LMFDB - Embedded newform 961.2.d.n.628.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6,-9,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			628.3
Root			$-0.176392i$ of defining polynomial
Character	$\chi$	$=$	961.628
Dual form			961.2.d.n.531.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.380762 - 1.17187i) q^{2} +(-0.641202 - 1.97342i) q^{3} +(0.389745 + 0.283166i) q^{4} -1.54562 q^{5} -2.55673 q^{6} +(3.07730 + 2.23579i) q^{7} +(2.47393 - 1.79742i) q^{8} +(-1.05619 + 0.767366i) q^{9} +(-0.588515 + 1.81126i) q^{10} +(-3.04314 - 2.21097i) q^{11} +(0.308900 - 0.950697i) q^{12} +(0.814279 + 2.50609i) q^{13} +(3.79177 - 2.75488i) q^{14} +(0.991057 + 3.05016i) q^{15} +(-0.866611 - 2.66715i) q^{16} +(3.05350 - 2.21850i) q^{17} +(0.497093 + 1.52989i) q^{18} +(1.88448 - 5.79984i) q^{19} +(-0.602399 - 0.437668i) q^{20} +(2.43898 - 7.50641i) q^{21} +(-3.74967 + 2.72429i) q^{22} +(0.736082 - 0.534795i) q^{23} +(-5.13334 - 3.72959i) q^{24} -2.61105 q^{25} +3.24685 q^{26} +(-2.84451 - 2.06665i) q^{27} +(0.566263 + 1.74278i) q^{28} +(2.10397 - 6.47535i) q^{29} +3.95173 q^{30} +2.66037 q^{32} +(-2.41190 + 7.42306i) q^{33} +(-1.43713 - 4.42302i) q^{34} +(-4.75635 - 3.45569i) q^{35} -0.628936 q^{36} +1.81406 q^{37} +(-6.07909 - 4.41672i) q^{38} +(4.42345 - 3.21383i) q^{39} +(-3.82376 + 2.77813i) q^{40} +(0.104183 - 0.320644i) q^{41} +(-7.86783 - 5.71631i) q^{42} +(-1.20022 + 3.69390i) q^{43} +(-0.559976 - 1.72343i) q^{44} +(1.63247 - 1.18606i) q^{45} +(-0.346435 - 1.06622i) q^{46} +(-0.367467 - 1.13095i) q^{47} +(-4.70774 + 3.42037i) q^{48} +(2.30792 + 7.10304i) q^{49} +(-0.994189 + 3.05980i) q^{50} +(-6.33595 - 4.60333i) q^{51} +(-0.392280 + 1.20731i) q^{52} +(-1.89644 + 1.37784i) q^{53} +(-3.50492 + 2.54647i) q^{54} +(4.70354 + 3.41732i) q^{55} +11.6317 q^{56} -12.6538 q^{57} +(-6.78713 - 4.93114i) q^{58} +(2.40379 + 7.39811i) q^{59} +(-0.477443 + 1.46942i) q^{60} +2.72343 q^{61} -4.96588 q^{63} +(2.74619 - 8.45191i) q^{64} +(-1.25857 - 3.87348i) q^{65} +(7.78047 + 5.65284i) q^{66} -7.42118 q^{67} +1.81829 q^{68} +(-1.52735 - 1.10969i) q^{69} +(-5.86065 + 4.25801i) q^{70} +(4.12451 - 2.99664i) q^{71} +(-1.23366 + 3.79682i) q^{72} +(4.36201 + 3.16919i) q^{73} +(0.690727 - 2.12584i) q^{74} +(1.67421 + 5.15269i) q^{75} +(2.37679 - 1.72684i) q^{76} +(-4.42139 - 13.6076i) q^{77} +(-2.08189 - 6.40740i) q^{78} +(-7.87758 + 5.72340i) q^{79} +(1.33945 + 4.12241i) q^{80} +(-3.46475 + 10.6634i) q^{81} +(-0.336082 - 0.244178i) q^{82} +(2.59424 - 7.98426i) q^{83} +(3.07614 - 2.23495i) q^{84} +(-4.71957 + 3.42897i) q^{85} +(3.87175 + 2.81299i) q^{86} -14.1277 q^{87} -11.5025 q^{88} +(4.12243 + 2.99512i) q^{89} +(-0.768318 - 2.36464i) q^{90} +(-3.09732 + 9.53258i) q^{91} +0.438320 q^{92} -1.46523 q^{94} +(-2.91270 + 8.96437i) q^{95} +(-1.70584 - 5.25003i) q^{96} +(-8.82979 - 6.41522i) q^{97} +9.20257 q^{98} +4.91075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 9 q^{3} - 14 q^{4} + 6 q^{5} + 22 q^{6} + 11 q^{7} + 17 q^{8} + 5 q^{9} + 19 q^{10} - 14 q^{11} - 5 q^{12} + q^{13} + 27 q^{14} - 14 q^{15} - 2 q^{16} + 3 q^{17} - 9 q^{18} + 13 q^{19}+ \cdots + 12 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 - 9 * q^3 - 14 * q^4 + 6 * q^5 + 22 * q^6 + 11 * q^7 + 17 * q^8 + 5 * q^9 + 19 * q^10 - 14 * q^11 - 5 * q^12 + q^13 + 27 * q^14 - 14 * q^15 - 2 * q^16 + 3 * q^17 - 9 * q^18 + 13 * q^19 - 29 * q^20 + 3 * q^21 - 12 * q^22 - q^23 - 25 * q^24 + 26 * q^25 + 18 * q^26 - 9 * q^27 - 15 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 - 49 * q^34 - 9 * q^35 - 2 * q^36 - 16 * q^37 - 31 * q^38 - 3 * q^39 + 2 * q^40 + 16 * q^41 + 18 * q^42 - 14 * q^43 + 33 * q^44 + 5 * q^45 - 34 * q^46 + 14 * q^47 + 38 * q^48 + 41 * q^49 - 6 * q^50 + 9 * q^51 - 17 * q^52 - 3 * q^53 + 46 * q^54 + q^55 + 60 * q^56 - 34 * q^57 + 15 * q^58 + 7 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 + 6 * q^65 - 30 * q^66 - 26 * q^67 + 60 * q^68 - q^69 + 12 * q^70 - 17 * q^71 + q^72 - 11 * q^73 + 56 * q^74 - 4 * q^75 + 24 * q^76 - 18 * q^77 - 15 * q^78 + 6 * q^79 - 42 * q^80 - q^81 - 13 * q^82 + 28 * q^83 + 31 * q^84 - 37 * q^85 - 7 * q^86 - 30 * q^87 - 34 * q^88 - q^89 + 16 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 + 16 * q^96 + 3 * q^97 + 20 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.380762	−	1.17187i	0.269240	−	0.828634i	−0.721447	−	0.692470i	$-0.756523\pi$
$2$	0.380762	−	1.17187i	0.269240	−	0.828634i	0.990686	−	0.136164i	$-0.0434774\pi$
$3$	−0.641202	−	1.97342i	−0.370198	−	1.13935i	−0.946661	−	0.322230i	$-0.895567\pi$
$3$	−0.641202	−	1.97342i	−0.370198	−	1.13935i	0.576463	−	0.817123i	$-0.304433\pi$
$4$	0.389745	+	0.283166i	0.194873	+	0.141583i
$5$	−1.54562			−0.691223			−0.345612	−	0.938378i	$-0.612329\pi$
$5$	−1.54562			−0.691223			−0.345612	+	0.938378i	$0.612329\pi$
$6$	−2.55673			−1.04378
$7$	3.07730	+	2.23579i	1.16311	+	0.845050i	0.990168	−	0.139881i	$-0.0446721\pi$
$7$	3.07730	+	2.23579i	1.16311	+	0.845050i	0.172944	+	0.984932i	$0.444672\pi$
$8$	2.47393	−	1.79742i	0.874666	−	0.635482i
$9$	−1.05619	+	0.767366i	−0.352063	+	0.255789i
$10$	−0.588515	+	1.81126i	−0.186105	+	0.572771i
$11$	−3.04314	−	2.21097i	−0.917540	−	0.666632i	0.0253702	−	0.999678i	$-0.491924\pi$
$11$	−3.04314	−	2.21097i	−0.917540	−	0.666632i	−0.942911	+	0.333046i	$0.891924\pi$
$12$	0.308900	−	0.950697i	0.0891718	−	0.274443i
$13$	0.814279	+	2.50609i	0.225840	+	0.695065i	0.998205	+	0.0598862i	$0.0190738\pi$
$13$	0.814279	+	2.50609i	0.225840	+	0.695065i	−0.772365	+	0.635179i	$0.780926\pi$
$14$	3.79177	−	2.75488i	1.01339	−	0.736273i
$15$	0.991057	+	3.05016i	0.255890	+	0.787548i
$16$	−0.866611	−	2.66715i	−0.216653	−	0.666789i
$17$	3.05350	−	2.21850i	0.740584	−	0.538066i	−0.152310	−	0.988333i	$-0.548671\pi$
$17$	3.05350	−	2.21850i	0.740584	−	0.538066i	0.892894	+	0.450267i	$0.148671\pi$
$18$	0.497093	+	1.52989i	0.117166	+	0.360599i
$19$	1.88448	−	5.79984i	0.432330	−	1.33057i	−0.463468	−	0.886114i	$-0.653395\pi$
$19$	1.88448	−	5.79984i	0.432330	−	1.33057i	0.895798	−	0.444461i	$-0.146605\pi$
$20$	−0.602399	−	0.437668i	−0.134701	−	0.0978657i
$21$	2.43898	−	7.50641i	0.532229	−	1.63803i
$22$	−3.74967	+	2.72429i	−0.799432	+	0.580821i
$23$	0.736082	−	0.534795i	0.153484	−	0.111512i	−0.508393	−	0.861125i	$-0.669760\pi$
$23$	0.736082	−	0.534795i	0.153484	−	0.111512i	0.661877	+	0.749613i	$0.269760\pi$
$24$	−5.13334	−	3.72959i	−1.04784	−	0.761300i
$25$	−2.61105			−0.522210
$26$	3.24685			0.636760
$27$	−2.84451	−	2.06665i	−0.547425	−	0.397728i
$28$	0.566263	+	1.74278i	0.107014	+	0.329354i
$29$	2.10397	−	6.47535i	0.390697	−	1.20244i	−0.541565	−	0.840659i	$-0.682168\pi$
$29$	2.10397	−	6.47535i	0.390697	−	1.20244i	0.932262	−	0.361784i	$-0.117832\pi$
$30$	3.95173			0.721485
$31$		0			0
$31$		0			0
$32$	2.66037			0.470292
$33$	−2.41190	+	7.42306i	−0.419858	+	1.29219i
$34$	−1.43713	−	4.42302i	−0.246465	−	0.758541i
$35$	−4.75635	−	3.45569i	−0.803970	−	0.584119i
$36$	−0.628936			−0.104823
$37$	1.81406			0.298230			0.149115	−	0.988820i	$-0.452357\pi$
$37$	1.81406			0.298230			0.149115	+	0.988820i	$0.452357\pi$
$38$	−6.07909	−	4.41672i	−0.986159	−	0.716487i
$39$	4.42345	−	3.21383i	0.708320	−	0.514624i
$40$	−3.82376	+	2.77813i	−0.604590	+	0.439260i
$41$	0.104183	−	0.320644i	0.0162707	−	0.0500761i	−0.942592	−	0.333948i	$-0.891619\pi$
$41$	0.104183	−	0.320644i	0.0162707	−	0.0500761i	0.958862	+	0.283872i	$0.0916190\pi$
$42$	−7.86783	−	5.71631i	−1.21403	−	0.882046i
$43$	−1.20022	+	3.69390i	−0.183032	+	0.563314i	−0.999909	−	0.0134976i	$-0.995703\pi$
$43$	−1.20022	+	3.69390i	−0.183032	+	0.563314i	0.816877	+	0.576812i	$0.195703\pi$
$44$	−0.559976	−	1.72343i	−0.0844195	−	0.259817i
$45$	1.63247	−	1.18606i	0.243354	−	0.176807i
$46$	−0.346435	−	1.06622i	−0.0510791	−	0.157205i
$47$	−0.367467	−	1.13095i	−0.0536005	−	0.164965i	0.920673	−	0.390335i	$-0.127641\pi$
$47$	−0.367467	−	1.13095i	−0.0536005	−	0.164965i	−0.974273	+	0.225370i	$0.927641\pi$
$48$	−4.70774	+	3.42037i	−0.679504	+	0.493688i
$49$	2.30792	+	7.10304i	0.329702	+	1.01472i
$50$	−0.994189	+	3.05980i	−0.140600	+	0.432721i
$51$	−6.33595	−	4.60333i	−0.887210	−	0.644596i
$52$	−0.392280	+	1.20731i	−0.0543995	+	0.167424i
$53$	−1.89644	+	1.37784i	−0.260496	+	0.189261i	−0.710366	−	0.703833i	$-0.751470\pi$
$53$	−1.89644	+	1.37784i	−0.260496	+	0.189261i	0.449870	+	0.893094i	$0.351470\pi$
$54$	−3.50492	+	2.54647i	−0.476959	+	0.346531i
$55$	4.70354	+	3.41732i	0.634225	+	0.460792i
$56$	11.6317			1.55435
$57$	−12.6538			−1.67604
$58$	−6.78713	−	4.93114i	−0.891194	−	0.647490i
$59$	2.40379	+	7.39811i	0.312947	+	0.963152i	0.976591	+	0.215103i	$0.0690089\pi$
$59$	2.40379	+	7.39811i	0.312947	+	0.963152i	−0.663644	+	0.748048i	$0.730991\pi$
$60$	−0.477443	+	1.46942i	−0.0616377	+	0.189701i
$61$	2.72343			0.348700			0.174350	−	0.984684i	$-0.444218\pi$
$61$	2.72343			0.348700			0.174350	+	0.984684i	$0.444218\pi$
$62$		0			0
$63$	−4.96588			−0.625642
$64$	2.74619	−	8.45191i	0.343274	−	1.05649i
$65$	−1.25857	−	3.87348i	−0.156106	−	0.480446i
$66$	7.78047	+	5.65284i	0.957709	+	0.695817i
$67$	−7.42118			−0.906642			−0.453321	−	0.891347i	$-0.649761\pi$
$67$	−7.42118			−0.906642			−0.453321	+	0.891347i	$0.649761\pi$
$68$	1.81829			0.220501
$69$	−1.52735	−	1.10969i	−0.183871	−	0.133590i
$70$	−5.86065	+	4.25801i	−0.700481	+	0.508929i
$71$	4.12451	−	2.99664i	0.489490	−	0.355635i	−0.315498	−	0.948926i	$-0.602172\pi$
$71$	4.12451	−	2.99664i	0.489490	−	0.355635i	0.804988	+	0.593291i	$0.202172\pi$
$72$	−1.23366	+	3.79682i	−0.145388	+	0.447459i
$73$	4.36201	+	3.16919i	0.510535	+	0.370925i	0.813026	−	0.582227i	$-0.197818\pi$
$73$	4.36201	+	3.16919i	0.510535	+	0.370925i	−0.302492	+	0.953152i	$0.597818\pi$
$74$	0.690727	−	2.12584i	0.0802954	−	0.247124i
$75$	1.67421	+	5.15269i	0.193321	+	0.594982i
$76$	2.37679	−	1.72684i	0.272636	−	0.198082i
$77$	−4.42139	−	13.6076i	−0.503865	−	1.55074i
$78$	−2.08189	−	6.40740i	−0.235728	−	0.725495i
$79$	−7.87758	+	5.72340i	−0.886297	+	0.643933i	−0.934910	−	0.354885i	$-0.884520\pi$
$79$	−7.87758	+	5.72340i	−0.886297	+	0.643933i	0.0486128	+	0.998818i	$0.484520\pi$
$80$	1.33945	+	4.12241i	0.149755	+	0.460900i
$81$	−3.46475	+	10.6634i	−0.384973	+	1.18482i
$82$	−0.336082	−	0.244178i	−0.0371141	−	0.0269649i
$83$	2.59424	−	7.98426i	0.284755	−	0.876386i	−0.701717	−	0.712456i	$-0.747583\pi$
$83$	2.59424	−	7.98426i	0.284755	−	0.876386i	0.986472	−	0.163930i	$-0.0524172\pi$
$84$	3.07614	−	2.23495i	0.335635	−	0.243853i
$85$	−4.71957	+	3.42897i	−0.511909	+	0.371924i
$86$	3.87175	+	2.81299i	0.417502	+	0.303333i
$87$	−14.1277			−1.51464
$88$	−11.5025			−1.22617
$89$	4.12243	+	2.99512i	0.436976	+	0.317482i	0.784432	−	0.620214i	$-0.212954\pi$
$89$	4.12243	+	2.99512i	0.436976	+	0.317482i	−0.347456	+	0.937696i	$0.612954\pi$
$90$	−0.768318	−	2.36464i	−0.0809878	−	0.249255i
$91$	−3.09732	+	9.53258i	−0.324688	+	0.999285i
$92$	0.438320			0.0456980
$93$		0			0
$94$	−1.46523			−0.151127
$95$	−2.91270	+	8.96437i	−0.298837	+	0.919725i
$96$	−1.70584	−	5.25003i	−0.174101	−	0.535829i
$97$	−8.82979	−	6.41522i	−0.896530	−	0.651367i	0.0410427	−	0.999157i	$-0.486932\pi$
$97$	−8.82979	−	6.41522i	−0.896530	−	0.651367i	−0.937572	+	0.347791i	$0.886932\pi$
$98$	9.20257			0.929600
$99$	4.91075			0.493549
$100$	−1.01764	−	0.739362i	−0.101764	−	0.0739362i
$101$	0.322577	−	0.234366i	0.0320976	−	0.0233203i	−0.571621	−	0.820518i	$-0.693685\pi$
$101$	0.322577	−	0.234366i	0.0320976	−	0.0233203i	0.603718	+	0.797198i	$0.293685\pi$
$102$	−7.80698	+	5.67210i	−0.773006	+	0.561622i
$103$	1.01259	−	3.11642i	0.0997732	−	0.307070i	−0.888695	−	0.458499i	$-0.848387\pi$
$103$	1.01259	−	3.11642i	0.0997732	−	0.307070i	0.988468	+	0.151428i	$0.0483873\pi$
$104$	6.51896	+	4.73630i	0.639237	+	0.464433i
$105$	−3.76974	+	11.6021i	−0.367889	+	1.13225i
$106$	0.892554	+	2.74700i	0.0866925	+	0.266812i
$107$	−2.55394	+	1.85555i	−0.246899	+	0.179383i	−0.704351	−	0.709852i	$-0.748762\pi$
$107$	−2.55394	+	1.85555i	−0.246899	+	0.179383i	0.457452	+	0.889234i	$0.348762\pi$
$108$	−0.523425	−	1.61094i	−0.0503666	−	0.155013i
$109$	2.14959	+	6.61576i	0.205893	+	0.633675i	0.999676	+	0.0254724i	$0.00810899\pi$
$109$	2.14959	+	6.61576i	0.205893	+	0.633675i	−0.793782	+	0.608202i	$0.791891\pi$
$110$	5.79557	−	4.21073i	0.552586	−	0.401477i
$111$	−1.16318	−	3.57991i	−0.110404	−	0.339790i
$112$	3.29638	−	10.1452i	0.311479	−	0.958632i
$113$	12.3349	+	8.96184i	1.16037	+	0.843059i	0.989825	−	0.142291i	$-0.0454469\pi$
$113$	12.3349	+	8.96184i	1.16037	+	0.843059i	0.170546	+	0.985350i	$0.445447\pi$
$114$	−4.81811	+	14.8286i	−0.451257	+	1.38883i
$115$	−1.13770	+	0.826591i	−0.106092	+	0.0770800i
$116$	2.65362	−	1.92796i	0.246382	−	0.179007i
$117$	−2.78312	−	2.02206i	−0.257300	−	0.186939i
$118$	9.58486			0.882358
$119$	14.3567			1.31607
$120$	7.93421	+	5.76454i	0.724291	+	0.526228i
$121$	0.973115	+	2.99494i	0.0884650	+	0.272267i
$122$	1.03698	−	3.19150i	0.0938838	−	0.288945i
$123$	−0.699567			−0.0630778
$124$		0			0
$125$	11.7638			1.05219
$126$	−1.89082	+	5.81935i	−0.168448	+	0.518429i
$127$	6.25029	+	19.2364i	0.554624	+	1.70696i	0.696935	+	0.717134i	$0.254547\pi$
$127$	6.25029	+	19.2364i	0.554624	+	1.70696i	−0.142311	+	0.989822i	$0.545453\pi$
$128$	−4.55428	−	3.30888i	−0.402545	−	0.292466i
$129$	8.05919			0.709572
$130$	−5.01841			−0.440143
$131$	−10.2351	−	7.43624i	−0.894245	−	0.649707i	0.0427363	−	0.999086i	$-0.486392\pi$
$131$	−10.2351	−	7.43624i	−0.894245	−	0.649707i	−0.936981	+	0.349379i	$0.886392\pi$
$132$	−3.04199	+	2.21013i	−0.264771	+	0.192367i
$133$	18.7664	−	13.6346i	1.62725	−	1.18227i
$134$	−2.82570	+	8.69663i	−0.244104	+	0.751274i
$135$	4.39653	+	3.19427i	0.378393	+	0.274919i
$136$	3.56659	−	10.9768i	0.305832	−	0.941256i
$137$	3.05247	+	9.39455i	0.260790	+	0.802630i	0.992633	+	0.121157i	$0.0386605\pi$
$137$	3.05247	+	9.39455i	0.260790	+	0.802630i	−0.731843	+	0.681473i	$0.761340\pi$
$138$	−1.88196	+	1.36732i	−0.160203	+	0.116394i
$139$	4.78945	+	14.7404i	0.406236	+	1.25026i	0.919859	+	0.392249i	$0.128303\pi$
$139$	4.78945	+	14.7404i	0.406236	+	1.25026i	−0.513623	+	0.858016i	$0.671697\pi$
$140$	−0.875229	−	2.69368i	−0.0739704	−	0.227657i
$141$	−1.99621	+	1.45033i	−0.168111	+	0.122140i
$142$	−1.94119	−	5.97438i	−0.162901	−	0.501359i
$143$	3.06293	−	9.42673i	0.256135	−	0.788303i
$144$	2.96199	+	2.15201i	0.246832	+	0.179334i
$145$	−3.25194	+	10.0085i	−0.270059	+	0.831157i
$146$	5.37475	−	3.90499i	0.444818	−	0.323179i
$147$	12.5374	−	9.10897i	1.03407	−	0.751295i
$148$	0.707023	+	0.513682i	0.0581169	+	0.0422244i
$149$	−15.2432			−1.24878			−0.624388	−	0.781115i	$-0.714651\pi$
$149$	−15.2432			−1.24878			−0.624388	+	0.781115i	$0.714651\pi$
$150$	6.67574			0.545072
$151$	−0.211823	−	0.153899i	−0.0172379	−	0.0125241i	0.579133	−	0.815233i	$-0.303391\pi$
$151$	−0.211823	−	0.153899i	−0.0172379	−	0.0125241i	−0.596371	+	0.802709i	$0.703391\pi$
$152$	−5.76265	−	17.7356i	−0.467412	−	1.43855i
$153$	−1.52267	+	4.68631i	−0.123101	+	0.378866i
$154$	−17.6298			−1.42065
$155$		0			0
$156$	2.63407			0.210894
$157$	4.92157	−	15.1470i	0.392784	−	1.20886i	−0.537890	−	0.843015i	$-0.680778\pi$
$157$	4.92157	−	15.1470i	0.392784	−	1.20886i	0.930674	−	0.365850i	$-0.119222\pi$
$158$	3.70757	+	11.4107i	0.294958	+	0.907788i
$159$	3.93506	+	2.85899i	0.312071	+	0.226733i
$160$	−4.11193			−0.325077
$161$	3.46084			0.272752
$162$	11.1768	+	8.12045i	0.878135	+	0.638003i
$163$	0.107741	−	0.0782785i	0.00843894	−	0.00613125i	−0.583558	−	0.812072i	$-0.698340\pi$
$163$	0.107741	−	0.0782785i	0.00843894	−	0.00613125i	0.591997	+	0.805940i	$0.298340\pi$
$164$	0.131401	−	0.0954681i	0.0102607	−	0.00745480i
$165$	3.72789	−	11.4733i	0.290215	−	0.893191i
$166$	−8.36869	−	6.08021i	−0.649536	−	0.471916i
$167$	1.22024	−	3.75551i	0.0944250	−	0.290610i	−0.892678	−	0.450694i	$-0.851176\pi$
$167$	1.22024	−	3.75551i	0.0944250	−	0.290610i	0.987103	+	0.160084i	$0.0511765\pi$
$168$	−7.45826	−	22.9542i	−0.575418	−	1.77095i
$169$	4.89976	−	3.55989i	0.376905	−	0.273837i
$170$	2.22125	+	6.83632i	0.170362	+	0.524322i
$171$	2.46023	+	7.57181i	0.188139	+	0.579031i
$172$	−1.51377	+	1.09982i	−0.115424	+	0.0838603i
$173$	−4.46744	−	13.7494i	−0.339653	−	1.04535i	−0.964384	−	0.264505i	$-0.914791\pi$
$173$	−4.46744	−	13.7494i	−0.339653	−	1.04535i	0.624731	−	0.780840i	$-0.285209\pi$
$174$	−5.37928	+	16.5557i	−0.407802	+	1.25509i
$175$	−8.03500	−	5.83777i	−0.607389	−	0.441294i
$176$	−3.25978	+	10.0326i	−0.245715	+	0.756233i
$177$	13.0582	−	9.48737i	0.981518	−	0.713114i
$178$	5.07954	−	3.69050i	0.380727	−	0.276615i
$179$	−14.3357	−	10.4155i	−1.07150	−	0.778490i	−0.0953185	−	0.995447i	$-0.530387\pi$
$179$	−14.3357	−	10.4155i	−1.07150	−	0.778490i	−0.976181	+	0.216957i	$0.930387\pi$
$180$	0.972098			0.0724559
$181$	12.0592			0.896350			0.448175	−	0.893946i	$-0.352074\pi$
$181$	12.0592			0.896350			0.448175	+	0.893946i	$0.352074\pi$
$182$	9.99155	+	7.25929i	0.740623	+	0.538094i
$183$	−1.74627	−	5.37447i	−0.129088	−	0.397292i
$184$	0.859766	−	2.64609i	0.0633828	−	0.195072i
$185$	−2.80386			−0.206144
$186$		0			0
$187$	−14.1973			−1.03821
$188$	0.177028	−	0.544835i	0.0129111	−	0.0397362i
$189$	−4.13280	−	12.7195i	−0.300617	−	0.925204i
$190$	9.39599	+	6.82658i	0.681656	+	0.495252i
$191$	5.07152			0.366962			0.183481	−	0.983023i	$-0.441263\pi$
$191$	5.07152			0.366962			0.183481	+	0.983023i	$0.441263\pi$
$192$	−18.4400			−1.33079
$193$	16.2141	+	11.7802i	1.16712	+	0.847960i	0.990661	−	0.136348i	$-0.0435366\pi$
$193$	16.2141	+	11.7802i	1.16712	+	0.847960i	0.176456	+	0.984308i	$0.443537\pi$
$194$	−10.8798	+	7.90466i	−0.781126	+	0.567521i
$195$	−6.83699	+	4.96736i	−0.489607	+	0.355720i
$196$	−1.11184	+	3.42190i	−0.0794173	+	0.244421i
$197$	17.5624	+	12.7599i	1.25127	+	0.909102i	0.998295	−	0.0583705i	$-0.0185905\pi$
$197$	17.5624	+	12.7599i	1.25127	+	0.909102i	0.252976	+	0.967472i	$0.418590\pi$
$198$	1.86983	−	5.75473i	0.132883	−	0.408971i
$199$	−4.68640	−	14.4233i	−0.332210	−	1.02244i	−0.968080	−	0.250641i	$-0.919359\pi$
$199$	−4.68640	−	14.4233i	−0.332210	−	1.02244i	0.635870	−	0.771796i	$-0.280641\pi$
$200$	−6.45956	+	4.69314i	−0.456760	+	0.331855i
$201$	4.75848	+	14.6451i	0.335637	+	1.03299i
$202$	−0.151820	−	0.467255i	−0.0106820	−	0.0328759i
$203$	20.9521	−	15.2226i	1.47055	−	1.06842i
$204$	−1.16589	−	3.58825i	−0.0816289	−	0.251228i
$205$	−0.161028	+	0.495594i	−0.0112467	+	0.0346138i
$206$	−3.26647	−	2.37323i	−0.227586	−	0.165351i
$207$	−0.367058	+	1.12969i	−0.0255123	+	0.0785187i
$208$	5.97848	−	4.34362i	0.414533	−	0.301176i
$209$	−18.5580	+	13.4832i	−1.28368	+	0.932651i
$210$	12.1607	+	8.83526i	0.839167	+	0.609691i
$211$	6.30441			0.434013			0.217007	−	0.976170i	$-0.430371\pi$
$211$	6.30441			0.434013			0.217007	+	0.976170i	$0.430371\pi$
$212$	−1.12929			−0.0775597
$213$	−8.55826	−	6.21794i	−0.586403	−	0.426046i
$214$	1.20201	+	3.69940i	0.0821676	+	0.252886i
$215$	1.85509	−	5.70937i	0.126516	−	0.389376i
$216$	−10.7517			−0.731564
$217$		0			0
$218$	8.57126			0.580519
$219$	3.45720	−	10.6402i	0.233616	−	0.718996i
$220$	0.865512	+	2.66377i	0.0583528	+	0.179591i
$221$	8.04618	+	5.84589i	0.541245	+	0.393237i
$222$	−4.63806			−0.311287
$223$	−7.38911			−0.494811			−0.247406	−	0.968912i	$-0.579578\pi$
$223$	−7.38911			−0.494811			−0.247406	+	0.968912i	$0.579578\pi$
$224$	8.18678	+	5.94804i	0.547002	+	0.397420i
$225$	2.75776	−	2.00363i	0.183851	−	0.133575i
$226$	15.1987	−	11.0425i	1.01100	−	0.734538i
$227$	5.94542	−	18.2981i	0.394611	−	1.21449i	−0.534652	−	0.845072i	$-0.679557\pi$
$227$	5.94542	−	18.2981i	0.394611	−	1.21449i	0.929264	−	0.369417i	$-0.120443\pi$
$228$	−4.93178	−	3.58315i	−0.326615	−	0.237300i
$229$	1.88102	−	5.78918i	0.124301	−	0.382560i	−0.869472	−	0.493982i	$-0.835541\pi$
$229$	1.88102	−	5.78918i	0.124301	−	0.382560i	0.993773	+	0.111423i	$0.0355407\pi$
$230$	0.535458	+	1.64797i	0.0353071	+	0.108664i
$231$	−24.0186	+	17.4505i	−1.58031	+	1.14816i
$232$	−6.43383	−	19.8013i	−0.422401	−	1.30002i
$233$	5.41646	+	16.6702i	0.354844	+	1.09210i	0.956100	+	0.293042i	$0.0946675\pi$
$233$	5.41646	+	16.6702i	0.354844	+	1.09210i	−0.601255	+	0.799057i	$0.705333\pi$
$234$	−3.42929	+	2.49152i	−0.224179	+	0.162876i
$235$	0.567965	+	1.74802i	0.0370499	+	0.114028i
$236$	−1.15803	+	3.56405i	−0.0753813	+	0.232000i
$237$	16.3458	+	11.8759i	1.06177	+	0.771423i
$238$	5.46648	−	16.8241i	0.354339	−	1.09054i
$239$	−22.5813	+	16.4063i	−1.46066	+	1.06123i	−0.477475	+	0.878646i	$0.658448\pi$
$239$	−22.5813	+	16.4063i	−1.46066	+	1.06123i	−0.983189	+	0.182589i	$0.941552\pi$
$240$	7.27639	−	5.28660i	0.469689	−	0.341249i
$241$	18.4049	+	13.3720i	1.18557	+	0.861364i	0.992789	−	0.119879i	$-0.0382507\pi$
$241$	18.4049	+	13.3720i	1.18557	+	0.861364i	0.192777	+	0.981243i	$0.438251\pi$
$242$	3.88019			0.249428
$243$	12.7170			0.815794
$244$	1.06144	+	0.771185i	0.0679520	+	0.0493701i
$245$	−3.56717	−	10.9786i	−0.227898	−	0.701398i
$246$	−0.266369	+	0.819798i	−0.0169830	+	0.0522684i
$247$	16.0694			1.02247
$248$		0			0
$249$	−17.4197			−1.10393
$250$	4.47921	−	13.7856i	0.283290	−	0.871878i
$251$	5.01674	+	15.4399i	0.316654	+	0.974559i	0.975068	+	0.221904i	$0.0712273\pi$
$251$	5.01674	+	15.4399i	0.316654	+	0.974559i	−0.658415	+	0.752655i	$0.728773\pi$
$252$	−1.93543	−	1.40617i	−0.121921	−	0.0885805i
$253$	−3.42241			−0.215165
$254$	24.9224			1.56377
$255$	9.79298	+	7.11502i	0.613260	+	0.445560i
$256$	8.76759	−	6.37002i	0.547974	−	0.398126i
$257$	−18.8922	+	13.7260i	−1.17847	+	0.856206i	−0.991998	−	0.126255i	$-0.959704\pi$
$257$	−18.8922	+	13.7260i	−1.17847	+	0.856206i	−0.186468	+	0.982461i	$0.559704\pi$
$258$	3.06864	−	9.44429i	0.191045	−	0.587976i
$259$	5.58243	+	4.05587i	0.346875	+	0.252020i
$260$	0.606317	−	1.86605i	0.0376022	−	0.115728i
$261$	2.74678	+	8.45371i	0.170021	+	0.523271i
$262$	−12.6114	+	9.16272i	−0.779135	+	0.566075i
$263$	3.21203	+	9.88562i	0.198062	+	0.609574i	0.999927	+	0.0120680i	$0.00384144\pi$
$263$	3.21203	+	9.88562i	0.198062	+	0.609574i	−0.801865	+	0.597506i	$0.796159\pi$
$264$	7.37545	+	22.6993i	0.453928	+	1.39705i
$265$	2.93118	−	2.12962i	0.180061	−	0.130822i
$266$	−8.83235	−	27.1832i	−0.541546	−	1.66671i
$267$	3.26731	−	10.0557i	0.199956	−	0.615402i
$268$	−2.89237	−	2.10143i	−0.176680	−	0.128365i
$269$	1.36525	−	4.20181i	0.0832408	−	0.256189i	−0.900770	−	0.434296i	$-0.856997\pi$
$269$	1.36525	−	4.20181i	0.0832408	−	0.256189i	0.984011	+	0.178107i	$0.0569973\pi$
$270$	5.41729	−	3.93589i	0.329686	−	0.239531i
$271$	4.97777	−	3.61656i	0.302378	−	0.219691i	−0.426241	−	0.904610i	$-0.640162\pi$
$271$	4.97777	−	3.61656i	0.302378	−	0.219691i	0.728619	+	0.684919i	$0.240162\pi$
$272$	−8.56329	−	6.22159i	−0.519225	−	0.377239i
$273$	20.7978			1.25874
$274$	12.1714			0.735302
$275$	7.94578	+	5.77295i	0.479149	+	0.348122i
$276$	−0.281052	−	0.864989i	−0.0169173	−	0.0520662i
$277$	−6.81302	+	20.9683i	−0.409355	+	1.25987i	0.507849	+	0.861446i	$0.330441\pi$
$277$	−6.81302	+	20.9683i	−0.409355	+	1.25987i	−0.917204	+	0.398419i	$0.869559\pi$
$278$	19.0974			1.14539
$279$		0			0
$280$	−17.9782			−1.07440
$281$	−9.50955	+	29.2674i	−0.567292	+	1.74595i	0.0937474	+	0.995596i	$0.470115\pi$
$281$	−9.50955	+	29.2674i	−0.567292	+	1.74595i	−0.661040	+	0.750351i	$0.729885\pi$
$282$	0.939512	+	2.89152i	0.0559471	+	0.172188i
$283$	17.2687	+	12.5464i	1.02652	+	0.745807i	0.967608	−	0.252456i	$-0.0812383\pi$
$283$	17.2687	+	12.5464i	1.02652	+	0.745807i	0.0589075	+	0.998263i	$0.481238\pi$
$284$	2.45606			0.145740
$285$	19.5581			1.15852
$286$	−9.88062	−	7.17869i	−0.584253	−	0.424485i
$287$	1.03750	−	0.753786i	0.0612415	−	0.0444946i
$288$	−2.80985	+	2.04148i	−0.165572	+	0.120295i
$289$	−0.851145	+	2.61955i	−0.0500673	+	0.154091i
$290$	10.4903	+	7.62168i	0.616014	+	0.447561i
$291$	−6.99823	+	21.5383i	−0.410243	+	1.26260i
$292$	0.802666	+	2.47035i	0.0469725	+	0.144566i
$293$	1.45544	−	1.05744i	0.0850279	−	0.0617764i	−0.544459	−	0.838787i	$-0.683265\pi$
$293$	1.45544	−	1.05744i	0.0850279	−	0.0617764i	0.629487	+	0.777011i	$0.283265\pi$
$294$	−5.90071	−	18.1605i	−0.344136	−	1.05914i
$295$	−3.71535	−	11.4347i	−0.216316	−	0.665753i
$296$	4.48787	−	3.26063i	0.260852	−	0.189520i
$297$	4.08691	+	12.5782i	0.237147	+	0.729863i
$298$	−5.80405	+	17.8630i	−0.336220	+	1.03478i
$299$	1.93962	+	1.40922i	0.112171	+	0.0814972i
$300$	−0.806554	+	2.48232i	−0.0465664	+	0.143317i
$301$	−11.9522	+	8.68381i	−0.688916	+	0.500526i
$302$	−0.261003	+	0.189630i	−0.0150190	+	0.0109120i
$303$	−0.669339	−	0.486303i	−0.0384525	−	0.0279374i
$304$	−17.1022			−0.980878
$305$	−4.20940			−0.241030
$306$	4.91195	+	3.56874i	0.280797	+	0.204011i
$307$	8.27220	+	25.4592i	0.472119	+	1.45303i	0.849803	+	0.527100i	$0.176721\pi$
$307$	8.27220	+	25.4592i	0.472119	+	1.45303i	−0.377684	+	0.925935i	$0.623279\pi$
$308$	2.13001	−	6.55551i	0.121369	−	0.373535i
$309$	−6.79928			−0.386798
$310$		0			0
$311$	4.18114			0.237090			0.118545	−	0.992949i	$-0.462177\pi$
$311$	4.18114			0.237090			0.118545	+	0.992949i	$0.462177\pi$
$312$	5.16673	−	15.9016i	0.292509	−	0.900249i
$313$	3.50513	+	10.7877i	0.198121	+	0.609755i	0.999926	+	0.0121688i	$0.00387354\pi$
$313$	3.50513	+	10.7877i	0.198121	+	0.609755i	−0.801804	+	0.597586i	$0.796126\pi$
$314$	−15.8763	−	11.5348i	−0.895953	−	0.650948i
$315$	7.67538			0.432459
$316$	−4.69092			−0.263885
$317$	−20.9384	−	15.2127i	−1.17602	−	0.854429i	−0.184303	−	0.982869i	$-0.559003\pi$
$317$	−20.9384	−	15.2127i	−1.17602	−	0.854429i	−0.991717	+	0.128441i	$0.959003\pi$
$318$	4.84867	−	3.52277i	0.271900	−	0.197547i
$319$	−20.7195	+	15.0536i	−1.16007	+	0.842839i
$320$	−4.24458	+	13.0635i	−0.237279	+	0.730270i
$321$	5.29937	+	3.85021i	0.295782	+	0.214898i
$322$	1.31776	−	4.05564i	0.0734357	−	0.226012i
$323$	−7.11268	−	21.8906i	−0.395760	−	1.21802i
$324$	−4.36989	+	3.17491i	−0.242772	+	0.176384i
$325$	−2.12612	−	6.54354i	−0.117936	−	0.362970i
$326$	−0.0507081	−	0.156064i	−0.00280846	−	0.00864356i
$327$	11.6773	−	8.48408i	0.645758	−	0.469171i
$328$	−0.318587	−	0.980511i	−0.0175910	−	0.0541396i
$329$	1.39775	−	4.30185i	0.0770607	−	0.237168i
$330$	−12.0257	−	8.73716i	−0.661991	−	0.480965i
$331$	−0.236641	+	0.728307i	−0.0130070	+	0.0400314i	−0.957349	−	0.288933i	$-0.906700\pi$
$331$	−0.236641	+	0.728307i	−0.0130070	+	0.0400314i	0.944342	+	0.328964i	$0.106700\pi$
$332$	3.27197	−	2.37722i	0.179573	−	0.130467i
$333$	−1.91599	+	1.39205i	−0.104996	+	0.0762839i
$334$	−3.93633	−	2.85991i	−0.215387	−	0.156488i
$335$	11.4703			0.626692
$336$	−22.1344			−1.20753
$337$	1.93706	+	1.40736i	0.105519	+	0.0766637i	0.639293	−	0.768963i	$-0.279227\pi$
$337$	1.93706	+	1.40736i	0.105519	+	0.0766637i	−0.533775	+	0.845627i	$0.679227\pi$
$338$	−2.30606	−	7.09733i	−0.125433	−	0.386044i
$339$	9.77628	−	30.0883i	0.530974	−	1.63417i
$340$	−2.81040			−0.152415
$341$		0			0
$342$	9.80991			0.530459
$343$	−0.550776	+	1.69511i	−0.0297391	+	0.0915276i
$344$	3.67021	+	11.2957i	0.197884	+	0.609026i
$345$	2.36071	+	1.71516i	0.127096	+	0.0923408i
$346$	−17.8134			−0.957656
$347$	−5.65780			−0.303727			−0.151863	−	0.988402i	$-0.548527\pi$
$347$	−5.65780			−0.303727			−0.151863	+	0.988402i	$0.548527\pi$
$348$	−5.50619	−	4.00048i	−0.295163	−	0.214448i
$349$	−23.5162	+	17.0855i	−1.25879	+	0.914566i	−0.998698	−	0.0510167i	$-0.983754\pi$
$349$	−23.5162	+	17.0855i	−1.25879	+	0.914566i	−0.260095	+	0.965583i	$0.583754\pi$
$350$	−9.90050	+	7.19314i	−0.529204	+	0.384489i
$351$	2.86301	−	8.81143i	0.152816	−	0.470320i
$352$	−8.09588	−	5.88200i	−0.431512	−	0.313512i
$353$	5.95637	−	18.3318i	0.317025	−	0.975704i	−0.657887	−	0.753116i	$-0.728550\pi$
$353$	5.95637	−	18.3318i	0.317025	−	0.975704i	0.974913	−	0.222587i	$-0.0714503\pi$
$354$	−6.14584	−	18.9149i	−0.326648	−	1.00532i
$355$	−6.37494	+	4.63167i	−0.338347	+	0.245823i
$356$	0.758579	+	2.33467i	0.0402046	+	0.123737i
$357$	−9.20553	−	28.3317i	−0.487209	−	1.49947i
$358$	−17.6640	+	12.8337i	−0.933573	+	0.678281i
$359$	3.19656	+	9.83799i	0.168708	+	0.519229i	0.999290	−	0.0376663i	$-0.0119924\pi$
$359$	3.19656	+	9.83799i	0.168708	+	0.519229i	−0.830583	+	0.556895i	$0.811992\pi$
$360$	1.90677	−	5.86845i	0.100496	−	0.309294i
$361$	−14.7156	−	10.6915i	−0.774503	−	0.562710i
$362$	4.59167	−	14.1317i	0.241333	−	0.742746i
$363$	5.28630	−	3.84072i	0.277459	−	0.201586i
$364$	−3.90647	+	2.83822i	−0.204755	+	0.148763i
$365$	−6.74203	−	4.89837i	−0.352894	−	0.256392i
$366$	−6.96307			−0.363966
$367$	0.136564			0.00712857			0.00356428	−	0.999994i	$-0.498865\pi$
$367$	0.136564			0.00712857			0.00356428	+	0.999994i	$0.498865\pi$
$368$	−2.06428	−	1.49978i	−0.107608	−	0.0781817i
$369$	0.136014	+	0.418607i	0.00708058	+	0.0217918i
$370$	−1.06760	+	3.28574i	−0.0555020	+	0.170818i
$371$	−8.91649			−0.462921
$372$		0			0
$373$	−7.36393			−0.381290			−0.190645	−	0.981659i	$-0.561058\pi$
$373$	−7.36393			−0.381290			−0.190645	+	0.981659i	$0.561058\pi$
$374$	−5.40578	+	16.6373i	−0.279526	+	0.860294i
$375$	−7.54299	−	23.2149i	−0.389518	−	1.19881i
$376$	−2.94187	−	2.13739i	−0.151715	−	0.110228i
$377$	17.9411			0.924012
$378$	−16.4791			−0.847593
$379$	3.72806	+	2.70859i	0.191498	+	0.139131i	0.679403	−	0.733765i	$-0.262239\pi$
$379$	3.72806	+	2.70859i	0.191498	+	0.139131i	−0.487905	+	0.872897i	$0.662239\pi$
$380$	−3.67362	+	2.66904i	−0.188453	+	0.136919i
$381$	33.9538	−	24.6689i	1.73951	−	1.26383i
$382$	1.93104	−	5.94314i	0.0988008	−	0.304077i
$383$	−26.1270	−	18.9824i	−1.33503	−	0.969955i	−0.999611	−	0.0278856i	$-0.991123\pi$
$383$	−26.1270	−	18.9824i	−1.33503	−	0.969955i	−0.335418	−	0.942070i	$-0.608877\pi$
$384$	−3.60959	+	11.1092i	−0.184201	+	0.566912i
$385$	6.83381	+	21.0323i	0.348283	+	1.07190i
$386$	19.9786	−	14.5153i	1.01688	−	0.738809i
$387$	−1.56691	−	4.82246i	−0.0796506	−	0.245139i
$388$	−1.62479	−	5.00060i	−0.0824864	−	0.253867i
$389$	−28.5351	+	20.7319i	−1.44678	+	1.05115i	−0.460216	+	0.887807i	$0.652228\pi$
$389$	−28.5351	+	20.7319i	−1.44678	+	1.05115i	−0.986569	+	0.163344i	$0.947772\pi$
$390$	3.21782	+	9.90342i	0.162940	+	0.501479i
$391$	1.06119	−	3.26600i	0.0536665	−	0.165169i
$392$	18.4767	+	13.4241i	0.933216	+	0.678021i
$393$	−8.11203	+	24.9663i	−0.409198	+	1.25938i
$394$	21.6399	−	15.7223i	1.09020	−	0.792080i
$395$	12.1758	−	8.84621i	0.612629	−	0.445101i
$396$	1.91394	+	1.39056i	0.0961791	+	0.0698782i
$397$	−4.03402			−0.202462			−0.101231	−	0.994863i	$-0.532278\pi$
$397$	−4.03402			−0.202462			−0.101231	+	0.994863i	$0.532278\pi$
$398$	−18.6865			−0.936671
$399$	−38.9398	−	28.2914i	−1.94943	−	1.41634i
$400$	2.26277	+	6.96408i	0.113138	+	0.348204i
$401$	−7.68933	+	23.6653i	−0.383987	+	1.18179i	0.553225	+	0.833032i	$0.313397\pi$
$401$	−7.68933	+	23.6653i	−0.383987	+	1.18179i	−0.937212	+	0.348759i	$0.886603\pi$
$402$	18.9739			0.946334
$403$		0			0
$404$	0.192087			0.00955671
$405$	5.35520	−	16.4816i	0.266102	−	0.818978i
$406$	−9.86107	−	30.3492i	−0.489397	−	1.50621i
$407$	−5.52044	−	4.01084i	−0.273638	−	0.198810i
$408$	−23.9488			−1.18564
$409$	−3.50722			−0.173421			−0.0867105	−	0.996234i	$-0.527636\pi$
$409$	−3.50722			−0.173421			−0.0867105	+	0.996234i	$0.527636\pi$
$410$	0.519456	+	0.377407i	0.0256541	+	0.0186388i
$411$	16.5821	−	12.0476i	0.817936	−	0.594265i
$412$	1.27712	−	0.927881i	0.0629191	−	0.0457134i
$413$	−9.14344	+	28.1406i	−0.449919	+	1.38471i
$414$	1.18408	+	0.860285i	0.0581944	+	0.0422807i
$415$	−4.00972	+	12.3407i	−0.196829	+	0.605779i
$416$	2.16629	+	6.66714i	0.106211	+	0.326884i
$417$	26.0180	−	18.9032i	1.27411	−	0.925692i
$418$	8.73429	+	26.8814i	0.427208	+	1.31481i
$419$	1.27325	+	3.91865i	0.0622022	+	0.191439i	0.977328	−	0.211729i	$-0.0679093\pi$
$419$	1.27325	+	3.91865i	0.0622022	+	0.191439i	−0.915126	+	0.403167i	$0.867909\pi$
$420$	−4.75456	+	3.45439i	−0.231999	+	0.168557i
$421$	8.52930	+	26.2505i	0.415693	+	1.27937i	0.911630	+	0.411012i	$0.134825\pi$
$421$	8.52930	+	26.2505i	0.415693	+	1.27937i	−0.495937	+	0.868358i	$0.665175\pi$
$422$	2.40048	−	7.38792i	0.116854	−	0.359638i
$423$	1.25596	+	0.912511i	0.0610670	+	0.0443678i
$424$	−2.21510	+	6.81737i	−0.107575	+	0.331081i
$425$	−7.97286	+	5.79262i	−0.386740	+	0.280983i
$426$	−10.5453	+	7.66158i	−0.510919	+	0.371205i
$427$	8.38083	+	6.08903i	0.405577	+	0.294669i
$428$	−1.52082			−0.0735114
$429$	−20.5668			−0.992977
$430$	−5.98427	−	4.34783i	−0.288587	−	0.209671i
$431$	−4.59630	−	14.1460i	−0.221396	−	0.681387i	−0.998637	−	0.0521843i	$-0.983382\pi$
$431$	−4.59630	−	14.1460i	−0.221396	−	0.681387i	0.777242	−	0.629202i	$-0.216618\pi$
$432$	−3.04701	+	9.37772i	−0.146599	+	0.451186i
$433$	−9.26195			−0.445101			−0.222550	−	0.974921i	$-0.571438\pi$
$433$	−9.26195			−0.445101			−0.222550	+	0.974921i	$0.571438\pi$
$434$		0			0
$435$	21.8360			1.04696
$436$	−1.03557	+	3.18715i	−0.0495947	+	0.152637i
$437$	−1.71459	−	5.27697i	−0.0820200	−	0.252432i
$438$	−11.1525	−	8.10275i	−0.532886	−	0.387164i
$439$	17.7182			0.845643			0.422821	−	0.906213i	$-0.361040\pi$
$439$	17.7182			0.845643			0.422821	+	0.906213i	$0.361040\pi$
$440$	17.7786			0.847561
$441$	−7.88822	−	5.73113i	−0.375630	−	0.272911i
$442$	9.91428	−	7.20314i	0.471574	−	0.342619i
$443$	14.9266	−	10.8448i	0.709182	−	0.515251i	−0.173728	−	0.984794i	$-0.555581\pi$
$443$	14.9266	−	10.8448i	0.709182	−	0.515251i	0.882910	+	0.469543i	$0.155581\pi$
$444$	0.560365	−	1.72463i	0.0265937	−	0.0818471i
$445$	−6.37171	−	4.62932i	−0.302048	−	0.219451i
$446$	−2.81349	+	8.65904i	−0.133223	+	0.410017i
$447$	9.77401	+	30.0813i	0.462295	+	1.42280i
$448$	27.3476	−	19.8692i	1.29205	−	0.938731i
$449$	−7.01784	−	21.5987i	−0.331192	−	1.01931i	−0.968567	−	0.248752i	$-0.919980\pi$
$449$	−7.01784	−	21.5987i	−0.331192	−	1.01931i	0.637375	−	0.770554i	$-0.280020\pi$
$450$	−1.29793	−	3.99463i	−0.0611852	−	0.188309i
$451$	−1.02598	+	0.745416i	−0.0483114	+	0.0351003i
$452$	2.26978	+	6.98566i	0.106761	+	0.328578i
$453$	−0.167885	+	0.516696i	−0.00788791	+	0.0242765i
$454$	−19.1791	−	13.9345i	−0.900122	−	0.653977i
$455$	4.78729	−	14.7338i	0.224432	−	0.690730i
$456$	−31.3047	+	22.7442i	−1.46598	+	1.06510i
$457$	−13.0752	+	9.49970i	−0.611633	+	0.444377i	−0.849989	−	0.526800i	$-0.823392\pi$
$457$	−13.0752	+	9.49970i	−0.611633	+	0.444377i	0.238356	+	0.971178i	$0.423392\pi$
$458$	−6.06792	−	4.40860i	−0.283535	−	0.206000i
$459$	−13.2706			−0.619418
$460$	−0.677478			−0.0315876
$461$	17.4252	+	12.6602i	0.811573	+	0.589642i	0.914286	−	0.405069i	$-0.132752\pi$
$461$	17.4252	+	12.6602i	0.811573	+	0.589642i	−0.102713	+	0.994711i	$0.532752\pi$
$462$	11.3043	+	34.7910i	0.525923	+	1.61863i
$463$	5.41083	−	16.6528i	0.251462	−	0.773922i	−0.743044	−	0.669243i	$-0.766619\pi$
$463$	5.41083	−	16.6528i	0.251462	−	0.773922i	0.994506	−	0.104679i	$-0.0333815\pi$
$464$	−19.0941			−0.886421
$465$		0			0
$466$	21.5976			1.00049
$467$	−3.64845	+	11.2288i	−0.168830	+	0.519605i	−0.999298	−	0.0374608i	$-0.988073\pi$
$467$	−3.64845	+	11.2288i	−0.168830	+	0.519605i	0.830468	+	0.557066i	$0.188073\pi$
$468$	−0.512130	−	1.57617i	−0.0236732	−	0.0728587i
$469$	−22.8372	−	16.5922i	−1.05453	−	0.766158i
$470$	2.26470			0.104463
$471$	−33.0472			−1.52273
$472$	19.2443	+	13.9818i	0.885790	+	0.643564i
$473$	11.8195	−	8.58739i	0.543463	−	0.394849i
$474$	20.1408	−	14.6332i	0.925098	−	0.672123i
$475$	−4.92048	+	15.1437i	−0.225767	+	0.694840i
$476$	5.59544	+	4.06533i	0.256467	+	0.186334i
$477$	0.945686	−	2.91052i	0.0433000	−	0.133264i
$478$	10.6278	+	32.7092i	0.486107	+	1.49608i
$479$	12.7895	−	9.29213i	0.584368	−	0.424568i	−0.255928	−	0.966696i	$-0.582381\pi$
$479$	12.7895	−	9.29213i	0.584368	−	0.424568i	0.840296	+	0.542127i	$0.182381\pi$
$480$	2.63658	+	8.11456i	0.120343	+	0.370377i
$481$	1.47715	+	4.54621i	0.0673525	+	0.207290i
$482$	22.6780	−	16.4766i	1.03296	−	0.750487i
$483$	−2.21910	−	6.82968i	−0.100972	−	0.310761i
$484$	−0.468800	+	1.44282i	−0.0213091	+	0.0655826i
$485$	13.6475	+	9.91551i	0.619702	+	0.450240i
$486$	4.84214	−	14.9026i	0.219644	−	0.675995i
$487$	10.3487	−	7.51874i	0.468942	−	0.340707i	−0.328087	−	0.944648i	$-0.606404\pi$
$487$	10.3487	−	7.51874i	0.468942	−	0.340707i	0.797029	+	0.603941i	$0.206404\pi$
$488$	6.73758	−	4.89514i	0.304996	−	0.221593i
$489$	−0.223560	−	0.162426i	−0.0101097	−	0.00734515i
$490$	−14.2237			−0.642561
$491$	18.5282			0.836166			0.418083	−	0.908409i	$-0.362702\pi$
$491$	18.5282			0.836166			0.418083	+	0.908409i	$0.362702\pi$
$492$	−0.272653	−	0.198094i	−0.0122921	−	0.00893076i
$493$	−7.94110	−	24.4402i	−0.357649	−	1.10073i
$494$	6.11864	−	18.8312i	0.275290	−	0.847257i
$495$	−7.59016			−0.341152
$496$		0			0
$497$	19.3922			0.869861
$498$	−6.63277	+	20.4136i	−0.297221	+	0.914754i
$499$	−12.6349	−	38.8861i	−0.565614	−	1.74078i	−0.666121	−	0.745844i	$-0.732046\pi$
$499$	−12.6349	−	38.8861i	−0.565614	−	1.74078i	0.100507	−	0.994936i	$-0.467954\pi$
$500$	4.58489	+	3.33112i	0.205042	+	0.148972i
$501$	−8.19362			−0.366064
$502$	20.0037			0.892809
$503$	−16.2427	−	11.8010i	−0.724227	−	0.526182i	0.163505	−	0.986543i	$-0.447720\pi$
$503$	−16.2427	−	11.8010i	−0.724227	−	0.526182i	−0.887732	+	0.460361i	$0.847720\pi$
$504$	−12.2852	+	8.92575i	−0.547228	+	0.397585i
$505$	−0.498582	+	0.362241i	−0.0221866	+	0.0161195i
$506$	−1.30312	+	4.01061i	−0.0579310	+	0.178293i
$507$	−10.1669	−	7.38668i	−0.451527	−	0.328054i
$508$	−3.01109	+	9.26718i	−0.133595	+	0.411164i
$509$	9.86111	+	30.3494i	0.437086	+	1.34521i	0.890934	+	0.454133i	$0.150051\pi$
$509$	9.86111	+	30.3494i	0.437086	+	1.34521i	−0.453848	+	0.891079i	$0.649949\pi$
$510$	12.0666	−	8.76693i	0.534320	−	0.388206i
$511$	6.33760	+	19.5051i	0.280359	+	0.862855i
$512$	−7.60561	−	23.4076i	−0.336123	−	1.03448i
$513$	−17.3467	+	12.6031i	−0.765875	+	0.556441i
$514$	8.89160	+	27.3655i	0.392192	+	1.20704i
$515$	−1.56508	+	4.81682i	−0.0689656	+	0.212254i
$516$	3.14103	+	2.28209i	0.138276	+	0.100464i
$517$	−1.38223	+	4.25408i	−0.0607906	+	0.187094i
$518$	6.87851	−	4.99753i	0.302224	−	0.219579i
$519$	−24.2687	+	17.6323i	−1.06528	+	0.773970i
$520$	−10.0759	−	7.32054i	−0.441855	−	0.321027i
$521$	2.10756			0.0923339			0.0461670	−	0.998934i	$-0.485299\pi$
$521$	2.10756			0.0923339			0.0461670	+	0.998934i	$0.485299\pi$
$522$	10.9525			0.479377
$523$	3.97047	+	2.88471i	0.173616	+	0.126140i	0.671200	−	0.741276i	$-0.265779\pi$
$523$	3.97047	+	2.88471i	0.173616	+	0.126140i	−0.497584	+	0.867416i	$0.665779\pi$
$524$	−1.88339	−	5.79648i	−0.0822762	−	0.253220i
$525$	−6.36830	+	19.5996i	−0.277935	+	0.855397i
$526$	12.8076			0.558440
$527$		0			0
$528$	21.8886			0.952580
$529$	−6.85158	+	21.0870i	−0.297895	+	0.916826i
$530$	−1.37955	−	4.24583i	−0.0599239	−	0.184427i
$531$	−8.21591	−	5.96921i	−0.356540	−	0.259042i
$532$	11.1750			0.484496
$533$	0.888398			0.0384808
$534$	−10.5399	−	7.65770i	−0.456107	−	0.331381i
$535$	3.94743	−	2.86798i	0.170662	−	0.123993i
$536$	−18.3595	+	13.3389i	−0.793009	+	0.576155i
$537$	−11.3620	+	34.9687i	−0.490308	+	1.50901i
$538$	−4.40412	−	3.19978i	−0.189875	−	0.137952i
$539$	8.68129	−	26.7182i	0.373929	−	1.15084i
$540$	0.809018	+	2.48990i	0.0348146	+	0.107148i
$541$	10.0618	−	7.31030i	0.432589	−	0.314294i	−0.350094	−	0.936714i	$-0.613850\pi$
$541$	10.0618	−	7.31030i	0.432589	−	0.314294i	0.782683	+	0.622420i	$0.213850\pi$
$542$	−2.34278	−	7.21033i	−0.100631	−	0.309710i
$543$	−7.73236	−	23.7978i	−0.331827	−	1.02126i
$544$	8.12346	−	5.90204i	0.348290	−	0.253048i
$545$	−3.32245	−	10.2255i	−0.142318	−	0.438011i
$546$	7.91900	−	24.3722i	0.338902	−	1.04303i
$547$	11.2979	+	8.20843i	0.483065	+	0.350967i	0.802511	−	0.596637i	$-0.203497\pi$
$547$	11.2979	+	8.20843i	0.483065	+	0.350967i	−0.319446	+	0.947604i	$0.603497\pi$
$548$	−1.47053	+	4.52584i	−0.0628181	+	0.193334i
$549$	−2.87646	+	2.08987i	−0.122764	+	0.0891934i
$550$	9.79058	−	7.11327i	0.417472	−	0.303311i
$551$	−33.5911	−	24.4054i	−1.43103	−	1.03970i
$552$	−5.77312			−0.245721
$553$	−37.0381			−1.57502
$554$	21.9779	+	15.9679i	0.933752	+	0.678411i
$555$	1.79784	+	5.53318i	0.0763141	+	0.234871i
$556$	−2.30732	+	7.10121i	−0.0978523	+	0.301159i
$557$	37.2207			1.57709			0.788546	−	0.614976i	$-0.210834\pi$
$557$	37.2207			1.57709			0.788546	+	0.614976i	$0.210834\pi$
$558$		0			0
$559$	−10.2346			−0.432876
$560$	−5.09496	+	15.6807i	−0.215301	+	0.662629i
$561$	9.10332	+	28.0172i	0.384343	+	1.18289i
$562$	30.6766	+	22.2878i	1.29401	+	0.940156i
$563$	−30.0267			−1.26548			−0.632738	−	0.774366i	$-0.718069\pi$
$563$	−30.0267			−1.26548			−0.632738	+	0.774366i	$0.718069\pi$
$564$	−1.18870			−0.0500532
$565$	−19.0651	−	13.8516i	−0.802075	−	0.582742i
$566$	21.2780	−	15.4594i	0.894380	−	0.649805i
$567$	−34.5033	+	25.0681i	−1.44900	+	1.05276i
$568$	4.81756	−	14.8269i	0.202140	−	0.622124i
$569$	−32.6611	−	23.7297i	−1.36922	−	0.994799i	−0.997797	−	0.0663367i	$-0.978869\pi$
$569$	−32.6611	−	23.7297i	−1.36922	−	0.994799i	−0.371426	−	0.928462i	$-0.621131\pi$
$570$	7.44698	−	22.9194i	0.311919	−	0.959989i
$571$	−13.1646	−	40.5165i	−0.550921	−	1.69556i	−0.706478	−	0.707735i	$-0.749717\pi$
$571$	−13.1646	−	40.5165i	−0.550921	−	1.69556i	0.155557	−	0.987827i	$-0.450283\pi$
$572$	3.86310	−	2.80670i	0.161524	−	0.117354i
$573$	−3.25187	−	10.0082i	−0.135849	−	0.418100i
$574$	−0.488296	−	1.50282i	−0.0203811	−	0.0627265i
$575$	−1.92195	+	1.39638i	−0.0801507	+	0.0582329i
$576$	3.58521	+	11.0341i	0.149384	+	0.459756i
$577$	−2.02028	+	6.21779i	−0.0841054	+	0.258850i	−0.984262	−	0.176717i	$-0.943452\pi$
$577$	−2.02028	+	6.21779i	−0.0841054	+	0.258850i	0.900156	+	0.435567i	$0.143452\pi$
$578$	2.74568	+	1.99485i	0.114205	+	0.0829750i
$579$	12.8508	−	39.5507i	0.534062	−	1.64367i
$580$	−4.10149	+	2.97991i	−0.170305	+	0.123734i
$581$	25.8344	−	18.7698i	1.07179	−	0.778703i
$582$	22.5754	+	16.4020i	0.935779	+	0.679883i
$583$	8.81749			0.365183
$584$	16.4877			0.682264
$585$	4.30166	+	3.12534i	0.177852	+	0.129217i
$586$	−0.685001	−	2.10822i	−0.0282971	−	0.0870897i
$587$	6.60607	−	20.3314i	0.272662	−	0.839167i	−0.717167	−	0.696902i	$-0.754561\pi$
$587$	6.60607	−	20.3314i	0.272662	−	0.839167i	0.989829	−	0.142265i	$-0.0454386\pi$
$588$	7.46576			0.307883
$589$		0			0
$590$	−14.8146			−0.609907
$591$	13.9195	−	42.8397i	0.572570	−	1.76219i
$592$	−1.57209	−	4.83839i	−0.0646124	−	0.198857i
$593$	−21.0268	−	15.2769i	−0.863468	−	0.627347i	0.0653579	−	0.997862i	$-0.479181\pi$
$593$	−21.0268	−	15.2769i	−0.863468	−	0.627347i	−0.928826	+	0.370515i	$0.879181\pi$
$594$	16.2961			0.668638
$595$	−22.1900			−0.909701
$596$	−5.94098	−	4.31638i	−0.243352	−	0.176806i
$597$	−25.4582	+	18.4965i	−1.04193	+	0.757010i
$598$	2.38995	−	1.73640i	0.0977323	−	0.0710066i
$599$	−2.83923	+	8.73827i	−0.116008	+	0.357036i	−0.992156	−	0.125006i	$-0.960105\pi$
$599$	−2.83923	+	8.73827i	−0.116008	+	0.357036i	0.876148	+	0.482042i	$0.160105\pi$
$600$	13.4034	+	9.73815i	0.547192	+	0.397558i
$601$	−10.2961	+	31.6883i	−0.419989	+	1.29259i	0.487723	+	0.872998i	$0.337828\pi$
$601$	−10.2961	+	31.6883i	−0.419989	+	1.29259i	−0.907712	+	0.419594i	$0.862172\pi$
$602$	5.62530	+	17.3129i	0.229270	+	0.705620i
$603$	7.83816	−	5.69476i	0.319195	−	0.231908i
$604$	−0.0389782	−	0.119962i	−0.00158600	−	0.00488120i
$605$	−1.50407	−	4.62905i	−0.0611491	−	0.188197i
$606$	−0.824741	+	0.599210i	−0.0335028	+	0.0243412i
$607$	−15.0494	−	46.3172i	−0.610835	−	1.87996i	−0.450157	−	0.892949i	$-0.648632\pi$
$607$	−15.0494	−	46.3172i	−0.610835	−	1.87996i	−0.160678	−	0.987007i	$-0.551368\pi$
$608$	5.01342	−	15.4297i	0.203321	−	0.625758i
$609$	−43.4751	−	31.5865i	−1.76170	−	1.27995i
$610$	−1.60278	+	4.93285i	−0.0648947	+	0.199725i
$611$	2.53504	−	1.84181i	0.102557	−	0.0745118i
$612$	−1.92046	+	1.39530i	−0.0776300	+	0.0564015i
$613$	16.9198	+	12.2929i	0.683384	+	0.496507i	0.874479	−	0.485064i	$-0.161204\pi$
$613$	16.9198	+	12.2929i	0.683384	+	0.496507i	−0.191095	+	0.981572i	$0.561204\pi$
$614$	32.9845			1.33115
$615$	1.08127			0.0436009
$616$	−35.3968	−	25.7173i	−1.42618	−	1.03618i
$617$	14.0244	+	43.1627i	0.564602	+	1.73767i	0.669132	+	0.743144i	$0.266666\pi$
$617$	14.0244	+	43.1627i	0.564602	+	1.73767i	−0.104530	+	0.994522i	$0.533334\pi$
$618$	−2.58891	+	7.96784i	−0.104141	+	0.320514i
$619$	10.2462			0.411832			0.205916	−	0.978570i	$-0.433983\pi$
$619$	10.2462			0.411832			0.205916	+	0.978570i	$0.433983\pi$
$620$		0			0
$621$	−3.19902			−0.128372
$622$	1.59202	−	4.89973i	0.0638341	−	0.196461i
$623$	5.98950	+	18.4338i	0.239964	+	0.738534i
$624$	−12.4052	−	9.01290i	−0.496605	−	0.360805i
$625$	−5.12716			−0.205086
$626$	13.9763			0.558606
$627$	38.5074	+	27.9773i	1.53784	+	1.11730i
$628$	6.20729	−	4.50986i	0.247698	−	0.179963i
$629$	5.53925	−	4.02450i	0.220864	−	0.160467i
$630$	2.92249	−	8.99451i	0.116435	−	0.358350i
$631$	−8.63785	−	6.27576i	−0.343867	−	0.249834i	0.402424	−	0.915453i	$-0.368168\pi$
$631$	−8.63785	−	6.27576i	−0.343867	−	0.249834i	−0.746292	+	0.665619i	$0.768168\pi$
$632$	−9.20126	+	28.3186i	−0.366006	+	1.12645i
$633$	−4.04240	−	12.4412i	−0.160671	−	0.494495i
$634$	−25.7998	+	18.7446i	−1.02464	+	0.744444i
$635$	−9.66059	−	29.7322i	−0.383369	−	1.17989i
$636$	0.724101	+	2.22855i	0.0287125	+	0.0883679i
$637$	−15.9216	+	11.5677i	−0.630836	+	0.458330i
$638$	9.75158	+	30.0123i	0.386069	+	1.18820i
$639$	−2.05675	+	6.33002i	−0.0813637	+	0.250412i
$640$	7.03920	+	5.11428i	0.278249	+	0.202160i
$641$	−7.37379	+	22.6942i	−0.291247	+	0.896367i	0.693209	+	0.720737i	$0.256196\pi$
$641$	−7.37379	+	22.6942i	−0.291247	+	0.896367i	−0.984456	+	0.175630i	$0.943804\pi$
$642$	6.52973	−	4.74413i	0.257708	−	0.187236i
$643$	−6.42300	+	4.66658i	−0.253298	+	0.184032i	−0.707187	−	0.707026i	$-0.750036\pi$
$643$	−6.42300	+	4.66658i	−0.253298	+	0.184032i	0.453889	+	0.891058i	$0.350036\pi$
$644$	1.34885	+	0.979993i	0.0531519	+	0.0386171i
$645$	−12.4565			−0.490473
$646$	−28.3610			−1.11585
$647$	2.00443	+	1.45630i	0.0788023	+	0.0572532i	0.626489	−	0.779430i	$-0.284491\pi$
$647$	2.00443	+	1.45630i	0.0788023	+	0.0572532i	−0.547687	+	0.836684i	$0.684491\pi$
$648$	10.5950	+	32.6081i	0.416212	+	1.28097i
$649$	9.04192	−	27.8282i	0.354926	−	1.09235i
$650$	−8.47769			−0.332523
$651$		0			0
$652$	0.0641574			0.00251260
$653$	6.95104	−	21.3931i	0.272015	−	0.837177i	−0.717978	−	0.696065i	$-0.754932\pi$
$653$	6.95104	−	21.3931i	0.272015	−	0.837177i	0.989994	−	0.141112i	$-0.0450677\pi$
$654$	−5.49591	−	16.9147i	−0.214907	−	0.661416i
$655$	15.8196	+	11.4936i	0.618123	+	0.449093i
$656$	−0.945493			−0.0369153
$657$	−7.03903			−0.274619
$658$	−4.50897	−	3.27596i	−0.175778	−	0.127710i
$659$	9.67555	−	7.02970i	0.376906	−	0.273838i	−0.383163	−	0.923681i	$-0.625165\pi$
$659$	9.67555	−	7.02970i	0.376906	−	0.273838i	0.760069	+	0.649843i	$0.225165\pi$
$660$	4.70177	−	3.41603i	0.183016	−	0.132969i
$661$	7.36572	−	22.6694i	0.286493	−	0.881736i	−0.699454	−	0.714678i	$-0.746573\pi$
$661$	7.36572	−	22.6694i	0.286493	−	0.881736i	0.985947	−	0.167058i	$-0.0534267\pi$
$662$	0.763374	+	0.554624i	0.0296694	+	0.0215561i
$663$	6.37716	−	19.6269i	0.247668	−	0.762245i
$664$	−7.93305	−	24.4154i	−0.307862	−	0.947502i
$665$	−29.0057	+	21.0739i	−1.12479	+	0.817211i
$666$	0.901758	+	2.77533i	0.0349424	+	0.107542i
$667$	−1.91429	−	5.89158i	−0.0741216	−	0.228123i
$668$	1.53902	−	1.11816i	0.0595464	−	0.0432630i
$669$	4.73791	+	14.5818i	0.183178	+	0.563765i
$670$	4.36747	−	13.4417i	0.168730	−	0.519298i
$671$	−8.28778	−	6.02142i	−0.319946	−	0.232455i
$672$	6.48859	−	19.9698i	0.250303	−	0.770353i
$673$	2.82680	−	2.05379i	0.108965	−	0.0791679i	−0.531968	−	0.846764i	$-0.678547\pi$
$673$	2.82680	−	2.05379i	0.108965	−	0.0791679i	0.640933	+	0.767596i	$0.278547\pi$
$674$	2.38679	−	1.73411i	0.0919359	−	0.0667953i
$675$	7.42715	+	5.39614i	0.285871	+	0.207698i
$676$	2.91770			0.112219
$677$	19.2457			0.739674			0.369837	−	0.929097i	$-0.379414\pi$
$677$	19.2457			0.739674			0.369837	+	0.929097i	$0.379414\pi$
$678$	−31.5370	−	22.9130i	−1.21117	−	0.879967i
$679$	−12.8289	−	39.4832i	−0.492326	−	1.51523i
$680$	−5.51260	+	16.9660i	−0.211399	+	0.650618i
$681$	−39.9221			−1.52982
$682$		0			0
$683$	−39.8738			−1.52573			−0.762865	−	0.646558i	$-0.776208\pi$
$683$	−39.8738			−1.52573			−0.762865	+	0.646558i	$0.776208\pi$
$684$	−1.18522	+	3.64773i	−0.0453180	+	0.139475i
$685$	−4.71797	−	14.5204i	−0.180264	−	0.554797i
$686$	1.77673	+	1.29087i	0.0678359	+	0.0492857i
$687$	−12.6306			−0.481887
$688$	10.8923			0.415266
$689$	−4.99723	−	3.63070i	−0.190379	−	0.138319i
$690$	2.90880	−	2.11337i	0.110736	−	0.0804545i
$691$	−31.0747	+	22.5771i	−1.18214	+	0.858873i	−0.992411	−	0.122964i	$-0.960760\pi$
$691$	−31.0747	+	22.5771i	−1.18214	+	0.858873i	−0.189726	+	0.981837i	$0.560760\pi$
$692$	2.15220	−	6.62378i	0.0818142	−	0.251798i
$693$	15.1119	+	10.9794i	0.574052	+	0.417073i
$694$	−2.15428	+	6.63018i	−0.0817752	+	0.251678i
$695$	−7.40268	−	22.7831i	−0.280800	−	0.864212i
$696$	−34.9508	+	25.3933i	−1.32481	+	0.962529i
$697$	−0.393224	−	1.21022i	−0.0148944	−	0.0458403i
$698$	11.0678	+	34.0633i	0.418924	+	1.28932i
$699$	29.4242	−	21.3779i	1.11292	−	0.808586i
$700$	−1.47854	−	4.55048i	−0.0558836	−	0.171992i
$701$	−10.9471	+	33.6916i	−0.413465	+	1.27251i	0.500151	+	0.865938i	$0.333278\pi$
$701$	−10.9471	+	33.6916i	−0.413465	+	1.27251i	−0.913617	+	0.406577i	$0.866722\pi$
$702$	−9.23569	−	6.71012i	−0.348579	−	0.253257i
$703$	3.41857	−	10.5213i	0.128934	−	0.396818i
$704$	−27.0439	+	19.6486i	−1.01926	+	0.740533i
$705$	3.08539	−	2.24166i	0.116202	−	0.0844260i
$706$	−19.2145	−	13.9601i	−0.723145	−	0.525396i
$707$	1.51666			0.0570399
$708$	7.77589			0.292236
$709$	−20.8801	−	15.1703i	−0.784170	−	0.569733i	0.122057	−	0.992523i	$-0.461051\pi$
$709$	−20.8801	−	15.1703i	−0.784170	−	0.569733i	−0.906228	+	0.422790i	$0.861051\pi$
$710$	3.00035	+	9.23414i	0.112601	+	0.346551i
$711$	3.92827	−	12.0900i	0.147322	−	0.453409i
$712$	15.5821			0.583962
$713$		0			0
$714$	−36.7061			−1.37369
$715$	−4.73414	+	14.5702i	−0.177047	+	0.544894i
$716$	−2.63795	−	8.11877i	−0.0985848	−	0.303413i
$717$	46.8557	+	34.0426i	1.74986	+	1.27135i
$718$	12.7459			0.475674
$719$	39.0467			1.45620			0.728099	−	0.685472i	$-0.240404\pi$
$719$	39.0467			1.45620			0.728099	+	0.685472i	$0.240404\pi$
$720$	−4.57811	−	3.32619i	−0.170616	−	0.123960i
$721$	10.0837	−	7.32625i	0.375537	−	0.272844i
$722$	−18.1321	+	13.1738i	−0.674807	+	0.490276i
$723$	14.5872	−	44.8947i	0.542503	−	1.66965i
$724$	4.70000	+	3.41475i	0.174674	+	0.126908i
$725$	−5.49357	+	16.9075i	−0.204026	+	0.627928i
$726$	−2.48799	−	7.65724i	−0.0923379	−	0.284187i
$727$	−20.2122	+	14.6850i	−0.749629	+	0.544637i	−0.895712	−	0.444635i	$-0.853333\pi$
$727$	−20.2122	+	14.6850i	−0.749629	+	0.544637i	0.146083	+	0.989272i	$0.453333\pi$
$728$	9.47144	+	29.1501i	0.351035	+	1.08037i
$729$	2.24010	+	6.89433i	0.0829668	+	0.255345i
$730$	−8.30734	+	6.03563i	−0.307468	+	0.223389i
$731$	4.53004	+	13.9420i	0.167550	+	0.515665i
$732$	0.841269	−	2.58916i	0.0310942	−	0.0956981i
$733$	13.7121	+	9.96240i	0.506467	+	0.367970i	0.811482	−	0.584378i	$-0.198661\pi$
$733$	13.7121	+	9.96240i	0.506467	+	0.367970i	−0.305015	+	0.952348i	$0.598661\pi$
$734$	0.0519983	−	0.160034i	0.00191929	−	0.00590697i
$735$	−19.3781	+	14.0790i	−0.714773	+	0.519313i
$736$	1.95825	−	1.42275i	0.0721821	−	0.0524434i
$737$	22.5837	+	16.4080i	0.831880	+	0.604396i
$738$	0.542340			0.0199638
$739$	−14.3821			−0.529055			−0.264528	−	0.964378i	$-0.585216\pi$
$739$	−14.3821			−0.529055			−0.264528	+	0.964378i	$0.585216\pi$
$740$	−1.09279	−	0.793959i	−0.0401718	−	0.0291865i
$741$	−10.3038	−	31.7117i	−0.378518	−	1.16496i
$742$	−3.39506	+	10.4489i	−0.124637	+	0.383592i
$743$	27.7705			1.01880			0.509400	−	0.860530i	$-0.329867\pi$
$743$	27.7705			1.01880			0.509400	+	0.860530i	$0.329867\pi$
$744$		0			0
$745$	23.5603			0.863183
$746$	−2.80390	+	8.62953i	−0.102658	+	0.315950i
$747$	3.38684	+	10.4236i	0.123918	+	0.381380i
$748$	−5.53332	−	4.02019i	−0.202318	−	0.146993i
$749$	−12.0079			−0.438758
$750$	−30.0768			−1.09825
$751$	35.2490	+	25.6099i	1.28626	+	0.934519i	0.999723	−	0.0235512i	$-0.00749727\pi$
$751$	35.2490	+	25.6099i	1.28626	+	0.934519i	0.286533	+	0.958070i	$0.407497\pi$
$752$	−2.69796	+	1.96018i	−0.0983844	+	0.0714804i
$753$	27.2527	−	19.8002i	0.993143	−	0.721561i
$754$	6.83128	−	21.0245i	0.248781	−	0.765668i
$755$	0.327399	+	0.237869i	0.0119153	+	0.00865695i
$756$	1.99098	−	6.12762i	0.0724114	−	0.222859i
$757$	−7.79251	−	23.9829i	−0.283224	−	0.871673i	−0.986925	−	0.161177i	$-0.948471\pi$
$757$	−7.79251	−	23.9829i	−0.283224	−	0.871673i	0.703702	−	0.710495i	$-0.251529\pi$
$758$	4.59361	−	3.33745i	0.166847	−	0.121222i
$759$	2.19446	+	6.75385i	0.0796538	+	0.245149i
$760$	8.90688	+	27.4125i	0.323086	+	0.994358i
$761$	−2.11633	+	1.53761i	−0.0767170	+	0.0557382i	−0.625483	−	0.780238i	$-0.715098\pi$
$761$	−2.11633	+	1.53761i	−0.0767170	+	0.0557382i	0.548766	+	0.835976i	$0.315098\pi$
$762$	−15.9803	−	49.1823i	−0.578905	−	1.78169i
$763$	−8.17652	+	25.1647i	−0.296010	+	0.911025i
$764$	1.97660	+	1.43608i	0.0715109	+	0.0519557i
$765$	2.35348	−	7.24326i	0.0850902	−	0.261881i
$766$	−32.1930	+	23.3896i	−1.16318	+	0.845100i
$767$	−16.5830	+	12.0483i	−0.598777	+	0.435037i
$768$	−18.1925	−	13.2176i	−0.656466	−	0.476950i
$769$	11.3507			0.409316			0.204658	−	0.978834i	$-0.434392\pi$
$769$	11.3507			0.409316			0.204658	+	0.978834i	$0.434392\pi$
$770$	27.2491			0.981988
$771$	39.2009	+	28.4811i	1.41179	+	1.02572i
$772$	2.98360	+	9.18259i	0.107382	+	0.330488i
$773$	3.52816	−	10.8586i	0.126899	−	0.390556i	−0.867343	−	0.497711i	$-0.834174\pi$
$773$	3.52816	−	10.8586i	0.126899	−	0.390556i	0.994242	+	0.107155i	$0.0341741\pi$
$774$	−6.24789			−0.224576
$775$		0			0
$776$	−33.3751			−1.19810
$777$	4.42446	−	13.6171i	0.158727	−	0.488511i
$778$	13.4300	+	41.3332i	0.481488	+	1.48187i
$779$	−1.66335	−	1.20849i	−0.0595957	−	0.0432988i
$780$	−4.07128			−0.145775
$781$	−19.1769			−0.686204
$782$	−3.42325	−	2.48714i	−0.122415	−	0.0889398i
$783$	−19.3671	+	14.0710i	−0.692123	+	0.502857i
$784$	16.9448	−	12.3111i	0.605173	−	0.439684i
$785$	−7.60689	+	23.4116i	−0.271502	+	0.835596i
$786$	26.1684	+	19.0124i	0.933394	+	0.678151i
$787$	8.37103	−	25.7634i	0.298395	−	0.918365i	−0.683665	−	0.729796i	$-0.739615\pi$
$787$	8.37103	−	25.7634i	0.298395	−	0.918365i	0.982060	−	0.188569i	$-0.0603849\pi$
$788$	3.23171	+	9.94618i	0.115125	+	0.354318i
$789$	17.4489	−	12.6774i	0.621197	−	0.451326i
$790$	−5.73050	−	17.6367i	−0.203882	−	0.627484i
$791$	17.9215	+	55.1566i	0.637214	+	1.96114i
$792$	12.1488	−	8.82665i	0.431690	−	0.313641i
$793$	2.21764	+	6.82518i	0.0787505	+	0.242369i
$794$	−1.53600	+	4.72733i	−0.0545106	+	0.167767i
$795$	−6.08212	−	4.41892i	−0.215710	−	0.156723i
$796$	2.25768	−	6.94843i	0.0800214	−	0.246280i
$797$	39.3634	−	28.5992i	1.39432	−	1.01303i	0.398947	−	0.916974i	$-0.369376\pi$
$797$	39.3634	−	28.5992i	1.39432	−	1.01303i	0.995375	−	0.0960610i	$-0.0306244\pi$
$798$	−47.9805	+	34.8599i	−1.69849	+	1.23403i
$799$	−3.63107	−	2.63812i	−0.128458	−	0.0933301i
$800$	−6.94637			−0.245591
$801$	−6.65241			−0.235051
$802$	24.8048	+	18.0217i	0.875887	+	0.636369i
$803$	−6.26723	−	19.2885i	−0.221166	−	0.680678i
$804$	−2.29240	+	7.05530i	−0.0808469	+	0.248821i
$805$	−5.34915			−0.188533
$806$		0			0
$807$	−9.16733			−0.322705
$808$	0.376780	−	1.15961i	0.0132551	−	0.0407949i
$809$	5.81234	+	17.8885i	0.204351	+	0.628928i	0.999739	+	0.0228278i	$0.00726693\pi$
$809$	5.81234	+	17.8885i	0.204351	+	0.628928i	−0.795388	+	0.606100i	$0.792733\pi$
$810$	−17.2752	−	12.5512i	−0.606988	−	0.441002i
$811$	−39.5385			−1.38839			−0.694193	−	0.719789i	$-0.744239\pi$
$811$	−39.5385			−1.38839			−0.694193	+	0.719789i	$0.744239\pi$
$812$	12.4765			0.437840
$813$	−10.3287	−	7.50428i	−0.362245	−	0.263186i
$814$	−6.80214	+	4.94204i	−0.238415	+	0.173219i
$815$	−0.166527	+	0.120989i	−0.00583319	+	0.00423806i
$816$	−6.78700	+	20.8882i	−0.237593	+	0.731235i
$817$	19.1622	+	13.9222i	0.670402	+	0.487075i
$818$	−1.33542	+	4.10999i	−0.0466918	+	0.143703i
$819$	−4.04362	−	12.4450i	−0.141295	−	0.434862i
$820$	−0.203096	+	0.147558i	−0.00709241	+	0.00515293i
$821$	4.52299	+	13.9203i	0.157854	+	0.485823i	0.998439	−	0.0558559i	$-0.0177887\pi$
$821$	4.52299	+	13.9203i	0.157854	+	0.485823i	−0.840585	+	0.541679i	$0.817789\pi$
$822$	−7.80434	−	24.0193i	−0.272208	−	0.837769i
$823$	33.8062	−	24.5616i	1.17841	−	0.856164i	0.186417	−	0.982471i	$-0.440312\pi$
$823$	33.8062	−	24.5616i	1.17841	−	0.856164i	0.991991	+	0.126307i	$0.0403124\pi$
$824$	−3.09644	−	9.52986i	−0.107870	−	0.331988i
$825$	6.29759	−	19.3820i	0.219254	−	0.674794i
$826$	29.4955	+	21.4298i	1.02628	+	0.745637i
$827$	2.90665	−	8.94576i	0.101074	−	0.311075i	−0.887715	−	0.460394i	$-0.847708\pi$
$827$	2.90665	−	8.94576i	0.101074	−	0.311075i	0.988789	+	0.149319i	$0.0477082\pi$
$828$	−0.462949	+	0.336352i	−0.0160886	+	0.0116890i
$829$	32.6283	−	23.7058i	1.13323	−	0.823337i	0.147065	−	0.989127i	$-0.453017\pi$
$829$	32.6283	−	23.7058i	1.13323	−	0.823337i	0.986161	+	0.165790i	$0.0530173\pi$
$830$	12.9348	+	9.39771i	0.448975	+	0.326199i
$831$	45.7478			1.58697
$832$	23.4174			0.811854
$833$	22.8053	+	16.5690i	0.790158	+	0.574083i
$834$	−12.2453	−	37.6872i	−0.424020	−	1.30500i
$835$	−1.88603	+	5.80460i	−0.0652688	+	0.200877i
$836$	−11.0509			−0.382203
$837$		0			0
$838$	5.07693			0.175380
$839$	2.20936	−	6.79972i	0.0762757	−	0.234752i	−0.905648	−	0.424031i	$-0.860615\pi$
$839$	2.20936	−	6.79972i	0.0762757	−	0.234752i	0.981923	+	0.189278i	$0.0606149\pi$
$840$	11.5277	+	35.4785i	0.397742	+	1.22412i
$841$	−14.0420	−	10.2021i	−0.484208	−	0.351798i
$842$	34.0097			1.17205
$843$	63.8544			2.19926
$844$	2.45711	+	1.78520i	0.0845773	+	0.0614490i
$845$	−7.57319	+	5.50224i	−0.260526	+	0.189283i
$846$	1.54756	−	1.12437i	0.0532063	−	0.0386566i
$847$	−3.70149	+	11.3920i	−0.127185	+	0.391435i
$848$	5.31839	+	3.86404i	0.182634	+	0.132692i
$849$	13.6866	−	42.1231i	0.469724	−	1.44566i
$850$	3.75241	+	11.5487i	0.128707	+	0.396118i
$851$	1.33530	−	0.970152i	0.0457735	−	0.0332564i
$852$	−1.57483	−	4.84683i	−0.0539528	−	0.166050i
$853$	0.348160	+	1.07153i	0.0119208	+	0.0366884i	0.956840	−	0.290615i	$-0.0938600\pi$
$853$	0.348160	+	1.07153i	0.0119208	+	0.0366884i	−0.944919	+	0.327304i	$0.893860\pi$
$854$	10.3266	−	7.50274i	0.353370	−	0.256738i
$855$	−3.80259	−	11.7032i	−0.130046	−	0.400240i
$856$	−2.98308	+	9.18099i	−0.101960	+	0.313800i
$857$	19.2983	+	14.0210i	0.659218	+	0.478950i	0.866399	−	0.499353i	$-0.166429\pi$
$857$	19.2983	+	14.0210i	0.659218	+	0.478950i	−0.207181	+	0.978303i	$0.566429\pi$
$858$	−7.83108	+	24.1016i	−0.267349	+	0.822814i
$859$	26.2653	−	19.0829i	0.896160	−	0.651098i	−0.0413167	−	0.999146i	$-0.513155\pi$
$859$	26.2653	−	19.0829i	0.896160	−	0.651098i	0.937477	+	0.348048i	$0.113155\pi$
$860$	2.33971	−	1.69990i	0.0797836	−	0.0579662i
$861$	−2.15278	−	1.56409i	−0.0733665	−	0.0533039i
$862$	−18.3273			−0.624229
$863$	23.8418			0.811585			0.405793	−	0.913965i	$-0.366996\pi$
$863$	23.8418			0.811585			0.405793	+	0.913965i	$0.366996\pi$
$864$	−7.56744	−	5.49807i	−0.257450	−	0.187048i
$865$	6.90498	+	21.2513i	0.234776	+	0.722567i
$866$	−3.52660	+	10.8538i	−0.119839	+	0.368826i
$867$	5.71523			0.194099
$868$		0			0
$869$	36.6268			1.24248
$870$	8.31433	−	25.5889i	0.281882	−	0.867544i
$871$	−6.04291	−	18.5982i	−0.204756	−	0.630175i
$872$	17.2092	+	12.5032i	0.582777	+	0.423412i
$873$	14.2487			0.482247
$874$	−6.83675			−0.231256
$875$	36.2008	+	26.3014i	1.22381	+	0.889151i
$876$	4.36037	−	3.16799i	0.147323	−	0.107036i
$877$	−23.6837	+	17.2072i	−0.799741	+	0.581046i	−0.910838	−	0.412764i	$-0.864564\pi$
$877$	−23.6837	+	17.2072i	−0.799741	+	0.581046i	0.111097	+	0.993810i	$0.464564\pi$
$878$	6.74641	−	20.7633i	0.227680	−	0.700728i
$879$	−3.02001	−	2.19416i	−0.101862	−	0.0740073i
$880$	5.03839	−	15.5066i	0.169844	−	0.522726i
$881$	−2.79045	−	8.58811i	−0.0940126	−	0.289341i	0.892983	−	0.450091i	$-0.148609\pi$
$881$	−2.79045	−	8.58811i	−0.0940126	−	0.289341i	−0.986995	+	0.160750i	$0.948609\pi$
$882$	−9.71965	+	7.06174i	−0.327278	+	0.237781i
$883$	−6.61531	−	20.3598i	−0.222623	−	0.685162i	−0.998524	−	0.0543083i	$-0.982705\pi$
$883$	−6.61531	−	20.3598i	−0.222623	−	0.685162i	0.775901	−	0.630854i	$-0.217295\pi$
$884$	1.48060	+	4.55682i	0.0497979	+	0.153262i
$885$	−20.1831	+	14.6639i	−0.678448	+	0.492921i
$886$	−7.02515	−	21.6212i	−0.236015	−	0.726378i
$887$	7.60028	−	23.3912i	0.255192	−	0.785401i	−0.738599	−	0.674145i	$-0.764512\pi$
$887$	7.60028	−	23.3912i	0.255192	−	0.785401i	0.993792	−	0.111257i	$-0.0354875\pi$
$888$	−9.31221	−	6.76572i	−0.312497	−	0.227043i
$889$	−23.7746	+	73.1707i	−0.797374	+	2.45407i
$890$	−7.85105	+	5.70412i	−0.263168	+	0.191203i
$891$	34.1202	−	24.7898i	1.14307	−	0.830489i
$892$	−2.87987	−	2.09235i	−0.0964251	−	0.0700570i
$893$	−7.25179			−0.242672
$894$	38.9728			1.30345
$895$	22.1576	+	16.0984i	0.740646	+	0.538111i
$896$	−6.61694	−	20.3649i	−0.221057	−	0.680342i
$897$	1.53729	−	4.73128i	0.0513285	−	0.157973i
$898$	−27.9829			−0.933801
$899$		0			0
$900$	1.64218			0.0547395
$901$	−2.73404	+	8.41450i	−0.0910839	+	0.280328i
$902$	0.482874	+	1.48613i	0.0160779	+	0.0494828i
$903$	24.8006	+	18.0187i	0.825312	+	0.599624i
$904$	46.6238			1.55069
$905$	−18.6389			−0.619578
$906$	0.541574	+	0.393477i	0.0179926	+	0.0130724i
$907$	15.9913	−	11.6183i	0.530981	−	0.385781i	−0.289743	−	0.957104i	$-0.593570\pi$
$907$	15.9913	−	11.6183i	0.530981	−	0.385781i	0.820725	+	0.571324i	$0.193570\pi$
$908$	7.49861	−	5.44806i	0.248850	−	0.180800i
$909$	−0.160858	+	0.495069i	−0.00533531	+	0.0164204i
$910$	−15.4432	−	11.2201i	−0.511936	−	0.371943i
$911$	11.0077	−	33.8781i	0.364701	−	1.12243i	−0.585468	−	0.810696i	$-0.699089\pi$
$911$	11.0077	−	33.8781i	0.364701	−	1.12243i	0.950168	−	0.311737i	$-0.100911\pi$
$912$	10.9660	+	33.7498i	0.363119	+	1.11757i
$913$	−25.5476	+	18.5614i	−0.845501	+	0.614293i
$914$	6.15383	+	18.9395i	0.203550	+	0.626464i
$915$	2.69908	+	8.30691i	0.0892287	+	0.274618i
$916$	2.37242	−	1.72366i	0.0783870	−	0.0569515i
$917$	−14.8706	−	45.7671i	−0.491072	−	1.51136i
$918$	−5.05294	+	15.5513i	−0.166772	+	0.513271i
$919$	13.8798	+	10.0842i	0.457851	+	0.332648i	0.792688	−	0.609628i	$-0.208681\pi$
$919$	13.8798	+	10.0842i	0.457851	+	0.332648i	−0.334837	+	0.942276i	$0.608681\pi$
$920$	−1.32887	+	4.08986i	−0.0438117	+	0.134839i
$921$	44.9375	−	32.6490i	1.48074	−	1.07582i
$922$	21.4709	−	15.5995i	0.707105	−	0.513742i
$923$	10.8684	+	7.89632i	0.357736	+	0.259911i
$924$	−14.3025			−0.470519
$925$	−4.73661			−0.155739
$926$	−17.4546	−	12.6815i	−0.573594	−	0.416741i
$927$	1.32195	+	4.06856i	0.0434187	+	0.133629i
$928$	5.59734	−	17.2268i	0.183742	−	0.565499i
$929$	−45.5222			−1.49353			−0.746767	−	0.665086i	$-0.768395\pi$
$929$	−45.5222			−1.49353			−0.746767	+	0.665086i	$0.768395\pi$
$930$		0			0
$931$	45.5457			1.49270
$932$	−2.60939	+	8.03088i	−0.0854734	+	0.263060i
$933$	−2.68095	−	8.25113i	−0.0877705	−	0.270130i
$934$	11.7694	+	8.55098i	0.385107	+	0.279797i
$935$	21.9436			0.717633
$936$	−10.5197			−0.343848
$937$	−20.7250	−	15.0576i	−0.677056	−	0.491910i	0.195324	−	0.980739i	$-0.437424\pi$
$937$	−20.7250	−	15.0576i	−0.677056	−	0.491910i	−0.872380	+	0.488829i	$0.837424\pi$
$938$	−28.1394	+	20.4445i	−0.918784	+	0.667536i
$939$	19.0411	−	13.8342i	0.621383	−	0.451461i
$940$	−0.273618	+	0.842110i	−0.00892443	+	0.0274666i
$941$	9.80839	+	7.12621i	0.319744	+	0.232308i	0.736066	−	0.676909i	$-0.236681\pi$
$941$	9.80839	+	7.12621i	0.319744	+	0.232308i	−0.416322	+	0.909217i	$0.636681\pi$
$942$	−12.5831	+	38.7268i	−0.409980	+	1.26179i
$943$	−0.0947910	−	0.291737i	−0.00308682	−	0.00950025i
$944$	17.6487	−	12.8226i	0.574418	−	0.417339i
$945$	6.38775	+	19.6595i	0.207794	+	0.639523i
$946$	−5.56284	−	17.1207i	−0.180863	−	0.556640i
$947$	−22.0061	+	15.9884i	−0.715103	+	0.519553i	−0.884816	−	0.465941i	$-0.845716\pi$
$947$	−22.0061	+	15.9884i	−0.715103	+	0.519553i	0.169713	+	0.985494i	$0.445716\pi$
$948$	3.00783	+	9.25715i	0.0976898	+	0.300658i
$949$	−4.39039	+	13.5122i	−0.142518	+	0.438625i
$950$	15.8728	+	11.5323i	0.514982	+	0.374157i
$951$	−16.5952	+	51.0747i	−0.538136	+	1.65621i
$952$	35.5174	−	25.8049i	1.15113	−	0.836342i
$953$	20.1386	−	14.6316i	0.652353	−	0.473962i	−0.211719	−	0.977331i	$-0.567906\pi$
$953$	20.1386	−	14.6316i	0.652353	−	0.473962i	0.864072	+	0.503368i	$0.167906\pi$
$954$	−3.05066	−	2.21643i	−0.0987687	−	0.0717597i
$955$	−7.83866			−0.253653
$956$	−13.4467			−0.434896
$957$	42.9924	+	31.2358i	1.38975	+	1.00971i
$958$	−6.01936	−	18.5257i	−0.194477	−	0.598538i
$959$	−11.6109	+	35.7346i	−0.374935	+	1.15393i
$960$	28.5013			0.919876
$961$		0			0
$962$	5.89000			0.189901
$963$	1.27356	−	3.91961i	0.0410399	−	0.126308i
$964$	3.38674	+	10.4233i	0.109080	+	0.335712i
$965$	−25.0609	−	18.2078i	−0.806739	−	0.586130i
$966$	−8.84842			−0.284693
$967$	−52.1998			−1.67863			−0.839316	−	0.543643i	$-0.817044\pi$
$967$	−52.1998			−1.67863			−0.839316	+	0.543643i	$0.817044\pi$
$968$	7.79057	+	5.66018i	0.250398	+	0.181925i
$969$	−38.6386	+	28.0726i	−1.24125	+	0.901821i
$970$	16.8161	−	12.2176i	0.539933	−	0.392284i
$971$	−6.16824	+	18.9839i	−0.197948	+	0.609222i	0.801981	+	0.597349i	$0.203779\pi$
$971$	−6.16824	+	18.9839i	−0.197948	+	0.609222i	−0.999930	+	0.0118727i	$0.996221\pi$
$972$	4.95638	+	3.60102i	0.158976	+	0.115503i
$973$	−18.2179	+	56.0689i	−0.584039	+	1.79749i
$974$	−4.87057	−	14.9901i	−0.156063	−	0.480313i
$975$	−11.5499	+	8.39147i	−0.369892	+	0.268742i
$976$	−2.36016	−	7.26382i	−0.0755468	−	0.232509i
$977$	−18.6185	−	57.3017i	−0.595657	−	1.83324i	−0.551426	−	0.834224i	$-0.685916\pi$
$977$	−18.6185	−	57.3017i	−0.595657	−	1.83324i	−0.0442310	−	0.999021i	$-0.514084\pi$
$978$	−0.275465	+	0.200137i	−0.00880839	+	0.00639967i
$979$	−5.92300	−	18.2291i	−0.189300	−	0.582605i
$980$	1.71849	−	5.28897i	0.0548951	−	0.168950i
$981$	−7.34707	−	5.33796i	−0.234574	−	0.170428i
$982$	7.05483	−	21.7125i	0.225129	−	0.692875i
$983$	−9.33502	+	6.78229i	−0.297741	+	0.216322i	−0.726619	−	0.687041i	$-0.758909\pi$
$983$	−9.33502	+	6.78229i	−0.297741	+	0.216322i	0.428877	+	0.903363i	$0.358909\pi$
$984$	−1.73068	+	1.25741i	−0.0551720	+	0.0400848i
$985$	−27.1449	−	19.7219i	−0.864908	−	0.628393i
$986$	−31.6643			−1.00840
$987$	−9.38559			−0.298746
$988$	6.26299	+	4.55033i	0.199252	+	0.144765i
$989$	1.09202	+	3.36088i	0.0347241	+	0.106870i
$990$	−2.89005	+	8.89465i	−0.0918517	+	0.282690i
$991$	−37.3423			−1.18622			−0.593109	−	0.805122i	$-0.702100\pi$
$991$	−37.3423			−1.18622			−0.593109	+	0.805122i	$0.702100\pi$
$992$		0			0
$993$	1.58899			0.0504251
$994$	7.38383	−	22.7251i	0.234201	−	0.720796i
$995$	7.24341	+	22.2929i	0.229631	+	0.706733i
$996$	−6.78925	−	4.93268i	−0.215126	−	0.156298i
$997$	20.8024			0.658820			0.329410	−	0.944187i	$-0.393150\pi$
$997$	20.8024			0.658820			0.329410	+	0.944187i	$0.393150\pi$
$998$	−50.3801			−1.59476
$999$	−5.16012	−	3.74904i	−0.163259	−	0.118614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.n.628.3		16
31.2	even	5		961.2.a.j.1.5		8
31.3	odd	30		961.2.g.s.816.1		16
31.4	even	5	inner	961.2.d.n.531.3		16
31.5	even	3		961.2.g.j.448.2		16
31.6	odd	6		31.2.g.a.9.2	yes	16
31.7	even	15		961.2.g.j.547.2		16
31.8	even	5		961.2.d.q.388.2		16
31.9	even	15		961.2.g.m.338.1		16
31.10	even	15		961.2.c.i.521.5		16
31.11	odd	30		31.2.g.a.7.2	✓	16
31.12	odd	30		961.2.c.j.439.5		16
31.13	odd	30		961.2.g.t.732.1		16
31.14	even	15		961.2.g.n.235.1		16
31.15	odd	10		961.2.d.p.374.2		16
31.16	even	5		961.2.d.q.374.2		16
31.17	odd	30		961.2.g.t.235.1		16
31.18	even	15		961.2.g.n.732.1		16
31.19	even	15		961.2.c.i.439.5		16
31.20	even	15		961.2.g.l.844.2		16
31.21	odd	30		961.2.c.j.521.5		16
31.22	odd	30		961.2.g.s.338.1		16
31.23	odd	10		961.2.d.p.388.2		16
31.24	odd	30		961.2.g.k.547.2		16
31.25	even	3		961.2.g.l.846.2		16
31.26	odd	6		961.2.g.k.448.2		16
31.27	odd	10		961.2.d.o.531.3		16
31.28	even	15		961.2.g.m.816.1		16
31.29	odd	10		961.2.a.i.1.5		8
31.30	odd	2		961.2.d.o.628.3		16
93.2	odd	10		8649.2.a.be.1.4		8
93.11	even	30		279.2.y.c.100.1		16
93.29	even	10		8649.2.a.bf.1.4		8
93.68	even	6		279.2.y.c.226.1		16
124.11	even	30		496.2.bg.c.193.2		16
124.99	even	6		496.2.bg.c.257.2		16
155.37	even	12		775.2.ck.a.474.3		32
155.42	even	60		775.2.ck.a.224.2		32
155.68	even	12		775.2.ck.a.474.2		32
155.73	even	60		775.2.ck.a.224.3		32
155.99	odd	6		775.2.bl.a.226.1		16
155.104	odd	30		775.2.bl.a.751.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.2	✓	16	31.11	odd	30
31.2.g.a.9.2	yes	16	31.6	odd	6
279.2.y.c.100.1		16	93.11	even	30
279.2.y.c.226.1		16	93.68	even	6
496.2.bg.c.193.2		16	124.11	even	30
496.2.bg.c.257.2		16	124.99	even	6
775.2.bl.a.226.1		16	155.99	odd	6
775.2.bl.a.751.1		16	155.104	odd	30
775.2.ck.a.224.2		32	155.42	even	60
775.2.ck.a.224.3		32	155.73	even	60
775.2.ck.a.474.2		32	155.68	even	12
775.2.ck.a.474.3		32	155.37	even	12
961.2.a.i.1.5		8	31.29	odd	10
961.2.a.j.1.5		8	31.2	even	5
961.2.c.i.439.5		16	31.19	even	15
961.2.c.i.521.5		16	31.10	even	15
961.2.c.j.439.5		16	31.12	odd	30
961.2.c.j.521.5		16	31.21	odd	30
961.2.d.n.531.3		16	31.4	even	5	inner
961.2.d.n.628.3		16	1.1	even	1	trivial
961.2.d.o.531.3		16	31.27	odd	10
961.2.d.o.628.3		16	31.30	odd	2
961.2.d.p.374.2		16	31.15	odd	10
961.2.d.p.388.2		16	31.23	odd	10
961.2.d.q.374.2		16	31.16	even	5
961.2.d.q.388.2		16	31.8	even	5
961.2.g.j.448.2		16	31.5	even	3
961.2.g.j.547.2		16	31.7	even	15
961.2.g.k.448.2		16	31.26	odd	6
961.2.g.k.547.2		16	31.24	odd	30
961.2.g.l.844.2		16	31.20	even	15
961.2.g.l.846.2		16	31.25	even	3
961.2.g.m.338.1		16	31.9	even	15
961.2.g.m.816.1		16	31.28	even	15
961.2.g.n.235.1		16	31.14	even	15
961.2.g.n.732.1		16	31.18	even	15
961.2.g.s.338.1		16	31.22	odd	30
961.2.g.s.816.1		16	31.3	odd	30
961.2.g.t.235.1		16	31.17	odd	30
961.2.g.t.732.1		16	31.13	odd	30
8649.2.a.be.1.4		8	93.2	odd	10
8649.2.a.bf.1.4		8	93.29	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.380762 - 1.17187i) q^{2} +(-0.641202 - 1.97342i) q^{3} +(0.389745 + 0.283166i) q^{4} -1.54562 q^{5} -2.55673 q^{6} +(3.07730 + 2.23579i) q^{7} +(2.47393 - 1.79742i) q^{8} +(-1.05619 + 0.767366i) q^{9} +(-0.588515 + 1.81126i) q^{10} +(-3.04314 - 2.21097i) q^{11} +(0.308900 - 0.950697i) q^{12} +(0.814279 + 2.50609i) q^{13} +(3.79177 - 2.75488i) q^{14} +(0.991057 + 3.05016i) q^{15} +(-0.866611 - 2.66715i) q^{16} +(3.05350 - 2.21850i) q^{17} +(0.497093 + 1.52989i) q^{18} +(1.88448 - 5.79984i) q^{19} +(-0.602399 - 0.437668i) q^{20} +(2.43898 - 7.50641i) q^{21} +(-3.74967 + 2.72429i) q^{22} +(0.736082 - 0.534795i) q^{23} +(-5.13334 - 3.72959i) q^{24} -2.61105 q^{25} +3.24685 q^{26} +(-2.84451 - 2.06665i) q^{27} +(0.566263 + 1.74278i) q^{28} +(2.10397 - 6.47535i) q^{29} +3.95173 q^{30} +2.66037 q^{32} +(-2.41190 + 7.42306i) q^{33} +(-1.43713 - 4.42302i) q^{34} +(-4.75635 - 3.45569i) q^{35} -0.628936 q^{36} +1.81406 q^{37} +(-6.07909 - 4.41672i) q^{38} +(4.42345 - 3.21383i) q^{39} +(-3.82376 + 2.77813i) q^{40} +(0.104183 - 0.320644i) q^{41} +(-7.86783 - 5.71631i) q^{42} +(-1.20022 + 3.69390i) q^{43} +(-0.559976 - 1.72343i) q^{44} +(1.63247 - 1.18606i) q^{45} +(-0.346435 - 1.06622i) q^{46} +(-0.367467 - 1.13095i) q^{47} +(-4.70774 + 3.42037i) q^{48} +(2.30792 + 7.10304i) q^{49} +(-0.994189 + 3.05980i) q^{50} +(-6.33595 - 4.60333i) q^{51} +(-0.392280 + 1.20731i) q^{52} +(-1.89644 + 1.37784i) q^{53} +(-3.50492 + 2.54647i) q^{54} +(4.70354 + 3.41732i) q^{55} +11.6317 q^{56} -12.6538 q^{57} +(-6.78713 - 4.93114i) q^{58} +(2.40379 + 7.39811i) q^{59} +(-0.477443 + 1.46942i) q^{60} +2.72343 q^{61} -4.96588 q^{63} +(2.74619 - 8.45191i) q^{64} +(-1.25857 - 3.87348i) q^{65} +(7.78047 + 5.65284i) q^{66} -7.42118 q^{67} +1.81829 q^{68} +(-1.52735 - 1.10969i) q^{69} +(-5.86065 + 4.25801i) q^{70} +(4.12451 - 2.99664i) q^{71} +(-1.23366 + 3.79682i) q^{72} +(4.36201 + 3.16919i) q^{73} +(0.690727 - 2.12584i) q^{74} +(1.67421 + 5.15269i) q^{75} +(2.37679 - 1.72684i) q^{76} +(-4.42139 - 13.6076i) q^{77} +(-2.08189 - 6.40740i) q^{78} +(-7.87758 + 5.72340i) q^{79} +(1.33945 + 4.12241i) q^{80} +(-3.46475 + 10.6634i) q^{81} +(-0.336082 - 0.244178i) q^{82} +(2.59424 - 7.98426i) q^{83} +(3.07614 - 2.23495i) q^{84} +(-4.71957 + 3.42897i) q^{85} +(3.87175 + 2.81299i) q^{86} -14.1277 q^{87} -11.5025 q^{88} +(4.12243 + 2.99512i) q^{89} +(-0.768318 - 2.36464i) q^{90} +(-3.09732 + 9.53258i) q^{91} +0.438320 q^{92} -1.46523 q^{94} +(-2.91270 + 8.96437i) q^{95} +(-1.70584 - 5.25003i) q^{96} +(-8.82979 - 6.41522i) q^{97} +9.20257 q^{98} +4.91075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 9 q^{3} - 14 q^{4} + 6 q^{5} + 22 q^{6} + 11 q^{7} + 17 q^{8} + 5 q^{9} + 19 q^{10} - 14 q^{11} - 5 q^{12} + q^{13} + 27 q^{14} - 14 q^{15} - 2 q^{16} + 3 q^{17} - 9 q^{18} + 13 q^{19}+ \cdots + 12 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 9 * q^3 - 14 * q^4 + 6 * q^5 + 22 * q^6 + 11 * q^7 + 17 * q^8 + 5 * q^9 + 19 * q^10 - 14 * q^11 - 5 * q^12 + q^13 + 27 * q^14 - 14 * q^15 - 2 * q^16 + 3 * q^17 - 9 * q^18 + 13 * q^19 - 29 * q^20 + 3 * q^21 - 12 * q^22 - q^23 - 25 * q^24 + 26 * q^25 + 18 * q^26 - 9 * q^27 - 15 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 - 49 * q^34 - 9 * q^35 - 2 * q^36 - 16 * q^37 - 31 * q^38 - 3 * q^39 + 2 * q^40 + 16 * q^41 + 18 * q^42 - 14 * q^43 + 33 * q^44 + 5 * q^45 - 34 * q^46 + 14 * q^47 + 38 * q^48 + 41 * q^49 - 6 * q^50 + 9 * q^51 - 17 * q^52 - 3 * q^53 + 46 * q^54 + q^55 + 60 * q^56 - 34 * q^57 + 15 * q^58 + 7 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 + 6 * q^65 - 30 * q^66 - 26 * q^67 + 60 * q^68 - q^69 + 12 * q^70 - 17 * q^71 + q^72 - 11 * q^73 + 56 * q^74 - 4 * q^75 + 24 * q^76 - 18 * q^77 - 15 * q^78 + 6 * q^79 - 42 * q^80 - q^81 - 13 * q^82 + 28 * q^83 + 31 * q^84 - 37 * q^85 - 7 * q^86 - 30 * q^87 - 34 * q^88 - q^89 + 16 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 + 16 * q^96 + 3 * q^97 + 20 * q^98 + 12 * q^99

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