LMFDB - Embedded newform 968.2.o.h.245.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [968,2,Mod(245,968)] 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("968.245"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(968, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,4,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			245.6
Character	$\chi$	$=$	968.245
Dual form			968.2.o.h.565.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.445829 + 1.34210i) q^{2} +(-1.27008 + 0.412674i) q^{3} +(-1.60247 + 1.19669i) q^{4} +(1.13513 - 1.56237i) q^{5} +(-1.12009 - 1.52059i) q^{6} +(0.568375 - 1.74928i) q^{7} +(-2.32051 - 1.61716i) q^{8} +(-0.984248 + 0.715098i) q^{9} +(2.60293 + 0.826906i) q^{10} +(1.54142 - 2.18120i) q^{12} +(-0.0944573 - 0.130009i) q^{13} +(2.60111 - 0.0170613i) q^{14} +(-0.796952 + 2.45277i) q^{15} +(1.13584 - 3.83534i) q^{16} +(4.38036 + 3.18252i) q^{17} +(-1.39854 - 1.00215i) q^{18} +(-2.66053 + 0.864457i) q^{19} +(0.0506664 + 3.86205i) q^{20} +2.45628i q^{21} +4.44137 q^{23} +(3.61460 + 1.09631i) q^{24} +(0.392607 + 1.20832i) q^{25} +(0.132374 - 0.184733i) q^{26} +(3.30983 - 4.55559i) q^{27} +(1.18255 + 3.48334i) q^{28} +(7.94083 + 2.58013i) q^{29} +(-3.64717 + 0.0239226i) q^{30} +(7.32836 - 5.32436i) q^{31} +(5.65381 - 0.185487i) q^{32} +(-2.31837 + 7.29774i) q^{34} +(-2.08784 - 2.87366i) q^{35} +(0.721478 - 2.32377i) q^{36} +(-0.572605 - 0.186051i) q^{37} +(-2.34633 - 3.18530i) q^{38} +(0.173620 + 0.126142i) q^{39} +(-5.16067 + 1.78981i) q^{40} +(3.63525 + 11.1881i) q^{41} +(-3.29657 + 1.09508i) q^{42} +4.47936i q^{43} +2.34948i q^{45} +(1.98009 + 5.96077i) q^{46} +(1.94544 + 5.98745i) q^{47} +(0.140134 + 5.33993i) q^{48} +(2.92620 + 2.12601i) q^{49} +(-1.44665 + 1.06562i) q^{50} +(-6.87675 - 2.23439i) q^{51} +(0.306947 + 0.0952999i) q^{52} +(-6.88946 - 9.48253i) q^{53} +(7.58968 + 2.41112i) q^{54} +(-4.14779 + 3.14007i) q^{56} +(3.02234 - 2.19586i) q^{57} +(0.0774495 + 11.8077i) q^{58} +(-9.15964 - 2.97615i) q^{59} +(-1.65812 - 4.88420i) q^{60} +(1.95681 - 2.69331i) q^{61} +(10.4130 + 7.46165i) q^{62} +(0.691483 + 2.12817i) q^{63} +(2.76957 + 7.50530i) q^{64} -0.310343 q^{65} -5.76864i q^{67} +(-10.8279 + 0.142052i) q^{68} +(-5.64090 + 1.83284i) q^{69} +(2.92593 - 4.08325i) q^{70} +(-7.79016 - 5.65988i) q^{71} +(3.44039 - 0.0677068i) q^{72} +(0.210731 - 0.648563i) q^{73} +(-0.00558480 - 0.851441i) q^{74} +(-0.997284 - 1.37264i) q^{75} +(3.22893 - 4.56911i) q^{76} +(-0.0918909 + 0.289253i) q^{78} +(4.67504 - 3.39662i) q^{79} +(-4.70288 - 6.12820i) q^{80} +(-1.19593 + 3.68068i) q^{81} +(-13.3949 + 9.86686i) q^{82} +(-1.71869 + 2.36557i) q^{83} +(-2.93941 - 3.93612i) q^{84} +(9.94451 - 3.23117i) q^{85} +(-6.01175 + 1.99703i) q^{86} -11.1502 q^{87} +5.74214 q^{89} +(-3.15324 + 1.04747i) q^{90} +(-0.281109 + 0.0913380i) q^{91} +(-7.11718 + 5.31497i) q^{92} +(-7.11037 + 9.78659i) q^{93} +(-7.16843 + 5.28035i) q^{94} +(-1.66943 + 5.13798i) q^{95} +(-7.10425 + 2.56876i) q^{96} +(4.35113 - 3.16128i) q^{97} +(-1.54873 + 4.87509i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{4} + 2 q^{6} + 10 q^{9} - 40 q^{10} - 16 q^{12} + 12 q^{14} - 8 q^{15} - 4 q^{17} - 10 q^{18} - 12 q^{20} - 48 q^{23} + 6 q^{25} + 20 q^{26} - 12 q^{28} + 18 q^{30} + 4 q^{31} + 80 q^{32} - 32 q^{36}+ \cdots - 96 q^{98}+O(q^{100}) $ 40 * q + 4 * q^4 + 2 * q^6 + 10 * q^9 - 40 * q^10 - 16 * q^12 + 12 * q^14 - 8 * q^15 - 4 * q^17 - 10 * q^18 - 12 * q^20 - 48 * q^23 + 6 * q^25 + 20 * q^26 - 12 * q^28 + 18 * q^30 + 4 * q^31 + 80 * q^32 - 32 * q^36 - 8 * q^38 + 24 * q^39 + 20 * q^40 + 4 * q^41 - 20 * q^42 + 2 * q^46 + 4 * q^47 - 32 * q^48 + 6 * q^49 - 6 * q^50 - 20 * q^52 + 152 * q^54 - 32 * q^56 + 16 * q^57 - 36 * q^58 + 4 * q^60 + 22 * q^62 - 40 * q^63 + 16 * q^64 - 64 * q^65 - 28 * q^68 - 28 * q^70 + 12 * q^71 - 4 * q^72 - 4 * q^73 - 14 * q^74 - 176 * q^76 - 32 * q^78 + 16 * q^79 + 56 * q^80 + 6 * q^81 + 4 * q^82 - 52 * q^84 + 20 * q^86 - 128 * q^87 - 16 * q^89 - 36 * q^90 + 36 * q^92 + 24 * q^95 + 60 * q^96 + 20 * q^97 - 96 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.445829	+	1.34210i	0.315248	+	0.949009i
$2$	0.445829	+	1.34210i	0.315248	+	0.949009i
$3$	−1.27008	+	0.412674i	−0.733281	+	0.238257i	−0.651772	−	0.758415i	$-0.725974\pi$
$3$	−1.27008	+	0.412674i	−0.733281	+	0.238257i	−0.0815092	+	0.996673i	$0.525974\pi$
$4$	−1.60247	+	1.19669i	−0.801237	+	0.598347i
$5$	1.13513	−	1.56237i	0.507643	−	0.698711i	−0.475876	−	0.879512i	$-0.657869\pi$
$5$	1.13513	−	1.56237i	0.507643	−	0.698711i	0.983520	+	0.180801i	$0.0578690\pi$
$6$	−1.12009	−	1.52059i	−0.457274	−	0.620780i
$7$	0.568375	−	1.74928i	0.214826	−	0.661165i	−0.784340	−	0.620331i	$-0.786998\pi$
$7$	0.568375	−	1.74928i	0.214826	−	0.661165i	0.999166	−	0.0408343i	$-0.0130016\pi$
$8$	−2.32051	−	1.61716i	−0.820426	−	0.571753i
$9$	−0.984248	+	0.715098i	−0.328083	+	0.238366i
$10$	2.60293	+	0.826906i	0.823117	+	0.261491i
$11$		0			0
$11$		0			0
$12$	1.54142	−	2.18120i	0.444971	−	0.629657i
$13$	−0.0944573	−	0.130009i	−0.0261977	−	0.0360581i	0.795717	−	0.605668i	$-0.207094\pi$
$13$	−0.0944573	−	0.130009i	−0.0261977	−	0.0360581i	−0.821915	+	0.569610i	$0.807094\pi$
$14$	2.60111	−	0.0170613i	0.695175	−	0.00455982i
$15$	−0.796952	+	2.45277i	−0.205772	+	0.633302i
$16$	1.13584	−	3.83534i	0.283961	−	0.958836i
$17$	4.38036	+	3.18252i	1.06239	+	0.771874i	0.974530	−	0.224259i	$-0.0719962\pi$
$17$	4.38036	+	3.18252i	1.06239	+	0.771874i	0.0878632	+	0.996133i	$0.471996\pi$
$18$	−1.39854	−	1.00215i	−0.329639	−	0.236209i
$19$	−2.66053	+	0.864457i	−0.610367	+	0.198320i	−0.597859	−	0.801602i	$-0.703982\pi$
$19$	−2.66053	+	0.864457i	−0.610367	+	0.198320i	−0.0125081	+	0.999922i	$0.503982\pi$
$20$	0.0506664	+	3.86205i	0.0113293	+	0.863580i
$21$			2.45628i			0.536003i
$22$		0			0
$23$	4.44137			0.926090			0.463045	−	0.886335i	$-0.346757\pi$
$23$	4.44137			0.926090			0.463045	+	0.886335i	$0.346757\pi$
$24$	3.61460	+	1.09631i	0.737827	+	0.223783i
$25$	0.392607	+	1.20832i	0.0785214	+	0.241664i
$26$	0.132374	−	0.184733i	0.0259607	−	0.0362291i
$27$	3.30983	−	4.55559i	0.636977	−	0.876723i
$28$	1.18255	+	3.48334i	0.223480	+	0.658290i
$29$	7.94083	+	2.58013i	1.47457	+	0.479118i	0.932487	−	0.361203i	$-0.117634\pi$
$29$	7.94083	+	2.58013i	1.47457	+	0.479118i	0.542088	+	0.840322i	$0.317634\pi$
$30$	−3.64717	+	0.0239226i	−0.665878	+	0.00436765i
$31$	7.32836	−	5.32436i	1.31621	−	0.956284i	0.316241	−	0.948679i	$-0.397579\pi$
$31$	7.32836	−	5.32436i	1.31621	−	0.956284i	0.999971	−	0.00760506i	$-0.00242079\pi$
$32$	5.65381	−	0.185487i	0.999462	−	0.0327898i
$33$		0			0
$34$	−2.31837	+	7.29774i	−0.397597	+	1.25155i
$35$	−2.08784	−	2.87366i	−0.352909	−	0.485737i
$36$	0.721478	−	2.32377i	0.120246	−	0.387295i
$37$	−0.572605	−	0.186051i	−0.0941357	−	0.0305865i	0.261570	−	0.965184i	$-0.415760\pi$
$37$	−0.572605	−	0.186051i	−0.0941357	−	0.0305865i	−0.355706	+	0.934598i	$0.615760\pi$
$38$	−2.34633	−	3.18530i	−0.380625	−	0.516723i
$39$	0.173620	+	0.126142i	0.0278014	+	0.0201989i
$40$	−5.16067	+	1.78981i	−0.815974	+	0.282994i
$41$	3.63525	+	11.1881i	0.567730	+	1.74729i	0.659698	+	0.751531i	$0.270684\pi$
$41$	3.63525	+	11.1881i	0.567730	+	1.74729i	−0.0919677	+	0.995762i	$0.529316\pi$
$42$	−3.29657	+	1.09508i	−0.508672	+	0.168974i
$43$			4.47936i			0.683096i	0.939864	+	0.341548i	$0.110951\pi$
$43$			4.47936i			0.683096i	−0.939864	+	0.341548i	$0.889049\pi$
$44$		0			0
$45$			2.34948i			0.350240i
$46$	1.98009	+	5.96077i	0.291948	+	0.878868i
$47$	1.94544	+	5.98745i	0.283772	+	0.873359i	0.986764	+	0.162162i	$0.0518467\pi$
$47$	1.94544	+	5.98745i	0.283772	+	0.873359i	−0.702993	+	0.711197i	$0.748153\pi$
$48$	0.140134	+	5.33993i	0.0202265	+	0.770752i
$49$	2.92620	+	2.12601i	0.418028	+	0.303715i
$50$	−1.44665	+	1.06562i	−0.204588	+	0.150702i
$51$	−6.87675	−	2.23439i	−0.962937	−	0.312877i
$52$	0.306947	+	0.0952999i	0.0425658	+	0.0132157i
$53$	−6.88946	−	9.48253i	−0.946340	−	1.30253i	−0.953134	−	0.302549i	$-0.902162\pi$
$53$	−6.88946	−	9.48253i	−0.946340	−	1.30253i	0.00679344	−	0.999977i	$-0.497838\pi$
$54$	7.58968	+	2.41112i	1.03282	+	0.328111i
$55$		0			0
$56$	−4.14779	+	3.14007i	−0.554271	+	0.419610i
$57$	3.02234	−	2.19586i	0.400319	−	0.290849i
$58$	0.0774495	+	11.8077i	0.0101696	+	1.55043i
$59$	−9.15964	−	2.97615i	−1.19248	−	0.387461i	−0.355493	−	0.934679i	$-0.615687\pi$
$59$	−9.15964	−	2.97615i	−1.19248	−	0.387461i	−0.836991	+	0.547217i	$0.815687\pi$
$60$	−1.65812	−	4.88420i	−0.214062	−	0.630548i
$61$	1.95681	−	2.69331i	0.250543	−	0.344843i	−0.665158	−	0.746703i	$-0.731636\pi$
$61$	1.95681	−	2.69331i	0.250543	−	0.344843i	0.915701	+	0.401859i	$0.131636\pi$
$62$	10.4130	+	7.46165i	1.32246	+	0.947630i
$63$	0.691483	+	2.12817i	0.0871187	+	0.268124i
$64$	2.76957	+	7.50530i	0.346197	+	0.938162i
$65$	−0.310343			−0.0384933
$66$		0			0
$67$		−	5.76864i		−	0.704751i	−0.935859	−	0.352376i	$-0.885374\pi$
$67$		−	5.76864i		−	0.704751i	0.935859	−	0.352376i	$-0.114626\pi$
$68$	−10.8279	+	0.142052i	−1.31308	+	0.0172263i
$69$	−5.64090	+	1.83284i	−0.679084	+	0.220648i
$70$	2.92593	−	4.08325i	0.349715	−	0.488041i
$71$	−7.79016	−	5.65988i	−0.924521	−	0.671704i	0.0201239	−	0.999797i	$-0.493594\pi$
$71$	−7.79016	−	5.65988i	−0.924521	−	0.671704i	−0.944645	+	0.328093i	$0.893594\pi$
$72$	3.44039	−	0.0677068i	0.405454	−	0.00797932i
$73$	0.210731	−	0.648563i	0.0246642	−	0.0759086i	−0.937967	−	0.346725i	$-0.887294\pi$
$73$	0.210731	−	0.648563i	0.0246642	−	0.0759086i	0.962631	+	0.270817i	$0.0872937\pi$
$74$	−0.00558480	−	0.851441i	−0.000649220	−	0.0989780i
$75$	−0.997284	−	1.37264i	−0.115156	−	0.158499i
$76$	3.22893	−	4.56911i	0.370384	−	0.524113i
$77$		0			0
$78$	−0.0918909	+	0.289253i	−0.0104046	+	0.0327515i
$79$	4.67504	−	3.39662i	0.525983	−	0.382149i	−0.292870	−	0.956152i	$-0.594610\pi$
$79$	4.67504	−	3.39662i	0.525983	−	0.382149i	0.818853	+	0.574003i	$0.194610\pi$
$80$	−4.70288	−	6.12820i	−0.525798	−	0.685154i
$81$	−1.19593	+	3.68068i	−0.132881	+	0.408965i
$82$	−13.3949	+	9.86686i	−1.47922	+	1.08961i
$83$	−1.71869	+	2.36557i	−0.188650	+	0.259655i	−0.892857	−	0.450340i	$-0.851303\pi$
$83$	−1.71869	+	2.36557i	−0.188650	+	0.259655i	0.704207	+	0.709995i	$0.251303\pi$
$84$	−2.93941	−	3.93612i	−0.320716	−	0.429466i
$85$	9.94451	−	3.23117i	1.07863	−	0.350469i
$86$	−6.01175	+	1.99703i	−0.648264	+	0.215345i
$87$	−11.1502			−1.19543
$88$		0			0
$89$	5.74214			0.608666			0.304333	−	0.952566i	$-0.401566\pi$
$89$	5.74214			0.608666			0.304333	+	0.952566i	$0.401566\pi$
$90$	−3.15324	+	1.04747i	−0.332381	+	0.110413i
$91$	−0.281109	+	0.0913380i	−0.0294683	+	0.00957482i
$92$	−7.11718	+	5.31497i	−0.742018	+	0.554124i
$93$	−7.11037	+	9.78659i	−0.737311	+	1.01482i
$94$	−7.16843	+	5.28035i	−0.739367	+	0.544627i
$95$	−1.66943	+	5.13798i	−0.171280	+	0.527146i
$96$	−7.10425	+	2.56876i	−0.725074	+	0.262173i
$97$	4.35113	−	3.16128i	0.441790	−	0.320979i	−0.344556	−	0.938766i	$-0.611970\pi$
$97$	4.35113	−	3.16128i	0.441790	−	0.320979i	0.786346	+	0.617787i	$0.211970\pi$
$98$	−1.54873	+	4.87509i	−0.156446	+	0.492458i
$99$		0			0
$100$	−2.07513	−	1.46647i	−0.207513	−	0.146647i
$101$	5.47738	+	7.53897i	0.545020	+	0.750156i	0.989326	−	0.145719i	$-0.0465497\pi$
$101$	5.47738	+	7.53897i	0.545020	+	0.750156i	−0.444306	+	0.895875i	$0.646550\pi$
$102$	−0.0670711	−	10.2254i	−0.00664103	−	1.01247i
$103$	0.518716	−	1.59644i	0.0511106	−	0.157302i	−0.922243	−	0.386610i	$-0.873646\pi$
$103$	0.518716	−	1.59644i	0.0511106	−	0.157302i	0.973354	+	0.229307i	$0.0736461\pi$
$104$	0.00894339	+	0.454441i	0.000876971	+	0.0445616i
$105$	3.83760	+	2.78818i	0.374512	+	0.272099i
$106$	9.65500	−	13.4739i	0.937777	−	1.30870i
$107$	10.7249	−	3.48472i	1.03681	−	0.336881i	0.259332	−	0.965788i	$-0.416497\pi$
$107$	10.7249	−	3.48472i	1.03681	−	0.336881i	0.777480	+	0.628907i	$0.216497\pi$
$108$	0.147734	+	11.2611i	0.0142157	+	1.08360i
$109$			19.6373i			1.88092i	0.339910	+	0.940458i	$0.389603\pi$
$109$			19.6373i			1.88092i	−0.339910	+	0.940458i	$0.610397\pi$
$110$		0			0
$111$	0.804032			0.0763154
$112$	−6.06350	−	4.16682i	−0.572947	−	0.393727i
$113$	−3.99113	−	12.2834i	−0.375454	−	1.15553i	−0.943172	−	0.332305i	$-0.892174\pi$
$113$	−3.99113	−	12.2834i	−0.375454	−	1.15553i	0.567718	−	0.823223i	$-0.307826\pi$
$114$	4.29451	+	3.07731i	0.402218	+	0.288217i
$115$	5.04151	−	6.93905i	0.470124	−	0.647070i
$116$	−15.8126	+	5.36815i	−1.46816	+	0.498421i
$117$	0.185939	+	0.0604151i	0.0171900	+	0.00558538i
$118$	−0.0893370	−	13.6200i	−0.00822413	−	1.25382i
$119$	8.05679	−	5.85360i	0.738565	−	0.536599i
$120$	5.81586	−	4.40288i	0.530913	−	0.401926i
$121$		0			0
$122$	4.48710	+	1.42548i	0.406243	+	0.129057i
$123$	−9.23410	−	12.7097i	−0.832611	−	1.14599i
$124$	−5.37186	+	17.3020i	−0.482408	+	1.55376i
$125$	11.5169	+	3.74205i	1.03010	+	0.334699i
$126$	−2.54793	+	1.87684i	−0.226988	+	0.167202i
$127$	0.911890	+	0.662527i	0.0809172	+	0.0587898i	0.627508	−	0.778610i	$-0.284075\pi$
$127$	0.911890	+	0.662527i	0.0809172	+	0.0587898i	−0.546591	+	0.837400i	$0.684075\pi$
$128$	−8.83811	+	7.06313i	−0.781186	+	0.624298i
$129$	−1.84851	−	5.68914i	−0.162753	−	0.500901i
$130$	−0.138360	−	0.416512i	−0.0121350	−	0.0365305i
$131$		−	10.9554i		−	0.957178i	−0.878039	−	0.478589i	$-0.841148\pi$
$131$		−	10.9554i		−	0.957178i	0.878039	−	0.478589i	$-0.158852\pi$
$132$		0			0
$133$			5.14534i			0.446157i
$134$	7.74210	−	2.57182i	0.668815	−	0.222172i
$135$	−3.36043	−	10.3423i	−0.289219	−	0.890126i
$136$	−5.01804	−	14.4688i	−0.430293	−	1.24069i
$137$	8.23202	+	5.98091i	0.703309	+	0.510984i	0.881008	−	0.473101i	$-0.156865\pi$
$137$	8.23202	+	5.98091i	0.703309	+	0.510984i	−0.177699	+	0.984085i	$0.556865\pi$
$138$	−4.97473	−	6.75353i	−0.423477	−	0.574898i
$139$	−17.4373	−	5.66574i	−1.47902	−	0.480562i	−0.545198	−	0.838307i	$-0.683545\pi$
$139$	−17.4373	−	5.66574i	−1.47902	−	0.480562i	−0.933819	+	0.357746i	$0.883545\pi$
$140$	6.78459	+	2.10646i	0.573403	+	0.178029i
$141$	−4.94173	−	6.80171i	−0.416169	−	0.572807i
$142$	4.12306	−	12.9785i	0.345999	−	1.08913i
$143$		0			0
$144$	1.62469	+	4.58717i	0.135391	+	0.382264i
$145$	13.0449	−	9.47771i	1.08332	−	0.787081i
$146$	0.964388	−	0.00632565i	0.0798133	−	0.000523514i
$147$	−4.59385	−	1.49263i	−0.378894	−	0.123110i
$148$	1.14023	−	0.387092i	0.0937264	−	0.0318188i
$149$	4.97791	−	6.85150i	0.407806	−	0.561297i	−0.554876	−	0.831933i	$-0.687234\pi$
$149$	4.97791	−	6.85150i	0.407806	−	0.561297i	0.962682	+	0.270636i	$0.0872341\pi$
$150$	1.39761	−	1.95042i	0.114114	−	0.159251i
$151$	3.11197	+	9.57765i	0.253248	+	0.779418i	0.994170	+	0.107826i	$0.0343890\pi$
$151$	3.11197	+	9.57765i	0.253248	+	0.779418i	−0.740922	+	0.671592i	$0.765611\pi$
$152$	7.57176	+	2.29652i	0.614151	+	0.186272i
$153$	−6.58717			−0.532541
$154$		0			0
$155$		−	17.4934i		−	1.40510i
$156$	−0.429175	+	0.00563036i	−0.0343615	+	0.000450789i
$157$	8.31194	−	2.70071i	0.663365	−	0.215540i	0.0420671	−	0.999115i	$-0.486606\pi$
$157$	8.31194	−	2.70071i	0.663365	−	0.215540i	0.621298	+	0.783574i	$0.286606\pi$
$158$	6.64287	+	4.76007i	0.528478	+	0.378691i
$159$	12.6634	+	9.20047i	1.00427	+	0.729645i
$160$	6.12799	−	9.04388i	0.484460	−	0.714981i
$161$	2.52436	−	7.76919i	0.198948	−	0.612298i
$162$	−5.47303	+	0.0358989i	−0.430002	+	0.00282048i
$163$	14.3559	+	19.7592i	1.12444	+	1.54766i	0.798219	+	0.602368i	$0.205776\pi$
$163$	14.3559	+	19.7592i	1.12444	+	1.54766i	0.326223	+	0.945293i	$0.394224\pi$
$164$	−19.2142	−	13.5784i	−1.50037	−	1.06030i
$165$		0			0
$166$	−3.94107	−	1.25201i	−0.305887	−	0.0971751i
$167$	−5.95829	+	4.32895i	−0.461066	+	0.334984i	−0.793949	−	0.607984i	$-0.791978\pi$
$167$	−5.95829	+	4.32895i	−0.461066	+	0.334984i	0.332883	+	0.942968i	$0.391978\pi$
$168$	3.97220	−	5.69982i	0.306462	−	0.439751i
$169$	4.00924	−	12.3392i	0.308403	−	0.949167i
$170$	8.77010	+	11.9060i	0.672636	+	0.913148i
$171$	2.00045	−	2.75338i	0.152978	−	0.210556i
$172$	−5.36042	−	7.17805i	−0.408728	−	0.547321i
$173$	−1.31533	+	0.427378i	−0.100003	+	0.0324929i	−0.358591	−	0.933495i	$-0.616743\pi$
$173$	−1.31533	+	0.427378i	−0.100003	+	0.0324929i	0.258588	+	0.965988i	$0.416743\pi$
$174$	−4.97110	−	14.9648i	−0.376858	−	1.13448i
$175$	2.33684			0.176648
$176$		0			0
$177$	12.8617			0.966741
$178$	2.56001	+	7.70654i	0.191881	+	0.577630i
$179$	9.41240	−	3.05827i	0.703516	−	0.228586i	0.0646542	−	0.997908i	$-0.479406\pi$
$179$	9.41240	−	3.05827i	0.703516	−	0.228586i	0.638862	+	0.769322i	$0.279406\pi$
$180$	−2.81161	−	3.76498i	−0.209565	−	0.280625i
$181$	−6.86552	+	9.44958i	−0.510310	+	0.702382i	−0.983972	−	0.178325i	$-0.942932\pi$
$181$	−6.86552	+	9.44958i	−0.510310	+	0.702382i	0.473661	+	0.880707i	$0.342932\pi$
$182$	−0.247912	−	0.336556i	−0.0183764	−	0.0249472i
$183$	−1.37384	+	4.22825i	−0.101557	+	0.312561i
$184$	−10.3063	−	7.18242i	−0.759788	−	0.529495i
$185$	−0.940658	+	0.683428i	−0.0691585	+	0.0502466i
$186$	−16.3046	−	5.17970i	−1.19551	−	0.379794i
$187$		0			0
$188$	−10.2827	−	7.26663i	−0.749940	−	0.529974i
$189$	−6.08777	−	8.37909i	−0.442820	−	0.609489i
$190$	−7.63998	+	0.0501124i	−0.554262	+	0.00363554i
$191$	3.73607	−	11.4984i	0.270332	−	0.831997i	−0.720085	−	0.693886i	$-0.755897\pi$
$191$	3.73607	−	11.4984i	0.270332	−	0.831997i	0.990417	−	0.138111i	$-0.0441030\pi$
$192$	−6.61482	−	8.38939i	−0.477384	−	0.605452i
$193$	−10.7292	−	7.79523i	−0.772305	−	0.561113i	0.130354	−	0.991467i	$-0.458388\pi$
$193$	−10.7292	−	7.79523i	−0.772305	−	0.561113i	−0.902660	+	0.430355i	$0.858388\pi$
$194$	6.18261	+	4.43027i	0.443886	+	0.318075i
$195$	0.394160	−	0.128070i	0.0282264	−	0.00917131i
$196$	−7.23333	+	0.0948944i	−0.516666	+	0.00677817i
$197$		−	11.6835i		−	0.832415i	−0.909270	−	0.416208i	$-0.863359\pi$
$197$		−	11.6835i		−	0.832415i	0.909270	−	0.416208i	$-0.136641\pi$
$198$		0			0
$199$	−24.9329			−1.76745			−0.883725	−	0.468007i	$-0.844972\pi$
$199$	−24.9329			−1.76745			−0.883725	+	0.468007i	$0.844972\pi$
$200$	1.04300	−	3.43883i	0.0737512	−	0.243162i
$201$	2.38057	+	7.32663i	0.167912	+	0.516780i
$202$	−7.67609	+	10.7123i	−0.540088	+	0.753715i
$203$	9.02674	−	12.4242i	0.633553	−	0.872010i
$204$	13.6937	−	4.64881i	0.958750	−	0.325482i
$205$	21.6064	+	7.02035i	1.50906	+	0.490323i
$206$	2.37385	−	0.0155706i	0.165394	−	0.00108486i
$207$	−4.37141	+	3.17602i	−0.303834	+	0.220748i
$208$	−0.605919	+	0.214606i	−0.0420129	+	0.0148802i
$209$		0			0
$210$	−2.03111	+	6.39350i	−0.140160	+	0.441194i
$211$	3.50464	+	4.82372i	0.241269	+	0.332079i	0.912430	−	0.409233i	$-0.134204\pi$
$211$	3.50464	+	4.82372i	0.241269	+	0.332079i	−0.671160	+	0.741312i	$0.734204\pi$
$212$	22.3879	+	6.95093i	1.53761	+	0.477392i
$213$	12.2298	+	3.97370i	0.837972	+	0.272274i
$214$	9.45831	+	12.8403i	0.646557	+	0.877744i
$215$	6.99840	+	5.08463i	0.477287	+	0.346769i
$216$	−15.0476	+	5.21878i	−1.02386	+	0.355093i
$217$	−5.14854	−	15.8456i	−0.349506	−	1.07567i
$218$	−26.3553	+	8.75489i	−1.78501	+	0.592956i
$219$			0.910690i			0.0615387i
$220$		0			0
$221$		−	0.870099i		−	0.0585292i
$222$	0.358461	+	1.07909i	0.0240583	+	0.0724240i
$223$	0.320763	+	0.987207i	0.0214799	+	0.0661082i	0.961222	−	0.275776i	$-0.0889349\pi$
$223$	0.320763	+	0.987207i	0.0214799	+	0.0661082i	−0.939742	+	0.341884i	$0.888935\pi$
$224$	2.88902	−	9.99552i	0.193030	−	0.667853i
$225$	−1.25049	−	0.908534i	−0.0833660	−	0.0605689i
$226$	14.7062	−	10.8328i	0.978245	−	0.720587i
$227$	−6.33034	−	2.05685i	−0.420160	−	0.136518i	0.0913041	−	0.995823i	$-0.470896\pi$
$227$	−6.33034	−	2.05685i	−0.420160	−	0.136518i	−0.511464	+	0.859305i	$0.670896\pi$
$228$	−2.21545	+	7.13563i	−0.146722	+	0.472569i
$229$	−9.63291	−	13.2586i	−0.636561	−	0.876150i	0.361866	−	0.932230i	$-0.382140\pi$
$229$	−9.63291	−	13.2586i	−0.636561	−	0.876150i	−0.998426	+	0.0560798i	$0.982140\pi$
$230$	11.5606	+	3.67260i	0.762281	+	0.242164i
$231$		0			0
$232$	−14.2543	−	18.8288i	−0.935842	−	1.23617i
$233$	−13.0043	+	9.44820i	−0.851942	+	0.618972i	−0.925681	−	0.378305i	$-0.876507\pi$
$233$	−13.0043	+	9.44820i	−0.851942	+	0.618972i	0.0737385	+	0.997278i	$0.476507\pi$
$234$	0.00181352	+	0.276483i	0.000118554	+	0.0180743i
$235$	11.5629	+	3.75702i	0.754281	+	0.245081i
$236$	18.2396	−	6.19209i	1.18730	−	0.403071i
$237$	−4.53598	+	6.24324i	−0.294644	+	0.405542i
$238$	11.4481	+	8.20333i	0.742068	+	0.531743i
$239$	0.778914	+	2.39725i	0.0503837	+	0.155065i	0.973083	−	0.230456i	$-0.0740217\pi$
$239$	0.778914	+	2.39725i	0.0503837	+	0.155065i	−0.922699	+	0.385521i	$0.874022\pi$
$240$	8.50199	+	5.84255i	0.548801	+	0.377135i
$241$	−6.11179			−0.393695			−0.196848	−	0.980434i	$-0.563070\pi$
$241$	−6.11179			−0.393695			−0.196848	+	0.980434i	$0.563070\pi$
$242$		0			0
$243$			11.7248i			0.752144i
$244$	0.0873421	+	6.65766i	0.00559151	+	0.426213i
$245$	6.64320	−	2.15851i	0.424418	−	0.137902i
$246$	12.9408	−	18.0594i	0.825077	−	1.15143i
$247$	0.363693	+	0.264239i	0.0231413	+	0.0168131i
$248$	−25.6159	+	0.504121i	−1.62661	+	0.0320117i
$249$	1.20666	−	3.71372i	0.0764690	−	0.235347i
$250$	0.112328	+	17.1251i	0.00710422	+	1.08309i
$251$	−0.287656	−	0.395925i	−0.0181567	−	0.0249905i	0.799842	−	0.600210i	$-0.204916\pi$
$251$	−0.287656	−	0.395925i	−0.0181567	−	0.0249905i	−0.817999	+	0.575220i	$0.804916\pi$
$252$	−3.65485	−	2.58284i	−0.230234	−	0.162703i
$253$		0			0
$254$	−0.482632	+	1.51922i	−0.0302830	+	0.0953245i
$255$	−11.2969	+	8.20768i	−0.707439	+	0.513985i
$256$	−13.4197	−	8.71270i	−0.838732	−	0.544544i
$257$	3.11755	−	9.59484i	0.194468	−	0.598510i	−0.805515	−	0.592576i	$-0.798111\pi$
$257$	3.11755	−	9.59484i	0.194468	−	0.598510i	0.999982	−	0.00593420i	$-0.00188893\pi$
$258$	6.81129	−	5.01728i	0.424052	−	0.312362i
$259$	−0.650909	+	0.895899i	−0.0404455	+	0.0556684i
$260$	0.497316	−	0.371386i	0.0308422	−	0.0230324i
$261$	−9.66079	+	3.13898i	−0.597988	+	0.194298i
$262$	14.7033	−	4.88423i	0.908370	−	0.301749i
$263$	−3.98466			−0.245705			−0.122852	−	0.992425i	$-0.539204\pi$
$263$	−3.98466			−0.245705			−0.122852	+	0.992425i	$0.539204\pi$
$264$		0			0
$265$	−22.6356			−1.39049
$266$	−6.90556	+	2.29394i	−0.423407	+	0.140650i
$267$	−7.29298	+	2.36963i	−0.446323	+	0.145019i
$268$	6.90330	+	9.24409i	0.421686	+	0.564673i
$269$	−1.58743	+	2.18490i	−0.0967871	+	0.133216i	−0.854664	−	0.519182i	$-0.826237\pi$
$269$	−1.58743	+	2.18490i	−0.0967871	+	0.133216i	0.757877	+	0.652398i	$0.226237\pi$
$270$	12.3823	−	9.12094i	0.753562	−	0.555083i
$271$	−6.90996	+	21.2667i	−0.419750	+	1.29186i	0.488182	+	0.872742i	$0.337660\pi$
$271$	−6.90996	+	21.2667i	−0.419750	+	1.29186i	−0.907932	+	0.419117i	$0.862340\pi$
$272$	17.1814	−	13.1853i	1.04178	−	0.799478i
$273$	0.319339	−	0.232013i	0.0193273	−	0.0140421i
$274$	−4.35692	+	13.7147i	−0.263211	+	0.828534i
$275$		0			0
$276$	6.84604	−	9.68751i	0.412083	−	0.583119i
$277$	18.5073	+	25.4731i	1.11200	+	1.53053i	0.818440	+	0.574592i	$0.194839\pi$
$277$	18.5073	+	25.4731i	1.11200	+	1.53053i	0.293557	+	0.955942i	$0.405161\pi$
$278$	−0.170072	−	25.9286i	−0.0102002	−	1.55510i
$279$	−3.40548	+	10.4810i	−0.203881	+	0.627480i
$280$	0.197680	+	10.0447i	0.0118136	+	0.600288i
$281$	−7.74293	−	5.62557i	−0.461905	−	0.335593i	0.332373	−	0.943148i	$-0.392151\pi$
$281$	−7.74293	−	5.62557i	−0.461905	−	0.335593i	−0.794278	+	0.607555i	$0.792151\pi$
$282$	6.92542	−	9.66470i	0.412403	−	0.575524i
$283$	−15.5970	+	5.06778i	−0.927147	+	0.301248i	−0.733395	−	0.679802i	$-0.762066\pi$
$283$	−15.5970	+	5.06778i	−0.927147	+	0.301248i	−0.193751	+	0.981051i	$0.562066\pi$
$284$	19.2567	−	0.252629i	1.14267	−	0.0149908i
$285$		−	7.21458i		−	0.427355i
$286$		0			0
$287$	21.6373			1.27721
$288$	−5.43211	+	4.22560i	−0.320090	+	0.248996i
$289$	3.80583	+	11.7132i	0.223873	+	0.689009i
$290$	18.5359	+	13.2822i	1.08846	+	0.779958i
$291$	−4.22170	+	5.81067i	−0.247481	+	0.340628i
$292$	0.438441	+	1.29149i	0.0256578	+	0.0755785i
$293$	9.51885	+	3.09286i	0.556097	+	0.180687i	0.573564	−	0.819161i	$-0.305560\pi$
$293$	9.51885	+	3.09286i	0.556097	+	0.180687i	−0.0174673	+	0.999847i	$0.505560\pi$
$294$	−0.0448053	−	6.83087i	−0.00261310	−	0.398384i
$295$	−15.0472	+	10.9324i	−0.876080	+	0.636510i
$296$	1.02786	+	1.35773i	0.0597434	+	0.0789164i
$297$		0			0
$298$	11.4147	+	3.62626i	0.661236	+	0.210064i
$299$	−0.419520	−	0.577419i	−0.0242615	−	0.0333930i
$300$	3.24076	+	1.00618i	0.187105	+	0.0580919i
$301$	7.83564	+	2.54595i	0.451639	+	0.146746i
$302$	−11.4668	+	8.44656i	−0.659839	+	0.486045i
$303$	−10.0679	−	7.31472i	−0.578383	−	0.420220i
$304$	0.293548	+	11.1859i	0.0168361	+	0.641557i
$305$	−1.98672	−	6.11450i	−0.113759	−	0.350115i
$306$	−2.93675	−	8.84065i	−0.167883	−	0.505386i
$307$		−	18.8436i		−	1.07546i	−0.843117	−	0.537731i	$-0.819282\pi$
$307$		−	18.8436i		−	1.07546i	0.843117	−	0.537731i	$-0.180718\pi$
$308$		0			0
$309$			2.24167i			0.127524i
$310$	23.4779	−	7.79906i	1.33346	−	0.442957i
$311$	−0.493381	−	1.51847i	−0.0279770	−	0.0861045i	0.936093	−	0.351752i	$-0.114414\pi$
$311$	−0.493381	−	1.51847i	−0.0279770	−	0.0861045i	−0.964070	+	0.265648i	$0.914414\pi$
$312$	−0.198895	−	0.573486i	−0.0112602	−	0.0324672i
$313$	−3.18863	−	2.31667i	−0.180232	−	0.130946i	0.494011	−	0.869455i	$-0.335530\pi$
$313$	−3.18863	−	2.31667i	−0.180232	−	0.130946i	−0.674243	+	0.738509i	$0.735530\pi$
$314$	7.33033	+	9.95141i	0.413675	+	0.561591i
$315$	4.10990	+	1.33539i	0.231566	+	0.0752405i
$316$	−3.42692	+	11.0376i	−0.192779	+	0.620913i
$317$	1.14256	+	1.57260i	0.0641725	+	0.0883258i	0.839897	−	0.542746i	$-0.182615\pi$
$317$	1.14256	+	1.57260i	0.0641725	+	0.0883258i	−0.775724	+	0.631072i	$0.782615\pi$
$318$	−6.70228	+	21.0974i	−0.375845	+	1.18308i
$319$		0			0
$320$	14.8698	+	4.19236i	0.831249	+	0.234360i
$321$	−12.1834	+	8.85175i	−0.680011	+	0.494057i
$322$	11.5525	−	0.0757755i	0.643795	−	0.00422280i
$323$	−14.4052	−	4.68054i	−0.801527	−	0.260432i
$324$	−2.48821	−	7.32936i	−0.138234	−	0.407186i
$325$	0.120008	−	0.165177i	0.00665686	−	0.00916238i
$326$	−20.1186	+	28.0763i	−1.11427	+	1.55500i
$327$	−8.10382	−	24.9410i	−0.448142	−	1.37924i
$328$	9.65739	−	31.8410i	0.533240	−	1.75813i
$329$	11.5795			0.638396
$330$		0			0
$331$		−	7.52148i		−	0.413418i	−0.978402	−	0.206709i	$-0.933725\pi$
$331$		−	7.52148i		−	0.413418i	0.978402	−	0.206709i	$-0.0662753\pi$
$332$	−0.0767137	−	5.84751i	−0.00421021	−	0.320924i
$333$	0.696630	−	0.226349i	0.0381751	−	0.0124038i
$334$	−8.46626	−	6.06666i	−0.463253	−	0.331953i
$335$	−9.01272	−	6.54812i	−0.492418	−	0.357762i
$336$	9.42066	+	2.78995i	0.513939	+	0.152204i
$337$	2.61809	−	8.05767i	0.142617	−	0.438929i	−0.854080	−	0.520142i	$-0.825879\pi$
$337$	2.61809	−	8.05767i	0.142617	−	0.438929i	0.996697	+	0.0812124i	$0.0258792\pi$
$338$	18.3479	−	0.120348i	0.997992	−	0.00654607i
$339$	10.1381	+	13.9539i	0.550626	+	0.757872i
$340$	−12.0691	+	17.0784i	−0.654539	+	0.926206i
$341$		0			0
$342$	4.58717	+	1.45727i	0.248046	+	0.0788000i
$343$	15.7983	−	11.4782i	0.853029	−	0.619762i
$344$	7.24385	−	10.3944i	0.390562	−	0.560429i
$345$	−3.53956	+	10.8936i	−0.190564	+	0.586494i
$346$	−1.16000	−	1.57477i	−0.0623619	−	0.0846604i
$347$	10.1385	−	13.9545i	0.544266	−	0.749117i	−0.444955	−	0.895553i	$-0.646780\pi$
$347$	10.1385	−	13.9545i	0.544266	−	0.749117i	0.989220	+	0.146436i	$0.0467802\pi$
$348$	17.8680	−	13.3434i	0.957824	−	0.715283i
$349$	4.44703	−	1.44493i	0.238044	−	0.0773452i	−0.187566	−	0.982252i	$-0.560060\pi$
$349$	4.44703	−	1.44493i	0.238044	−	0.0773452i	0.425610	+	0.904907i	$0.360060\pi$
$350$	1.04183	+	3.13627i	0.0556881	+	0.167641i
$351$	−0.904906			−0.0483003
$352$		0			0
$353$	−5.45055			−0.290104			−0.145052	−	0.989424i	$-0.546335\pi$
$353$	−5.45055			−0.290104			−0.145052	+	0.989424i	$0.546335\pi$
$354$	5.73409	+	17.2616i	0.304764	+	0.917446i
$355$	−17.6856	+	5.74640i	−0.938655	+	0.304987i
$356$	−9.20163	+	6.87159i	−0.487686	+	0.364194i
$357$	−7.81714	+	10.7594i	−0.413727	+	0.569446i
$358$	8.30083	+	11.2689i	0.438713	+	0.595582i
$359$	8.65793	−	26.6464i	0.456948	−	1.40634i	−0.411885	−	0.911236i	$-0.635129\pi$
$359$	8.65793	−	26.6464i	0.456948	−	1.40634i	0.868833	−	0.495105i	$-0.164871\pi$
$360$	3.79949	−	5.45201i	0.200251	−	0.287346i
$361$	−9.04021	+	6.56810i	−0.475800	+	0.345689i
$362$	−15.7431	−	5.00134i	−0.827441	−	0.262864i
$363$		0			0
$364$	0.341167	−	0.482769i	0.0178820	−	0.0253040i
$365$	−0.774087	−	1.06544i	−0.0405176	−	0.0557676i
$366$	−6.28723	+	0.0412395i	−0.328639	+	0.00215562i
$367$	−8.91183	+	27.4278i	−0.465194	+	1.43172i	0.393545	+	0.919305i	$0.371248\pi$
$367$	−8.91183	+	27.4278i	−0.465194	+	1.43172i	−0.858739	+	0.512413i	$0.828752\pi$
$368$	5.04471	−	17.0342i	0.262974	−	0.887968i
$369$	−11.5786	−	8.41234i	−0.602758	−	0.437929i
$370$	−1.33660	−	0.957767i	−0.0694866	−	0.0497919i
$371$	−20.5034	+	6.66195i	−1.06448	+	0.345871i
$372$	−0.317372	−	24.1917i	−0.0164550	−	1.25428i
$373$		−	1.34080i		−	0.0694239i	−0.999397	−	0.0347119i	$-0.988949\pi$
$373$		−	1.34080i		−	0.0694239i	0.999397	−	0.0347119i	$-0.0110514\pi$
$374$		0			0
$375$	−16.1716			−0.835096
$376$	5.16825	−	17.0401i	0.266532	−	0.878774i
$377$	−0.414628	−	1.27609i	−0.0213544	−	0.0657222i
$378$	8.53149	−	11.9060i	0.438813	−	0.612381i
$379$	−5.12693	+	7.05661i	−0.263353	+	0.362474i	−0.920132	−	0.391609i	$-0.871918\pi$
$379$	−5.12693	+	7.05661i	−0.263353	+	0.362474i	0.656779	+	0.754083i	$0.271918\pi$
$380$	−3.47338	−	10.2313i	−0.178180	−	0.524854i
$381$	−1.43158	−	0.465149i	−0.0733421	−	0.0238303i
$382$	17.0977	−	0.112148i	0.874795	−	0.00573799i
$383$	−6.28019	+	4.56283i	−0.320903	+	0.233150i	−0.736561	−	0.676371i	$-0.763551\pi$
$383$	−6.28019	+	4.56283i	−0.320903	+	0.233150i	0.415658	+	0.909521i	$0.363551\pi$
$384$	8.31034	−	12.6180i	0.424085	−	0.643909i
$385$		0			0
$386$	5.67860	−	17.8750i	0.289033	−	0.909815i
$387$	−3.20318	−	4.40880i	−0.162827	−	0.224112i
$388$	−3.18948	+	10.2728i	−0.161921	+	0.521524i
$389$	−36.7049	−	11.9261i	−1.86101	−	0.604679i	−0.994398	−	0.105699i	$-0.966292\pi$
$389$	−36.7049	−	11.9261i	−1.86101	−	0.604679i	−0.866613	−	0.498980i	$-0.833708\pi$
$390$	0.347611	+	0.471906i	0.0176020	+	0.0238959i
$391$	19.4548	+	14.1347i	0.983871	+	0.714824i
$392$	−3.35218	−	9.66556i	−0.169311	−	0.488184i
$393$	4.52101	+	13.9142i	0.228055	+	0.701880i
$394$	15.6804	−	5.20884i	0.789970	−	0.262418i
$395$		−	11.1597i		−	0.561506i
$396$		0			0
$397$			20.4200i			1.02485i	0.858732	+	0.512426i	$0.171253\pi$
$397$			20.4200i			1.02485i	−0.858732	+	0.512426i	$0.828747\pi$
$398$	−11.1158	−	33.4625i	−0.557186	−	1.67733i
$399$	−2.12335	−	6.53499i	−0.106300	−	0.327159i
$400$	5.08026	−	0.133319i	0.254013	−	0.00666596i
$401$	−4.01473	−	2.91687i	−0.200486	−	0.145662i	0.483013	−	0.875613i	$-0.339542\pi$
$401$	−4.01473	−	2.91687i	−0.200486	−	0.145662i	−0.683499	+	0.729952i	$0.739542\pi$
$402$	−8.77176	+	6.46138i	−0.437495	+	0.322264i
$403$	−1.38443	−	0.449830i	−0.0689635	−	0.0224076i
$404$	−17.7992	−	5.52625i	−0.885544	−	0.274941i
$405$	4.39305	+	6.04651i	0.218292	+	0.300454i
$406$	20.6990	+	6.57572i	1.02727	+	0.326347i
$407$		0			0
$408$	12.3442	+	16.3057i	0.611130	+	0.807255i
$409$	12.4117	−	9.01766i	0.613721	−	0.445895i	−0.237001	−	0.971509i	$-0.576165\pi$
$409$	12.4117	−	9.01766i	0.613721	−	0.445895i	0.850723	+	0.525615i	$0.176165\pi$
$410$	0.210734	+	32.1279i	0.0104074	+	1.58668i
$411$	−12.9235	−	4.19910i	−0.637469	−	0.207126i
$412$	1.07923	+	3.17900i	0.0531697	+	0.156618i
$413$	−10.4122	+	14.3312i	−0.512352	+	0.705192i
$414$	−6.21144	−	4.45092i	−0.305275	−	0.218751i
$415$	1.74496	+	5.37043i	0.0856567	+	0.263624i
$416$	−0.558159	−	0.717527i	−0.0273660	−	0.0351797i
$417$	24.4849			1.19903
$418$		0			0
$419$			12.0628i			0.589306i	0.955604	+	0.294653i	$0.0952041\pi$
$419$			12.0628i			0.589306i	−0.955604	+	0.294653i	$0.904796\pi$
$420$	−9.48626	+	0.124451i	−0.462882	+	0.00607257i
$421$	−13.6041	+	4.42024i	−0.663023	+	0.215429i	−0.621148	−	0.783694i	$-0.713333\pi$
$421$	−13.6041	+	4.42024i	−0.663023	+	0.215429i	−0.0418753	+	0.999123i	$0.513333\pi$
$422$	−4.91146	+	6.85414i	−0.239086	+	0.333654i
$423$	−6.19641	−	4.50195i	−0.301280	−	0.218892i
$424$	0.652307	+	33.1457i	0.0316788	+	1.60970i
$425$	−2.12574	+	6.54235i	−0.103113	+	0.317351i
$426$	0.119281	+	18.1852i	0.00577920	+	0.881077i
$427$	−3.59915	−	4.95381i	−0.174175	−	0.239732i
$428$	−13.0162	+	18.4186i	−0.629161	+	0.890296i
$429$		0			0
$430$	−3.70401	+	11.6594i	−0.178623	+	0.562268i
$431$	−15.3325	+	11.1397i	−0.738540	+	0.536580i	−0.892253	−	0.451535i	$-0.850877\pi$
$431$	−15.3325	+	11.1397i	−0.738540	+	0.536580i	0.153714	+	0.988115i	$0.450877\pi$
$432$	−13.7128	−	17.8688i	−0.659757	−	0.859711i
$433$	−5.07190	+	15.6097i	−0.243740	+	0.750155i	0.752101	+	0.659048i	$0.229041\pi$
$433$	−5.07190	+	15.6097i	−0.243740	+	0.750155i	−0.995841	+	0.0911071i	$0.970959\pi$
$434$	18.9710	−	13.9743i	0.910637	−	0.670786i
$435$	−12.6569	+	17.4208i	−0.606853	+	0.835261i
$436$	−23.4999	−	31.4683i	−1.12544	−	1.50706i
$437$	−11.8164	+	3.83938i	−0.565255	+	0.183662i
$438$	−1.22224	+	0.406012i	−0.0584008	+	0.0194000i
$439$	24.5482			1.17162			0.585810	−	0.810448i	$-0.300776\pi$
$439$	24.5482			1.17162			0.585810	+	0.810448i	$0.300776\pi$
$440$		0			0
$441$	−4.40040			−0.209543
$442$	1.16776	−	0.387915i	0.0555447	−	0.0184512i
$443$	10.5262	−	3.42018i	0.500117	−	0.162498i	−0.0480860	−	0.998843i	$-0.515312\pi$
$443$	10.5262	−	3.42018i	0.500117	−	0.162498i	0.548203	+	0.836345i	$0.315312\pi$
$444$	−1.28844	+	0.962181i	−0.0611467	+	0.0456631i
$445$	6.51805	−	8.97133i	0.308985	−	0.425282i
$446$	−1.18193	+	0.870621i	−0.0559658	+	0.0412251i
$447$	−3.49490	+	10.7562i	−0.165303	+	0.508751i
$448$	14.7030	−	0.578934i	0.694652	−	0.0273520i
$449$	−21.5722	+	15.6731i	−1.01805	+	0.739660i	−0.965883	−	0.258978i	$-0.916614\pi$
$449$	−21.5722	+	15.6731i	−1.01805	+	0.739660i	−0.0521715	+	0.998638i	$0.516614\pi$
$450$	0.661841	−	2.08333i	0.0311995	−	0.0982093i
$451$		0			0
$452$	21.0952	+	14.9077i	0.992234	+	0.701200i
$453$	−7.90489	−	10.8801i	−0.371404	−	0.511194i
$454$	−0.0617419	−	9.41297i	−0.00289769	−	0.441772i
$455$	−0.176391	+	0.542876i	−0.00826934	+	0.0254504i
$456$	−10.5644	+	0.207908i	−0.494726	+	0.00973619i
$457$	2.65597	+	1.92967i	0.124241	+	0.0902663i	0.648170	−	0.761495i	$-0.275534\pi$
$457$	2.65597	+	1.92967i	0.124241	+	0.0902663i	−0.523929	+	0.851762i	$0.675534\pi$
$458$	13.4997	−	18.8394i	0.630800	−	0.880307i
$459$	28.9965	−	9.42152i	1.35344	−	0.439759i
$460$	0.225028	+	17.1528i	0.0104920	+	0.799753i
$461$		−	3.17514i		−	0.147881i	−0.997263	−	0.0739406i	$-0.976442\pi$
$461$		−	3.17514i		−	0.147881i	0.997263	−	0.0739406i	$-0.0235575\pi$
$462$		0			0
$463$	21.8696			1.01637			0.508184	−	0.861248i	$-0.330317\pi$
$463$	21.8696			1.01637			0.508184	+	0.861248i	$0.330317\pi$
$464$	18.9152	−	27.5252i	0.878118	−	1.27782i
$465$	7.21907	+	22.2180i	0.334776	+	1.03034i
$466$	−18.4782	−	13.2409i	−0.855984	−	0.613371i
$467$	2.91385	−	4.01058i	0.134837	−	0.185587i	−0.736259	−	0.676700i	$-0.763410\pi$
$467$	2.91385	−	4.01058i	0.134837	−	0.185587i	0.871096	+	0.491112i	$0.163410\pi$
$468$	−0.370260	+	0.125698i	−0.0171153	+	0.00581040i
$469$	−10.0909	−	3.27875i	−0.465957	−	0.151398i
$470$	0.112777	+	17.1936i	0.00520200	+	0.793081i
$471$	−9.44231	+	6.86024i	−0.435079	+	0.316103i
$472$	16.4422	+	21.7188i	0.756812	+	0.999690i
$473$		0			0
$474$	−10.4013	−	3.30433i	−0.477749	−	0.151773i
$475$	−2.08908	−	2.87538i	−0.0958537	−	0.131931i
$476$	−5.90582	+	19.0218i	−0.270693	+	0.871861i
$477$	13.5619	+	4.40652i	0.620956	+	0.201761i
$478$	−2.87009	+	2.11414i	−0.131275	+	0.0966987i
$479$	−28.7543	−	20.8912i	−1.31382	−	0.954544i	−0.999987	−	0.00506526i	$-0.998388\pi$
$479$	−28.7543	−	20.8912i	−1.31382	−	0.954544i	−0.313830	−	0.949479i	$-0.601612\pi$
$480$	−4.05086	+	14.0153i	−0.184896	+	0.639708i
$481$	0.0298984	+	0.0920178i	0.00136325	+	0.00419565i
$482$	−2.72481	−	8.20265i	−0.124112	−	0.373620i
$483$			10.9092i			0.496387i
$484$		0			0
$485$		−	10.3865i		−	0.471627i
$486$	−15.7358	+	5.22723i	−0.713791	+	0.237112i
$487$	3.13797	+	9.65768i	0.142195	+	0.437631i	0.996640	−	0.0819113i	$-0.0261024\pi$
$487$	3.13797	+	9.65768i	0.142195	+	0.437631i	−0.854445	+	0.519542i	$0.826102\pi$
$488$	−8.89632	+	3.08540i	−0.402718	+	0.139669i
$489$	−26.3873	−	19.1715i	−1.19327	−	0.866964i
$490$	5.85866	+	7.95352i	0.264667	+	0.359304i
$491$	−0.349574	−	0.113583i	−0.0157760	−	0.00512595i	0.301118	−	0.953587i	$-0.402640\pi$
$491$	−0.349574	−	0.113583i	−0.0157760	−	0.00512595i	−0.316894	+	0.948461i	$0.602640\pi$
$492$	30.0070	+	9.31648i	1.35282	+	0.420020i
$493$	26.5724	+	36.5737i	1.19676	+	1.64720i
$494$	−0.192490	+	0.605919i	−0.00866055	+	0.0272616i
$495$		0			0
$496$	−12.0969	−	34.1544i	−0.543166	−	1.53358i
$497$	−14.3284	+	10.4102i	−0.642718	+	0.466962i
$498$	5.52215	−	0.0362211i	0.247454	−	0.00162311i
$499$	29.6562	+	9.63588i	1.32759	+	0.431361i	0.885096	−	0.465409i	$-0.154093\pi$
$499$	29.6562	+	9.63588i	1.32759	+	0.431361i	0.442497	+	0.896770i	$0.354093\pi$
$500$	−22.9335	+	7.78562i	−1.02562	+	0.348183i
$501$	5.78105	−	7.95694i	0.258278	−	0.355490i
$502$	0.403126	−	0.562578i	0.0179924	−	0.0251091i
$503$	−6.24227	−	19.2117i	−0.278329	−	0.856609i	−0.988319	−	0.152397i	$-0.951301\pi$
$503$	−6.24227	−	19.2117i	−0.278329	−	0.856609i	0.709990	−	0.704212i	$-0.248699\pi$
$504$	1.83699	−	6.05668i	0.0818262	−	0.269786i
$505$	17.9962			0.800818
$506$		0			0
$507$			17.3262i			0.769486i
$508$	−2.25412	+	0.0295719i	−0.100011	+	0.00131204i
$509$	−20.9431	+	6.80482i	−0.928286	+	0.301618i	−0.733862	−	0.679299i	$-0.762284\pi$
$509$	−20.9431	+	6.80482i	−0.928286	+	0.301618i	−0.194425	+	0.980917i	$0.562284\pi$
$510$	−16.0520	−	11.5024i	−0.710796	−	0.509334i
$511$	−1.01474	−	0.737254i	−0.0448896	−	0.0326142i
$512$	5.71044	−	21.8950i	0.252368	−	0.967631i
$513$	−4.86777	+	14.9815i	−0.214917	+	0.661448i
$514$	14.2672	−	0.0935816i	0.629297	−	0.00412771i
$515$	−1.90542	−	2.62259i	−0.0839629	−	0.115565i
$516$	9.77036	+	6.90459i	0.430116	+	0.303958i
$517$		0			0
$518$	−1.49258	−	0.474168i	−0.0655802	−	0.0208338i
$519$	1.49421	−	1.08561i	0.0655886	−	0.0476529i
$520$	0.720155	+	0.501875i	0.0315809	+	0.0220087i
$521$	11.1592	−	34.3445i	0.488894	−	1.50466i	−0.337367	−	0.941373i	$-0.609536\pi$
$521$	11.1592	−	34.3445i	0.488894	−	1.50466i	0.826261	−	0.563287i	$-0.190464\pi$
$522$	−8.51989	−	11.5663i	−0.372905	−	0.506244i
$523$	−20.3014	+	27.9425i	−0.887719	+	1.22184i	0.0865036	+	0.996252i	$0.472431\pi$
$523$	−20.3014	+	27.9425i	−0.887719	+	1.22184i	−0.974223	+	0.225589i	$0.927569\pi$
$524$	13.1103	+	17.5557i	0.572725	+	0.766926i
$525$	−2.96797	+	0.964351i	−0.129533	+	0.0420877i
$526$	−1.77648	−	5.34782i	−0.0774580	−	0.233176i
$527$	49.0457			2.13646
$528$		0			0
$529$	−3.27421			−0.142357
$530$	−10.0916	−	30.3793i	−0.438351	−	1.31959i
$531$	11.1436	−	3.62077i	0.483591	−	0.157128i
$532$	−6.15740	−	8.24527i	−0.266957	−	0.357478i
$533$	1.11119	−	1.52942i	0.0481308	−	0.0662464i
$534$	−6.43171	−	8.73147i	−0.278327	−	0.377848i
$535$	6.72966	−	20.7118i	0.290949	−	0.895448i
$536$	−9.32882	+	13.3862i	−0.402944	+	0.578196i
$537$	−10.6924	+	7.76851i	−0.461412	+	0.335236i
$538$	−3.64008	−	1.15639i	−0.156935	−	0.0498557i
$539$		0			0
$540$	17.7616	+	12.5519i	0.764338	+	0.540148i
$541$	−3.61210	−	4.97162i	−0.155296	−	0.213747i	0.724279	−	0.689507i	$-0.242173\pi$
$541$	−3.61210	−	4.97162i	−0.155296	−	0.213747i	−0.879575	+	0.475761i	$0.842173\pi$
$542$	−31.6227	+	0.207421i	−1.35831	+	0.00890949i
$543$	4.82017	−	14.8349i	0.206853	−	0.636628i
$544$	25.3560	+	17.1808i	1.08713	+	0.736623i
$545$	30.6807	+	22.2908i	1.31422	+	0.954835i
$546$	0.453755	+	0.325147i	0.0194189	+	0.0139150i
$547$	−16.4848	+	5.35622i	−0.704837	+	0.229016i	−0.639437	−	0.768844i	$-0.720832\pi$
$547$	−16.4848	+	5.35622i	−0.704837	+	0.229016i	−0.0654005	+	0.997859i	$0.520832\pi$
$548$	−20.3489	+	0.266958i	−0.869263	+	0.0114039i
$549$			4.05020i			0.172858i
$550$		0			0
$551$	−23.3572			−0.995050
$552$	16.0538	+	4.86912i	0.683294	+	0.207243i
$553$	−3.28445	−	10.1085i	−0.139669	−	0.429857i
$554$	−25.9365	+	36.1954i	−1.10193	+	1.53779i
$555$	0.912678	−	1.25619i	0.0387410	−	0.0533224i
$556$	34.7231	−	11.7880i	1.47259	−	0.499922i
$557$	−36.2951	−	11.7930i	−1.53787	−	0.499686i	−0.587085	−	0.809525i	$-0.699725\pi$
$557$	−36.2951	−	11.7930i	−1.53787	−	0.499686i	−0.950789	+	0.309840i	$0.899725\pi$
$558$	−15.5848	+	0.102224i	−0.659758	+	0.00432751i
$559$	0.582358	−	0.423108i	0.0246311	−	0.0178956i
$560$	−13.3929	+	4.74354i	−0.565954	+	0.200451i
$561$		0			0
$562$	4.09806	−	12.8998i	0.172866	−	0.544147i
$563$	19.5222	+	26.8699i	0.822761	+	1.13243i	0.989228	+	0.146386i	$0.0467642\pi$
$563$	19.5222	+	26.8699i	0.822761	+	1.13243i	−0.166467	+	0.986047i	$0.553236\pi$
$564$	16.0586	+	4.98581i	0.676187	+	0.209941i
$565$	−23.7216	−	7.70763i	−0.997977	−	0.324262i
$566$	−13.7551	−	18.6734i	−0.578169	−	0.784903i
$567$	5.75880	+	4.18402i	0.241847	+	0.175712i
$568$	8.92423	+	25.7318i	0.374452	+	1.07968i
$569$	−2.54477	−	7.83199i	−0.106682	−	0.328334i	0.883439	−	0.468545i	$-0.155222\pi$
$569$	−2.54477	−	7.83199i	−0.106682	−	0.328334i	−0.990122	+	0.140211i	$0.955222\pi$
$570$	9.68270	−	3.21647i	0.405564	−	0.134723i
$571$			32.7618i			1.37104i	0.728055	+	0.685518i	$0.240424\pi$
$571$			32.7618i			1.37104i	−0.728055	+	0.685518i	$0.759576\pi$
$572$		0			0
$573$			16.1457i			0.674496i
$574$	9.64654	+	29.0395i	0.402639	+	1.21209i
$575$	1.74371	+	5.36660i	0.0727179	+	0.223803i
$576$	−8.09297	−	5.40655i	−0.337207	−	0.225273i
$577$	5.26520	+	3.82539i	0.219193	+	0.159253i	0.691963	−	0.721933i	$-0.256746\pi$
$577$	5.26520	+	3.82539i	0.219193	+	0.159253i	−0.472770	+	0.881186i	$0.656746\pi$
$578$	−14.0235	+	10.3299i	−0.583300	+	0.429666i
$579$	16.8438	+	5.47290i	0.700006	+	0.227446i
$580$	−9.56226	+	30.7986i	−0.397051	+	1.27884i
$581$	3.16118	+	4.35099i	0.131148	+	0.180510i
$582$	−9.68067	−	3.07539i	−0.401277	−	0.127479i
$583$		0			0
$584$	−1.53784	+	1.16421i	−0.0636361	+	0.0481755i
$585$	0.305454	−	0.221926i	0.0126290	−	0.00917549i
$586$	0.0928404	+	14.1541i	0.00383520	+	0.584702i
$587$	−9.46611	−	3.07572i	−0.390708	−	0.126949i	0.107074	−	0.994251i	$-0.465852\pi$
$587$	−9.46611	−	3.07572i	−0.390708	−	0.126949i	−0.497782	+	0.867302i	$0.665852\pi$
$588$	9.14775	−	3.10553i	0.377247	−	0.128070i
$589$	−14.8946	+	20.5007i	−0.613721	+	0.844715i
$590$	−21.3809	−	15.3209i	−0.880236	−	0.630750i
$591$	4.82148	+	14.8390i	0.198329	+	0.610394i
$592$	−1.36396	+	1.98481i	−0.0560583	+	0.0815753i
$593$	−8.80877			−0.361733			−0.180867	−	0.983508i	$-0.557890\pi$
$593$	−8.80877			−0.361733			−0.180867	+	0.983508i	$0.557890\pi$
$594$		0			0
$595$		−	19.2322i		−	0.788444i
$596$	0.222189	+	16.9364i	0.00910122	+	0.693741i
$597$	31.6668	−	10.2892i	1.29604	−	0.421108i
$598$	0.587922	−	0.820468i	0.0240419	−	0.0335514i
$599$	−25.8194	−	18.7589i	−1.05495	−	0.766467i	−0.0818036	−	0.996648i	$-0.526068\pi$
$599$	−25.8194	−	18.7589i	−1.05495	−	0.766467i	−0.973148	+	0.230181i	$0.926068\pi$
$600$	0.0944247	+	4.79801i	0.00385487	+	0.195878i
$601$	−3.40890	+	10.4915i	−0.139052	+	0.427957i	−0.996198	−	0.0871154i	$-0.972235\pi$
$601$	−3.40890	+	10.4915i	−0.139052	+	0.427957i	0.857146	+	0.515073i	$0.172235\pi$
$602$	0.0764236	+	11.6513i	0.00311479	+	0.474871i
$603$	4.12514	+	5.67777i	0.167989	+	0.231217i
$604$	−16.4484	−	11.6239i	−0.669274	−	0.472968i
$605$		0			0
$606$	5.32857	−	16.7732i	0.216458	−	0.681364i
$607$	9.88287	−	7.18032i	0.401133	−	0.291440i	−0.368869	−	0.929481i	$-0.620255\pi$
$607$	9.88287	−	7.18032i	0.401133	−	0.291440i	0.770002	+	0.638041i	$0.220255\pi$
$608$	−14.8818	+	5.38097i	−0.603536	+	0.218227i
$609$	−6.33752	+	19.5049i	−0.256809	+	0.790377i
$610$	7.32054	−	5.39240i	0.296400	−	0.218332i
$611$	0.594663	−	0.818483i	0.0240575	−	0.0331123i
$612$	10.5558	−	7.88283i	0.426692	−	0.318644i
$613$	3.39986	−	1.10468i	0.137319	−	0.0446176i	−0.239551	−	0.970884i	$-0.577000\pi$
$613$	3.39986	−	1.10468i	0.137319	−	0.0446176i	0.376870	+	0.926266i	$0.377000\pi$
$614$	25.2900	−	8.40102i	1.02062	−	0.339038i
$615$	−30.3390			−1.22339
$616$		0			0
$617$	30.5057			1.22811			0.614057	−	0.789262i	$-0.289537\pi$
$617$	30.5057			1.22811			0.614057	+	0.789262i	$0.289537\pi$
$618$	−3.00855	+	0.999401i	−0.121022	+	0.0402018i
$619$	−10.0925	+	3.27924i	−0.405650	+	0.131804i	−0.504733	−	0.863275i	$-0.668409\pi$
$619$	−10.0925	+	3.27924i	−0.405650	+	0.131804i	0.0990828	+	0.995079i	$0.468409\pi$
$620$	20.9343	+	28.0327i	0.840740	+	1.12582i
$621$	14.7002	−	20.2331i	0.589898	−	0.811925i
$622$	1.81798	−	1.33914i	0.0728942	−	0.0536948i
$623$	3.26369	−	10.0446i	0.130757	−	0.402429i
$624$	0.681003	−	0.522613i	0.0272619	−	0.0209213i
$625$	13.7802	−	10.0119i	0.551209	−	0.400477i
$626$	1.68763	−	5.31230i	0.0674513	−	0.212322i
$627$		0			0
$628$	−10.0877	+	14.2747i	−0.402545	+	0.569622i
$629$	−1.91611	−	2.63729i	−0.0764001	−	0.105156i
$630$	0.0400852	+	6.11125i	0.00159703	+	0.243478i
$631$	1.32641	−	4.08227i	0.0528035	−	0.162513i	−0.921177	−	0.389143i	$-0.872771\pi$
$631$	1.32641	−	4.08227i	0.0528035	−	0.162513i	0.973981	+	0.226631i	$0.0727711\pi$
$632$	−16.3414	+	0.321598i	−0.650025	+	0.0127925i
$633$	−6.44180	−	4.68024i	−0.256038	−	0.186023i
$634$	−1.60120	+	2.23454i	−0.0635918	+	0.0887448i
$635$	2.07022	−	0.672655i	0.0821541	−	0.0266935i
$636$	−31.3029	+	0.410663i	−1.24124	+	0.0162839i
$637$		−	0.581249i		−	0.0230299i
$638$		0			0
$639$	11.7148			0.463431
$640$	1.00282	+	21.8259i	0.0396399	+	0.862745i
$641$	−8.20767	−	25.2606i	−0.324184	−	0.997735i	−0.971808	−	0.235775i	$-0.924237\pi$
$641$	−8.20767	−	25.2606i	−0.324184	−	0.997735i	0.647624	−	0.761960i	$-0.275763\pi$
$642$	−17.3117	−	12.4050i	−0.683237	−	0.489586i
$643$	−16.4941	+	22.7022i	−0.650463	+	0.895286i	−0.999119	−	0.0419648i	$-0.986638\pi$
$643$	−16.4941	+	22.7022i	−0.650463	+	0.895286i	0.348656	+	0.937251i	$0.386638\pi$
$644$	5.25213	+	15.4708i	0.206963	+	0.609636i
$645$	−10.9868	−	3.56983i	−0.432606	−	0.140562i
$646$	−0.140499	−	21.4200i	−0.00552785	−	0.842757i
$647$	26.1298	−	18.9844i	1.02727	−	0.746356i	0.0595098	−	0.998228i	$-0.481046\pi$
$647$	26.1298	−	18.9844i	1.02727	−	0.746356i	0.967761	+	0.251872i	$0.0810463\pi$
$648$	8.72742	−	6.60707i	0.342846	−	0.259550i
$649$		0			0
$650$	0.275188	+	0.0874225i	0.0107937	+	0.00342899i
$651$	13.0781	+	18.0005i	0.512571	+	0.705494i
$652$	−46.6507	−	14.4840i	−1.82698	−	0.567236i
$653$	31.3088	+	10.1728i	1.22521	+	0.398094i	0.848976	−	0.528431i	$-0.177220\pi$
$653$	31.3088	+	10.1728i	1.22521	+	0.398094i	0.376232	+	0.926526i	$0.377220\pi$
$654$	29.8604	−	21.9956i	1.16764	−	0.860094i
$655$	−17.1163	−	12.4358i	−0.668791	−	0.485905i
$656$	47.0394	−	1.23444i	1.83658	−	0.0481966i
$657$	0.256375	+	0.789040i	0.0100021	+	0.0307834i
$658$	5.16245	+	15.5408i	0.201253	+	0.605843i
$659$			3.99602i			0.155663i	0.996967	+	0.0778314i	$0.0247996\pi$
$659$			3.99602i			0.155663i	−0.996967	+	0.0778314i	$0.975200\pi$
$660$		0			0
$661$		−	19.2377i		−	0.748258i	−0.927377	−	0.374129i	$-0.877942\pi$
$661$		−	19.2377i		−	0.748258i	0.927377	−	0.374129i	$-0.122058\pi$
$662$	10.0946	−	3.35329i	0.392337	−	0.130329i
$663$	0.359067	+	1.10509i	0.0139450	+	0.0429183i
$664$	7.81375	−	2.70994i	0.303232	−	0.105166i
$665$	8.03890	+	5.84060i	0.311735	+	0.226489i
$666$	0.614361	+	0.834035i	0.0238060	+	0.0323182i
$667$	35.2682	+	11.4593i	1.36559	+	0.443707i
$668$	4.36757	−	14.0673i	0.168986	−	0.544279i
$669$	−0.814789	−	1.12146i	−0.0315016	−	0.0433582i
$670$	4.77012	−	15.0153i	0.184286	−	0.580093i
$671$		0			0
$672$	0.455608	+	13.8873i	0.0175755	+	0.535715i
$673$	4.37842	−	3.18111i	0.168776	−	0.122623i	−0.500191	−	0.865915i	$-0.666737\pi$
$673$	4.37842	−	3.18111i	0.168776	−	0.122623i	0.668967	+	0.743292i	$0.266737\pi$
$674$	11.9814	−	0.0785891i	0.461507	−	0.00302714i
$675$	6.80407	+	2.21078i	0.261889	+	0.0850928i
$676$	8.34152	+	24.5710i	0.320828	+	0.945040i
$677$	24.1616	−	33.2556i	0.928607	−	1.27812i	−0.0317931	−	0.999494i	$-0.510122\pi$
$677$	24.1616	−	33.2556i	0.928607	−	1.27812i	0.960400	−	0.278624i	$-0.0898782\pi$
$678$	−14.2077	+	19.8274i	−0.545643	+	0.761467i
$679$	−3.05688	−	9.40812i	−0.117312	−	0.361051i
$680$	−28.3017	−	8.58391i	−1.08532	−	0.329178i
$681$	8.88885			0.340621
$682$		0			0
$683$			35.8592i			1.37211i	0.727548	+	0.686057i	$0.240660\pi$
$683$			35.8592i			1.37211i	−0.727548	+	0.686057i	$0.759340\pi$
$684$	0.0892900	+	6.80614i	0.00341409	+	0.260239i
$685$	18.6888	−	6.07234i	0.714061	−	0.232012i
$686$	22.4482	+	16.0857i	0.857076	+	0.614154i
$687$	17.7060	+	12.8642i	0.675527	+	0.490799i
$688$	17.1799	+	5.08785i	0.654977	+	0.193973i
$689$	−0.582057	+	1.79139i	−0.0221746	+	0.0682464i
$690$	−16.1984	+	0.106249i	−0.616663	+	0.00404484i
$691$	−26.5363	−	36.5240i	−1.00949	−	1.38944i	−0.919319	−	0.393513i	$-0.871260\pi$
$691$	−26.5363	−	36.5240i	−1.00949	−	1.38944i	−0.0901675	−	0.995927i	$-0.528740\pi$
$692$	1.59635	−	2.25891i	0.0606840	−	0.0858710i
$693$		0			0
$694$	23.2484	+	7.38564i	0.882498	+	0.280355i
$695$	−28.6455	+	20.8122i	−1.08659	+	0.789452i
$696$	25.8743	+	18.0317i	0.980762	+	0.683491i
$697$	−19.6827	+	60.5773i	−0.745537	+	2.29453i
$698$	3.92185	+	5.32417i	0.148444	+	0.201523i
$699$	12.6175	−	17.3665i	0.477238	−	0.656862i
$700$	−3.74472	+	2.79648i	−0.141537	+	0.105697i
$701$	−17.6770	+	5.74360i	−0.667651	+	0.216933i	−0.623181	−	0.782078i	$-0.714160\pi$
$701$	−17.6770	+	5.74360i	−0.667651	+	0.216933i	−0.0444699	+	0.999011i	$0.514160\pi$
$702$	−0.403433	−	1.21448i	−0.0152266	−	0.0458374i
$703$	1.68426			0.0635232
$704$		0			0
$705$	−16.2362			−0.611492
$706$	−2.43001	−	7.31519i	−0.0914547	−	0.275311i
$707$	16.3010	−	5.29650i	0.613061	−	0.199196i
$708$	−20.6105	+	15.3915i	−0.774589	+	0.578447i
$709$	16.0291	−	22.0621i	0.601985	−	0.828561i	−0.393903	−	0.919152i	$-0.628876\pi$
$709$	16.0291	−	22.0621i	0.601985	−	0.828561i	0.995888	+	0.0905907i	$0.0288755\pi$
$710$	−15.5970	−	21.1740i	−0.585345	−	0.794645i
$711$	−2.17249	+	6.68622i	−0.0814746	+	0.250753i
$712$	−13.3247	−	9.28598i	−0.499365	−	0.348007i
$713$	32.5480	−	23.6475i	1.21893	−	0.885605i
$714$	−17.9253	−	5.69456i	−0.670836	−	0.213114i
$715$		0			0
$716$	−11.4233	+	16.1646i	−0.426909	+	0.604099i
$717$	−1.97856	−	2.72326i	−0.0738909	−	0.101702i
$718$	39.6221	−	0.259891i	1.47868	−	0.00969903i
$719$	10.5622	−	32.5071i	0.393903	−	1.21231i	−0.535909	−	0.844276i	$-0.680031\pi$
$719$	10.5622	−	32.5071i	0.393903	−	1.21231i	0.929812	−	0.368034i	$-0.119969\pi$
$720$	9.01107	+	2.66864i	0.335823	+	0.0994545i
$721$	−2.49780	−	1.81476i	−0.0930228	−	0.0675850i
$722$	−12.8454	−	9.20463i	−0.478058	−	0.342561i
$723$	7.76247	−	2.52218i	0.288689	−	0.0938008i
$724$	−0.306443	−	23.3586i	−0.0113889	−	0.868117i
$725$			10.6080i			0.393973i
$726$		0			0
$727$	−25.0380			−0.928608			−0.464304	−	0.885676i	$-0.653696\pi$
$727$	−25.0380			−0.928608			−0.464304	+	0.885676i	$0.653696\pi$
$728$	0.800027	+	0.242648i	0.0296510	+	0.00899315i
$729$	−8.42628	−	25.9334i	−0.312085	−	0.960497i
$730$	1.08482	−	1.51391i	0.0401509	−	0.0560322i
$731$	−14.2556	+	19.6212i	−0.527263	+	0.725716i
$732$	−2.85838	−	8.41972i	−0.105649	−	0.311202i
$733$	16.4242	+	5.33655i	0.606643	+	0.197110i	0.596201	−	0.802835i	$-0.296676\pi$
$733$	16.4242	+	5.33655i	0.606643	+	0.197110i	0.0104418	+	0.999945i	$0.496676\pi$
$734$	−40.7840	+	0.267512i	−1.50537	+	0.00987405i
$735$	−7.54663	+	5.48295i	−0.278362	+	0.202242i
$736$	25.1107	−	0.823818i	0.925592	−	0.0303663i
$737$		0			0
$738$	6.12815	−	19.2901i	0.225580	−	0.710079i
$739$	−10.1503	−	13.9707i	−0.373385	−	0.513920i	0.580432	−	0.814309i	$-0.302884\pi$
$739$	−10.1503	−	13.9707i	−0.373385	−	0.513920i	−0.953817	+	0.300389i	$0.902884\pi$
$740$	0.689525	−	2.22086i	0.0253474	−	0.0816403i
$741$	−0.570964	−	0.185518i	−0.0209749	−	0.00681516i
$742$	−18.0820	−	24.5475i	−0.663811	−	0.901168i
$743$	28.0222	+	20.3593i	1.02804	+	0.746911i	0.967915	−	0.251280i	$-0.0808514\pi$
$743$	28.0222	+	20.3593i	1.02804	+	0.746911i	0.0601209	+	0.998191i	$0.480851\pi$
$744$	32.3262	−	11.2113i	1.18514	−	0.411026i
$745$	−5.05400	−	15.5546i	−0.185164	−	0.569877i
$746$	1.79949	−	0.597766i	0.0658839	−	0.0218858i
$747$		−	3.55734i		−	0.130156i
$748$		0			0
$749$		−	20.7414i		−	0.757875i
$750$	−7.20975	−	21.7039i	−0.263263	−	0.792514i
$751$	15.9306	+	49.0294i	0.581317	+	1.78911i	0.613583	+	0.789631i	$0.289728\pi$
$751$	15.9306	+	49.0294i	0.581317	+	1.78911i	−0.0322656	+	0.999479i	$0.510272\pi$
$752$	25.1736	−	0.660622i	0.917988	−	0.0240904i
$753$	0.528734	+	0.384148i	0.0192681	+	0.0139991i
$754$	1.52779	−	1.12539i	0.0556390	−	0.0409843i
$755$	18.4963	+	6.00980i	0.673148	+	0.218719i
$756$	19.7827	+	6.14208i	0.719490	+	0.223385i
$757$	19.1647	+	26.3779i	0.696551	+	0.958721i	0.999983	+	0.00586732i	$0.00186764\pi$
$757$	19.1647	+	26.3779i	0.696551	+	0.958721i	−0.303432	+	0.952853i	$0.598132\pi$
$758$	−11.7564	−	3.73482i	−0.427012	−	0.135655i
$759$		0			0
$760$	12.1829	−	9.22302i	0.441920	−	0.334554i
$761$	−2.25792	+	1.64048i	−0.0818496	+	0.0594672i	−0.627958	−	0.778248i	$-0.716109\pi$
$761$	−2.25792	+	1.64048i	−0.0818496	+	0.0594672i	0.546108	+	0.837715i	$0.316109\pi$
$762$	−0.0139627	−	2.12870i	−0.000505814	−	0.0771148i
$763$	34.3512	+	11.1614i	1.24360	+	0.404069i
$764$	7.77316	+	22.8969i	0.281223	+	0.828379i
$765$	−7.47726	+	10.2916i	−0.270341	+	0.372092i
$766$	−8.92367	−	6.39442i	−0.322425	−	0.231040i
$767$	0.478268	+	1.47196i	0.0172692	+	0.0531493i
$768$	20.6396	+	5.52786i	0.744768	+	0.199470i
$769$	−23.1604			−0.835187			−0.417593	−	0.908634i	$-0.637126\pi$
$769$	−23.1604			−0.835187			−0.417593	+	0.908634i	$0.637126\pi$
$770$		0			0
$771$			13.4728i			0.485209i
$772$	26.5218	−	0.347940i	0.954540	−	0.0125226i
$773$	−19.7737	+	6.42486i	−0.711210	+	0.231086i	−0.642208	−	0.766530i	$-0.721982\pi$
$773$	−19.7737	+	6.42486i	−0.711210	+	0.231086i	−0.0690021	+	0.997617i	$0.521982\pi$
$774$	4.48899	−	6.26456i	0.161353	−	0.225175i
$775$	9.31070	+	6.76462i	0.334450	+	0.242992i
$776$	−15.2092	+	0.299316i	−0.545977	+	0.0107448i
$777$	0.456992	−	1.40648i	0.0163945	−	0.0504571i
$778$	−0.357995	−	54.5787i	−0.0128347	−	1.95674i
$779$	−19.3433	−	26.6238i	−0.693047	−	0.953897i
$780$	−0.478370	+	0.676919i	−0.0171284	+	0.0242376i
$781$		0			0
$782$	−10.2968	+	32.4120i	−0.368211	+	1.15905i
$783$	38.0368	−	27.6354i	1.35932	−	0.987607i
$784$	11.4777	−	8.80815i	0.409917	−	0.314577i
$785$	5.21559	−	16.0519i	0.186152	−	0.572918i
$786$	−16.6587	+	12.2710i	−0.594197	+	0.437693i
$787$	23.7391	−	32.6741i	0.846208	−	1.16470i	−0.138478	−	0.990365i	$-0.544221\pi$
$787$	23.7391	−	32.6741i	0.846208	−	1.16470i	0.984686	−	0.174339i	$-0.0557789\pi$
$788$	13.9816	+	18.7225i	0.498073	+	0.666962i
$789$	5.06084	−	1.64437i	0.180171	−	0.0585410i
$790$	14.9775	−	4.97532i	0.532874	−	0.177014i
$791$	−23.7556			−0.844651
$792$		0			0
$793$	−0.534990			−0.0189981
$794$	−27.4057	+	9.10383i	−0.972593	+	0.323083i
$795$	28.7490	−	9.34112i	1.01962	−	0.331295i
$796$	39.9544	−	29.8371i	1.41615	−	1.05755i
$797$	18.2913	−	25.1758i	0.647910	−	0.891772i	−0.351096	−	0.936339i	$-0.614191\pi$
$797$	18.2913	−	25.1758i	0.647910	−	0.891772i	0.999006	+	0.0445674i	$0.0141909\pi$
$798$	7.82397	−	5.76323i	0.276966	−	0.204016i
$799$	−10.5334	+	32.4186i	−0.372646	+	1.14689i
$800$	2.44385	+	6.75879i	0.0864033	+	0.238959i
$801$	−5.65169	+	4.10620i	−0.199693	+	0.145085i
$802$	2.12486	−	6.68859i	0.0750313	−	0.236182i
$803$		0			0
$804$	−12.5825	−	8.89192i	−0.443752	−	0.313594i
$805$	−9.27286	−	12.7630i	−0.326825	−	0.449836i
$806$	−0.0135028	−	2.05860i	−0.000475617	−	0.0725110i
$807$	1.11450	−	3.43009i	0.0392324	−	0.120745i
$808$	−0.518609	−	26.3521i	−0.0182446	−	0.927064i
$809$	19.1132	+	13.8866i	0.671984	+	0.488225i	0.870689	−	0.491834i	$-0.163673\pi$
$809$	19.1132	+	13.8866i	0.671984	+	0.488225i	−0.198704	+	0.980059i	$0.563673\pi$
$810$	−6.15649	+	8.59162i	−0.216317	+	0.301879i
$811$	−25.0107	+	8.12648i	−0.878245	+	0.285359i	−0.713229	−	0.700932i	$-0.752768\pi$
$811$	−25.0107	+	8.12648i	−0.878245	+	0.285359i	−0.165017	+	0.986291i	$0.552768\pi$
$812$	0.402909	+	30.7118i	0.0141393	+	1.07777i
$813$		−	29.8619i		−	1.04730i
$814$		0			0
$815$	47.1669			1.65218
$816$	−16.3806	+	23.8368i	−0.573434	+	0.834453i
$817$	−3.87221	−	11.9174i	−0.135472	−	0.416939i
$818$	17.6361	+	12.6375i	0.616633	+	0.441860i
$819$	0.211366	−	0.290920i	0.00738572	−	0.0101656i
$820$	−43.0249	+	14.6064i	−1.50250	+	0.510076i
$821$	−52.9038	−	17.1895i	−1.84636	−	0.599917i	−0.997450	−	0.0713743i	$-0.977262\pi$
$821$	−52.9038	−	17.1895i	−1.84636	−	0.599917i	−0.848906	−	0.528543i	$-0.822738\pi$
$822$	−0.126047	−	19.2167i	−0.00439639	−	0.670260i
$823$	−22.7310	+	16.5150i	−0.792353	+	0.575678i	−0.908661	−	0.417535i	$-0.862894\pi$
$823$	−22.7310	+	16.5150i	−0.792353	+	0.575678i	0.116308	+	0.993213i	$0.462894\pi$
$824$	−3.78539	+	2.86572i	−0.131870	+	0.0998321i
$825$		0			0
$826$	−23.8760	−	7.58500i	−0.830752	−	0.263916i
$827$	22.6623	+	31.1920i	0.788047	+	1.08465i	0.994349	+	0.106165i	$0.0338571\pi$
$827$	22.6623	+	31.1920i	0.788047	+	1.08465i	−0.206302	+	0.978488i	$0.566143\pi$
$828$	3.20435	−	10.3207i	0.111359	−	0.358670i
$829$	−42.2822	−	13.7383i	−1.46852	−	0.477151i	−0.537860	−	0.843034i	$-0.680767\pi$
$829$	−42.2822	−	13.7383i	−1.46852	−	0.477151i	−0.930661	+	0.365883i	$0.880767\pi$
$830$	−6.42972	+	4.73621i	−0.223179	+	0.164396i
$831$	−34.0179	−	24.7154i	−1.18007	−	0.857369i
$832$	0.714151	−	1.06900i	0.0247587	−	0.0370609i
$833$	6.05174	+	18.6253i	0.209680	+	0.645329i
$834$	10.9161	+	32.8613i	0.377993	+	1.13789i
$835$			14.2229i			0.492204i
$836$		0			0
$837$		−	51.0077i		−	1.76308i
$838$	−16.1895	+	5.37794i	−0.559257	+	0.185778i
$839$	−12.2952	−	37.8407i	−0.424477	−	1.30641i	−0.903494	−	0.428600i	$-0.859007\pi$
$839$	−12.2952	−	37.8407i	−0.424477	−	1.30641i	0.479018	−	0.877805i	$-0.340993\pi$
$840$	−4.39627	−	12.6760i	−0.151686	−	0.437365i
$841$	32.9382	+	23.9310i	1.13580	+	0.825207i
$842$	−11.9975	−	16.2874i	−0.413461	−	0.561301i
$843$	12.1557	+	3.94962i	0.418663	+	0.136032i
$844$	−11.3886	−	3.53591i	−0.392012	−	0.121711i
$845$	−14.7273	−	20.2704i	−0.506635	−	0.697323i
$846$	3.27954	−	10.3233i	0.112753	−	0.354923i
$847$		0			0
$848$	−44.1941	+	15.6528i	−1.51763	+	0.537518i
$849$	17.7181	−	12.8730i	0.608084	−	0.441799i
$850$	−9.72822	+	0.0638097i	−0.333675	+	0.00218865i
$851$	−2.54315	−	0.826320i	−0.0871781	−	0.0283259i
$852$	−24.3533	+	8.26758i	−0.834329	+	0.283243i
$853$	−2.46590	+	3.39402i	−0.0844307	+	0.116209i	−0.849143	−	0.528163i	$-0.822881\pi$
$853$	−2.46590	+	3.39402i	−0.0844307	+	0.116209i	0.764712	+	0.644372i	$0.222881\pi$
$854$	5.04391	−	7.03898i	0.172599	−	0.240869i
$855$	−2.03103	−	6.25086i	−0.0694596	−	0.213775i
$856$	−30.5226	−	9.25751i	−1.04324	−	0.316415i
$857$	−43.4106			−1.48288			−0.741438	−	0.671021i	$-0.765856\pi$
$857$	−43.4106			−1.48288			−0.741438	+	0.671021i	$0.765856\pi$
$858$		0			0
$859$		−	31.7672i		−	1.08388i	−0.840416	−	0.541941i	$-0.817690\pi$
$859$		−	31.7672i		−	1.08388i	0.840416	−	0.541941i	$-0.182310\pi$
$860$	−17.2995	+	0.226953i	−0.589908	+	0.00773903i
$861$	−27.4811	+	8.92917i	−0.936555	+	0.304305i
$862$	−21.7863	−	15.6114i	−0.742043	−	0.531725i
$863$	41.3382	+	30.0340i	1.40717	+	1.02237i	0.993726	+	0.111839i	$0.0356740\pi$
$863$	41.3382	+	30.0340i	1.40717	+	1.02237i	0.413443	+	0.910530i	$0.364326\pi$
$864$	17.8681	−	26.3704i	0.607887	−	0.897138i
$865$	−0.825348	+	2.54016i	−0.0280627	+	0.0863680i
$866$	−23.2110	+	0.152247i	−0.788743	+	0.00517355i
$867$	−9.66743	−	13.3061i	−0.328323	−	0.451898i
$868$	27.2127	+	19.2309i	0.923659	+	0.652739i
$869$		0			0
$870$	−29.0232	−	9.22020i	−0.983980	−	0.312594i
$871$	−0.749976	+	0.544889i	−0.0254120	+	0.0184629i
$872$	31.7568	−	45.5687i	1.07542	−	1.54315i
$873$	−2.02196	+	6.22296i	−0.0684331	+	0.210615i
$874$	−10.4209	−	14.1471i	−0.352493	−	0.478532i
$875$	13.0918	−	18.0193i	0.442583	−	0.609163i
$876$	−1.08982	−	1.45936i	−0.0368215	−	0.0493071i
$877$	43.6451	−	14.1812i	1.47379	−	0.478863i	0.541539	−	0.840676i	$-0.317842\pi$
$877$	43.6451	−	14.1812i	1.47379	−	0.478863i	0.932251	+	0.361812i	$0.117842\pi$
$878$	10.9443	+	32.9461i	0.369351	+	1.11188i
$879$	−13.3660			−0.450825
$880$		0			0
$881$	−19.3333			−0.651356			−0.325678	−	0.945481i	$-0.605593\pi$
$881$	−19.3333			−0.651356			−0.325678	+	0.945481i	$0.605593\pi$
$882$	−1.96183	−	5.90579i	−0.0660581	−	0.198858i
$883$	−21.4808	+	6.97953i	−0.722886	+	0.234880i	−0.647274	−	0.762257i	$-0.724091\pi$
$883$	−21.4808	+	6.97953i	−0.722886	+	0.234880i	−0.0756122	+	0.997137i	$0.524091\pi$
$884$	1.04124	+	1.39431i	0.0350208	+	0.0468957i
$885$	14.5996	−	20.0946i	0.490760	−	0.675473i
$886$	9.28313	+	12.6025i	0.311873	+	0.423388i
$887$	10.5685	−	32.5266i	0.354856	−	1.09214i	−0.601236	−	0.799071i	$-0.705325\pi$
$887$	10.5685	−	32.5266i	0.354856	−	1.09214i	0.956093	−	0.293064i	$-0.0946750\pi$
$888$	−1.86577	−	1.30025i	−0.0626111	−	0.0436336i
$889$	1.67724	−	1.21859i	0.0562528	−	0.0408701i
$890$	14.9464	+	4.74821i	0.501003	+	0.159160i
$891$		0			0
$892$	−1.69540	−	1.19812i	−0.0567662	−	0.0401159i
$893$	−10.3518	−	14.2480i	−0.346409	−	0.476792i
$894$	−15.9941	+	0.104909i	−0.534921	+	0.00350867i
$895$	5.90611	−	18.1771i	0.197420	−	0.607595i
$896$	7.33201	+	19.4748i	0.244945	+	0.650608i
$897$	0.771110	+	0.560244i	0.0257466	+	0.0187060i
$898$	−30.6524	−	21.9646i	−1.02288	−	0.732967i
$899$	71.9308	−	23.3717i	2.39903	−	0.779491i
$900$	3.09111	−	0.0405525i	0.103037	−	0.00135175i
$901$		−	63.4627i		−	2.11425i
$902$		0			0
$903$	−11.0025			−0.366142
$904$	−10.6028	+	34.9582i	−0.352645	+	1.16269i
$905$	6.97048	+	21.4529i	0.231706	+	0.713119i
$906$	11.0780	−	15.4598i	0.368043	−	0.513619i
$907$	−10.1278	+	13.9398i	−0.336289	+	0.462862i	−0.943353	−	0.331791i	$-0.892347\pi$
$907$	−10.1278	+	13.9398i	−0.336289	+	0.462862i	0.607064	+	0.794653i	$0.292347\pi$
$908$	12.6056	−	4.27943i	0.418333	−	0.142018i
$909$	−10.7822	−	3.50335i	−0.357623	−	0.116199i
$910$	−0.807235	+	0.00529485i	−0.0267596	+	0.000175522i
$911$	22.7766	−	16.5481i	0.754621	−	0.548265i	−0.142634	−	0.989775i	$-0.545557\pi$
$911$	22.7766	−	16.5481i	0.754621	−	0.548265i	0.897256	+	0.441511i	$0.145557\pi$
$912$	−4.98897	−	14.0859i	−0.165201	−	0.466430i
$913$		0			0
$914$	−1.40571	+	4.42488i	−0.0464968	+	0.146362i
$915$	5.04659	+	6.94603i	0.166835	+	0.229629i
$916$	31.3029	+	9.71885i	1.03428	+	0.321120i
$917$	−19.1640	−	6.22677i	−0.632852	−	0.205626i
$918$	25.5721	+	34.7158i	0.844005	+	1.14579i
$919$	1.51662	+	1.10189i	0.0500285	+	0.0363479i	0.612518	−	0.790456i	$-0.290157\pi$
$919$	1.51662	+	1.10189i	0.0500285	+	0.0363479i	−0.562490	+	0.826804i	$0.690157\pi$
$920$	−22.9205	+	7.94922i	−0.755666	+	0.262078i
$921$	7.77627	+	23.9329i	0.256237	+	0.788615i
$922$	4.26137	−	1.41557i	0.140341	−	0.0466193i
$923$			1.54741i			0.0509336i
$924$		0			0
$925$		−	0.764935i		−	0.0251509i
$926$	9.75011	+	29.3513i	0.320408	+	0.964543i
$927$	0.631068	+	1.94223i	0.0207270	+	0.0637911i
$928$	45.3745	+	13.1147i	1.48949	+	0.430510i
$929$	−18.8141	−	13.6693i	−0.617271	−	0.448474i	0.234696	−	0.972069i	$-0.424591\pi$
$929$	−18.8141	−	13.6693i	−0.617271	−	0.448474i	−0.851967	+	0.523595i	$0.824591\pi$
$930$	−26.6004	+	19.5942i	−0.872260	+	0.642518i
$931$	−9.62306	−	3.12672i	−0.315383	−	0.102474i
$932$	9.53249	−	30.7027i	0.312247	−	1.00570i
$933$	1.25327	+	1.72497i	0.0410301	+	0.0564730i
$934$	6.68168	+	2.12266i	0.218631	+	0.0694555i
$935$		0			0
$936$	−0.333772	−	0.440887i	−0.0109097	−	0.0144109i
$937$	−9.00160	+	6.54004i	−0.294069	+	0.213654i	−0.725031	−	0.688716i	$-0.758174\pi$
$937$	−9.00160	+	6.54004i	−0.294069	+	0.213654i	0.430961	+	0.902370i	$0.358174\pi$
$938$	−0.0984203	−	15.0048i	−0.00321354	−	0.489925i
$939$	5.00584	+	1.62650i	0.163359	+	0.0530787i
$940$	−23.0253	+	7.81675i	−0.751001	+	0.254954i
$941$	13.8672	−	19.0866i	0.452058	−	0.622205i	−0.520780	−	0.853691i	$-0.674359\pi$
$941$	13.8672	−	19.0866i	0.452058	−	0.622205i	0.972838	+	0.231486i	$0.0743588\pi$
$942$	−13.4168	−	9.61405i	−0.437143	−	0.313243i
$943$	16.1455	+	49.6907i	0.525769	+	1.61815i
$944$	−21.8185	+	31.7499i	−0.710131	+	1.03337i
$945$	−20.0016			−0.650652
$946$		0			0
$947$			23.1038i			0.750772i	0.926869	+	0.375386i	$0.122490\pi$
$947$			23.1038i			0.750772i	−0.926869	+	0.375386i	$0.877510\pi$
$948$	−0.202464	−	15.4328i	−0.00657571	−	0.501234i
$949$	−0.104224	+	0.0338645i	−0.00338326	+	0.00109929i
$950$	2.92767	−	4.08569i	0.0949863	−	0.132557i
$951$	−2.10011	−	1.52582i	−0.0681007	−	0.0494781i
$952$	−28.1621	+	0.554230i	−0.912740	+	0.0179627i
$953$	−0.852775	+	2.62457i	−0.0276241	+	0.0850182i	−0.963918	−	0.266199i	$-0.914232\pi$
$953$	−0.852775	+	2.62457i	−0.0276241	+	0.0850182i	0.936294	+	0.351217i	$0.114232\pi$
$954$	0.132273	+	20.1660i	0.00428251	+	0.652897i
$955$	−13.7239	−	18.8893i	−0.444093	−	0.611242i
$956$	−4.11696	−	2.90941i	−0.133152	−	0.0940970i
$957$		0			0
$958$	15.2187	−	47.9051i	0.491692	−	1.54774i
$959$	15.1412	−	11.0007i	0.488933	−	0.355231i
$960$	−20.6160	+	0.811757i	−0.665377	+	0.0261993i
$961$	15.7765	−	48.5549i	0.508918	−	1.56629i
$962$	−0.110168	+	0.0811508i	−0.00355195	+	0.00261641i
$963$	−8.06402	+	11.0992i	−0.259859	+	0.357666i
$964$	9.79399	−	7.31395i	0.315443	−	0.235567i
$965$	−24.3580	+	7.91439i	−0.784112	+	0.254773i
$966$	−14.6413	+	4.86365i	−0.471076	+	0.156485i
$967$	−50.7176			−1.63097			−0.815484	−	0.578780i	$-0.803529\pi$
$967$	−50.7176			−1.63097			−0.815484	+	0.578780i	$0.803529\pi$
$968$		0			0
$969$	20.2273			0.649794
$970$	13.9397	−	4.63060i	0.447578	−	0.148680i
$971$	−36.9878	+	12.0181i	−1.18700	+	0.385679i	−0.834962	−	0.550308i	$-0.814510\pi$
$971$	−36.9878	+	12.0181i	−1.18700	+	0.385679i	−0.352035	+	0.935987i	$0.614510\pi$
$972$	−14.0310	−	18.7886i	−0.450043	−	0.602645i
$973$	−19.8219	+	27.2825i	−0.635461	+	0.874637i
$974$	−11.5626	+	8.51714i	−0.370489	+	0.272907i
$975$	−0.0842557	+	0.259312i	−0.00269834	+	0.00830464i
$976$	−8.10715	−	10.5642i	−0.259504	−	0.338152i
$977$	13.8493	−	10.0621i	0.443077	−	0.321914i	−0.343779	−	0.939050i	$-0.611707\pi$
$977$	13.8493	−	10.0621i	0.443077	−	0.321914i	0.786856	+	0.617136i	$0.211707\pi$
$978$	13.9659	−	43.9616i	0.446579	−	1.40574i
$979$		0			0
$980$	−8.06248	+	11.4088i	−0.257546	+	0.364442i
$981$	−14.0426	−	19.3280i	−0.448346	−	0.617096i
$982$	−0.00340951	−	0.519802i	−0.000108802	−	0.0165876i
$983$	−1.78805	+	5.50305i	−0.0570299	+	0.175520i	−0.975514	−	0.219939i	$-0.929414\pi$
$983$	−1.78805	+	5.50305i	−0.0570299	+	0.175520i	0.918484	+	0.395459i	$0.129414\pi$
$984$	0.874302	+	44.4260i	0.0278717	+	1.41625i
$985$	−18.2539	−	13.2622i	−0.581618	−	0.422570i
$986$	−37.2389	+	51.9684i	−1.18593	+	1.65501i
$987$	−14.7068	+	4.77854i	−0.468123	+	0.152103i
$988$	−0.899022	+	0.0117943i	−0.0286017	+	0.000375227i
$989$			19.8945i			0.632608i
$990$		0			0
$991$	−4.97362			−0.157992			−0.0789961	−	0.996875i	$-0.525171\pi$
$991$	−4.97362			−0.157992			−0.0789961	+	0.996875i	$0.525171\pi$
$992$	40.4456	−	31.4623i	1.28415	−	0.998928i
$993$	3.10392	+	9.55288i	0.0984999	+	0.303151i
$994$	−20.3596	−	14.5890i	−0.645767	−	0.462736i
$995$	−28.3020	+	38.9544i	−0.897234	+	1.23494i
$996$	2.51055	+	7.39514i	0.0795497	+	0.234324i
$997$	21.2468	+	6.90350i	0.672892	+	0.218636i	0.625481	−	0.780239i	$-0.284903\pi$
$997$	21.2468	+	6.90350i	0.672892	+	0.218636i	0.0474115	+	0.998875i	$0.484903\pi$
$998$	0.289246	+	44.0976i	0.00915593	+	1.39588i
$999$	−2.74279	+	1.99276i	−0.0867782	+	0.0630480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.h.245.6		40
8.5	even	2	inner	968.2.o.h.245.2		40
11.2	odd	10		88.2.c.a.45.4	yes	10
11.3	even	5	inner	968.2.o.h.269.10		40
11.4	even	5	inner	968.2.o.h.565.2		40
11.5	even	5	inner	968.2.o.h.493.3		40
11.6	odd	10		968.2.o.g.493.8		40
11.7	odd	10		968.2.o.g.565.9		40
11.8	odd	10		968.2.o.g.269.1		40
11.9	even	5		968.2.c.d.485.7		10
11.10	odd	2		968.2.o.g.245.5		40
33.2	even	10		792.2.f.g.397.7		10
44.31	odd	10		3872.2.c.f.1937.4		10
44.35	even	10		352.2.c.a.177.4		10
88.5	even	10	inner	968.2.o.h.493.10		40
88.13	odd	10		88.2.c.a.45.3	✓	10
88.21	odd	2		968.2.o.g.245.9		40
88.29	odd	10		968.2.o.g.565.5		40
88.35	even	10		352.2.c.a.177.7		10
88.37	even	10	inner	968.2.o.h.565.6		40
88.53	even	10		968.2.c.d.485.8		10
88.61	odd	10		968.2.o.g.493.1		40
88.69	even	10	inner	968.2.o.h.269.3		40
88.75	odd	10		3872.2.c.f.1937.7		10
88.85	odd	10		968.2.o.g.269.8		40
132.35	odd	10		3168.2.f.g.1585.3		10
176.13	odd	20		2816.2.a.r.1.2		5
176.35	even	20		2816.2.a.q.1.4		5
176.101	odd	20		2816.2.a.o.1.4		5
176.123	even	20		2816.2.a.p.1.2		5
264.35	odd	10		3168.2.f.g.1585.8		10
264.101	even	10		792.2.f.g.397.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.3	✓	10	88.13	odd	10
88.2.c.a.45.4	yes	10	11.2	odd	10
352.2.c.a.177.4		10	44.35	even	10
352.2.c.a.177.7		10	88.35	even	10
792.2.f.g.397.7		10	33.2	even	10
792.2.f.g.397.8		10	264.101	even	10
968.2.c.d.485.7		10	11.9	even	5
968.2.c.d.485.8		10	88.53	even	10
968.2.o.g.245.5		40	11.10	odd	2
968.2.o.g.245.9		40	88.21	odd	2
968.2.o.g.269.1		40	11.8	odd	10
968.2.o.g.269.8		40	88.85	odd	10
968.2.o.g.493.1		40	88.61	odd	10
968.2.o.g.493.8		40	11.6	odd	10
968.2.o.g.565.5		40	88.29	odd	10
968.2.o.g.565.9		40	11.7	odd	10
968.2.o.h.245.2		40	8.5	even	2	inner
968.2.o.h.245.6		40	1.1	even	1	trivial
968.2.o.h.269.3		40	88.69	even	10	inner
968.2.o.h.269.10		40	11.3	even	5	inner
968.2.o.h.493.3		40	11.5	even	5	inner
968.2.o.h.493.10		40	88.5	even	10	inner
968.2.o.h.565.2		40	11.4	even	5	inner
968.2.o.h.565.6		40	88.37	even	10	inner
2816.2.a.o.1.4		5	176.101	odd	20
2816.2.a.p.1.2		5	176.123	even	20
2816.2.a.q.1.4		5	176.35	even	20
2816.2.a.r.1.2		5	176.13	odd	20
3168.2.f.g.1585.3		10	132.35	odd	10
3168.2.f.g.1585.8		10	264.35	odd	10
3872.2.c.f.1937.4		10	44.31	odd	10
3872.2.c.f.1937.7		10	88.75	odd	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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.445829 + 1.34210i) q^{2} +(-1.27008 + 0.412674i) q^{3} +(-1.60247 + 1.19669i) q^{4} +(1.13513 - 1.56237i) q^{5} +(-1.12009 - 1.52059i) q^{6} +(0.568375 - 1.74928i) q^{7} +(-2.32051 - 1.61716i) q^{8} +(-0.984248 + 0.715098i) q^{9} +(2.60293 + 0.826906i) q^{10} +(1.54142 - 2.18120i) q^{12} +(-0.0944573 - 0.130009i) q^{13} +(2.60111 - 0.0170613i) q^{14} +(-0.796952 + 2.45277i) q^{15} +(1.13584 - 3.83534i) q^{16} +(4.38036 + 3.18252i) q^{17} +(-1.39854 - 1.00215i) q^{18} +(-2.66053 + 0.864457i) q^{19} +(0.0506664 + 3.86205i) q^{20} +2.45628i q^{21} +4.44137 q^{23} +(3.61460 + 1.09631i) q^{24} +(0.392607 + 1.20832i) q^{25} +(0.132374 - 0.184733i) q^{26} +(3.30983 - 4.55559i) q^{27} +(1.18255 + 3.48334i) q^{28} +(7.94083 + 2.58013i) q^{29} +(-3.64717 + 0.0239226i) q^{30} +(7.32836 - 5.32436i) q^{31} +(5.65381 - 0.185487i) q^{32} +(-2.31837 + 7.29774i) q^{34} +(-2.08784 - 2.87366i) q^{35} +(0.721478 - 2.32377i) q^{36} +(-0.572605 - 0.186051i) q^{37} +(-2.34633 - 3.18530i) q^{38} +(0.173620 + 0.126142i) q^{39} +(-5.16067 + 1.78981i) q^{40} +(3.63525 + 11.1881i) q^{41} +(-3.29657 + 1.09508i) q^{42} +4.47936i q^{43} +2.34948i q^{45} +(1.98009 + 5.96077i) q^{46} +(1.94544 + 5.98745i) q^{47} +(0.140134 + 5.33993i) q^{48} +(2.92620 + 2.12601i) q^{49} +(-1.44665 + 1.06562i) q^{50} +(-6.87675 - 2.23439i) q^{51} +(0.306947 + 0.0952999i) q^{52} +(-6.88946 - 9.48253i) q^{53} +(7.58968 + 2.41112i) q^{54} +(-4.14779 + 3.14007i) q^{56} +(3.02234 - 2.19586i) q^{57} +(0.0774495 + 11.8077i) q^{58} +(-9.15964 - 2.97615i) q^{59} +(-1.65812 - 4.88420i) q^{60} +(1.95681 - 2.69331i) q^{61} +(10.4130 + 7.46165i) q^{62} +(0.691483 + 2.12817i) q^{63} +(2.76957 + 7.50530i) q^{64} -0.310343 q^{65} -5.76864i q^{67} +(-10.8279 + 0.142052i) q^{68} +(-5.64090 + 1.83284i) q^{69} +(2.92593 - 4.08325i) q^{70} +(-7.79016 - 5.65988i) q^{71} +(3.44039 - 0.0677068i) q^{72} +(0.210731 - 0.648563i) q^{73} +(-0.00558480 - 0.851441i) q^{74} +(-0.997284 - 1.37264i) q^{75} +(3.22893 - 4.56911i) q^{76} +(-0.0918909 + 0.289253i) q^{78} +(4.67504 - 3.39662i) q^{79} +(-4.70288 - 6.12820i) q^{80} +(-1.19593 + 3.68068i) q^{81} +(-13.3949 + 9.86686i) q^{82} +(-1.71869 + 2.36557i) q^{83} +(-2.93941 - 3.93612i) q^{84} +(9.94451 - 3.23117i) q^{85} +(-6.01175 + 1.99703i) q^{86} -11.1502 q^{87} +5.74214 q^{89} +(-3.15324 + 1.04747i) q^{90} +(-0.281109 + 0.0913380i) q^{91} +(-7.11718 + 5.31497i) q^{92} +(-7.11037 + 9.78659i) q^{93} +(-7.16843 + 5.28035i) q^{94} +(-1.66943 + 5.13798i) q^{95} +(-7.10425 + 2.56876i) q^{96} +(4.35113 - 3.16128i) q^{97} +(-1.54873 + 4.87509i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{4} + 2 q^{6} + 10 q^{9} - 40 q^{10} - 16 q^{12} + 12 q^{14} - 8 q^{15} - 4 q^{17} - 10 q^{18} - 12 q^{20} - 48 q^{23} + 6 q^{25} + 20 q^{26} - 12 q^{28} + 18 q^{30} + 4 q^{31} + 80 q^{32} - 32 q^{36}+ \cdots - 96 q^{98}+O(q^{100}) \) 40 * q + 4 * q^4 + 2 * q^6 + 10 * q^9 - 40 * q^10 - 16 * q^12 + 12 * q^14 - 8 * q^15 - 4 * q^17 - 10 * q^18 - 12 * q^20 - 48 * q^23 + 6 * q^25 + 20 * q^26 - 12 * q^28 + 18 * q^30 + 4 * q^31 + 80 * q^32 - 32 * q^36 - 8 * q^38 + 24 * q^39 + 20 * q^40 + 4 * q^41 - 20 * q^42 + 2 * q^46 + 4 * q^47 - 32 * q^48 + 6 * q^49 - 6 * q^50 - 20 * q^52 + 152 * q^54 - 32 * q^56 + 16 * q^57 - 36 * q^58 + 4 * q^60 + 22 * q^62 - 40 * q^63 + 16 * q^64 - 64 * q^65 - 28 * q^68 - 28 * q^70 + 12 * q^71 - 4 * q^72 - 4 * q^73 - 14 * q^74 - 176 * q^76 - 32 * q^78 + 16 * q^79 + 56 * q^80 + 6 * q^81 + 4 * q^82 - 52 * q^84 + 20 * q^86 - 128 * q^87 - 16 * q^89 - 36 * q^90 + 36 * q^92 + 24 * q^95 + 60 * q^96 + 20 * q^97 - 96 * q^98

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