$0.792497\pi$
$510$	−5.33017	+	3.87260i	−0.236024	+	0.171482i
$511$	−1.35730	+	4.17733i	−0.0600433	+	0.184794i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	4.10317	−	2.98113i	0.181159	−	0.131620i
$514$	15.6887	+	11.3985i	0.691999	+	0.502767i
$515$	4.49184	+	13.8245i	0.197934	+	0.609179i
$516$		0			0
$517$		0			0
$518$	−34.0526			−1.49618
$519$	−0.993610	−	3.05802i	−0.0436146	−	0.134232i
$520$	4.20378	+	3.05422i	0.184348	+	0.133936i
$521$	−7.65662	+	5.56286i	−0.335443	+	0.243713i	−0.742736	−	0.669584i	$-0.766472\pi$
$521$	−7.65662	+	5.56286i	−0.335443	+	0.243713i	0.407294	+	0.913297i	$0.366472\pi$
$522$	2.28435	−	7.03050i	0.0999832	−	0.307717i
$523$	0.783636	−	2.41178i	0.0342660	−	0.105460i	−0.932461	−	0.361272i	$-0.882343\pi$
$523$	0.783636	−	2.41178i	0.0342660	−	0.105460i	0.966727	+	0.255812i	$0.0823427\pi$
$524$		0			0
$525$	5.60503	+	4.07230i	0.244624	+	0.177730i
$526$	3.02956	+	9.32401i	0.132095	+	0.406546i
$527$	−1.01924			−0.0443987
$528$		0			0
$529$	−21.3923			−0.930100
$530$	−5.99255	−	18.4432i	−0.260300	−	0.801120i
$531$	18.8667	+	13.7075i	0.818744	+	0.594853i
$532$	−4.85410	+	3.52671i	−0.210452	+	0.152902i
$533$	−0.745208	+	2.29351i	−0.0322785	+	0.0993431i
$534$	1.46228	−	4.50045i	0.0632792	−	0.194753i
$535$	17.6397	−	12.8160i	0.762630	−	0.554083i
$536$	8.24886	+	5.99315i	0.356297	+	0.258865i
$537$	−3.13454	−	9.64713i	−0.135266	−	0.416304i
$538$	9.58846			0.413388
$539$		0			0
$540$	6.92820			0.298142
$541$	−9.27051	−	28.5317i	−0.398570	−	1.22667i	−0.926146	−	0.377165i	$-0.876899\pi$
$541$	−9.27051	−	28.5317i	−0.398570	−	1.22667i	0.527576	−	0.849508i	$-0.323101\pi$
$542$	13.2617	+	9.63516i	0.569637	+	0.413865i
$543$	−4.26186	+	3.09642i	−0.182894	+	0.132880i
$544$	−1.60570	+	4.94183i	−0.0688438	+	0.211879i
$545$	1.10889	−	3.41283i	0.0474998	−	0.146189i
$546$	−8.40755	+	6.10844i	−0.359810	+	0.261417i
$547$	19.4164	+	14.1068i	0.830186	+	0.603165i	0.919612	−	0.392828i	$-0.128503\pi$
$547$	19.4164	+	14.1068i	0.830186	+	0.603165i	−0.0894262	+	0.995993i	$0.528503\pi$
$548$	−2.92457	−	9.00090i	−0.124931	−	0.384499i
$549$	−6.24871			−0.266688
$550$		0			0
$551$	−3.80385			−0.162049
$552$	−0.286831	−	0.882774i	−0.0122083	−	0.0375733i
$553$	18.1158	+	13.1619i	0.770360	+	0.559699i
$554$	6.73143	−	4.89067i	0.285991	−	0.207785i
$555$	2.81958	−	8.67778i	0.119685	−	0.368351i
$556$	6.24095	−	19.2077i	0.264675	−	0.814587i
$557$	−30.0768	+	21.8520i	−1.27439	+	0.925901i	−0.999368	−	0.0355364i	$-0.988686\pi$
$557$	−30.0768	+	21.8520i	−1.27439	+	0.925901i	−0.275025	+	0.961437i	$0.588686\pi$
$558$	0.391030	+	0.284100i	0.0165536	+	0.0120269i
$559$		0			0
$560$	−8.19615			−0.346351
$561$		0			0
$562$	18.0000			0.759284
$563$	−0.181843	−	0.559656i	−0.00766378	−	0.0235867i	0.947152	−	0.320787i	$-0.103947\pi$
$563$	−0.181843	−	0.559656i	−0.00766378	−	0.0235867i	−0.954815	+	0.297200i	$0.903947\pi$
$564$	4.85410	+	3.52671i	0.204395	+	0.148501i
$565$	15.2126	−	11.0526i	0.640000	−	0.464987i
$566$	2.14093	−	6.58911i	0.0899901	−	0.276961i
$567$	6.52778	−	20.0905i	0.274141	−	0.843720i
$568$	7.65662	−	5.56286i	0.321265	−	0.233412i
$569$	−33.9787	−	24.6870i	−1.42446	−	1.03493i	−0.991015	−	0.133753i	$-0.957297\pi$
$569$	−33.9787	−	24.6870i	−1.42446	−	1.03493i	−0.433447	−	0.901179i	$-0.642703\pi$
$570$	−0.496805	−	1.52901i	−0.0208089	−	0.0640431i
$571$	5.66025			0.236874			0.118437	−	0.992962i	$-0.462212\pi$
$571$	5.66025			0.236874			0.118437	+	0.992962i	$0.462212\pi$
$572$		0			0
$573$	−15.7128			−0.656412
$574$	−1.17545	−	3.61767i	−0.0490625	−	0.150999i
$575$	−2.05158	−	1.49056i	−0.0855570	−	0.0621608i
$576$	1.99350	−	1.44836i	0.0830625	−	0.0603484i
$577$	4.51403	−	13.8927i	0.187921	−	0.578362i	−0.812065	−	0.583567i	$-0.801657\pi$
$577$	4.51403	−	13.8927i	0.187921	−	0.578362i	0.999986	+	0.00520438i	$0.00165661\pi$
$578$	3.09017	−	9.51057i	0.128534	−	0.395587i
$579$	−6.08111	+	4.41818i	−0.252722	+	0.183613i
$580$	−4.20378	−	3.05422i	−0.174552	−	0.126820i
$581$	11.9851	+	36.8864i	0.497226	+	1.53030i
$582$	−0.732051			−0.0303445
$583$		0			0
$584$	−0.928203			−0.0384093
$585$	3.95661	+	12.1772i	0.163586	+	0.503465i
$586$	−19.2422	−	13.9802i	−0.794886	−	0.577519i
$587$	−24.7466	+	17.9794i	−1.02140	+	0.742091i	−0.966570	−	0.256405i	$-0.917462\pi$
$587$	−24.7466	+	17.9794i	−1.02140	+	0.742091i	−0.0548312	+	0.998496i	$0.517462\pi$
$588$	3.48199	−	10.7165i	0.143595	−	0.441939i
$589$	0.0768560	−	0.236539i	0.00316680	−	0.00974640i
$590$	13.2617	−	9.63516i	0.545974	−	0.396673i
$591$	7.93148	+	5.76256i	0.326257	+	0.237040i
$592$	−2.22373	−	6.84395i	−0.0913949	−	0.281285i
$593$	−23.1962			−0.952552			−0.476276	−	0.879296i	$-0.658014\pi$
$593$	−23.1962			−0.952552			−0.476276	+	0.879296i	$0.658014\pi$
$594$		0			0
$595$	42.5885			1.74596
$596$	−4.63525	−	14.2658i	−0.189867	−	0.584352i
$597$	0.232339	+	0.168804i	0.00950901	+	0.00690870i
$598$	3.07738	−	2.23585i	0.125843	−	0.0914305i
$599$	−1.17545	+	3.61767i	−0.0480277	+	0.147814i	−0.972194	−	0.234175i	$-0.924761\pi$
$599$	−1.17545	+	3.61767i	−0.0480277	+	0.147814i	0.924167	+	0.381990i	$0.124761\pi$
$600$	−0.452432	+	1.39244i	−0.0184705	+	0.0568463i
$601$	7.00629	−	5.09037i	0.285793	−	0.207641i	−0.435647	−	0.900117i	$-0.643481\pi$
$601$	7.00629	−	5.09037i	0.285793	−	0.207641i	0.721440	+	0.692477i	$0.243481\pi$
$602$		0			0
$603$	7.76385	+	23.8947i	0.316169	+	0.973067i
$604$	−4.39230			−0.178720
$605$		0			0
$606$	12.0000			0.487467
$607$	8.09506	+	24.9140i	0.328568	+	1.01123i	0.969804	+	0.243885i	$0.0784220\pi$
$607$	8.09506	+	24.9140i	0.328568	+	1.01123i	−0.641236	+	0.767344i	$0.721578\pi$
$608$	−1.02579	−	0.745282i	−0.0416014	−	0.0302252i
$609$	8.40755	−	6.10844i	0.340691	−	0.247527i
$610$	−1.35730	+	4.17733i	−0.0549553	+	0.169135i
$611$	−7.59825	+	23.3850i	−0.307392	+	0.946056i
$612$	−10.3585	+	7.52591i	−0.418719	+	0.304217i
$613$	−16.4396	−	11.9441i	−0.663991	−	0.482417i	0.204018	−	0.978967i	$-0.434600\pi$
$613$	−16.4396	−	11.9441i	−0.663991	−	0.482417i	−0.868008	+	0.496550i	$0.834600\pi$
$614$	7.80823	+	24.0312i	0.315114	+	0.969822i
$615$	1.01924			0.0410996
$616$		0			0
$617$	10.6077			0.427050			0.213525	−	0.976938i	$-0.431506\pi$
$617$	10.6077			0.427050			0.213525	+	0.976938i	$0.431506\pi$
$618$	−1.89847	−	5.84290i	−0.0763679	−	0.235036i
$619$	24.4292	+	17.7489i	0.981892	+	0.713387i	0.958131	−	0.286331i	$-0.0924357\pi$
$619$	24.4292	+	17.7489i	0.981892	+	0.713387i	0.0237617	+	0.999718i	$0.492436\pi$
$620$	0.274860	−	0.199698i	0.0110387	−	0.00802005i
$621$	1.56727	−	4.82357i	0.0628924	−	0.193563i
$622$	2.71459	−	8.35466i	0.108845	−	0.334991i
$623$	−24.7466	+	17.9794i	−0.991451	+	0.720331i
$624$	−1.77672	−	1.29087i	−0.0711259	−	0.0516760i
$625$	−3.39919	−	10.4616i	−0.135967	−	0.418465i
$626$	−31.7846			−1.27037
$627$		0			0
$628$	4.00000			0.159617
$629$	11.5549	+	35.5622i	0.460722	+	1.41796i
$630$	−16.3390	−	11.8710i	−0.650963	−	0.472952i
$631$	16.6564	−	12.1016i	0.663081	−	0.481757i	−0.204621	−	0.978841i	$-0.565596\pi$
$631$	16.6564	−	12.1016i	0.663081	−	0.481757i	0.867702	+	0.497085i	$0.165596\pi$
$632$	−1.46228	+	4.50045i	−0.0581665	+	0.179018i
$633$	−5.84914	+	18.0018i	−0.232482	+	0.715507i
$634$	6.35597	−	4.61788i	0.252428	−	0.183399i
$635$	19.4164	+	14.1068i	0.770517	+	0.559813i
$636$	2.53275	+	7.79500i	0.100430	+	0.309092i
$637$	46.1769			1.82960
$638$		0			0
$639$	23.3205			0.922545
$640$	−0.535233	−	1.64728i	−0.0211569	−	0.0651144i
$641$	−2.97677	−	2.16275i	−0.117575	−	0.0854235i	0.527444	−	0.849590i	$-0.323151\pi$
$641$	−2.97677	−	2.16275i	−0.117575	−	0.0854235i	−0.645019	+	0.764166i	$0.723151\pi$
$642$	−7.45541	+	5.41667i	−0.294241	+	0.213779i
$643$	−7.97383	+	24.5409i	−0.314457	+	0.967799i	0.661520	+	0.749927i	$0.269912\pi$
$643$	−7.97383	+	24.5409i	−0.314457	+	0.967799i	−0.975977	+	0.217872i	$0.930088\pi$
$644$	−1.85410	+	5.70634i	−0.0730619	+	0.224861i
$645$		0			0
$646$	5.33017	+	3.87260i	0.209713	+	0.152365i
$647$	−7.20643	−	22.1791i	−0.283314	−	0.871951i	−0.986899	−	0.161340i	$-0.948418\pi$
$647$	−7.20643	−	22.1791i	−0.283314	−	0.871951i	0.703585	−	0.710611i	$-0.251582\pi$
$648$	4.46410			0.175366
$649$		0			0
$650$	−6.00000			−0.235339
$651$	0.209975	+	0.646235i	0.00822955	+	0.0253280i
$652$	−17.9571	−	13.0466i	−0.703253	−	0.510943i
$653$	1.50186	−	1.09117i	0.0587725	−	0.0427007i	−0.558011	−	0.829833i	$-0.688435\pi$
$653$	1.50186	−	1.09117i	0.0587725	−	0.0427007i	0.616784	+	0.787133i	$0.288435\pi$
$654$	−0.468674	+	1.44243i	−0.0183266	+	0.0564035i
$655$		0			0
$656$	0.650326	−	0.472490i	0.0253910	−	0.0184476i
$657$	−1.85037	−	1.34437i	−0.0721899	−	0.0524491i
$658$	−11.9851	−	36.8864i	−0.467228	−	1.43798i
$659$	16.9808			0.661477			0.330738	−	0.943723i	$-0.392702\pi$
$659$	16.9808			0.661477			0.330738	+	0.943723i	$0.392702\pi$
$660$		0			0
$661$	−16.4115			−0.638335			−0.319168	−	0.947698i	$-0.603403\pi$
$661$	−16.4115			−0.638335			−0.319168	+	0.947698i	$0.603403\pi$
$662$	8.89493	+	27.3758i	0.345711	+	1.06399i
$663$	9.23213	+	6.70754i	0.358546	+	0.260499i
$664$	−6.63083	+	4.81758i	−0.257326	+	0.186958i
$665$	−3.21140	+	9.88367i	−0.124533	+	0.383272i
$666$	5.47951	−	16.8642i	0.212327	−	0.653474i
$667$	−3.07738	+	2.23585i	−0.119157	+	0.0865723i
$668$	−13.2617	−	9.63516i	−0.513109	−	0.372795i
$669$	−4.61307	−	14.1976i	−0.178352	−	0.548910i
$670$	17.6603			0.682275
$671$		0			0
$672$	3.46410			0.133631
$673$	0.286831	+	0.882774i	0.0110565	+	0.0340284i	0.956433	−	0.291953i	$-0.0943052\pi$
$673$	0.286831	+	0.882774i	0.0110565	+	0.0340284i	−0.945376	+	0.325982i	$0.894305\pi$
$674$	−2.15219	−	1.56366i	−0.0828993	−	0.0602299i
$675$	−6.47214	+	4.70228i	−0.249113	+	0.180991i
$676$	−1.23607	+	3.80423i	−0.0475411	+	0.146316i
$677$	1.42386	−	4.38218i	0.0547232	−	0.168421i	−0.919959	−	0.392014i	$-0.871779\pi$
$677$	1.42386	−	4.38218i	0.0547232	−	0.168421i	0.974683	+	0.223593i	$0.0717786\pi$
$678$	−6.42961	+	4.67139i	−0.246928	+	0.179404i
$679$	3.82831	+	2.78143i	0.146917	+	0.106741i
$680$	2.78115	+	8.55951i	0.106652	+	0.328242i
$681$	−12.0000			−0.459841
$682$		0			0
$683$	−5.41154			−0.207067			−0.103533	−	0.994626i	$-0.533015\pi$
$683$	−5.41154			−0.207067			−0.103533	+	0.994626i	$0.533015\pi$
$684$	−0.965479	−	2.97144i	−0.0369160	−	0.113616i
$685$	−13.2617	−	9.63516i	−0.506702	−	0.368140i
$686$	−32.1283	+	23.3426i	−1.22667	+	0.891225i
$687$	−2.98518	+	9.18745i	−0.113892	+	0.350523i
$688$		0			0
$689$	−27.1736	+	19.7428i	−1.03523	+	0.752141i
$690$	−1.30065	−	0.944980i	−0.0495150	−	0.0359748i
$691$	−12.7244	−	39.1616i	−0.484058	−	1.48978i	−0.833341	−	0.552759i	$-0.813575\pi$
$691$	−12.7244	−	39.1616i	−0.484058	−	1.48978i	0.349283	−	0.937017i	$-0.386425\pi$
$692$	−4.39230			−0.166970
$693$		0			0
$694$	−28.3923			−1.07776
$695$	−10.8096	−	33.2687i	−0.410033	−	1.26195i
$696$	1.77672	+	1.29087i	0.0673466	+	0.0489301i
$697$	−3.37919	+	2.45513i	−0.127996	+	0.0929946i
$698$	−6.77619	+	20.8550i	−0.256482	+	0.789372i
$699$	−1.53914	+	4.73699i	−0.0582156	+	0.179169i
$700$	7.65662	−	5.56286i	0.289393	−	0.210256i
$701$	14.3881	+	10.4535i	0.543429	+	0.394824i	0.825357	−	0.564611i	$-0.190974\pi$
$701$	14.3881	+	10.4535i	0.543429	+	0.394824i	−0.281928	+	0.959436i	$0.590974\pi$
$702$	−3.70820	−	11.4127i	−0.139957	−	0.430744i
$703$	−9.12436			−0.344132
$704$		0			0
$705$	10.3923			0.391397
$706$	6.77619	+	20.8550i	0.255025	+	0.784887i
$707$	−62.7548	−	45.5940i	−2.36014	−	1.71474i
$708$	−5.60503	+	4.07230i	−0.210650	+	0.153046i
$709$	−11.7426	+	36.1401i	−0.441004	+	1.35727i	0.445802	+	0.895131i	$0.352918\pi$
$709$	−11.7426	+	36.1401i	−0.441004	+	1.35727i	−0.886807	+	0.462140i	$0.847082\pi$
$710$	5.06550	−	15.5900i	0.190105	−	0.585083i
$711$	−9.43334	+	6.85373i	−0.353778	+	0.257035i
$712$	−5.22957	−	3.79950i	−0.195986	−	0.142392i
$713$	−0.0768560	−	0.236539i	−0.00287828	−	0.00885844i
$714$	−18.0000			−0.673633
$715$		0			0
$716$	−13.8564			−0.517838
$717$	−3.21140	−	9.88367i	−0.119932	−	0.369112i
$718$	5.33017	+	3.87260i	0.198920	+	0.144524i
$719$	37.8070	−	27.4684i	1.40996	−	1.02440i	0.416636	−	0.909073i	$-0.363209\pi$
$719$	37.8070	−	27.4684i	1.40996	−	1.02440i	0.993328	−	0.115326i	$-0.0367911\pi$
$720$	1.31887	−	4.05906i	0.0491513	−	0.151272i
$721$	−12.2719	+	37.7691i	−0.457031	+	1.40660i
$722$	14.0707	−	10.2229i	0.523656	−	0.380458i
$723$	−15.8630	−	11.5251i	−0.589950	−	0.428624i
$724$	2.22373	+	6.84395i	0.0826444	+	0.254353i
$725$	6.00000			0.222834
$726$		0			0
$727$	−36.9808			−1.37154			−0.685770	−	0.727818i	$-0.740535\pi$
$727$	−36.9808			−1.37154			−0.685770	+	0.727818i	$0.740535\pi$
$728$	4.38685	+	13.5013i	0.162588	+	0.500393i
$729$	1.79229	+	1.30217i	0.0663811	+	0.0482287i
$730$	−1.30065	+	0.944980i	−0.0481393	+	0.0349753i
$731$		0			0
$732$	0.573661	−	1.76555i	0.0212031	−	0.0652565i
$733$	−13.4359	+	9.76176i	−0.496267	+	0.360559i	−0.807589	−	0.589746i	$-0.799228\pi$
$733$	−13.4359	+	9.76176i	−0.496267	+	0.360559i	0.311323	+	0.950304i	$0.399228\pi$
$734$	−6.94821	−	5.04817i	−0.256463	−	0.186331i
$735$	−6.03098	−	18.5614i	−0.222456	−	0.684649i
$736$	−1.26795			−0.0467372
$737$		0			0
$738$	1.98076			0.0729129
$739$	3.31639	+	10.2068i	0.121995	+	0.375463i	0.993342	−	0.115206i	$-0.0367527\pi$
$739$	3.31639	+	10.2068i	0.121995	+	0.375463i	−0.871346	+	0.490668i	$0.836753\pi$
$740$	−10.0837	−	7.32622i	−0.370683	−	0.269317i
$741$	−2.25280	+	1.63675i	−0.0827585	+	0.0601276i
$742$	16.3720	−	50.3877i	0.601033	−	1.84979i
$743$	−11.8033	+	36.3267i	−0.433020	+	1.33270i	0.462083	+	0.886837i	$0.347102\pi$
$743$	−11.8033	+	36.3267i	−0.433020	+	1.33270i	−0.895102	+	0.445861i	$0.852898\pi$
$744$	−0.116170	+	0.0844022i	−0.00425898	+	0.00309433i
$745$	−21.0189	−	15.2711i	−0.770072	−	0.559490i
$746$	−3.49823	−	10.7664i	−0.128079	−	0.394187i
$747$	−20.1962			−0.738939
$748$		0			0
$749$	59.5692			2.17661
$750$	2.74272	+	8.44124i	0.100150	+	0.308230i
$751$	−3.23607	−	2.35114i	−0.118086	−	0.0857944i	0.527175	−	0.849757i	$-0.323251\pi$
$751$	−3.23607	−	2.35114i	−0.118086	−	0.0857944i	−0.645261	+	0.763962i	$0.723251\pi$
$752$	6.63083	−	4.81758i	0.241801	−	0.175679i
$753$	2.06408	−	6.35257i	0.0752191	−	0.231501i
$754$	−2.78115	+	8.55951i	−0.101284	+	0.311719i
$755$	−6.15475	+	4.47169i	−0.223994	+	0.162741i
$756$	15.3132	+	11.1257i	0.556937	+	0.404638i
$757$	−4.07784	−	12.5503i	−0.148211	−	0.456148i	0.849199	−	0.528074i	$-0.177086\pi$
$757$	−4.07784	−	12.5503i	−0.148211	−	0.456148i	−0.997410	+	0.0719258i	$0.977086\pi$
$758$	3.60770			0.131037
$759$		0			0
$760$	−2.19615			−0.0796628
$761$	6.17440	+	19.0028i	0.223822	+	0.688852i	0.998409	+	0.0563854i	$0.0179575\pi$
$761$	6.17440	+	19.0028i	0.223822	+	0.688852i	−0.774587	+	0.632467i	$0.782042\pi$
$762$	−8.20634	−	5.96225i	−0.297284	−	0.215990i
$763$	7.93148	−	5.76256i	0.287139	−	0.208619i
$764$	−6.63277	+	20.4136i	−0.239965	+	0.738537i
$765$	−6.85304	+	21.0915i	−0.247772	+	0.762565i
$766$	0.549721	−	0.399395i	0.0198622	−	0.0144307i
$767$	−22.9699	−	16.6886i	−0.829393	−	0.602590i
$768$	0.226216	+	0.696222i	0.00816287	+	0.0251227i
$769$	34.5167			1.24470			0.622351	−	0.782738i	$-0.286178\pi$
$769$	34.5167			1.24470			0.622351	+	0.782738i	$0.286178\pi$
$770$		0			0
$771$	−14.1962			−0.511262
$772$	3.17297	+	9.76540i	0.114198	+	0.351464i
$773$	14.5623	+	10.5801i	0.523770	+	0.380541i	0.818022	−	0.575187i	$-0.195071\pi$
$773$	14.5623	+	10.5801i	0.523770	+	0.380541i	−0.294252	+	0.955728i	$0.595071\pi$
$774$		0			0
$775$	−0.121229	+	0.373104i	−0.00435467	+	0.0134023i
$776$	−0.309017	+	0.951057i	−0.0110931	+	0.0341409i
$777$	20.1673	−	14.6524i	0.723499	−	0.525653i
$778$	−26.4227	−	19.1972i	−0.947300	−	0.688254i
$779$	−0.314962	−	0.969353i	−0.0112847	−	0.0347307i
$780$	−3.80385			−0.136200
$781$		0			0
$782$	6.58846			0.235603
$783$	3.70820	+	11.4127i	0.132520	+	0.407856i
$784$	−12.4526	−	9.04737i	−0.444737	−	0.323120i
$785$	5.60503	−	4.07230i	0.200052	−	0.145346i
$786$		0			0
$787$	13.8392	−	42.5927i	0.493314	−	1.51827i	−0.326253	−	0.945283i	$-0.605786\pi$
$787$	13.8392	−	42.5927i	0.493314	−	1.51827i	0.819567	−	0.572983i	$-0.194214\pi$
$788$	10.8346	−	7.87180i	0.385967	−	0.280421i
$789$	−5.80625	−	4.21848i	−0.206708	−	0.150182i
$790$	2.53275	+	7.79500i	0.0901112	+	0.277334i
$791$	51.3731			1.82662
$792$		0			0
$793$	7.60770			0.270157
$794$	1.72693	+	5.31494i	0.0612864	+	0.188620i
$795$	11.4849	+	8.34429i	0.407328	+	0.295941i
$796$	0.317381	−	0.230591i	0.0112493	−	0.00817308i
$797$	11.4114	−	35.1208i	0.404214	−	1.24404i	−0.517336	−	0.855783i	$-0.673076\pi$
$797$	11.4114	−	35.1208i	0.404214	−	1.24404i	0.921550	−	0.388260i	$-0.126924\pi$
$798$	1.35730	−	4.17733i	0.0480478	−	0.147876i
$799$	−34.4548	+	25.0329i	−1.21892	+	0.885599i
$800$	1.61803	+	1.17557i	0.0572061	+	0.0415627i
$801$	−4.92209	−	15.1486i	−0.173913	−	0.535250i
$802$	−7.39230			−0.261031
$803$		0			0
$804$	−7.46410			−0.263239
$805$	3.21140	+	9.88367i	0.113187	+	0.348354i
$806$	−0.476072	−	0.345887i	−0.0167689	−	0.0121833i
$807$	−5.67868	+	4.12580i	−0.199899	+	0.145235i
$808$	5.06550	−	15.5900i	0.178204	−	0.548455i
$809$	5.56231	−	17.1190i	0.195560	−	0.601873i	−0.804409	−	0.594075i	$-0.797518\pi$
$809$	5.56231	−	17.1190i	0.195560	−	0.601873i	0.999970	−	0.00779717i	$-0.00248194\pi$
$810$	6.25536	−	4.54479i	0.219791	−	0.159687i
$811$	−5.60503	−	4.07230i	−0.196819	−	0.142998i	0.485011	−	0.874508i	$-0.338816\pi$
$811$	−5.60503	−	4.07230i	−0.196819	−	0.142998i	−0.681830	+	0.731511i	$0.738816\pi$
$812$	−4.38685	−	13.5013i	−0.153948	−	0.473804i
$813$	−12.0000			−0.420858
$814$		0			0
$815$	−38.4449			−1.34666
$816$	−1.17545	−	3.61767i	−0.0411491	−	0.126644i
$817$		0			0
$818$	2.15219	−	1.56366i	0.0752496	−	0.0546720i
$819$	−10.8096	+	33.2687i	−0.377720	+	1.16250i
$820$	0.430246	−	1.32416i	0.0150248	−	0.0462417i
$821$	13.2617	−	9.63516i	0.462835	−	0.336269i	−0.331807	−	0.943347i	$-0.607658\pi$
$821$	13.2617	−	9.63516i	0.462835	−	0.336269i	0.794642	+	0.607078i	$0.207658\pi$
$822$	5.60503	+	4.07230i	0.195498	+	0.142038i
$823$	9.88854	+	30.4338i	0.344693	+	1.06086i	0.961748	+	0.273936i	$0.0883256\pi$
$823$	9.88854	+	30.4338i	0.344693	+	1.06086i	−0.617055	+	0.786920i	$0.711674\pi$
$824$	−8.39230			−0.292360
$825$		0			0
$826$	44.7846			1.55826
$827$	−6.24095	−	19.2077i	−0.217019	−	0.667917i	−0.999004	−	0.0446191i	$-0.985793\pi$
$827$	−6.24095	−	19.2077i	−0.217019	−	0.667917i	0.781985	−	0.623297i	$-0.214207\pi$
$828$	−2.52766	−	1.83645i	−0.0878421	−	0.0638211i
$829$	−11.9766	+	8.70148i	−0.415963	+	0.302215i	−0.776012	−	0.630719i	$-0.782760\pi$
$829$	−11.9766	+	8.70148i	−0.415963	+	0.302215i	0.360048	+	0.932934i	$0.382760\pi$
$830$	−4.38685	+	13.5013i	−0.152270	+	0.468638i
$831$	−1.88223	+	5.79292i	−0.0652939	+	0.200954i
$832$	−2.42705	+	1.76336i	−0.0841429	+	0.0611334i
$833$	64.7058	+	47.0115i	2.24192	+	1.62885i
$834$	4.56870	+	14.0610i	0.158201	+	0.486893i
$835$	−28.3923			−0.982556
$836$		0			0
$837$	−0.784610			−0.0271201
$838$	−12.1669	−	37.4460i	−0.420300	−	1.29355i
$839$	40.8108	+	29.6507i	1.40894	+	1.02366i	0.993475	+	0.114050i	$0.0363824\pi$
$839$	40.8108	+	29.6507i	1.40894	+	1.02366i	0.415469	+	0.909608i	$0.363618\pi$
$840$	4.85410	−	3.52671i	0.167482	−	0.121683i
$841$	−6.18034	+	19.0211i	−0.213115	+	0.655901i
$842$	2.34496	−	7.21705i	0.0808127	−	0.248716i
$843$	−10.6603	+	7.74520i	−0.367162	+	0.266759i
$844$	20.9183	+	15.1980i	0.720037	+	0.523137i
$845$	2.14093	+	6.58911i	0.0736503	+	0.226672i
$846$	20.1962			0.694358
$847$		0			0
$848$	11.1962			0.384477
$849$	1.56727	+	4.82357i	0.0537886	+	0.165544i
$850$	−8.40755	−	6.10844i	−0.288377	−	0.209518i
$851$	−7.38176	+	5.36316i	−0.253043	+	0.183847i
$852$	−2.14093	+	6.58911i	−0.0733471	+	0.225739i
$853$	−3.35481	+	10.3251i	−0.114867	+	0.353523i	−0.991919	−	0.126871i	$-0.959506\pi$
$853$	−3.35481	+	10.3251i	−0.114867	+	0.353523i	0.877053	+	0.480394i	$0.159506\pi$
$854$	−9.70820	+	7.05342i	−0.332208	+	0.241363i
$855$	−4.37803	−	3.18083i	−0.149725	−	0.108782i
$856$	3.89005	+	11.9723i	0.132959	+	0.409206i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	−24.7846			−0.845640			−0.422820	−	0.906214i	$-0.638960\pi$
$859$	−24.7846			−0.845640			−0.422820	+	0.906214i	$0.638960\pi$
$860$		0			0
$861$	2.25280	+	1.63675i	0.0767751	+	0.0557804i
$862$	−13.2617	+	9.63516i	−0.451694	+	0.328175i
$863$	−1.17545	+	3.61767i	−0.0400129	+	0.123147i	−0.969068	−	0.246795i	$-0.920623\pi$
$863$	−1.17545	+	3.61767i	−0.0400129	+	0.123147i	0.929055	+	0.369942i	$0.120623\pi$
$864$	−1.23607	+	3.80423i	−0.0420519	+	0.129422i
$865$	−6.15475	+	4.47169i	−0.209268	+	0.152042i
$866$	−25.7143	−	18.6825i	−0.873807	−	0.634858i
$867$	2.26216	+	6.96222i	0.0768270	+	0.236449i
$868$	0.928203			0.0315053
$869$		0			0
$870$	3.80385			0.128963
$871$	−9.45235	−	29.0914i	−0.320281	−	0.985723i
$872$	1.67612	+	1.21777i	0.0567605	+	0.0412389i
$873$	−1.99350	+	1.44836i	−0.0674698	+	0.0490196i
$874$	−0.496805	+	1.52901i	−0.0168047	+	0.0517195i
$875$	17.7293	−	54.5650i	0.599358	−	1.84463i
$876$	0.549721	−	0.399395i	0.0185733	−	0.0134943i
$877$	5.22957	+	3.79950i	0.176590	+	0.128300i	0.672569	−	0.740034i	$-0.265191\pi$
$877$	5.22957	+	3.79950i	0.176590	+	0.128300i	−0.495979	+	0.868334i	$0.665191\pi$
$878$	−6.52778	−	20.0905i	−0.220302	−	0.678020i
$879$	17.4115			0.587277
$880$		0			0
$881$	41.5359			1.39938			0.699690	−	0.714447i	$-0.253321\pi$
$881$	41.5359			1.39938			0.699690	+	0.714447i	$0.253321\pi$
$882$	−11.7205	−	36.0719i	−0.394648	−	1.21460i
$883$	12.6269	+	9.17397i	0.424929	+	0.308729i	0.779618	−	0.626255i	$-0.215413\pi$
$883$	12.6269	+	9.17397i	0.424929	+	0.308729i	−0.354689	+	0.934984i	$0.615413\pi$
$884$	12.6113	−	9.16267i	0.424165	−	0.308174i
$885$	−3.70820	+	11.4127i	−0.124650	+	0.383633i
$886$	5.27548	−	16.2362i	0.177233	−	0.545467i
$887$	37.0561	−	26.9228i	1.24422	−	0.903980i	0.246350	−	0.969181i	$-0.420769\pi$
$887$	37.0561	−	26.9228i	1.24422	−	0.903980i	0.997872	+	0.0652010i	$0.0207689\pi$
$888$	4.26186	+	3.09642i	0.143019	+	0.103909i
$889$	20.2620	+	62.3600i	0.679566	+	2.09149i
$890$	−11.1962			−0.375296
$891$		0			0
$892$	−20.3923			−0.682785
$893$	−3.21140	−	9.88367i	−0.107465	−	0.330744i
$894$	8.88362	+	6.45433i	0.297113	+	0.215865i
$895$	−19.4164	+	14.1068i	−0.649019	+	0.471540i
$896$	1.46228	−	4.50045i	0.0488515	−	0.150349i
$897$	−0.860492	+	2.64832i	−0.0287310	+	0.0884249i
$898$	8.03209	−	5.83565i	0.268034	−	0.194738i
$899$	0.476072	+	0.345887i	0.0158779	+	0.0115360i
$900$	1.52290	+	4.68700i	0.0507633	+	0.156233i
$901$	−58.1769			−1.93815
$902$		0			0
$903$		0			0
$904$	3.35481	+	10.3251i	0.111579	+	0.343406i
$905$	10.0837	+	7.32622i	0.335193	+	0.243532i
$906$	2.60131	−	1.88996i	0.0864226	−	0.0627897i
$907$	11.6095	−	35.7305i	0.385488	−	1.18641i	−0.550638	−	0.834744i	$-0.685615\pi$
$907$	11.6095	−	35.7305i	0.385488	−	1.18641i	0.936126	−	0.351666i	$-0.114385\pi$
$908$	−5.06550	+	15.5900i	−0.168105	+	0.517373i
$909$	32.6781	−	23.7420i	1.08386	−	0.787472i
$910$	19.8925	+	14.4527i	0.659429	+	0.479103i
$911$	−9.76731	−	30.0607i	−0.323606	−	0.995956i	−0.972066	−	0.234707i	$-0.924587\pi$
$911$	−9.76731	−	30.0607i	−0.323606	−	0.995956i	0.648461	−	0.761248i	$-0.275413\pi$
$912$	0.928203			0.0307359
$913$		0			0
$914$	−5.19615			−0.171873
$915$	−0.993610	−	3.05802i	−0.0328477	−	0.101095i
$916$	10.6759	+	7.75650i	0.352742	+	0.256282i
$917$		0			0
$918$	6.42280	−	19.7673i	0.211984	−	0.652419i
$919$	6.84275	−	21.0598i	0.225721	−	0.694699i	−0.772496	−	0.635019i	$-0.780992\pi$
$919$	6.84275	−	21.0598i	0.225721	−	0.694699i	0.998218	−	0.0596796i	$-0.0190079\pi$
$920$	−1.77672	+	1.29087i	−0.0585769	+	0.0425586i
$921$	−14.9647	−	10.8725i	−0.493105	−	0.358261i
$922$	10.1976	+	31.3849i	0.335839	+	1.03361i
$923$	−28.3923			−0.934544
$924$		0			0
$925$	14.3923			0.473216
$926$	8.89493	+	27.3758i	0.292306	+	0.899624i
$927$	−16.7301	−	12.1551i	−0.549487	−	0.399226i
$928$	2.42705	−	1.76336i	0.0796719	−	0.0578850i
$929$	12.0517	−	37.0912i	0.395402	−	1.21692i	−0.533246	−	0.845960i	$-0.679028\pi$
$929$	12.0517	−	37.0912i	0.395402	−	1.21692i	0.928648	−	0.370962i	$-0.120972\pi$
$930$	−0.0768560	+	0.236539i	−0.00252021	+	0.00775640i
$931$	−15.7893	+	11.4716i	−0.517474	+	0.375967i
$932$	5.50443	+	3.99920i	0.180304	+	0.130998i
$933$	1.98722	+	6.11604i	0.0650587	+	0.200230i
$934$	21.4641			0.702327
$935$		0			0
$936$	−7.39230			−0.241625
$937$	10.9531	+	33.7101i	0.357821	+	1.10126i	0.954356	+	0.298673i	$0.0965438\pi$
$937$	10.9531	+	33.7101i	0.357821	+	1.10126i	−0.596535	+	0.802587i	$0.703456\pi$
$938$	39.0340	+	28.3599i	1.27451	+	0.925983i
$939$	18.8242	−	13.6766i	0.614303	−	0.446318i
$940$	4.38685	−	13.5013i	0.143083	−	0.440365i
$941$	−10.6944	+	32.9139i	−0.348626	+	1.07296i	0.610987	+	0.791640i	$0.290773\pi$
$941$	−10.6944	+	32.9139i	−0.348626	+	1.07296i	−0.959614	+	0.281321i	$0.909227\pi$
$942$	−2.36897	+	1.72115i	−0.0771851	+	0.0560782i
$943$	−0.824581	−	0.599093i	−0.0268520	−	0.0195092i
$944$	2.92457	+	9.00090i	0.0951866	+	0.292954i
$945$	32.7846			1.06648
$946$		0			0
$947$	5.90897			0.192016			0.0960078	−	0.995381i	$-0.469393\pi$
$947$	5.90897			0.192016			0.0960078	+	0.995381i	$0.469393\pi$
$948$	−1.07047	−	3.29456i	−0.0347671	−	0.107002i
$949$	2.25280	+	1.63675i	0.0731289	+	0.0531312i
$950$	2.05158	−	1.49056i	0.0665622	−	0.0483603i
$951$	−1.77725	+	5.46980i	−0.0576311	+	0.177370i
$952$	−7.59825	+	23.3850i	−0.246261	+	0.757913i
$953$	32.0277	−	23.2695i	1.03748	−	0.753773i	0.0676880	−	0.997707i	$-0.478438\pi$
$953$	32.0277	−	23.2695i	1.03748	−	0.753773i	0.969792	+	0.243933i	$0.0784377\pi$
$954$	22.3195	+	16.2161i	0.722621	+	0.525015i
$955$	11.4883	+	35.3573i	0.371753	+	1.14414i
$956$	−14.1962			−0.459136
$957$		0			0
$958$	−8.78461			−0.283818
$959$	−13.8392	−	42.5927i	−0.446891	−	1.37539i
$960$	1.02579	+	0.745282i	0.0331073	+	0.0240539i
$961$	25.0484	−	18.1987i	0.808013	−	0.587056i
$962$	−6.67120	+	20.5318i	−0.215088	+	0.661973i
$963$	−9.58547	+	29.5010i	−0.308888	+	0.950658i
$964$	−21.6692	+	15.7436i	−0.697918	+	0.507067i
$965$	14.3881	+	10.4535i	0.463168	+	0.336511i
$966$	−1.35730	−	4.17733i	−0.0436703	−	0.134403i
$967$	−32.4449			−1.04336			−0.521678	−	0.853142i	$-0.674694\pi$
$967$	−32.4449			−1.04336			−0.521678	+	0.853142i	$0.674694\pi$
$968$		0			0
$969$	−4.82309			−0.154940
$970$	0.535233	+	1.64728i	0.0171853	+	0.0528909i
$971$	3.27859	+	2.38203i	0.105215	+	0.0764431i	0.639149	−	0.769083i	$-0.279287\pi$
$971$	3.27859	+	2.38203i	0.105215	+	0.0764431i	−0.533934	+	0.845526i	$0.679287\pi$
$972$	−12.3520	+	8.97428i	−0.396192	+	0.287850i
$973$	29.5325	−	90.8917i	0.946769	−	2.91386i
$974$	−4.01128	+	12.3454i	−0.128530	+	0.395573i
$975$	3.55345	−	2.58173i	0.113801	−	0.0826816i
$976$	−2.05158	−	1.49056i	−0.0656696	−	0.0477118i
$977$	9.98759	+	30.7386i	0.319531	+	0.983416i	0.973849	+	0.227196i	$0.0729559\pi$
$977$	9.98759	+	30.7386i	0.319531	+	0.983416i	−0.654318	+	0.756220i	$0.727044\pi$
$978$	16.2487			0.519576
$979$		0			0
$980$	−26.6603			−0.851631
$981$	1.57757	+	4.85526i	0.0503679	+	0.155016i
$982$	26.9994	+	19.6162i	0.861585	+	0.625978i
$983$	−25.9736	+	18.8709i	−0.828429	+	0.601889i	−0.919114	−	0.393991i	$-0.871094\pi$
$983$	−25.9736	+	18.8709i	−0.828429	+	0.601889i	0.0906856	+	0.995880i	$0.471094\pi$
$984$	−0.181843	+	0.559656i	−0.00579695	+	0.0178412i
$985$	7.16801	−	22.0609i	0.228392	−	0.702917i
$986$	−12.6113	+	9.16267i	−0.401626	+	0.291799i
$987$	22.9699	+	16.6886i	0.731139	+	0.531203i
$988$	1.17545	+	3.61767i	0.0373962	+	0.115094i
$989$		0			0
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$	0.0606144	+	0.186552i	0.00192451	+	0.00592303i
$993$	−17.0474	−	12.3857i	−0.540984	−	0.393048i
$994$	36.2315	−	26.3237i	1.14919	−	0.834938i
$995$	0.209975	−	0.646235i	0.00665664	−	0.0204870i
$996$	1.85410	−	5.70634i	0.0587495	−	0.180812i
$997$	−10.0837	+	7.32622i	−0.319353	+	0.232024i	−0.735899	−	0.677091i	$-0.763240\pi$
$997$	−10.0837	+	7.32622i	−0.319353	+	0.232024i	0.416546	+	0.909114i	$0.363240\pi$
$998$	−12.9443	−	9.40456i	−0.409744	−	0.297696i
$999$	8.89493	+	27.3758i	0.281423	+	0.866132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.2.c.f.27.1		8
11.2	odd	10		242.2.c.g.9.1		8
11.3	even	5		242.2.a.e.1.2	yes	2
11.4	even	5	inner	242.2.c.f.3.2		8
11.5	even	5	inner	242.2.c.f.81.2		8
11.6	odd	10		242.2.c.g.81.2		8
11.7	odd	10		242.2.c.g.3.2		8
11.8	odd	10		242.2.a.c.1.2	✓	2
11.9	even	5	inner	242.2.c.f.9.1		8
11.10	odd	2		242.2.c.g.27.1		8
33.8	even	10		2178.2.a.y.1.2		2
33.14	odd	10		2178.2.a.s.1.2		2
44.3	odd	10		1936.2.a.v.1.1		2
44.19	even	10		1936.2.a.y.1.1		2
55.14	even	10		6050.2.a.cc.1.1		2
55.19	odd	10		6050.2.a.cv.1.1		2
88.3	odd	10		7744.2.a.bq.1.2		2
88.19	even	10		7744.2.a.bt.1.2		2
88.69	even	10		7744.2.a.cv.1.1		2
88.85	odd	10		7744.2.a.cs.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
242.2.a.c.1.2	✓	2	11.8	odd	10
242.2.a.e.1.2	yes	2	11.3	even	5
242.2.c.f.3.2		8	11.4	even	5	inner
242.2.c.f.9.1		8	11.9	even	5	inner
242.2.c.f.27.1		8	1.1	even	1	trivial
242.2.c.f.81.2		8	11.5	even	5	inner
242.2.c.g.3.2		8	11.7	odd	10
242.2.c.g.9.1		8	11.2	odd	10
242.2.c.g.27.1		8	11.10	odd	2
242.2.c.g.81.2		8	11.6	odd	10
1936.2.a.v.1.1		2	44.3	odd	10
1936.2.a.y.1.1		2	44.19	even	10
2178.2.a.s.1.2		2	33.14	odd	10
2178.2.a.y.1.2		2	33.8	even	10
6050.2.a.cc.1.1		2	55.14	even	10
6050.2.a.cv.1.1		2	55.19	odd	10
7744.2.a.bq.1.2		2	88.3	odd	10
7744.2.a.bt.1.2		2	88.19	even	10
7744.2.a.cs.1.1		2	88.85	odd	10
7744.2.a.cv.1.1		2	88.69	even	10

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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	242.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.592242 - 0.430289i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.535233 + 1.64728i) q^{5} +(0.226216 - 0.696222i) q^{6} +(-3.82831 + 2.78143i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.761449 - 2.34350i) q^{9} -1.73205 q^{10} +0.732051 q^{12} +(0.927051 + 2.85317i) q^{13} +(-3.82831 - 2.78143i) q^{14} +(1.02579 - 0.745282i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.60570 + 4.94183i) q^{17} +(1.99350 - 1.44836i) q^{18} +(-1.02579 - 0.745282i) q^{19} +(-0.535233 - 1.64728i) q^{20} +3.46410 q^{21} -1.26795 q^{23} +(0.226216 + 0.696222i) q^{24} +(1.61803 + 1.17557i) q^{25} +(-2.42705 + 1.76336i) q^{26} +(-1.23607 + 3.80423i) q^{27} +(1.46228 - 4.50045i) q^{28} +(2.42705 - 1.76336i) q^{29} +(1.02579 + 0.745282i) q^{30} +(0.0606144 + 0.186552i) q^{31} +1.00000 q^{32} -5.19615 q^{34} +(-2.53275 - 7.79500i) q^{35} +(1.99350 + 1.44836i) q^{36} +(5.82181 - 4.22979i) q^{37} +(0.391818 - 1.20589i) q^{38} +(0.678648 - 2.08867i) q^{39} +(1.40126 - 1.01807i) q^{40} +(0.650326 + 0.472490i) q^{41} +(1.07047 + 3.29456i) q^{42} +4.26795 q^{45} +(-0.391818 - 1.20589i) q^{46} +(6.63083 + 4.81758i) q^{47} +(-0.592242 + 0.430289i) q^{48} +(4.75648 - 14.6390i) q^{49} +(-0.618034 + 1.90211i) q^{50} +(3.07738 - 2.23585i) q^{51} +(-2.42705 - 1.76336i) q^{52} +(3.45980 + 10.6482i) q^{53} -4.00000 q^{54} +4.73205 q^{56} +(0.286831 + 0.882774i) q^{57} +(2.42705 + 1.76336i) q^{58} +(-7.65662 + 5.56286i) q^{59} +(-0.391818 + 1.20589i) q^{60} +(0.783636 - 2.41178i) q^{61} +(-0.158691 + 0.115296i) q^{62} +(9.43334 + 6.85373i) q^{63} +(0.309017 + 0.951057i) q^{64} -5.19615 q^{65} -10.1962 q^{67} +(-1.60570 - 4.94183i) q^{68} +(0.750932 + 0.545584i) q^{69} +(6.63083 - 4.81758i) q^{70} +(-2.92457 + 9.00090i) q^{71} +(-0.761449 + 2.34350i) q^{72} +(0.750932 - 0.545584i) q^{73} +(5.82181 + 4.22979i) q^{74} +(-0.452432 - 1.39244i) q^{75} +1.26795 q^{76} +2.19615 q^{78} +(-1.46228 - 4.50045i) q^{79} +(1.40126 + 1.01807i) q^{80} +(-3.61153 + 2.62393i) q^{81} +(-0.248403 + 0.764504i) q^{82} +(2.53275 - 7.79500i) q^{83} +(-2.80252 + 2.03615i) q^{84} +(-7.28115 - 5.29007i) q^{85} -2.19615 q^{87} +6.46410 q^{89} +(1.31887 + 4.05906i) q^{90} +(-11.4849 - 8.34429i) q^{91} +(1.02579 - 0.745282i) q^{92} +(0.0443728 - 0.136566i) q^{93} +(-2.53275 + 7.79500i) q^{94} +(1.77672 - 1.29087i) q^{95} +(-0.592242 - 0.430289i) q^{96} +(-0.309017 - 0.951057i) q^{97} +15.3923 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} - 6 q^{7} - 2 q^{8} - 2 q^{9} - 8 q^{12} - 6 q^{13} - 6 q^{14} + 6 q^{15} - 2 q^{16} - 2 q^{18} - 6 q^{19} - 24 q^{23} + 2 q^{24} + 4 q^{25} - 6 q^{26} + 8 q^{27}+ \cdots + 40 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 - 6 * q^7 - 2 * q^8 - 2 * q^9 - 8 * q^12 - 6 * q^13 - 6 * q^14 + 6 * q^15 - 2 * q^16 - 2 * q^18 - 6 * q^19 - 24 * q^23 + 2 * q^24 + 4 * q^25 - 6 * q^26 + 8 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 10 * q^31 + 8 * q^32 + 6 * q^35 - 2 * q^36 + 4 * q^37 - 6 * q^38 + 6 * q^39 + 12 * q^41 + 48 * q^45 + 6 * q^46 + 6 * q^47 + 2 * q^48 - 10 * q^49 + 4 * q^50 + 18 * q^51 - 6 * q^52 - 12 * q^53 - 32 * q^54 + 24 * q^56 + 12 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 - 12 * q^61 + 10 * q^62 + 6 * q^63 - 2 * q^64 - 40 * q^67 - 12 * q^69 + 6 * q^70 + 12 * q^71 - 2 * q^72 - 12 * q^73 + 4 * q^74 - 4 * q^75 + 24 * q^76 - 24 * q^78 + 6 * q^79 - 2 * q^81 + 12 * q^82 - 6 * q^83 - 18 * q^85 + 24 * q^87 + 24 * q^89 - 12 * q^90 - 18 * q^91 + 6 * q^92 - 28 * q^93 + 6 * q^94 - 6 * q^95 + 2 * q^96 + 2 * q^97 + 40 * q^98

Introduction

L-functions

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