LMFDB - Embedded newform 968.2.o.c.565.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			565.6
Character	$\chi$	$=$	968.565
Dual form			968.2.o.c.245.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.876503 + 1.10984i) q^{2} +(-1.40150 - 0.455375i) q^{3} +(-0.463486 + 1.94555i) q^{4} +(2.09113 + 2.87820i) q^{5} +(-0.723026 - 1.95458i) q^{6} +(-1.18995 - 3.66230i) q^{7} +(-2.56550 + 1.19089i) q^{8} +(-0.670212 - 0.486937i) q^{9} +(-1.36145 + 4.84357i) q^{10} +(1.53553 - 2.51564i) q^{12} +(-2.80839 + 3.86541i) q^{13} +(3.02157 - 4.53067i) q^{14} +(-1.62007 - 4.98605i) q^{15} +(-3.57036 - 1.80347i) q^{16} +(-1.29042 + 0.937542i) q^{17} +(-0.0470202 - 1.17063i) q^{18} +(-3.94104 - 1.28052i) q^{19} +(-6.56890 + 2.73441i) q^{20} +5.67459i q^{21} -3.24264 q^{23} +(4.13785 - 0.500766i) q^{24} +(-2.36610 + 7.28210i) q^{25} +(-6.75154 + 0.271187i) q^{26} +(3.31609 + 4.56421i) q^{27} +(7.67673 - 0.617693i) q^{28} +(-7.02929 + 2.28396i) q^{29} +(4.11372 - 6.16830i) q^{30} +(2.90096 + 2.10767i) q^{31} +(-1.12786 - 5.54328i) q^{32} +(-2.17157 - 0.610396i) q^{34} +(8.05247 - 11.0833i) q^{35} +(1.25800 - 1.07824i) q^{36} +(-0.580521 + 0.188623i) q^{37} +(-2.03316 - 5.49631i) q^{38} +(5.69617 - 4.13851i) q^{39} +(-8.79241 - 4.89371i) q^{40} +(2.87280 - 8.84157i) q^{41} +(-6.29789 + 4.97380i) q^{42} -3.06147i q^{43} -2.94725i q^{45} +(-2.84218 - 3.59881i) q^{46} +(-1.49207 + 4.59211i) q^{47} +(4.18261 + 4.15343i) q^{48} +(-6.33333 + 4.60143i) q^{49} +(-10.1559 + 3.75679i) q^{50} +(2.23545 - 0.726342i) q^{51} +(-6.21872 - 7.25543i) q^{52} +(2.44991 - 3.37202i) q^{53} +(-2.15897 + 7.68087i) q^{54} +(7.41421 + 7.97852i) q^{56} +(4.94026 + 3.58931i) q^{57} +(-8.69602 - 5.79949i) q^{58} +(-5.36555 + 1.74337i) q^{59} +(10.4515 - 0.840960i) q^{60} +(1.27243 + 1.75135i) q^{61} +(0.203524 + 5.06698i) q^{62} +(-0.985790 + 3.03395i) q^{63} +(5.16357 - 6.11045i) q^{64} -16.9981 q^{65} -1.47363i q^{67} +(-1.22595 - 2.94511i) q^{68} +(4.54457 + 1.47662i) q^{69} +(19.3587 - 0.777573i) q^{70} +(-8.42528 + 6.12132i) q^{71} +(2.29932 + 0.451090i) q^{72} +(2.87280 + 8.84157i) q^{73} +(-0.718169 - 0.478957i) q^{74} +(6.63218 - 9.12841i) q^{75} +(4.31795 - 7.07401i) q^{76} +(9.58579 + 2.69442i) q^{78} +(2.58083 + 1.87508i) q^{79} +(-2.27534 - 14.0475i) q^{80} +(-1.80108 - 5.54316i) q^{81} +(12.3307 - 4.56132i) q^{82} +(-7.41626 - 10.2076i) q^{83} +(-11.0402 - 2.63010i) q^{84} +(-5.39686 - 1.75355i) q^{85} +(3.39774 - 2.68338i) q^{86} +10.8916 q^{87} -10.6569 q^{89} +(3.27098 - 2.58327i) q^{90} +(17.4981 + 5.68549i) q^{91} +(1.50292 - 6.30873i) q^{92} +(-3.10592 - 4.27493i) q^{93} +(-6.40430 + 2.36904i) q^{94} +(-4.55565 - 14.0208i) q^{95} +(-0.943569 + 8.28251i) q^{96} +(13.8683 + 10.0759i) q^{97} +(-10.6580 - 2.99581i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{4} + 16 q^{9} - 64 q^{12} - 8 q^{14} + 8 q^{15} + 8 q^{16} - 24 q^{20} + 32 q^{23} + 16 q^{25} - 8 q^{26} + 40 q^{31} - 160 q^{34} + 24 q^{38} - 40 q^{42} + 16 q^{47} - 8 q^{48} - 40 q^{49}+ \cdots + 24 q^{97}+O(q^{100}) $ 32 * q - 8 * q^4 + 16 * q^9 - 64 * q^12 - 8 * q^14 + 8 * q^15 + 8 * q^16 - 24 * q^20 + 32 * q^23 + 16 * q^25 - 8 * q^26 + 40 * q^31 - 160 * q^34 + 24 * q^38 - 40 * q^42 + 16 * q^47 - 8 * q^48 - 40 * q^49 + 192 * q^56 + 32 * q^60 + 16 * q^64 - 8 * q^70 - 72 * q^71 + 352 * q^78 - 56 * q^80 + 24 * q^81 + 56 * q^82 + 32 * q^86 - 160 * q^89 + 16 * q^92 + 24 * q^97

Character values

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

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

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 $

$2$	0.876503	+	1.10984i	0.619781	+	0.784775i
$2$	0.876503	+	1.10984i	0.619781	+	0.784775i
$3$	−1.40150	−	0.455375i	−0.809157	−	0.262911i	−0.124916	−	0.992167i	$-0.539866\pi$
$3$	−1.40150	−	0.455375i	−0.809157	−	0.262911i	−0.684241	+	0.729256i	$0.739866\pi$
$4$	−0.463486	+	1.94555i	−0.231743	+	0.972777i
$5$	2.09113	+	2.87820i	0.935183	+	1.28717i	0.957803	+	0.287425i	$0.0927991\pi$
$5$	2.09113	+	2.87820i	0.935183	+	1.28717i	−0.0226203	+	0.999744i	$0.507201\pi$
$6$	−0.723026	−	1.95458i	−0.295174	−	0.797954i
$7$	−1.18995	−	3.66230i	−0.449760	−	1.38422i	−0.877178	−	0.480165i	$-0.840577\pi$
$7$	−1.18995	−	3.66230i	−0.449760	−	1.38422i	0.427418	−	0.904054i	$-0.359423\pi$
$8$	−2.56550	+	1.19089i	−0.907041	+	0.421043i
$9$	−0.670212	−	0.486937i	−0.223404	−	0.162312i
$10$	−1.36145	+	4.84357i	−0.430529	+	1.53167i
$11$		0			0
$11$		0			0
$12$	1.53553	−	2.51564i	0.443270	−	0.726202i
$13$	−2.80839	+	3.86541i	−0.778906	+	1.07207i	0.216496	+	0.976284i	$0.430537\pi$
$13$	−2.80839	+	3.86541i	−0.778906	+	1.07207i	−0.995402	+	0.0957885i	$0.969463\pi$
$14$	3.02157	−	4.53067i	0.807548	−	1.21087i
$15$	−1.62007	−	4.98605i	−0.418299	−	1.28739i
$16$	−3.57036	−	1.80347i	−0.892590	−	0.450869i
$17$	−1.29042	+	0.937542i	−0.312972	+	0.227387i	−0.733171	−	0.680045i	$-0.761960\pi$
$17$	−1.29042	+	0.937542i	−0.312972	+	0.227387i	0.420199	+	0.907432i	$0.361960\pi$
$18$	−0.0470202	−	1.17063i	−0.0110828	−	0.275920i
$19$	−3.94104	−	1.28052i	−0.904138	−	0.293772i	−0.180194	−	0.983631i	$-0.557673\pi$
$19$	−3.94104	−	1.28052i	−0.904138	−	0.293772i	−0.723944	+	0.689859i	$0.757673\pi$
$20$	−6.56890	+	2.73441i	−1.46885	+	0.611432i
$21$			5.67459i			1.23830i
$22$		0			0
$23$	−3.24264			−0.676137			−0.338069	−	0.941121i	$-0.609774\pi$
$23$	−3.24264			−0.676137			−0.338069	+	0.941121i	$0.609774\pi$
$24$	4.13785	−	0.500766i	0.844635	−	0.102219i
$25$	−2.36610	+	7.28210i	−0.473220	+	1.45642i
$26$	−6.75154	+	0.271187i	−1.32409	+	0.0531841i
$27$	3.31609	+	4.56421i	0.638182	+	0.878382i
$28$	7.67673	−	0.617693i	1.45077	−	0.116733i
$29$	−7.02929	+	2.28396i	−1.30531	+	0.424120i	−0.877425	−	0.479714i	$-0.840740\pi$
$29$	−7.02929	+	2.28396i	−1.30531	+	0.424120i	−0.427882	+	0.903834i	$0.640740\pi$
$30$	4.11372	−	6.16830i	0.751059	−	1.12617i
$31$	2.90096	+	2.10767i	0.521028	+	0.378549i	0.816991	−	0.576650i	$-0.195640\pi$
$31$	2.90096	+	2.10767i	0.521028	+	0.378549i	−0.295963	+	0.955199i	$0.595640\pi$
$32$	−1.12786	−	5.54328i	−0.199380	−	0.979922i
$33$		0			0
$34$	−2.17157	−	0.610396i	−0.372422	−	0.104682i
$35$	8.05247	−	11.0833i	1.36112	−	1.87342i
$36$	1.25800	−	1.07824i	0.209666	−	0.179707i
$37$	−0.580521	+	0.188623i	−0.0954370	+	0.0310094i	−0.356346	−	0.934354i	$-0.615978\pi$
$37$	−0.580521	+	0.188623i	−0.0954370	+	0.0310094i	0.260909	+	0.965363i	$0.415978\pi$
$38$	−2.03316	−	5.49631i	−0.329822	−	0.891619i
$39$	5.69617	−	4.13851i	0.912117	−	0.662692i
$40$	−8.79241	−	4.89371i	−1.39020	−	0.773763i
$41$	2.87280	−	8.84157i	0.448656	−	1.38082i	−0.429768	−	0.902939i	$-0.641405\pi$
$41$	2.87280	−	8.84157i	0.448656	−	1.38082i	0.878424	−	0.477882i	$-0.158595\pi$
$42$	−6.29789	+	4.97380i	−0.971785	+	0.767473i
$43$		−	3.06147i		−	0.466869i	−0.972372	−	0.233435i	$-0.925003\pi$
$43$		−	3.06147i		−	0.466869i	0.972372	−	0.233435i	$-0.0749965\pi$
$44$		0			0
$45$		−	2.94725i		−	0.439350i
$46$	−2.84218	−	3.59881i	−0.419057	−	0.530616i
$47$	−1.49207	+	4.59211i	−0.217640	+	0.669828i	0.781315	+	0.624136i	$0.214549\pi$
$47$	−1.49207	+	4.59211i	−0.217640	+	0.669828i	−0.998956	+	0.0456913i	$0.985451\pi$
$48$	4.18261	+	4.15343i	0.603707	+	0.599496i
$49$	−6.33333	+	4.60143i	−0.904762	+	0.657348i
$50$	−10.1559	+	3.75679i	−1.43625	+	0.531291i
$51$	2.23545	−	0.726342i	0.313026	−	0.101708i
$52$	−6.21872	−	7.25543i	−0.862381	−	1.00615i
$53$	2.44991	−	3.37202i	0.336522	−	0.463182i	−0.606900	−	0.794778i	$-0.707587\pi$
$53$	2.44991	−	3.37202i	0.336522	−	0.463182i	0.943421	+	0.331596i	$0.107587\pi$
$54$	−2.15897	+	7.68087i	−0.293799	+	1.04523i
$55$		0			0
$56$	7.41421	+	7.97852i	0.990766	+	1.06618i
$57$	4.94026	+	3.58931i	0.654354	+	0.475416i
$58$	−8.69602	−	5.79949i	−1.14184	−	0.761511i
$59$	−5.36555	+	1.74337i	−0.698535	+	0.226968i	−0.636692	−	0.771118i	$-0.719698\pi$
$59$	−5.36555	+	1.74337i	−0.698535	+	0.226968i	−0.0618426	+	0.998086i	$0.519698\pi$
$60$	10.4515	−	0.840960i	1.34928	−	0.108568i
$61$	1.27243	+	1.75135i	0.162918	+	0.224237i	0.882669	−	0.469995i	$-0.155744\pi$
$61$	1.27243	+	1.75135i	0.162918	+	0.224237i	−0.719751	+	0.694232i	$0.755744\pi$
$62$	0.203524	+	5.06698i	0.0258475	+	0.643507i
$63$	−0.985790	+	3.03395i	−0.124198	+	0.382242i
$64$	5.16357	−	6.11045i	0.645446	−	0.763806i
$65$	−16.9981			−2.10836
$66$		0			0
$67$		−	1.47363i		−	0.180032i	−0.995940	−	0.0900160i	$-0.971308\pi$
$67$		−	1.47363i		−	0.180032i	0.995940	−	0.0900160i	$-0.0286918\pi$
$68$	−1.22595	−	2.94511i	−0.148668	−	0.357147i
$69$	4.54457	+	1.47662i	0.547101	+	0.177764i
$70$	19.3587	−	0.777573i	2.31380	−	0.0929377i
$71$	−8.42528	+	6.12132i	−0.999896	+	0.726467i	−0.962066	−	0.272817i	$-0.912045\pi$
$71$	−8.42528	+	6.12132i	−0.999896	+	0.726467i	−0.0378303	+	0.999284i	$0.512045\pi$
$72$	2.29932	+	0.451090i	0.270977	+	0.0531614i
$73$	2.87280	+	8.84157i	0.336236	+	1.03483i	0.966110	+	0.258131i	$0.0831065\pi$
$73$	2.87280	+	8.84157i	0.336236	+	1.03483i	−0.629874	+	0.776697i	$0.716894\pi$
$74$	−0.718169	−	0.478957i	−0.0834854	−	0.0556776i
$75$	6.63218	−	9.12841i	0.765818	−	1.05406i
$76$	4.31795	−	7.07401i	0.495302	−	0.811445i
$77$		0			0
$78$	9.58579	+	2.69442i	1.08538	+	0.305083i
$79$	2.58083	+	1.87508i	0.290366	+	0.210963i	0.723426	−	0.690402i	$-0.242566\pi$
$79$	2.58083	+	1.87508i	0.290366	+	0.210963i	−0.433060	+	0.901365i	$0.642566\pi$
$80$	−2.27534	−	14.0475i	−0.254391	−	1.57056i
$81$	−1.80108	−	5.54316i	−0.200120	−	0.615907i
$82$	12.3307	−	4.56132i	1.36170	−	0.503713i
$83$	−7.41626	−	10.2076i	−0.814040	−	1.12043i	−0.990687	−	0.136156i	$-0.956525\pi$
$83$	−7.41626	−	10.2076i	−0.814040	−	1.12043i	0.176648	−	0.984274i	$-0.443475\pi$
$84$	−11.0402	−	2.63010i	−1.20459	−	0.286967i
$85$	−5.39686	−	1.75355i	−0.585372	−	0.190199i
$86$	3.39774	−	2.68338i	0.366387	−	0.289357i
$87$	10.8916			1.16770
$88$		0			0
$89$	−10.6569			−1.12962			−0.564812	−	0.825220i	$-0.691051\pi$
$89$	−10.6569			−1.12962			−0.564812	+	0.825220i	$0.691051\pi$
$90$	3.27098	−	2.58327i	0.344791	−	0.272301i
$91$	17.4981	+	5.68549i	1.83430	+	0.596001i
$92$	1.50292	−	6.30873i	0.156690	−	0.657731i
$93$	−3.10592	−	4.27493i	−0.322069	−	0.443290i
$94$	−6.40430	+	2.36904i	−0.660553	+	0.244348i
$95$	−4.55565	−	14.0208i	−0.467400	−	1.43851i
$96$	−0.943569	+	8.28251i	−0.0963026	+	0.845330i
$97$	13.8683	+	10.0759i	1.40811	+	1.02305i	0.993594	+	0.113010i	$0.0360493\pi$
$97$	13.8683	+	10.0759i	1.40811	+	1.02305i	0.414517	+	0.910042i	$0.363951\pi$
$98$	−10.6580	−	2.99581i	−1.07662	−	0.302622i
$99$		0			0
$100$	−13.0711	−	7.97852i	−1.30711	−	0.797852i
$101$	−2.80839	+	3.86541i	−0.279445	+	0.384623i	−0.925550	−	0.378626i	$-0.876397\pi$
$101$	−2.80839	+	3.86541i	−0.279445	+	0.384623i	0.646105	+	0.763248i	$0.276397\pi$
$102$	2.76550	+	1.84435i	0.273826	+	0.182618i
$103$	2.87809	+	8.85786i	0.283587	+	0.872791i	0.986819	+	0.161830i	$0.0517397\pi$
$103$	2.87809	+	8.85786i	0.283587	+	0.872791i	−0.703232	+	0.710961i	$0.748260\pi$
$104$	2.60164	−	13.2612i	0.255112	−	1.30037i
$105$	−16.3326	+	11.8663i	−1.59390	+	1.15803i
$106$	5.88975	−	0.236572i	0.572063	−	0.0229779i
$107$	6.85267	+	2.22657i	0.662473	+	0.215251i	0.620906	−	0.783885i	$-0.286765\pi$
$107$	6.85267	+	2.22657i	0.662473	+	0.215251i	0.0415672	+	0.999136i	$0.486765\pi$
$108$	−10.4169	+	4.33619i	−1.00236	+	0.417250i
$109$		−	4.32957i		−	0.414697i	−0.978267	−	0.207349i	$-0.933517\pi$
$109$		−	4.32957i		−	0.414697i	0.978267	−	0.207349i	$-0.0664835\pi$
$110$		0			0
$111$	0.899495			0.0853763
$112$	−2.35630	+	15.2218i	−0.222650	+	1.43832i
$113$	1.07701	−	3.31470i	0.101317	−	0.311821i	−0.887532	−	0.460747i	$-0.847582\pi$
$113$	1.07701	−	3.31470i	0.101317	−	0.311821i	0.988848	+	0.148926i	$0.0475816\pi$
$114$	0.346595	+	8.62893i	0.0324616	+	0.808174i
$115$	−6.78079	−	9.33296i	−0.632312	−	0.870303i
$116$	−1.18558	−	14.7345i	−0.110078	−	1.36806i
$117$	3.76442	−	1.22314i	0.348021	−	0.113079i
$118$	−6.63778	−	4.42682i	−0.611057	−	0.407522i
$119$	4.96909	+	3.61026i	0.455516	+	0.330952i
$120$	10.0941	+	10.8624i	0.921461	+	0.991595i
$121$		0			0
$122$	−0.828427	+	2.94725i	−0.0750023	+	0.266832i
$123$	−8.05247	+	11.0833i	−0.726067	+	0.999345i
$124$	−5.44515	+	4.66710i	−0.488989	+	0.419118i
$125$	−8.98953	+	2.92088i	−0.804048	+	0.261251i
$126$	−4.23124	+	1.56520i	−0.376949	+	0.139439i
$127$	11.9268	−	8.66536i	1.05834	−	0.768926i	0.0845565	−	0.996419i	$-0.473053\pi$
$127$	11.9268	−	8.66536i	1.05834	−	0.768926i	0.973780	+	0.227492i	$0.0730527\pi$
$128$	11.3075	+	0.374911i	0.999451	+	0.0331378i
$129$	−1.39412	+	4.29065i	−0.122745	+	0.377771i
$130$	−14.8989	−	18.8652i	−1.30672	−	1.65459i
$131$			10.6382i			0.929465i	0.885451	+	0.464732i	$0.153850\pi$
$131$			10.6382i			0.929465i	−0.885451	+	0.464732i	$0.846150\pi$
$132$		0			0
$133$			15.9570i			1.38365i
$134$	1.63549	−	1.29164i	0.141285	−	0.111580i
$135$	−6.20230	+	19.0887i	−0.533809	+	1.64290i
$136$	2.19405	−	3.94200i	0.188138	−	0.338024i
$137$	−2.42705	+	1.76336i	−0.207357	+	0.150654i	−0.686617	−	0.727019i	$-0.740905\pi$
$137$	−2.42705	+	1.76336i	−0.207357	+	0.150654i	0.479260	+	0.877673i	$0.340905\pi$
$138$	2.34451	+	6.33800i	0.199578	+	0.539526i
$139$	−8.05871	+	2.61843i	−0.683531	+	0.222093i	−0.630141	−	0.776481i	$-0.717003\pi$
$139$	−8.05871	+	2.61843i	−0.683531	+	0.222093i	−0.0533903	+	0.998574i	$0.517003\pi$
$140$	17.8309	+	20.8035i	1.50699	+	1.75821i
$141$	4.18227	−	5.75639i	0.352210	−	0.484776i
$142$	−14.1785	−	3.98535i	−1.18983	−	0.334443i
$143$		0			0
$144$	1.51472	+	2.94725i	0.126227	+	0.245604i
$145$	−21.2729	−	15.4556i	−1.76661	−	1.28352i
$146$	−7.29471	+	10.9380i	−0.603714	+	0.905236i
$147$	10.9716	−	3.56487i	0.904918	−	0.294026i
$148$	−0.0979122	−	1.21686i	−0.00804834	−	0.100025i
$149$	11.2788	+	15.5239i	0.923992	+	1.27177i	0.962157	+	0.272494i	$0.0878485\pi$
$149$	11.2788	+	15.5239i	0.923992	+	1.27177i	−0.0381659	+	0.999271i	$0.512152\pi$
$150$	15.9442	−	0.640425i	1.30184	−	0.0522905i
$151$	−2.37991	+	7.32460i	−0.193674	+	0.596067i	0.806315	+	0.591486i	$0.201458\pi$
$151$	−2.37991	+	7.32460i	−0.193674	+	0.596067i	−0.999990	+	0.00458168i	$0.998542\pi$
$152$	11.6357	−	1.40816i	0.943780	−	0.114217i
$153$	1.32138			0.106827
$154$		0			0
$155$			12.7570i			1.02466i
$156$	5.41160	+	13.0003i	0.433275	+	1.04086i
$157$	12.9536	+	4.20887i	1.03381	+	0.335904i	0.776295	−	0.630370i	$-0.217097\pi$
$157$	12.9536	+	4.20887i	1.03381	+	0.335904i	0.257513	+	0.966275i	$0.417097\pi$
$158$	0.181064	+	4.50782i	0.0144047	+	0.358623i
$159$	−4.96909	+	3.61026i	−0.394075	+	0.286312i
$160$	13.5961	−	14.8379i	1.07487	−	1.17304i
$161$	3.85859	+	11.8755i	0.304100	+	0.935922i
$162$	4.57337	−	6.85751i	0.359318	−	0.538777i
$163$	−11.8292	+	16.2815i	−0.926537	+	1.27527i	0.0346581	+	0.999399i	$0.488966\pi$
$163$	−11.8292	+	16.2815i	−0.926537	+	1.27527i	−0.961195	+	0.275870i	$0.911034\pi$
$164$	15.8703	+	9.68714i	1.23926	+	0.756438i
$165$		0			0
$166$	4.82843	−	17.1778i	0.374759	−	1.33326i
$167$	3.11534	+	2.26343i	0.241072	+	0.175149i	0.701761	−	0.712413i	$-0.252398\pi$
$167$	3.11534	+	2.26343i	0.241072	+	0.175149i	−0.460689	+	0.887562i	$0.652398\pi$
$168$	−6.75781	−	14.5582i	−0.521376	−	1.12319i
$169$	−3.03715	−	9.34739i	−0.233627	−	0.719030i
$170$	−2.78421	−	7.52663i	−0.213539	−	0.577266i
$171$	2.01780	+	2.77726i	0.154305	+	0.212383i
$172$	5.95625	+	1.41895i	0.454160	+	0.108194i
$173$	−4.97046	−	1.61500i	−0.377897	−	0.122786i	0.113908	−	0.993491i	$-0.463663\pi$
$173$	−4.97046	−	1.61500i	−0.377897	−	0.122786i	−0.491806	+	0.870705i	$0.663663\pi$
$174$	9.54654	+	12.0879i	0.723721	+	0.916385i
$175$	29.4848			2.22884
$176$		0			0
$177$	8.31371			0.624897
$178$	−9.34076	−	11.8274i	−0.700120	−	0.886501i
$179$	−18.8996	−	6.14087i	−1.41263	−	0.458990i	−0.499374	−	0.866386i	$-0.666437\pi$
$179$	−18.8996	−	6.14087i	−1.41263	−	0.458990i	−0.913251	+	0.407397i	$0.866437\pi$
$180$	5.73404	+	1.36601i	0.427390	+	0.101816i
$181$	9.02054	+	12.4157i	0.670491	+	0.922852i	0.999771	−	0.0213803i	$-0.00680607\pi$
$181$	9.02054	+	12.4157i	0.670491	+	0.922852i	−0.329280	+	0.944232i	$0.606806\pi$
$182$	9.02719	+	24.4035i	0.669140	+	1.80891i
$183$	−0.985790	−	3.03395i	−0.0728717	−	0.224276i
$184$	8.31899	−	3.86162i	0.613284	−	0.284683i
$185$	−1.75684	−	1.27642i	−0.129165	−	0.0938442i
$186$	2.02214	−	7.19406i	0.148271	−	0.527494i
$187$		0			0
$188$	−8.24264	−	5.03127i	−0.601156	−	0.366943i
$189$	12.7695	−	17.5757i	0.928844	−	1.27844i
$190$	11.5678	−	17.3453i	0.839220	−	1.25836i
$191$	−3.73017	−	11.4803i	−0.269905	−	0.830683i	−0.990523	−	0.137350i	$-0.956141\pi$
$191$	−3.73017	−	11.4803i	−0.269905	−	0.830683i	0.720617	−	0.693333i	$-0.243859\pi$
$192$	−10.0193	+	6.21243i	−0.723081	+	0.448344i
$193$	−2.58083	+	1.87508i	−0.185772	+	0.134971i	−0.676784	−	0.736181i	$-0.736627\pi$
$193$	−2.58083	+	1.87508i	−0.185772	+	0.134971i	0.491012	+	0.871153i	$0.336627\pi$
$194$	0.972961	+	24.2231i	0.0698545	+	1.73912i
$195$	23.8229	+	7.74053i	1.70599	+	0.554311i
$196$	−6.01693	−	14.4545i	−0.429781	−	1.03247i
$197$		−	15.6788i		−	1.11707i	−0.829483	−	0.558533i	$-0.811365\pi$
$197$		−	15.6788i		−	1.11707i	0.829483	−	0.558533i	$-0.188635\pi$
$198$		0			0
$199$	16.8284			1.19294			0.596468	−	0.802637i	$-0.296570\pi$
$199$	16.8284			1.19294			0.596468	+	0.802637i	$0.296570\pi$
$200$	−2.60195	−	21.5000i	−0.183985	−	1.52028i
$201$	−0.671053	+	2.06529i	−0.0473324	+	0.145674i
$202$	−6.75154	+	0.271187i	−0.475037	+	0.0190806i
$203$	16.7291	+	23.0256i	1.17415	+	1.61608i
$204$	0.377037	+	4.68584i	0.0263979	+	0.328075i
$205$	31.4552	−	10.2204i	2.19693	−	0.713825i
$206$	−7.30815	+	10.9582i	−0.509183	+	0.763491i
$207$	2.17326	+	1.57896i	0.151052	+	0.109745i
$208$	16.9981	−	8.73606i	1.17861	−	0.605737i
$209$		0			0
$210$	−27.4853	−	7.72569i	−1.89666	−	0.533123i
$211$	−13.5601	+	18.6639i	−0.933515	+	1.28487i	0.0249581	+	0.999688i	$0.492055\pi$
$211$	−13.5601	+	18.6639i	−0.933515	+	1.28487i	−0.958473	+	0.285184i	$0.907945\pi$
$212$	5.42494	+	6.32932i	0.372587	+	0.434700i
$213$	14.5955	−	4.74238i	1.00007	−	0.324942i
$214$	3.53525	+	9.55696i	0.241665	+	0.653300i
$215$	8.81151	−	6.40193i	0.600940	−	0.436608i
$216$	−13.9429	−	7.76037i	−0.948693	−	0.528027i
$217$	4.26692	−	13.1322i	0.289657	−	0.891473i
$218$	4.80513	−	3.79488i	0.325444	−	0.257022i
$219$		−	13.6997i		−	0.925739i
$220$		0			0
$221$		−	7.62096i		−	0.512641i
$222$	0.788410	+	0.998295i	0.0529146	+	0.0670012i
$223$	7.95037	−	24.4687i	0.532396	−	1.63855i	−0.216814	−	0.976213i	$-0.569566\pi$
$223$	7.95037	−	24.4687i	0.532396	−	1.63855i	0.749210	−	0.662333i	$-0.230434\pi$
$224$	−18.9590	+	10.7268i	−1.26675	+	0.716716i
$225$	5.13171	−	3.72841i	0.342114	−	0.248561i
$226$	4.62279	−	1.71003i	0.307503	−	0.113750i
$227$	2.73501	−	0.888658i	0.181529	−	0.0589823i	−0.216842	−	0.976207i	$-0.569576\pi$
$227$	2.73501	−	0.888658i	0.181529	−	0.0589823i	0.398371	+	0.917224i	$0.369576\pi$
$228$	−9.27294	+	7.94795i	−0.614115	+	0.526366i
$229$	−12.1880	+	16.7754i	−0.805407	+	1.10855i	0.186609	+	0.982434i	$0.440250\pi$
$229$	−12.1880	+	16.7754i	−0.805407	+	1.10855i	−0.992016	+	0.126113i	$0.959750\pi$
$230$	4.41470	−	15.7060i	0.291097	−	1.03562i
$231$		0			0
$232$	15.3137	−	14.2306i	1.00539	−	0.934284i
$233$	8.81151	+	6.40193i	0.577261	+	0.419405i	0.837736	−	0.546076i	$-0.183879\pi$
$233$	8.81151	+	6.40193i	0.577261	+	0.419405i	−0.260475	+	0.965481i	$0.583879\pi$
$234$	4.65701	+	3.10582i	0.304438	+	0.203034i
$235$	−16.3371	+	5.30824i	−1.06571	+	0.346272i
$236$	−0.904968	−	11.2470i	−0.0589084	−	0.732117i
$237$	−2.76317	−	3.80318i	−0.179487	−	0.247043i
$238$	0.348618	+	8.67929i	0.0225976	+	0.562595i
$239$	−7.13972	+	21.9738i	−0.461830	+	1.42137i	0.401096	+	0.916036i	$0.368629\pi$
$239$	−7.13972	+	21.9738i	−0.461830	+	1.42137i	−0.862926	+	0.505331i	$0.831371\pi$
$240$	−3.20799	+	20.7237i	−0.207075	+	1.33771i
$241$	−29.4848			−1.89928			−0.949641	−	0.313340i	$-0.898552\pi$
$241$	−29.4848			−1.89928			−0.949641	+	0.313340i	$0.898552\pi$
$242$		0			0
$243$		−	8.33609i		−	0.534760i
$244$	−3.99709	+	1.66385i	−0.255888	+	0.106517i
$245$	−26.4877	−	8.60637i	−1.69224	−	0.549840i
$246$	−19.3587	+	0.777573i	−1.23426	+	0.0495762i
$247$	16.0177	−	11.6376i	1.01918	−	0.740480i
$248$	−9.95242	−	1.95251i	−0.631979	−	0.123984i
$249$	5.74560	+	17.6831i	0.364113	+	1.12062i
$250$	−11.1210	−	7.41678i	−0.703357	−	0.469078i
$251$	8.51314	−	11.7173i	0.537345	−	0.739592i	−0.450883	−	0.892583i	$-0.648891\pi$
$251$	8.51314	−	11.7173i	0.537345	−	0.739592i	0.988227	+	0.152992i	$0.0488907\pi$
$252$	−5.44581	−	3.32410i	−0.343054	−	0.209399i
$253$		0			0
$254$	20.0711	+	5.64167i	1.25937	+	0.353990i
$255$	6.76518	+	4.91519i	0.423652	+	0.307801i
$256$	9.49496	+	12.8781i	0.593435	+	0.804882i
$257$	5.71227	+	17.5805i	0.356321	+	1.09664i	0.955239	+	0.295834i	$0.0955975\pi$
$257$	5.71227	+	17.5805i	0.356321	+	1.09664i	−0.598918	+	0.800810i	$0.704402\pi$
$258$	−5.98388	+	2.21352i	−0.372540	+	0.137808i
$259$	1.38159	+	1.90159i	0.0858475	+	0.118159i
$260$	7.87839	−	33.0708i	0.488597	−	2.05096i
$261$	5.82326	+	1.89209i	0.360451	+	0.117117i
$262$	−11.8067	+	9.32442i	−0.729421	+	0.576065i
$263$	7.04085			0.434158			0.217079	−	0.976154i	$-0.430347\pi$
$263$	7.04085			0.434158			0.217079	+	0.976154i	$0.430347\pi$
$264$		0			0
$265$	14.8284			0.910903
$266$	−17.7098	+	13.9864i	−1.08585	+	0.857561i
$267$	14.9356	+	4.85287i	0.914044	+	0.296991i
$268$	2.86702	+	0.683005i	0.175131	+	0.0417212i
$269$	−4.47949	−	6.16549i	−0.273119	−	0.375916i	0.650320	−	0.759660i	$-0.274635\pi$
$269$	−4.47949	−	6.16549i	−0.273119	−	0.375916i	−0.923440	+	0.383744i	$0.874635\pi$
$270$	−26.6217	+	9.84776i	−1.62015	+	0.599315i
$271$	4.96398	+	15.2775i	0.301540	+	0.928045i	0.980946	+	0.194282i	$0.0622377\pi$
$271$	4.96398	+	15.2775i	0.301540	+	0.928045i	−0.679406	+	0.733763i	$0.737762\pi$
$272$	6.29808	−	1.02013i	0.381877	−	0.0618545i
$273$	−21.9346	−	15.9364i	−1.32754	−	0.964517i
$274$	−4.08436	−	1.14805i	−0.246745	−	0.0693563i
$275$		0			0
$276$	−4.97918	+	8.15731i	−0.299712	+	0.491012i
$277$	3.29023	−	4.52861i	0.197691	−	0.272098i	−0.698650	−	0.715463i	$-0.746216\pi$
$277$	3.29023	−	4.52861i	0.197691	−	0.272098i	0.896341	+	0.443366i	$0.146216\pi$
$278$	−9.96952	−	6.64881i	−0.597932	−	0.398769i
$279$	−0.917954	−	2.82517i	−0.0549565	−	0.169139i
$280$	−7.45966	+	38.0237i	−0.445800	+	2.27235i
$281$	−18.6920	+	13.5806i	−1.11507	+	0.810148i	−0.983455	−	0.181153i	$-0.942017\pi$
$281$	−18.6920	+	13.5806i	−1.11507	+	0.810148i	−0.131618	+	0.991301i	$0.542017\pi$
$282$	10.0544	−	0.403853i	0.598733	−	0.0240491i
$283$	−16.9702	−	5.51396i	−1.00877	−	0.327771i	−0.242408	−	0.970174i	$-0.577937\pi$
$283$	−16.9702	−	5.51396i	−1.00877	−	0.327771i	−0.766366	+	0.642404i	$0.777937\pi$
$284$	−8.00436	−	19.2290i	−0.474972	−	1.14103i
$285$			21.7248i			1.28686i
$286$		0			0
$287$	−35.7990			−2.11315
$288$	−1.94332	+	4.26437i	−0.114511	+	0.251280i
$289$	−4.46710	+	13.7483i	−0.262771	+	0.808725i
$290$	−1.49245	−	37.1564i	−0.0876395	−	2.18190i
$291$	−14.8481	−	20.4367i	−0.870411	−	1.19802i
$292$	−18.5333	+	1.49124i	−1.08458	+	0.0872684i
$293$	2.83847	−	0.922275i	0.165825	−	0.0538799i	−0.224928	−	0.974375i	$-0.572215\pi$
$293$	2.83847	−	0.922275i	0.165825	−	0.0538799i	0.390753	+	0.920496i	$0.372215\pi$
$294$	13.5730	+	9.05204i	0.791595	+	0.527926i
$295$	−16.2378	−	11.7975i	−0.945403	−	0.686876i
$296$	1.26470	−	1.17525i	0.0735090	−	0.0683098i
$297$		0			0
$298$	−7.34315	+	26.1243i	−0.425377	+	1.51334i
$299$	9.10658	−	12.5341i	0.526647	−	0.724868i
$300$	14.6859	+	17.1342i	0.847891	+	0.989241i
$301$	−11.2120	+	3.64300i	−0.646250	+	0.209979i
$302$	−10.2151	+	3.77872i	−0.587814	+	0.217441i
$303$	5.69617	−	4.13851i	0.327236	−	0.237751i
$304$	11.7616	+	11.6795i	0.674572	+	0.669865i
$305$	−2.37991	+	7.32460i	−0.136273	+	0.419405i
$306$	1.15819	+	1.46651i	0.0662093	+	0.0838350i
$307$		−	28.1103i		−	1.60434i	−0.597095	−	0.802171i	$-0.703678\pi$
$307$		−	28.1103i		−	1.60434i	0.597095	−	0.802171i	$-0.296322\pi$
$308$		0			0
$309$		−	13.7249i		−	0.780783i
$310$	−14.1582	+	11.1815i	−0.804130	+	0.635067i
$311$	3.24013	−	9.97210i	0.183731	−	0.565466i	−0.816193	−	0.577779i	$-0.803920\pi$
$311$	3.24013	−	9.97210i	0.183731	−	0.565466i	0.999924	+	0.0123133i	$0.00391956\pi$
$312$	−9.68501	+	17.4008i	−0.548306	+	0.985129i
$313$	1.47923	−	1.07472i	0.0836109	−	0.0607469i	−0.545194	−	0.838310i	$-0.683544\pi$
$313$	1.47923	−	1.07472i	0.0836109	−	0.0607469i	0.628805	+	0.777563i	$0.283544\pi$
$314$	6.68267	+	18.0655i	0.377125	+	1.01949i
$315$	−10.7937	+	3.50709i	−0.608157	+	0.197602i
$316$	−4.84425	+	4.15207i	−0.272511	+	0.233572i
$317$	−1.07634	+	1.48146i	−0.0604536	+	0.0832072i	−0.838173	−	0.545404i	$-0.816376\pi$
$317$	−1.07634	+	1.48146i	−0.0604536	+	0.0832072i	0.777720	+	0.628611i	$0.216376\pi$
$318$	−8.36223	−	2.35049i	−0.468930	−	0.131809i
$319$		0			0
$320$	28.3848	+	2.08402i	1.58676	+	0.116500i
$321$	−8.59011	−	6.24108i	−0.479453	−	0.348343i
$322$	−9.79785	+	14.6913i	−0.546013	+	0.818716i
$323$	6.28613	−	2.04249i	0.349770	−	0.113647i
$324$	11.6193	−	0.934925i	0.645517	−	0.0519403i
$325$	−21.5034	−	29.5969i	−1.19279	−	1.64174i
$326$	−28.4382	+	1.14227i	−1.57505	+	0.0632644i
$327$	−1.97158	+	6.06790i	−0.109029	+	0.335555i
$328$	3.15916	+	26.1042i	0.174435	+	1.44137i
$329$	18.5932			1.02507
$330$		0			0
$331$		−	12.7570i		−	0.701186i	−0.936528	−	0.350593i	$-0.885980\pi$
$331$		−	12.7570i		−	0.701186i	0.936528	−	0.350593i	$-0.114020\pi$
$332$	23.2968	−	9.69765i	1.27858	−	0.532227i
$333$	0.480919	+	0.156260i	0.0263542	+	0.00856300i
$334$	0.218564	+	5.44142i	0.0119593	+	0.297741i
$335$	4.24139	−	3.08155i	0.231732	−	0.168363i
$336$	10.2340	−	20.2603i	0.558310	−	1.10529i
$337$	−1.88701	−	5.80763i	−0.102792	−	0.316361i	0.886414	−	0.462894i	$-0.153189\pi$
$337$	−1.88701	−	5.80763i	−0.102792	−	0.316361i	−0.989206	+	0.146532i	$0.953189\pi$
$338$	7.71203	−	11.5638i	0.419479	−	0.628986i
$339$	−3.01887	+	4.15511i	−0.163962	+	0.225675i
$340$	5.91299	−	9.68714i	0.320677	−	0.525359i
$341$		0			0
$342$	−1.31371	+	4.67371i	−0.0710372	+	0.252725i
$343$	2.58083	+	1.87508i	0.139352	+	0.101245i
$344$	3.64587	+	7.85419i	0.196572	+	0.423470i
$345$	5.25329	+	16.1680i	0.282828	+	0.870454i
$346$	−2.56423	−	6.93196i	−0.137854	−	0.372665i
$347$	0.636214	+	0.875674i	0.0341538	+	0.0470086i	0.825752	−	0.564033i	$-0.190751\pi$
$347$	0.636214	+	0.875674i	0.0341538	+	0.0470086i	−0.791599	+	0.611041i	$0.790751\pi$
$348$	−5.04812	+	21.1902i	−0.270607	+	1.13592i
$349$	17.7499	+	5.76728i	0.950128	+	0.308715i	0.742768	−	0.669549i	$-0.233513\pi$
$349$	17.7499	+	5.76728i	0.950128	+	0.308715i	0.207360	+	0.978265i	$0.433513\pi$
$350$	25.8435	+	32.7234i	1.38139	+	1.74914i
$351$	−26.9554			−1.43877
$352$		0			0
$353$	−16.7990			−0.894120			−0.447060	−	0.894504i	$-0.647529\pi$
$353$	−16.7990			−0.894120			−0.447060	+	0.894504i	$0.647529\pi$
$354$	7.28699	+	9.22688i	0.387299	+	0.490403i
$355$	−35.2367	−	11.4491i	−1.87017	−	0.607656i
$356$	4.93930	−	20.7335i	0.261783	−	1.09887i
$357$	−5.32017	−	7.32258i	−0.281573	−	0.387552i
$358$	−9.75021	−	26.3580i	−0.515315	−	1.39307i
$359$	−5.54144	−	17.0548i	−0.292466	−	0.900118i	−0.984061	−	0.177832i	$-0.943092\pi$
$359$	−5.54144	−	17.0548i	−0.292466	−	0.900118i	0.691595	−	0.722286i	$-0.256908\pi$
$360$	3.50985	+	7.56117i	0.184985	+	0.398509i
$361$	−1.47923	−	1.07472i	−0.0778541	−	0.0565643i
$362$	−5.87291	+	20.8937i	−0.308673	+	1.09815i
$363$		0			0
$364$	−19.1716	+	31.4084i	−1.00486	+	1.64625i
$365$	−19.4404	+	26.7574i	−1.01756	+	1.40055i
$366$	2.50315	−	3.75333i	0.130842	−	0.196190i
$367$	−1.83214	−	5.63875i	−0.0956370	−	0.294340i	0.891782	−	0.452465i	$-0.149455\pi$
$367$	−1.83214	−	5.63875i	−0.0956370	−	0.294340i	−0.987419	+	0.158125i	$0.949455\pi$
$368$	11.5774	+	5.84802i	0.603514	+	0.304849i
$369$	−6.23068	+	4.52685i	−0.324356	+	0.235658i
$370$	−0.123255	−	3.06859i	−0.00640773	−	0.159529i
$371$	−15.2646	−	4.95978i	−0.792500	−	0.257499i
$372$	9.75666	−	4.06136i	0.505859	−	0.210572i
$373$			28.7444i			1.48833i	0.667997	+	0.744164i	$0.267152\pi$
$373$			28.7444i			1.48833i	−0.667997	+	0.744164i	$0.732848\pi$
$374$		0			0
$375$	13.9289			0.719287
$376$	−1.64079	−	13.5579i	−0.0846174	−	0.699197i
$377$	10.9125	−	33.5853i	0.562024	−	1.72973i
$378$	30.6987	−	1.23306i	1.57897	−	0.0634220i
$379$	−1.58374	−	2.17983i	−0.0813512	−	0.111970i	0.766402	−	0.642361i	$-0.222045\pi$
$379$	−1.58374	−	2.17983i	−0.0813512	−	0.111970i	−0.847753	+	0.530391i	$0.822045\pi$
$380$	29.3898	−	2.36479i	1.50766	−	0.121311i
$381$	−20.6615	+	6.71332i	−1.05852	+	0.343934i
$382$	9.47175	−	14.2024i	0.484617	−	0.726656i
$383$	−1.00532	−	0.730406i	−0.0513693	−	0.0373220i	0.561804	−	0.827270i	$-0.310107\pi$
$383$	−1.00532	−	0.730406i	−0.0513693	−	0.0373220i	−0.613174	+	0.789948i	$0.710107\pi$
$384$	−15.6767	−	5.67459i	−0.800001	−	0.289580i
$385$		0			0
$386$	−4.34315	−	1.22079i	−0.221060	−	0.0621367i
$387$	−1.49074	+	2.05183i	−0.0757787	+	0.104300i
$388$	−26.0310	+	22.3114i	−1.32152	+	1.13269i
$389$	15.7566	−	5.11962i	0.798890	−	0.259575i	0.119005	−	0.992894i	$-0.462030\pi$
$389$	15.7566	−	5.11962i	0.798890	−	0.259575i	0.679885	+	0.733319i	$0.262030\pi$
$390$	12.2901	+	33.2242i	0.622333	+	1.68237i
$391$	4.18435	−	3.04011i	0.211612	−	0.153745i
$392$	10.7684	−	19.3473i	0.543884	−	0.977184i
$393$	4.84438	−	14.9095i	0.244367	−	0.752083i
$394$	17.4009	−	13.7425i	0.876645	−	0.692336i
$395$			11.3492i			0.571040i
$396$		0			0
$397$		−	36.0821i		−	1.81091i	−0.424441	−	0.905455i	$-0.639530\pi$
$397$		−	36.0821i		−	1.81091i	0.424441	−	0.905455i	$-0.360470\pi$
$398$	14.7502	+	18.6768i	0.739359	+	0.936186i
$399$	7.26645	−	22.3638i	0.363777	−	1.11959i
$400$	21.5809	−	21.7325i	1.07905	−	1.08663i
$401$	9.26797	−	6.73358i	0.462820	−	0.336259i	−0.331816	−	0.943344i	$-0.607661\pi$
$401$	9.26797	−	6.73358i	0.462820	−	0.336259i	0.794637	+	0.607085i	$0.207661\pi$
$402$	−2.88032	+	1.06547i	−0.143657	+	0.0531408i
$403$	−16.2940	+	5.29425i	−0.811664	+	0.263726i
$404$	−6.21872	−	7.25543i	−0.309393	−	0.360971i
$405$	12.1880	−	16.7754i	0.605627	−	0.833574i
$406$	−10.8916	+	38.7485i	−0.540542	+	1.92306i
$407$		0			0
$408$	−4.87006	+	4.52560i	−0.241104	+	0.224051i
$409$	−5.16166	−	3.75017i	−0.255228	−	0.185434i	0.452813	−	0.891606i	$-0.350421\pi$
$409$	−5.16166	−	3.75017i	−0.255228	−	0.185434i	−0.708040	+	0.706172i	$0.750421\pi$
$410$	38.9136	+	25.9520i	1.92180	+	1.28168i
$411$	4.20450	−	1.36613i	0.207393	−	0.0673860i
$412$	−18.5674	+	1.49399i	−0.914751	+	0.0736037i
$413$	12.7695	+	17.5757i	0.628346	+	0.864844i
$414$	0.152470	+	3.79593i	0.00749348	+	0.186560i
$415$	13.8711	−	42.6909i	0.680906	−	2.09561i
$416$	24.5945	+	11.2080i	1.20585	+	0.549517i
$417$	12.4867			0.611474
$418$		0			0
$419$		−	11.7890i		−	0.575931i	−0.957641	−	0.287965i	$-0.907021\pi$
$419$		−	11.7890i		−	0.575931i	0.957641	−	0.287965i	$-0.0929788\pi$
$420$	−15.5166	−	37.2758i	−0.757135	−	1.81887i
$421$	3.96404	+	1.28800i	0.193196	+	0.0627731i	0.404017	−	0.914752i	$-0.367614\pi$
$421$	3.96404	+	1.28800i	0.193196	+	0.0627731i	−0.210821	+	0.977525i	$0.567614\pi$
$422$	−32.5993	+	1.30941i	−1.58691	+	0.0637409i
$423$	3.23607	−	2.35114i	0.157343	−	0.114316i
$424$	−2.26956	+	11.5685i	−0.110219	+	0.561815i
$425$	−3.77402	−	11.6153i	−0.183067	−	0.563422i
$426$	18.0563	+	12.0420i	0.874831	+	0.583436i
$427$	4.89983	−	6.74404i	0.237119	−	0.326367i
$428$	−7.50803	+	12.3003i	−0.362914	+	0.594556i
$429$		0			0
$430$	14.8284	+	4.16804i	0.715090	+	0.201001i
$431$	−20.7384	−	15.0673i	−0.998931	−	0.725766i	−0.0370725	−	0.999313i	$-0.511803\pi$
$431$	−20.7384	−	15.0673i	−0.998931	−	0.725766i	−0.961859	+	0.273547i	$0.911803\pi$
$432$	−3.60821	−	22.2763i	−0.173600	−	1.07177i
$433$	−1.03309	−	3.17952i	−0.0496471	−	0.152798i	0.923159	−	0.384417i	$-0.125598\pi$
$433$	−1.03309	−	3.17952i	−0.0496471	−	0.152798i	−0.972806	+	0.231619i	$0.925598\pi$
$434$	18.3146	−	6.77484i	0.879130	−	0.325203i
$435$	22.7758	+	31.3482i	1.09202	+	1.50303i
$436$	8.42341	+	2.00670i	0.403408	+	0.0961033i
$437$	12.7794	+	4.15228i	0.611321	+	0.198630i
$438$	15.2044	−	12.0078i	0.726496	−	0.573755i
$439$	4.51146			0.215320			0.107660	−	0.994188i	$-0.465664\pi$
$439$	4.51146			0.215320			0.107660	+	0.994188i	$0.465664\pi$
$440$		0			0
$441$	6.48528			0.308823
$442$	8.45804	−	6.67979i	0.402308	−	0.317725i
$443$	5.84647	+	1.89963i	0.277774	+	0.0902542i	0.444591	−	0.895734i	$-0.353349\pi$
$443$	5.84647	+	1.89963i	0.277774	+	0.0902542i	−0.166817	+	0.985988i	$0.553349\pi$
$444$	−0.416903	+	1.75002i	−0.0197854	+	0.0830521i
$445$	−22.2849	−	30.6725i	−1.05641	−	1.45402i
$446$	34.1248	−	12.6233i	1.61586	−	0.597729i
$447$	−8.73800	−	26.8928i	−0.413293	−	1.27199i
$448$	−28.5227	−	11.6394i	−1.34757	−	0.549910i
$449$	−14.0309	−	10.1940i	−0.662159	−	0.481087i	0.205232	−	0.978713i	$-0.434205\pi$
$449$	−14.0309	−	10.1940i	−0.662159	−	0.481087i	−0.867391	+	0.497627i	$0.834205\pi$
$450$	8.63589	+	2.42742i	0.407100	+	0.114430i
$451$		0			0
$452$	5.94975	+	3.63170i	0.279853	+	0.170821i
$453$	6.67088	−	9.18168i	0.313426	−	0.431393i
$454$	3.38351	+	2.25651i	0.158796	+	0.105903i
$455$	20.2270	+	62.2522i	0.948255	+	2.91843i
$456$	−16.9487	−	3.32507i	−0.793696	−	0.155711i
$457$	21.2729	−	15.4556i	0.995102	−	0.722984i	0.0340698	−	0.999419i	$-0.489153\pi$
$457$	21.2729	−	15.4556i	0.995102	−	0.722984i	0.961033	+	0.276435i	$0.0891531\pi$
$458$	−29.3008	+	1.17691i	−1.36914	+	0.0549936i
$459$	−8.55827	−	2.78075i	−0.399466	−	0.129794i
$460$	21.3006	−	8.86670i	0.993145	−	0.413412i
$461$			4.85483i			0.226112i	0.993589	+	0.113056i	$0.0360640\pi$
$461$			4.85483i			0.226112i	−0.993589	+	0.113056i	$0.963936\pi$
$462$		0			0
$463$	7.72792			0.359147			0.179573	−	0.983745i	$-0.442528\pi$
$463$	7.72792			0.359147			0.179573	+	0.983745i	$0.442528\pi$
$464$	29.2162	+	4.52260i	1.35633	+	0.209957i
$465$	5.80921	−	17.8789i	0.269396	−	0.829114i
$466$	0.618191	+	15.3907i	0.0286372	+	0.712959i
$467$	−16.8777	−	23.2301i	−0.781006	−	1.07496i	−0.995170	−	0.0981644i	$-0.968703\pi$
$467$	−16.8777	−	23.2301i	−0.781006	−	1.07496i	0.214165	−	0.976798i	$-0.431297\pi$
$468$	0.634918	+	7.89080i	0.0293491	+	0.364752i
$469$	−5.39686	+	1.75355i	−0.249204	+	0.0809712i
$470$	−20.2108	−	13.4789i	−0.932255	−	0.621733i
$471$	−16.2378	−	11.7975i	−0.748200	−	0.543599i
$472$	11.6891	−	10.8624i	0.538036	−	0.499982i
$473$		0			0
$474$	1.79899	−	6.40017i	0.0826303	−	0.293970i
$475$	18.6498	−	25.6692i	0.855711	−	1.17779i
$476$	−9.32705	+	7.99433i	−0.427505	+	0.366420i
$477$	−3.28392	+	1.06701i	−0.150360	+	0.0488551i
$478$	−30.6454	+	11.3362i	−1.40169	+	0.518504i
$479$	−3.11534	+	2.26343i	−0.142343	+	0.103419i	−0.656678	−	0.754171i	$-0.728039\pi$
$479$	−3.11534	+	2.26343i	−0.142343	+	0.103419i	0.514335	+	0.857590i	$0.328039\pi$
$480$	−25.8118	+	14.6041i	−1.17814	+	0.666581i
$481$	0.901222	−	2.77368i	0.0410922	−	0.126469i
$482$	−25.8435	−	32.7234i	−1.17714	−	1.49051i
$483$		−	18.4007i		−	0.837259i
$484$		0			0
$485$			60.9857i			2.76922i
$486$	9.25172	−	7.30660i	0.419666	−	0.331434i
$487$	−10.7845	+	33.1914i	−0.488694	+	1.50405i	0.337865	+	0.941195i	$0.390295\pi$
$487$	−10.7845	+	33.1914i	−0.488694	+	1.50405i	−0.826559	+	0.562851i	$0.809705\pi$
$488$	−5.35007	−	2.97776i	−0.242186	−	0.134797i
$489$	23.9929	−	17.4319i	1.08500	−	0.788296i
$490$	−13.6648	−	36.9406i	−0.617314	−	1.66880i
$491$	22.2939	−	7.24373i	1.00611	−	0.326905i	0.240806	−	0.970573i	$-0.422588\pi$
$491$	22.2939	−	7.24373i	1.00611	−	0.326905i	0.765305	+	0.643668i	$0.222588\pi$
$492$	−17.8309	−	20.8035i	−0.803879	−	0.937892i
$493$	6.92940	−	9.53751i	0.312085	−	0.429548i
$494$	26.9554	+	7.57675i	1.21278	+	0.340894i
$495$		0			0
$496$	−6.55635	−	12.7570i	−0.294389	−	0.572805i
$497$	32.4438	+	23.5718i	1.45530	+	1.05734i
$498$	−14.5894	+	21.8760i	−0.653767	+	0.980288i
$499$	30.3521	−	9.86200i	1.35875	−	0.441484i	0.463122	−	0.886294i	$-0.346729\pi$
$499$	30.3521	−	9.86200i	1.35875	−	0.441484i	0.895625	+	0.444811i	$0.146729\pi$
$500$	−1.51620	−	18.8434i	−0.0678065	−	0.842702i
$501$	−3.33544	−	4.59084i	−0.149017	−	0.205104i
$502$	20.4662	−	0.822057i	0.913449	−	0.0366902i
$503$	−3.36570	+	10.3585i	−0.150069	+	0.461865i	−0.997628	−	0.0688364i	$-0.978071\pi$
$503$	−3.36570	+	10.3585i	−0.150069	+	0.461865i	0.847559	+	0.530701i	$0.178071\pi$
$504$	−1.08405	−	8.95756i	−0.0482875	−	0.399001i
$505$	−16.9981			−0.756406
$506$		0			0
$507$			14.4834i			0.643231i
$508$	11.3310	+	27.2206i	0.502732	+	1.20772i
$509$	−2.90260	−	0.943113i	−0.128656	−	0.0418028i	0.243981	−	0.969780i	$-0.421546\pi$
$509$	−2.90260	−	0.943113i	−0.128656	−	0.0418028i	−0.372637	+	0.927977i	$0.621546\pi$
$510$	0.474627	+	11.8164i	0.0210168	+	0.523241i
$511$	28.9620	−	21.0421i	1.28120	−	0.930849i
$512$	−5.97028	+	21.8256i	−0.263851	+	0.964563i
$513$	−7.22429	−	22.2341i	−0.318960	−	0.981658i
$514$	−14.5048	+	21.7491i	−0.639778	+	0.959311i
$515$	−19.4762	+	26.8067i	−0.858224	+	1.18124i
$516$	−7.70154	−	4.70099i	−0.339041	−	0.206949i
$517$		0			0
$518$	−0.899495	+	3.20009i	−0.0395215	+	0.140604i
$519$	6.23068	+	4.52685i	0.273496	+	0.198707i
$520$	43.6087	−	20.2429i	1.91237	−	0.887708i
$521$	0.458977	+	1.41259i	0.0201082	+	0.0618865i	0.960607	−	0.277910i	$-0.0896417\pi$
$521$	0.458977	+	1.41259i	0.0201082	+	0.0618865i	−0.940499	+	0.339797i	$0.889642\pi$
$522$	3.00418	+	8.12130i	0.131490	+	0.355460i
$523$	−16.9595	−	23.3427i	−0.741586	−	1.02071i	−0.998526	−	0.0542779i	$-0.982714\pi$
$523$	−16.9595	−	23.3427i	−0.741586	−	1.02071i	0.256940	−	0.966427i	$-0.417286\pi$
$524$	−20.6972	−	4.93066i	−0.904162	−	0.215397i
$525$	−41.3230	−	13.4266i	−1.80348	−	0.585987i
$526$	6.17133	+	7.81421i	0.269083	+	0.340716i
$527$	−5.71948			−0.249144
$528$		0			0
$529$	−12.4853			−0.542838
$530$	12.9972	+	16.4572i	0.564560	+	0.714854i
$531$	4.44496	+	1.44426i	0.192895	+	0.0626754i
$532$	−31.0453	−	7.39587i	−1.34598	−	0.320652i
$533$	26.1084	+	35.9351i	1.13088	+	1.55652i
$534$	7.70519	+	20.8297i	0.333436	+	0.901388i
$535$	7.92135	+	24.3794i	0.342470	+	1.05401i
$536$	1.75492	+	3.78059i	0.0758012	+	0.163296i
$537$	23.6915	+	17.2129i	1.02236	+	0.742790i
$538$	2.91642	−	10.3756i	0.125736	−	0.447323i
$539$		0			0
$540$	−34.2635	−	20.9143i	−1.47446	−	0.900007i
$541$	−2.80839	+	3.86541i	−0.120742	+	0.166187i	−0.865109	−	0.501583i	$-0.832751\pi$
$541$	−2.80839	+	3.86541i	−0.120742	+	0.166187i	0.744367	+	0.667770i	$0.232751\pi$
$542$	−12.6047	+	18.9000i	−0.541418	+	0.811826i
$543$	−6.98849	−	21.5084i	−0.299905	−	0.923012i
$544$	6.65247	+	6.09571i	0.285222	+	0.261351i
$545$	12.4614	−	9.05370i	0.533786	−	0.387818i
$546$	−1.53887	−	38.3123i	−0.0658577	−	1.63961i
$547$	−38.5577	−	12.5281i	−1.64861	−	0.535665i	−0.670169	−	0.742209i	$-0.733778\pi$
$547$	−38.5577	−	12.5281i	−1.64861	−	0.535665i	−0.978437	+	0.206544i	$0.933778\pi$
$548$	−2.30580	−	5.53925i	−0.0984989	−	0.236625i
$549$		−	1.79337i		−	0.0765390i
$550$		0			0
$551$	30.6274			1.30477
$552$	−13.4176	+	1.62381i	−0.571090	+	0.0691138i
$553$	3.79605	−	11.6830i	0.161424	−	0.496813i
$554$	7.90992	−	0.317715i	0.336060	−	0.0134984i
$555$	1.88096	+	2.58892i	0.0798424	+	0.109894i
$556$	−1.35920	−	16.8923i	−0.0576431	−	0.716391i
$557$	−23.2199	+	7.54459i	−0.983857	+	0.319675i	−0.756397	−	0.654113i	$-0.773042\pi$
$557$	−23.2199	+	7.54459i	−0.983857	+	0.319675i	−0.227460	+	0.973787i	$0.573042\pi$
$558$	2.33090	−	3.49505i	0.0986748	−	0.147957i
$559$	11.8338	+	8.59778i	0.500518	+	0.363647i
$560$	−48.7386	+	25.0489i	−2.05958	+	1.05851i
$561$		0			0
$562$	−31.4558	−	8.84175i	−1.32688	−	0.372967i
$563$	10.7065	−	14.7362i	0.451224	−	0.621057i	−0.521436	−	0.853291i	$-0.674603\pi$
$563$	10.7065	−	14.7362i	0.451224	−	0.621057i	0.972660	+	0.232233i	$0.0746033\pi$
$564$	9.26095	+	10.8048i	0.389957	+	0.454965i
$565$	11.7925	−	3.83163i	0.496116	−	0.161198i
$566$	−8.75483	−	23.6672i	−0.367993	−	0.994807i
$567$	−18.1575	+	13.1922i	−0.762544	+	0.554021i
$568$	14.3252	−	25.7378i	0.601073	−	1.07993i
$569$	−4.35149	+	13.3925i	−0.182424	+	0.561443i	−0.999894	−	0.0145276i	$-0.995376\pi$
$569$	−4.35149	+	13.3925i	−0.182424	+	0.561443i	0.817471	+	0.575970i	$0.195376\pi$
$570$	−24.1110	+	19.0418i	−1.00990	+	0.797574i
$571$			40.3881i			1.69019i	0.534618	+	0.845094i	$0.320456\pi$
$571$			40.3881i			1.69019i	−0.534618	+	0.845094i	$0.679544\pi$
$572$		0			0
$573$			17.7882i			0.743114i
$574$	−31.3779	−	39.7311i	−1.30969	−	1.65835i
$575$	7.67241	−	23.6132i	0.319961	−	0.984740i
$576$	−6.43609	+	1.58096i	−0.268170	+	0.0658732i
$577$	20.5030	−	14.8963i	0.853553	−	0.620142i	−0.0725707	−	0.997363i	$-0.523120\pi$
$577$	20.5030	−	14.8963i	0.853553	−	0.620142i	0.926123	+	0.377221i	$0.123120\pi$
$578$	−19.1739	+	7.09268i	−0.797527	+	0.295017i
$579$	4.47090	−	1.45268i	0.185804	−	0.0603715i
$580$	39.9295	−	34.2240i	1.65798	−	1.42108i
$581$	−28.5583	+	39.3071i	−1.18480	+	1.63073i
$582$	9.66700	−	34.3918i	0.400710	−	1.42559i
$583$		0			0
$584$	−17.8995	−	19.2619i	−0.740686	−	0.797062i
$585$	11.3923	+	8.27702i	0.471015	+	0.342213i
$586$	3.51150	+	2.34187i	0.145059	+	0.0967417i
$587$	6.28613	−	2.04249i	0.259456	−	0.0843025i	−0.176401	−	0.984318i	$-0.556445\pi$
$587$	6.28613	−	2.04249i	0.259456	−	0.0843025i	0.435857	+	0.900016i	$0.356445\pi$
$588$	1.85049	+	22.9980i	0.0763130	+	0.948422i
$589$	−8.73390	−	12.0212i	−0.359874	−	0.495324i
$590$	−1.13920	−	28.3619i	−0.0469002	−	1.16764i
$591$	−7.13972	+	21.9738i	−0.293689	+	0.903881i
$592$	2.41285	+	0.373504i	0.0991673	+	0.0153509i
$593$	21.7832			0.894531			0.447265	−	0.894401i	$-0.352398\pi$
$593$	21.7832			0.894531			0.447265	+	0.894401i	$0.352398\pi$
$594$		0			0
$595$			21.8516i			0.895826i
$596$	−35.4301	+	14.7483i	−1.45127	+	0.604115i
$597$	−23.5851	−	7.66325i	−0.965272	−	0.313636i
$598$	21.8928	−	0.879361i	0.895264	−	0.0359598i
$599$	−34.6013	+	25.1393i	−1.41377	+	1.02716i	−0.421010	+	0.907056i	$0.638324\pi$
$599$	−34.6013	+	25.1393i	−1.41377	+	1.02716i	−0.992761	+	0.120108i	$0.961676\pi$
$600$	−6.14393	+	31.3171i	−0.250825	+	1.27852i
$601$	−8.21008	−	25.2680i	−0.334896	−	1.03070i	−0.966773	−	0.255635i	$-0.917715\pi$
$601$	−8.21008	−	25.2680i	−0.334896	−	1.03070i	0.631877	−	0.775068i	$-0.282285\pi$
$602$	−13.8705	−	9.25043i	−0.565320	−	0.377019i
$603$	−0.717563	+	0.987641i	−0.0292214	+	0.0402199i
$604$	−13.1474	−	8.02509i	−0.534958	−	0.326536i
$605$		0			0
$606$	9.58579	+	2.69442i	0.389396	+	0.109453i
$607$	26.4345	+	19.2058i	1.07294	+	0.779540i	0.976439	−	0.215793i	$-0.0692336\pi$
$607$	26.4345	+	19.2058i	1.07294	+	0.779540i	0.0965050	+	0.995333i	$0.469234\pi$
$608$	−2.65333	+	23.2906i	−0.107607	+	0.944557i
$609$	−12.9605	−	39.8884i	−0.525187	−	1.61636i
$610$	−10.2151	+	3.77872i	−0.413598	+	0.152996i
$611$	−13.5601	−	18.6639i	−0.548582	−	0.755059i
$612$	−0.612439	+	2.57081i	−0.0247564	+	0.103919i
$613$	−18.1763	−	5.90582i	−0.734132	−	0.238534i	−0.0819924	−	0.996633i	$-0.526128\pi$
$613$	−18.1763	−	5.90582i	−0.734132	−	0.238534i	−0.652139	+	0.758099i	$0.726128\pi$
$614$	31.1980	−	24.6388i	1.25905	−	0.994340i
$615$	−48.7386			−1.96533
$616$		0			0
$617$	13.7990			0.555526			0.277763	−	0.960650i	$-0.410407\pi$
$617$	13.7990			0.555526			0.277763	+	0.960650i	$0.410407\pi$
$618$	15.2325	−	12.0299i	0.612739	−	0.483915i
$619$	2.56254	+	0.832621i	0.102997	+	0.0334659i	0.360062	−	0.932928i	$-0.382755\pi$
$619$	2.56254	+	0.832621i	0.102997	+	0.0334659i	−0.257065	+	0.966394i	$0.582755\pi$
$620$	−24.8194	−	5.91268i	−0.996770	−	0.237459i
$621$	−10.7529	−	14.8001i	−0.431499	−	0.593907i
$622$	13.9074	−	5.14454i	0.557636	−	0.206277i
$623$	12.6812	+	39.0286i	0.508060	+	1.56365i
$624$	−27.8011	+	4.50308i	−1.11293	+	0.180267i
$625$	3.76747	+	2.73723i	0.150699	+	0.109489i
$626$	2.48932	+	0.699709i	0.0994931	+	0.0279660i
$627$		0			0
$628$	−14.1924	+	23.2511i	−0.566338	+	0.927821i
$629$	0.572271	−	0.787664i	0.0228180	−	0.0314062i
$630$	−13.3530	−	8.90532i	−0.531997	−	0.354796i
$631$	2.04422	+	6.29145i	0.0813790	+	0.250459i	0.983465	−	0.181097i	$-0.0579648\pi$
$631$	2.04422	+	6.29145i	0.0813790	+	0.250459i	−0.902086	+	0.431556i	$0.857965\pi$
$632$	−8.85413	−	1.73704i	−0.352198	−	0.0690959i
$633$	27.5035	−	19.9825i	1.09317	−	0.794233i
$634$	−2.58760	+	0.103935i	−0.102767	+	0.00412780i
$635$	49.8812	+	16.2074i	1.97948	+	0.643171i
$636$	−4.72084	−	11.3409i	−0.187194	−	0.449698i
$637$		−	37.4035i		−	1.48198i
$638$		0			0
$639$	8.62742			0.341295
$640$	22.5664	+	33.3292i	0.892015	+	1.31745i
$641$	0.671053	−	2.06529i	0.0265050	−	0.0815740i	−0.936929	−	0.349520i	$-0.886345\pi$
$641$	0.671053	−	2.06529i	0.0265050	−	0.0815740i	0.963434	+	0.267946i	$0.0863448\pi$
$642$	−0.602659	−	15.0040i	−0.0237850	−	0.592159i
$643$	23.8071	+	32.7676i	0.938859	+	1.29223i	0.956302	+	0.292381i	$0.0944476\pi$
$643$	23.8071	+	32.7676i	0.938859	+	1.29223i	−0.0174423	+	0.999848i	$0.505552\pi$
$644$	−24.8929	+	2.00296i	−0.980917	+	0.0789276i
$645$	−15.2646	+	4.95978i	−0.601044	+	0.195291i
$646$	7.77664	+	5.18635i	0.305968	+	0.204054i
$647$	−22.1547	−	16.0964i	−0.870993	−	0.632814i	0.0598602	−	0.998207i	$-0.480935\pi$
$647$	−22.1547	−	16.0964i	−0.870993	−	0.632814i	−0.930853	+	0.365393i	$0.880935\pi$
$648$	11.2220	+	12.0761i	0.440840	+	0.474394i
$649$		0			0
$650$	14.0000	−	49.8071i	0.549125	−	1.95359i
$651$	−11.9602	+	16.4618i	−0.468757	+	0.645188i
$652$	−26.1939	−	30.5607i	−1.02583	−	1.19685i
$653$	2.90260	−	0.943113i	0.113588	−	0.0369069i	−0.251672	−	0.967813i	$-0.580980\pi$
$653$	2.90260	−	0.943113i	0.113588	−	0.0369069i	0.365259	+	0.930906i	$0.380980\pi$
$654$	−8.46248	+	3.13039i	−0.330909	+	0.122408i
$655$	−30.6189	+	22.2459i	−1.19638	+	0.869220i
$656$	−26.2025	+	26.3866i	−1.02304	+	1.03022i
$657$	2.37991	−	7.32460i	0.0928490	−	0.285760i
$658$	16.2970	+	20.6354i	0.635321	+	0.804452i
$659$			49.2011i			1.91660i	0.285763	+	0.958300i	$0.407753\pi$
$659$			49.2011i			1.91660i	−0.285763	+	0.958300i	$0.592247\pi$
$660$		0			0
$661$		−	28.5659i		−	1.11108i	−0.831488	−	0.555542i	$-0.812511\pi$
$661$		−	28.5659i		−	1.11108i	0.831488	−	0.555542i	$-0.187489\pi$
$662$	14.1582	−	11.1815i	0.550273	−	0.434582i
$663$	−3.47040	+	10.6808i	−0.134779	+	0.414808i
$664$	31.1825	+	17.3557i	1.21012	+	0.673530i
$665$	−45.9275	+	33.3683i	−1.78099	+	1.29397i
$666$	0.248103	+	0.670705i	0.00961381	+	0.0259893i
$667$	22.7935	−	7.40605i	0.882567	−	0.286763i
$668$	−5.84753	+	5.01199i	−0.226248	+	0.193920i
$669$	−22.2849	+	30.6725i	−0.861584	+	1.18587i
$670$	7.13761	+	2.00627i	0.275750	+	0.0775090i
$671$		0			0
$672$	31.4558	−	6.40017i	1.21344	−	0.246892i
$673$	−7.74249	−	5.62525i	−0.298451	−	0.216837i	0.428474	−	0.903554i	$-0.359051\pi$
$673$	−7.74249	−	5.62525i	−0.298451	−	0.216837i	−0.726925	+	0.686717i	$0.759051\pi$
$674$	4.79156	−	7.18468i	0.184564	−	0.276743i
$675$	−41.0832	+	13.3487i	−1.58129	+	0.513793i
$676$	19.5935	−	1.57656i	0.753597	−	0.0606368i
$677$	19.4404	+	26.7574i	0.747155	+	1.02837i	0.998175	+	0.0603883i	$0.0192339\pi$
$677$	19.4404	+	26.7574i	0.747155	+	1.02837i	−0.251020	+	0.967982i	$0.580766\pi$
$678$	−7.25755	+	0.291511i	−0.278725	+	0.0111954i
$679$	20.3983	−	62.7796i	0.782816	−	2.40926i
$680$	15.9339	−	1.92834i	0.611038	−	0.0739483i
$681$	−4.23779			−0.162393
$682$		0			0
$683$			16.6722i			0.637943i	0.947764	+	0.318971i	$0.103337\pi$
$683$			16.6722i			0.637943i	−0.947764	+	0.318971i	$0.896663\pi$
$684$	−6.33854	+	2.63852i	−0.242360	+	0.100886i
$685$	−10.1506	−	3.29812i	−0.387833	−	0.126015i
$686$	0.181064	+	4.50782i	0.00691306	+	0.172109i
$687$	24.7206	−	17.9606i	0.943150	−	0.685239i
$688$	−5.52128	+	10.9305i	−0.210497	+	0.416723i
$689$	6.15393	+	18.9398i	0.234446	+	0.721551i
$690$	−13.3393	+	20.0016i	−0.507819	+	0.761447i
$691$	13.7102	−	18.8705i	0.521560	−	0.717866i	−0.464255	−	0.885702i	$-0.653678\pi$
$691$	13.7102	−	18.8705i	0.521560	−	0.717866i	0.985815	+	0.167835i	$0.0536777\pi$
$692$	5.44581	−	8.92177i	0.207019	−	0.339155i
$693$		0			0
$694$	−0.414214	+	1.47363i	−0.0157233	+	0.0559381i
$695$	−24.3882	−	17.7191i	−0.925097	−	0.672122i
$696$	−27.9424	+	12.9707i	−1.05916	+	0.491653i
$697$	4.58224	+	14.1027i	0.173565	+	0.534177i
$698$	9.15704	+	24.7545i	0.346599	+	0.936972i
$699$	−9.43406	−	12.9849i	−0.356829	−	0.491133i
$700$	−13.6658	+	57.3642i	−0.516518	+	2.16816i
$701$	26.4847	+	8.60541i	1.00031	+	0.325022i	0.762991	−	0.646409i	$-0.223730\pi$
$701$	26.4847	+	8.60541i	1.00031	+	0.325022i	0.237323	+	0.971431i	$0.423730\pi$
$702$	−23.6265	−	29.9161i	−0.891724	−	1.12911i
$703$	2.52939			0.0953979
$704$		0			0
$705$	25.3137			0.953369
$706$	−14.7244	−	18.6442i	−0.554159	−	0.701683i
$707$	17.4981	+	5.68549i	0.658085	+	0.213825i
$708$	−3.85329	+	16.1748i	−0.144815	+	0.607885i
$709$	−4.54105	−	6.25021i	−0.170543	−	0.234732i	0.715187	−	0.698933i	$-0.246341\pi$
$709$	−4.54105	−	6.25021i	−0.170543	−	0.234732i	−0.885730	+	0.464201i	$0.846341\pi$
$710$	−18.1784	−	49.1423i	−0.682224	−	1.84428i
$711$	−0.816655	−	2.51341i	−0.0306269	−	0.0942601i
$712$	27.3401	−	12.6911i	1.02462	−	0.475620i
$713$	−9.40678	−	6.83442i	−0.352287	−	0.255951i
$714$	3.46375	−	12.3228i	0.129628	−	0.461169i
$715$		0			0
$716$	20.7071	−	33.9241i	0.773861	−	1.26780i
$717$	20.0127	−	27.5451i	0.747386	−	1.02869i
$718$	14.0710	−	21.0987i	0.525125	−	0.787396i
$719$	−10.9966	−	33.8441i	−0.410104	−	1.26217i	−0.916557	−	0.399904i	$-0.869043\pi$
$719$	−10.9966	−	33.8441i	−0.410104	−	1.26217i	0.506453	−	0.862268i	$-0.330957\pi$
$720$	−5.31529	+	10.5228i	−0.198089	+	0.392160i
$721$	29.0154	−	21.0809i	1.08059	−	0.785093i
$722$	−0.103779	−	2.58370i	−0.00386224	−	0.0961555i
$723$	41.3230	+	13.4266i	1.53682	+	0.499342i
$724$	−28.3363	+	11.7954i	−1.05311	+	0.438374i
$725$		−	56.5921i		−	2.10178i
$726$		0			0
$727$	−8.07107			−0.299339			−0.149670	−	0.988736i	$-0.547821\pi$
$727$	−8.07107			−0.299339			−0.149670	+	0.988736i	$0.547821\pi$
$728$	−51.6622	+	6.25221i	−1.91473	+	0.231722i
$729$	−9.19930	+	28.3125i	−0.340715	+	1.04861i
$730$	−46.7359	+	1.87723i	−1.72978	+	0.0694793i
$731$	2.87025	+	3.95056i	0.106160	+	0.146117i
$732$	6.35961	−	0.511714i	0.235058	−	0.0189135i
$733$	6.17650	−	2.00687i	0.228134	−	0.0741253i	−0.192719	−	0.981254i	$-0.561731\pi$
$733$	6.17650	−	2.00687i	0.228134	−	0.0741253i	0.420853	+	0.907129i	$0.361731\pi$
$734$	4.65223	−	6.97576i	0.171717	−	0.257480i
$735$	33.2034	+	24.1237i	1.22472	+	0.889815i
$736$	3.65726	+	17.9749i	0.134808	+	0.662562i
$737$		0			0
$738$	−10.4853	−	2.94725i	−0.385969	−	0.108490i
$739$	−13.5601	+	18.6639i	−0.498816	+	0.686561i	−0.981983	−	0.188967i	$-0.939486\pi$
$739$	−13.5601	+	18.6639i	−0.498816	+	0.686561i	0.483168	+	0.875528i	$0.339486\pi$
$740$	3.29761	−	2.82642i	0.121223	−	0.103901i
$741$	−27.7483	+	9.01597i	−1.01936	+	0.331210i
$742$	−7.87493	−	21.2885i	−0.289098	−	0.781527i
$743$	−31.1534	+	22.6343i	−1.14291	+	0.830370i	−0.987522	−	0.157484i	$-0.949662\pi$
$743$	−31.1534	+	22.6343i	−1.14291	+	0.830370i	−0.155385	+	0.987854i	$0.549662\pi$
$744$	13.0592	+	7.26853i	0.478774	+	0.266477i
$745$	−21.0954	+	64.9250i	−0.772876	+	2.37867i
$746$	−31.9016	+	25.1945i	−1.16800	+	0.922437i
$747$			10.4525i			0.382437i
$748$		0			0
$749$		−	27.7461i		−	1.01382i
$750$	12.2087	+	15.4589i	0.445800	+	0.564478i
$751$	4.56027	−	14.0351i	0.166407	−	0.512147i	−0.832730	−	0.553679i	$-0.813224\pi$
$751$	4.56027	−	14.0351i	0.166407	−	0.512147i	0.999137	+	0.0415312i	$0.0132236\pi$
$752$	13.6090	−	13.7046i	0.496268	−	0.499755i
$753$	−17.2670	+	12.5452i	−0.629243	+	0.457172i
$754$	46.8392	−	17.3265i	1.70578	−	0.630993i
$755$	−26.0583	+	8.46687i	−0.948360	+	0.308141i
$756$	28.2760	+	32.9898i	1.02839	+	1.19983i
$757$	28.9786	−	39.8857i	1.05325	−	1.44967i	0.167286	−	0.985908i	$-0.446500\pi$
$757$	28.9786	−	39.8857i	1.05325	−	1.44967i	0.885960	−	0.463761i	$-0.153500\pi$
$758$	1.03111	−	3.66832i	0.0374516	−	0.133239i
$759$		0			0
$760$	28.3848	+	30.5452i	1.02962	+	1.10799i
$761$	−23.6323	−	17.1699i	−0.856670	−	0.622407i	0.0703071	−	0.997525i	$-0.477602\pi$
$761$	−23.6323	−	17.1699i	−0.856670	−	0.622407i	−0.926977	+	0.375118i	$0.877602\pi$
$762$	−25.5606	−	17.0467i	−0.925961	−	0.617536i
$763$	−15.8562	+	5.15198i	−0.574032	+	0.186514i
$764$	24.0644	−	1.93629i	0.870618	−	0.0700526i
$765$	2.76317	+	3.80318i	0.0999027	+	0.137504i
$766$	−0.0705303	−	1.75594i	−0.00254837	−	0.0634448i
$767$	8.32967	−	25.6361i	0.300767	−	0.925666i
$768$	−7.44282	−	22.3725i	−0.268570	−	0.807297i
$769$	40.1027			1.44614			0.723071	−	0.690774i	$-0.242730\pi$
$769$	40.1027			1.44614			0.723071	+	0.690774i	$0.242730\pi$
$770$		0			0
$771$		−	27.2404i		−	0.981039i
$772$	−2.45190	−	5.89022i	−0.0882457	−	0.211994i
$773$	46.2083	+	15.0140i	1.66200	+	0.540015i	0.981289	−	0.192540i	$-0.0616725\pi$
$773$	46.2083	+	15.0140i	1.66200	+	0.540015i	0.680707	+	0.732555i	$0.261672\pi$
$774$	−3.58384	+	0.143951i	−0.128819	+	0.00517421i
$775$	−22.2122	+	16.1381i	−0.797887	+	0.579699i
$776$	−47.5783	−	9.33413i	−1.70796	−	0.335076i
$777$	−1.07036	−	3.29422i	−0.0383988	−	0.118179i
$778$	19.4926	+	12.9999i	0.698845	+	0.466069i
$779$	−22.6437	+	31.1663i	−0.811294	+	1.11665i
$780$	−26.1012	+	42.7611i	−0.934572	+	1.53109i
$781$		0			0
$782$	7.04163	+	1.97929i	0.251808	+	0.0707794i
$783$	−33.7342	−	24.5093i	−1.20556	−	0.875892i
$784$	30.9108	−	5.00678i	1.10396	−	0.178814i
$785$	14.9737	+	46.0842i	0.534434	+	1.64482i
$786$	20.7932	−	7.69171i	0.741670	−	0.274354i
$787$	0.527057	+	0.725432i	0.0187876	+	0.0258589i	0.818307	−	0.574781i	$-0.194913\pi$
$787$	0.527057	+	0.725432i	0.0187876	+	0.0258589i	−0.799520	+	0.600640i	$0.794913\pi$
$788$	30.5039	+	7.26689i	1.08666	+	0.258872i
$789$	−9.86776	−	3.20623i	−0.351302	−	0.114145i
$790$	−12.5958	+	9.94759i	−0.448137	+	0.353919i
$791$	−13.4210			−0.477196
$792$		0			0
$793$	−10.3431			−0.367296
$794$	40.0454	−	31.6261i	1.42116	−	1.12237i
$795$	−20.7821	−	6.75250i	−0.737064	−	0.239487i
$796$	−7.79974	+	32.7406i	−0.276455	+	1.16046i
$797$	3.52626	+	4.85348i	0.124907	+	0.171919i	0.866891	−	0.498498i	$-0.166115\pi$
$797$	3.52626	+	4.85348i	0.124907	+	0.171919i	−0.741984	+	0.670417i	$0.766115\pi$
$798$	31.1893	−	11.5374i	1.10409	−	0.408418i
$799$	−2.37991	−	7.32460i	−0.0841950	−	0.259126i
$800$	43.0353	+	4.90272i	1.52153	+	0.173337i
$801$	7.14235	+	5.18922i	0.252362	+	0.183352i
$802$	15.5966	+	4.38396i	0.550735	+	0.154803i
$803$		0			0
$804$	−3.70711	−	2.26280i	−0.130740	−	0.0798029i
$805$	−26.1113	+	35.9391i	−0.920301	+	1.26669i
$806$	−20.1575	−	13.4433i	−0.710019	−	0.473521i
$807$	3.47040	+	10.6808i	0.122164	+	0.375982i
$808$	2.60164	−	13.2612i	0.0915253	−	0.466527i
$809$	7.52109	−	5.46439i	0.264427	−	0.192118i	−0.447669	−	0.894199i	$-0.647746\pi$
$809$	7.52109	−	5.46439i	0.264427	−	0.192118i	0.712097	+	0.702081i	$0.247746\pi$
$810$	29.3008	−	1.17691i	1.02952	−	0.0413525i
$811$	2.55839	+	0.831271i	0.0898372	+	0.0291899i	0.353591	−	0.935400i	$-0.384961\pi$
$811$	2.55839	+	0.831271i	0.0898372	+	0.0291899i	−0.263754	+	0.964590i	$0.584961\pi$
$812$	−52.5512	+	21.8753i	−1.84419	+	0.767671i
$813$		−	23.6720i		−	0.830213i
$814$		0			0
$815$	−71.5980			−2.50797
$816$	−9.29131	−	1.43828i	−0.325261	−	0.0503497i
$817$	−3.92028	+	12.0654i	−0.137153	+	0.422114i
$818$	−0.362128	−	9.01564i	−0.0126615	−	0.315225i
$819$	−8.95898	−	12.3310i	−0.313052	−	0.430879i
$820$	5.30532	+	65.9348i	0.185270	+	2.30254i
$821$	1.70559	−	0.554181i	0.0595256	−	0.0193410i	−0.279103	−	0.960261i	$-0.590037\pi$
$821$	1.70559	−	0.554181i	0.0595256	−	0.0193410i	0.338628	+	0.940920i	$0.390037\pi$
$822$	5.20144	+	3.46891i	0.181421	+	0.120992i
$823$	1.83815	+	1.33549i	0.0640739	+	0.0465524i	0.619361	−	0.785106i	$-0.287392\pi$
$823$	1.83815	+	1.33549i	0.0640739	+	0.0465524i	−0.555287	+	0.831659i	$0.687392\pi$
$824$	−17.9325	−	19.2974i	−0.624707	−	0.672255i
$825$		0			0
$826$	−8.31371	+	29.5772i	−0.289271	+	1.02912i
$827$	−13.4509	+	18.5136i	−0.467735	+	0.643781i	−0.976090	−	0.217366i	$-0.930254\pi$
$827$	−13.4509	+	18.5136i	−0.467735	+	0.643781i	0.508356	+	0.861147i	$0.330254\pi$
$828$	−4.07923	+	3.49636i	−0.141763	+	0.121507i
$829$	−29.9708	+	9.73810i	−1.04093	+	0.338218i	−0.779102	−	0.626897i	$-0.784325\pi$
$829$	−29.9708	+	9.73810i	−1.04093	+	0.338218i	−0.261826	+	0.965115i	$0.584325\pi$
$830$	59.5381	−	22.0240i	2.06660	−	0.764463i
$831$	−6.67348	+	4.84856i	−0.231500	+	0.168195i
$832$	9.11809	+	37.1198i	0.316113	+	1.28690i
$833$	3.85859	−	11.8755i	0.133692	−	0.411462i
$834$	10.9446	+	13.8582i	0.378980	+	0.479870i
$835$			13.6997i			0.474097i
$836$		0			0
$837$			20.2298i			0.699245i
$838$	13.0839	−	10.3331i	0.451976	−	0.356951i
$839$	−1.62007	+	4.98605i	−0.0559309	+	0.172137i	−0.975119	−	0.221680i	$-0.928846\pi$
$839$	−1.62007	+	4.98605i	−0.0559309	+	0.172137i	0.919189	+	0.393818i	$0.128846\pi$
$840$	27.7698	−	49.8934i	0.958149	−	1.72148i
$841$	20.7330	−	15.0634i	0.714932	−	0.519428i
$842$	2.04503	+	5.52838i	0.0704763	+	0.190521i
$843$	32.3812	−	10.5213i	1.11527	−	0.362372i
$844$	−30.0266	−	35.0323i	−1.03356	−	1.20586i
$845$	20.5525	−	28.2882i	0.707029	−	0.973142i
$846$	5.44581	+	1.53073i	0.187231	+	0.0526277i
$847$		0			0
$848$	−14.8284	+	7.62096i	−0.509210	+	0.261705i
$849$	21.2729	+	15.4556i	0.730083	+	0.530436i
$850$	9.58312	−	14.3694i	0.328698	−	0.492865i
$851$	1.88242	−	0.611636i	0.0645285	−	0.0209666i
$852$	2.46172	+	30.5944i	0.0843372	+	1.04815i
$853$	18.8681	+	25.9697i	0.646032	+	0.889187i	0.998919	−	0.0464793i	$-0.0148001\pi$
$853$	18.8681	+	25.9697i	0.646032	+	0.889187i	−0.352887	+	0.935666i	$0.614800\pi$
$854$	11.7795	−	0.473143i	0.403086	−	0.0161906i
$855$	−3.77402	+	11.6153i	−0.129069	+	0.397233i
$856$	−20.2321	+	2.44851i	−0.691520	+	0.0836883i
$857$	24.9733			0.853073			0.426536	−	0.904470i	$-0.359734\pi$
$857$	24.9733			0.853073			0.426536	+	0.904470i	$0.359734\pi$
$858$		0			0
$859$		−	49.5542i		−	1.69077i	−0.534159	−	0.845384i	$-0.679372\pi$
$859$		−	49.5542i		−	1.69077i	0.534159	−	0.845384i	$-0.320628\pi$
$860$	8.37130	+	20.1105i	0.285459	+	0.685761i
$861$	50.1723	+	16.3020i	1.70987	+	0.555570i
$862$	−1.45495	−	36.2228i	−0.0495557	−	1.23375i
$863$	−27.1140	+	19.6995i	−0.922971	+	0.670577i	−0.944262	−	0.329196i	$-0.893222\pi$
$863$	−27.1140	+	19.6995i	−0.922971	+	0.670577i	0.0212911	+	0.999773i	$0.493222\pi$
$864$	21.5606	−	23.5298i	0.733505	−	0.800500i
$865$	−5.74560	−	17.6831i	−0.195356	−	0.601245i
$866$	2.62325	−	3.93342i	0.0891417	−	0.133663i
$867$	12.5213	−	17.2341i	0.425246	−	0.585300i
$868$	23.5718	+	14.3881i	0.800079	+	0.488365i
$869$		0			0
$870$	−14.8284	+	52.7543i	−0.502731	+	1.78854i
$871$	5.69617	+	4.13851i	0.193007	+	0.140228i
$872$	5.15603	+	11.1075i	0.174605	+	0.376148i
$873$	−4.38835	−	13.5060i	−0.148523	−	0.457108i
$874$	6.59281	+	17.8226i	0.223005	+	0.602857i
$875$	21.3942	+	29.4466i	0.723257	+	0.995478i
$876$	26.6535	+	6.34961i	0.900537	+	0.214533i
$877$	13.2789	+	4.31459i	0.448398	+	0.145693i	0.524507	−	0.851406i	$-0.324250\pi$
$877$	13.2789	+	4.31459i	0.448398	+	0.145693i	−0.0761088	+	0.997100i	$0.524250\pi$
$878$	3.95430	+	5.00699i	0.133451	+	0.168978i
$879$	−4.39810			−0.148344
$880$		0			0
$881$	−24.1716			−0.814361			−0.407180	−	0.913348i	$-0.633488\pi$
$881$	−24.1716			−0.814361			−0.407180	+	0.913348i	$0.633488\pi$
$882$	5.68437	+	7.19762i	0.191403	+	0.242356i
$883$	25.4262	+	8.26148i	0.855661	+	0.278021i	0.703815	−	0.710383i	$-0.251478\pi$
$883$	25.4262	+	8.26148i	0.855661	+	0.278021i	0.151846	+	0.988404i	$0.451478\pi$
$884$	14.8270	+	3.53221i	0.498686	+	0.118801i
$885$	17.3851	+	23.9285i	0.584393	+	0.804347i
$886$	3.01616	+	8.15367i	0.101330	+	0.273928i
$887$	12.8853	+	39.6569i	0.432647	+	1.33155i	0.895479	+	0.445104i	$0.146833\pi$
$887$	12.8853	+	39.6569i	0.432647	+	1.33155i	−0.462832	+	0.886446i	$0.653167\pi$
$888$	−2.30765	+	1.07120i	−0.0774398	+	0.0359471i
$889$	−45.9275	−	33.3683i	−1.54036	−	1.11914i
$890$	14.5088	−	51.6172i	0.486336	−	1.73021i
$891$		0			0
$892$	43.9203	+	26.8088i	1.47056	+	0.897624i
$893$	11.7606	−	16.1871i	0.393553	−	0.541680i
$894$	22.1878	−	33.2694i	0.742071	−	1.11269i
$895$	−21.8470	−	67.2383i	−0.730266	−	2.24753i
$896$	−12.0824	−	41.8576i	−0.403643	−	1.39836i
$897$	−18.4706	+	13.4197i	−0.616716	+	0.448071i
$898$	−0.984370	−	24.5072i	−0.0328489	−	0.817814i
$899$	−25.2055	−	8.18978i	−0.840652	−	0.273144i
$900$	4.87534	+	11.7121i	0.162511	+	0.390403i
$901$			6.64820i			0.221484i
$902$		0			0
$903$	17.3726			0.578123
$904$	1.18437	+	9.78646i	0.0393914	+	0.325493i
$905$	−16.8717	+	51.9258i	−0.560834	+	1.72607i
$906$	16.0372	−	0.644162i	0.532802	−	0.0214009i
$907$	−26.5287	−	36.5136i	−0.880872	−	1.21242i	−0.976179	−	0.216968i	$-0.930383\pi$
$907$	−26.5287	−	36.5136i	−0.880872	−	1.21242i	0.0953071	−	0.995448i	$-0.469617\pi$
$908$	0.461294	+	5.73299i	0.0153086	+	0.190256i
$909$	3.76442	−	1.22314i	0.124858	−	0.0405689i
$910$	−51.3609	+	77.0129i	−1.70260	+	2.55295i
$911$	18.7462	+	13.6199i	0.621089	+	0.451248i	0.853302	−	0.521417i	$-0.174597\pi$
$911$	18.7462	+	13.6199i	0.621089	+	0.451248i	−0.232213	+	0.972665i	$0.574597\pi$
$912$	−11.1653	−	21.7248i	−0.369720	−	0.719379i
$913$		0			0
$914$	35.7990	+	10.0625i	1.18413	+	0.332839i
$915$	6.67088	−	9.18168i	0.220533	−	0.303537i
$916$	−26.9884	−	31.4876i	−0.891722	−	1.04038i
$917$	38.9603	−	12.6590i	1.28658	−	0.418036i
$918$	−4.41516	−	11.9356i	−0.145722	−	0.393935i
$919$	−26.4345	+	19.2058i	−0.871994	+	0.633541i	−0.931121	−	0.364709i	$-0.881168\pi$
$919$	−26.4345	+	19.2058i	−0.871994	+	0.633541i	0.0591270	+	0.998250i	$0.481168\pi$
$920$	28.5106	+	15.8685i	0.939967	+	0.523170i
$921$	−12.8008	+	39.3967i	−0.421799	+	1.29816i
$922$	−5.38808	+	4.25527i	−0.177447	+	0.140140i
$923$		−	49.7582i		−	1.63781i
$924$		0			0
$925$		−	4.67371i		−	0.153671i
$926$	6.77354	+	8.57675i	0.222592	+	0.281850i
$927$	2.38429	−	7.33809i	0.0783104	−	0.241015i
$928$	20.5887	+	36.3893i	0.675857	+	1.19454i
$929$	−46.9903	+	34.1405i	−1.54170	+	1.12011i	−0.592447	+	0.805610i	$0.701838\pi$
$929$	−46.9903	+	34.1405i	−1.54170	+	1.12011i	−0.949256	+	0.314503i	$0.898162\pi$
$930$	24.9345	−	9.22362i	0.817634	−	0.302454i
$931$	30.8522	−	10.0245i	1.01114	−	0.328539i
$932$	−16.5393	+	14.1761i	−0.541763	+	0.464352i
$933$	−9.08209	+	12.5004i	−0.297334	+	0.409246i
$934$	10.9884	−	39.0928i	0.359551	−	1.27915i
$935$		0			0
$936$	−8.20101	+	7.62096i	−0.268058	+	0.249099i
$937$	−31.3748	−	22.7951i	−1.02497	−	0.744684i	−0.0576738	−	0.998335i	$-0.518368\pi$
$937$	−31.3748	−	22.7951i	−1.02497	−	0.744684i	−0.967296	+	0.253652i	$0.918368\pi$
$938$	−6.67652	−	4.45266i	−0.217996	−	0.145384i
$939$	−2.56254	+	0.832621i	−0.0836254	+	0.0271716i
$940$	−2.75546	−	34.2450i	−0.0898732	−	1.11695i
$941$	−30.9375	−	42.5817i	−1.00853	−	1.38813i	−0.919941	−	0.392057i	$-0.871763\pi$
$941$	−30.9375	−	42.5817i	−1.00853	−	1.38813i	−0.0885913	−	0.996068i	$-0.528237\pi$
$942$	−1.13920	−	28.3619i	−0.0371172	−	0.924081i
$943$	−9.31546	+	28.6700i	−0.303353	+	0.933625i
$944$	22.3011	+	3.45216i	0.725838	+	0.112358i
$945$	77.2891			2.51421
$946$		0			0
$947$			29.9348i			0.972750i	0.873750	+	0.486375i	$0.161681\pi$
$947$			29.9348i			0.972750i	−0.873750	+	0.486375i	$0.838319\pi$
$948$	8.67998	−	3.61318i	0.281913	−	0.117351i
$949$	−42.2442	−	13.7260i	−1.37131	−	0.445564i
$950$	44.8353	−	1.80088i	1.45465	−	0.0584284i
$951$	2.18312	−	1.58613i	0.0707925	−	0.0514338i
$952$	−17.0476	−	3.34448i	−0.552516	−	0.108395i
$953$	−13.7865	−	42.4306i	−0.446590	−	1.37446i	−0.880731	−	0.473618i	$-0.842948\pi$
$953$	−13.7865	−	42.4306i	−0.446590	−	1.37446i	0.434141	−	0.900845i	$-0.357052\pi$
$954$	−4.06258	−	2.70939i	−0.131531	−	0.0877197i
$955$	25.2422	−	34.7429i	0.816819	−	1.12425i
$956$	−39.4421	−	24.0753i	−1.27565	−	0.778650i
$957$		0			0
$958$	−5.24264	−	1.47363i	−0.169382	−	0.0476107i
$959$	9.34601	+	6.79028i	0.301799	+	0.219269i
$960$	−38.8323	−	15.8465i	−1.25331	−	0.511443i
$961$	−5.60623	−	17.2542i	−0.180846	−	0.556587i
$962$	3.86826	−	1.43092i	0.124718	−	0.0461348i
$963$	−3.50854	−	4.82909i	−0.113061	−	0.155615i
$964$	13.6658	−	57.3642i	0.440145	−	1.84758i
$965$	−10.7937	−	3.50709i	−0.347462	−	0.112897i
$966$	20.4218	−	16.1282i	0.657060	−	0.518917i
$967$	33.9962			1.09325			0.546623	−	0.837379i	$-0.315913\pi$
$967$	33.9962			1.09325			0.546623	+	0.837379i	$0.315913\pi$
$968$		0			0
$969$	−9.74012			−0.312898
$970$	−67.6843	+	53.4541i	−2.17321	+	1.71631i
$971$	−23.3446	−	7.58512i	−0.749164	−	0.243418i	−0.0905426	−	0.995893i	$-0.528860\pi$
$971$	−23.3446	−	7.58512i	−0.749164	−	0.243418i	−0.658621	+	0.752474i	$0.728860\pi$
$972$	16.2183	+	3.86366i	0.520202	+	0.123927i
$973$	19.1790	+	26.3976i	0.614850	+	0.846268i
$974$	−46.2898	+	17.1232i	−1.48322	+	0.548664i
$975$	16.6593	+	51.2722i	0.533526	+	1.64202i
$976$	−1.38452	−	8.54773i	−0.0443174	−	0.273606i
$977$	48.7948	+	35.4515i	1.56108	+	1.13419i	0.935114	+	0.354348i	$0.115297\pi$
$977$	48.7948	+	35.4515i	1.56108	+	1.13419i	0.625971	+	0.779847i	$0.284703\pi$
$978$	40.3764	+	11.3492i	1.29110	+	0.362907i
$979$		0			0
$980$	29.0208	−	47.5443i	0.927036	−	1.51875i
$981$	−2.10823	+	2.90173i	−0.0673105	+	0.0926450i
$982$	27.5801	+	18.3935i	0.880115	+	0.586961i
$983$	13.5127	+	41.5877i	0.430987	+	1.32644i	0.897143	+	0.441740i	$0.145639\pi$
$983$	13.5127	+	41.5877i	0.430987	+	1.32644i	−0.466156	+	0.884703i	$0.654361\pi$
$984$	7.45966	−	38.0237i	0.237805	−	1.21215i
$985$	45.1265	−	32.7864i	1.43785	−	1.04466i
$986$	16.6587	−	0.669126i	0.530522	−	0.0213093i
$987$	−26.0583	−	8.46687i	−0.829446	−	0.269503i
$988$	15.2175	+	36.5572i	0.484133	+	1.16304i
$989$			9.92724i			0.315668i
$990$		0			0
$991$	−39.4558			−1.25336			−0.626678	−	0.779278i	$-0.715586\pi$
$991$	−39.4558			−1.25336			−0.626678	+	0.779278i	$0.715586\pi$
$992$	8.41152	−	18.4580i	0.267066	−	0.586042i
$993$	−5.80921	+	17.8789i	−0.184350	+	0.567370i
$994$	2.27617	+	56.6681i	0.0721957	+	1.79740i
$995$	35.1905	+	48.4355i	1.11561	+	1.53551i
$996$	−37.0665	+	2.98249i	−1.17450	+	0.0945037i
$997$	11.5734	−	3.76041i	0.366532	−	0.119093i	−0.119960	−	0.992779i	$-0.538276\pi$
$997$	11.5734	−	3.76041i	0.366532	−	0.119093i	0.486491	+	0.873685i	$0.338276\pi$
$998$	37.5489	+	25.0419i	1.18859	+	0.792687i
$999$	−2.78597	−	2.02413i	−0.0881443	−	0.0640405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.c.565.6		32
8.5	even	2	inner	968.2.o.c.565.7		32
11.2	odd	10	inner	968.2.o.c.269.5		32
11.3	even	5	inner	968.2.o.c.245.7		32
11.4	even	5	inner	968.2.o.c.493.2		32
11.5	even	5		968.2.c.c.485.1	✓	8
11.6	odd	10		968.2.c.c.485.8	yes	8
11.7	odd	10	inner	968.2.o.c.493.7		32
11.8	odd	10	inner	968.2.o.c.245.2		32
11.9	even	5	inner	968.2.o.c.269.4		32
11.10	odd	2	inner	968.2.o.c.565.3		32
44.27	odd	10		3872.2.c.c.1937.6		8
44.39	even	10		3872.2.c.c.1937.5		8
88.5	even	10		968.2.c.c.485.2	yes	8
88.13	odd	10	inner	968.2.o.c.269.7		32
88.21	odd	2	inner	968.2.o.c.565.2		32
88.27	odd	10		3872.2.c.c.1937.4		8
88.29	odd	10	inner	968.2.o.c.493.5		32
88.37	even	10	inner	968.2.o.c.493.4		32
88.53	even	10	inner	968.2.o.c.269.2		32
88.61	odd	10		968.2.c.c.485.7	yes	8
88.69	even	10	inner	968.2.o.c.245.6		32
88.83	even	10		3872.2.c.c.1937.3		8
88.85	odd	10	inner	968.2.o.c.245.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.2.c.c.485.1	✓	8	11.5	even	5
968.2.c.c.485.2	yes	8	88.5	even	10
968.2.c.c.485.7	yes	8	88.61	odd	10
968.2.c.c.485.8	yes	8	11.6	odd	10
968.2.o.c.245.2		32	11.8	odd	10	inner
968.2.o.c.245.3		32	88.85	odd	10	inner
968.2.o.c.245.6		32	88.69	even	10	inner
968.2.o.c.245.7		32	11.3	even	5	inner
968.2.o.c.269.2		32	88.53	even	10	inner
968.2.o.c.269.4		32	11.9	even	5	inner
968.2.o.c.269.5		32	11.2	odd	10	inner
968.2.o.c.269.7		32	88.13	odd	10	inner
968.2.o.c.493.2		32	11.4	even	5	inner
968.2.o.c.493.4		32	88.37	even	10	inner
968.2.o.c.493.5		32	88.29	odd	10	inner
968.2.o.c.493.7		32	11.7	odd	10	inner
968.2.o.c.565.2		32	88.21	odd	2	inner
968.2.o.c.565.3		32	11.10	odd	2	inner
968.2.o.c.565.6		32	1.1	even	1	trivial
968.2.o.c.565.7		32	8.5	even	2	inner
3872.2.c.c.1937.3		8	88.83	even	10
3872.2.c.c.1937.4		8	88.27	odd	10
3872.2.c.c.1937.5		8	44.39	even	10
3872.2.c.c.1937.6		8	44.27	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 $\F_{q}$

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+(0.876503 + 1.10984i) q^{2} +(-1.40150 - 0.455375i) q^{3} +(-0.463486 + 1.94555i) q^{4} +(2.09113 + 2.87820i) q^{5} +(-0.723026 - 1.95458i) q^{6} +(-1.18995 - 3.66230i) q^{7} +(-2.56550 + 1.19089i) q^{8} +(-0.670212 - 0.486937i) q^{9} +(-1.36145 + 4.84357i) q^{10} +(1.53553 - 2.51564i) q^{12} +(-2.80839 + 3.86541i) q^{13} +(3.02157 - 4.53067i) q^{14} +(-1.62007 - 4.98605i) q^{15} +(-3.57036 - 1.80347i) q^{16} +(-1.29042 + 0.937542i) q^{17} +(-0.0470202 - 1.17063i) q^{18} +(-3.94104 - 1.28052i) q^{19} +(-6.56890 + 2.73441i) q^{20} +5.67459i q^{21} -3.24264 q^{23} +(4.13785 - 0.500766i) q^{24} +(-2.36610 + 7.28210i) q^{25} +(-6.75154 + 0.271187i) q^{26} +(3.31609 + 4.56421i) q^{27} +(7.67673 - 0.617693i) q^{28} +(-7.02929 + 2.28396i) q^{29} +(4.11372 - 6.16830i) q^{30} +(2.90096 + 2.10767i) q^{31} +(-1.12786 - 5.54328i) q^{32} +(-2.17157 - 0.610396i) q^{34} +(8.05247 - 11.0833i) q^{35} +(1.25800 - 1.07824i) q^{36} +(-0.580521 + 0.188623i) q^{37} +(-2.03316 - 5.49631i) q^{38} +(5.69617 - 4.13851i) q^{39} +(-8.79241 - 4.89371i) q^{40} +(2.87280 - 8.84157i) q^{41} +(-6.29789 + 4.97380i) q^{42} -3.06147i q^{43} -2.94725i q^{45} +(-2.84218 - 3.59881i) q^{46} +(-1.49207 + 4.59211i) q^{47} +(4.18261 + 4.15343i) q^{48} +(-6.33333 + 4.60143i) q^{49} +(-10.1559 + 3.75679i) q^{50} +(2.23545 - 0.726342i) q^{51} +(-6.21872 - 7.25543i) q^{52} +(2.44991 - 3.37202i) q^{53} +(-2.15897 + 7.68087i) q^{54} +(7.41421 + 7.97852i) q^{56} +(4.94026 + 3.58931i) q^{57} +(-8.69602 - 5.79949i) q^{58} +(-5.36555 + 1.74337i) q^{59} +(10.4515 - 0.840960i) q^{60} +(1.27243 + 1.75135i) q^{61} +(0.203524 + 5.06698i) q^{62} +(-0.985790 + 3.03395i) q^{63} +(5.16357 - 6.11045i) q^{64} -16.9981 q^{65} -1.47363i q^{67} +(-1.22595 - 2.94511i) q^{68} +(4.54457 + 1.47662i) q^{69} +(19.3587 - 0.777573i) q^{70} +(-8.42528 + 6.12132i) q^{71} +(2.29932 + 0.451090i) q^{72} +(2.87280 + 8.84157i) q^{73} +(-0.718169 - 0.478957i) q^{74} +(6.63218 - 9.12841i) q^{75} +(4.31795 - 7.07401i) q^{76} +(9.58579 + 2.69442i) q^{78} +(2.58083 + 1.87508i) q^{79} +(-2.27534 - 14.0475i) q^{80} +(-1.80108 - 5.54316i) q^{81} +(12.3307 - 4.56132i) q^{82} +(-7.41626 - 10.2076i) q^{83} +(-11.0402 - 2.63010i) q^{84} +(-5.39686 - 1.75355i) q^{85} +(3.39774 - 2.68338i) q^{86} +10.8916 q^{87} -10.6569 q^{89} +(3.27098 - 2.58327i) q^{90} +(17.4981 + 5.68549i) q^{91} +(1.50292 - 6.30873i) q^{92} +(-3.10592 - 4.27493i) q^{93} +(-6.40430 + 2.36904i) q^{94} +(-4.55565 - 14.0208i) q^{95} +(-0.943569 + 8.28251i) q^{96} +(13.8683 + 10.0759i) q^{97} +(-10.6580 - 2.99581i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{4} + 16 q^{9} - 64 q^{12} - 8 q^{14} + 8 q^{15} + 8 q^{16} - 24 q^{20} + 32 q^{23} + 16 q^{25} - 8 q^{26} + 40 q^{31} - 160 q^{34} + 24 q^{38} - 40 q^{42} + 16 q^{47} - 8 q^{48} - 40 q^{49}+ \cdots + 24 q^{97}+O(q^{100}) \) 32 * q - 8 * q^4 + 16 * q^9 - 64 * q^12 - 8 * q^14 + 8 * q^15 + 8 * q^16 - 24 * q^20 + 32 * q^23 + 16 * q^25 - 8 * q^26 + 40 * q^31 - 160 * q^34 + 24 * q^38 - 40 * q^42 + 16 * q^47 - 8 * q^48 - 40 * q^49 + 192 * q^56 + 32 * q^60 + 16 * q^64 - 8 * q^70 - 72 * q^71 + 352 * q^78 - 56 * q^80 + 24 * q^81 + 56 * q^82 + 32 * q^86 - 160 * q^89 + 16 * q^92 + 24 * q^97

Introduction

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