LMFDB - Embedded newform 403.2.r.a.218.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(218,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("403.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (of order $6$, degree $2$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			218.5
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98176 + 1.14417i) q^{2} +(0.827863 + 1.43390i) q^{3} +(1.61825 - 2.80289i) q^{4} -1.16564i q^{5} +(-3.28125 - 1.89443i) q^{6} +(-2.58921 - 1.49488i) q^{7} +2.82952i q^{8} +(0.129286 - 0.223931i) q^{9} +O(q^{10})$	\(q+(-1.98176 + 1.14417i) q^{2} +(0.827863 + 1.43390i) q^{3} +(1.61825 - 2.80289i) q^{4} -1.16564i q^{5} +(-3.28125 - 1.89443i) q^{6} +(-2.58921 - 1.49488i) q^{7} +2.82952i q^{8} +(0.129286 - 0.223931i) q^{9} +(1.33368 + 2.31001i) q^{10} +(-1.16460 + 0.672380i) q^{11} +5.35875 q^{12} +(3.15059 + 1.75322i) q^{13} +6.84160 q^{14} +(1.67141 - 0.964986i) q^{15} +(-0.000955288 - 0.00165461i) q^{16} +(3.33708 - 5.77999i) q^{17} +0.591702i q^{18} +(2.43890 + 1.40810i) q^{19} +(-3.26714 - 1.88629i) q^{20} -4.95023i q^{21} +(1.53863 - 2.66499i) q^{22} +(-1.71975 - 2.97870i) q^{23} +(-4.05725 + 2.34245i) q^{24} +3.64129 q^{25} +(-8.24969 + 0.130344i) q^{26} +5.39530 q^{27} +(-8.37998 + 4.83818i) q^{28} +(0.110886 + 0.192060i) q^{29} +(-2.20822 + 3.82474i) q^{30} +1.00000i q^{31} +(-4.89709 - 2.82733i) q^{32} +(-1.92825 - 1.11328i) q^{33} +15.2727i q^{34} +(-1.74249 + 3.01808i) q^{35} +(-0.418435 - 0.724751i) q^{36} +(9.86577 - 5.69600i) q^{37} -6.44443 q^{38} +(0.0943101 + 5.96906i) q^{39} +3.29819 q^{40} +(-4.17402 + 2.40987i) q^{41} +(5.66391 + 9.81018i) q^{42} +(2.63099 - 4.55700i) q^{43} +4.35231i q^{44} +(-0.261022 - 0.150701i) q^{45} +(6.81627 + 3.93538i) q^{46} +6.66306i q^{47} +(0.00158169 - 0.00273958i) q^{48} +(0.969355 + 1.67897i) q^{49} +(-7.21617 + 4.16626i) q^{50} +11.0506 q^{51} +(10.0125 - 5.99360i) q^{52} +4.26104 q^{53} +(-10.6922 + 6.17314i) q^{54} +(0.783750 + 1.35750i) q^{55} +(4.22980 - 7.32623i) q^{56} +4.66286i q^{57} +(-0.439499 - 0.253745i) q^{58} +(-1.92911 - 1.11377i) q^{59} -6.24635i q^{60} +(-7.53621 + 13.0531i) q^{61} +(-1.14417 - 1.98176i) q^{62} +(-0.669501 + 0.386536i) q^{63} +12.9436 q^{64} +(2.04362 - 3.67244i) q^{65} +5.09511 q^{66} +(4.16970 - 2.40738i) q^{67} +(-10.8004 - 18.7069i) q^{68} +(2.84744 - 4.93191i) q^{69} -7.97481i q^{70} +(-9.09887 - 5.25324i) q^{71} +(0.633616 + 0.365819i) q^{72} -13.9653i q^{73} +(-13.0344 + 22.5762i) q^{74} +(3.01449 + 5.22125i) q^{75} +(7.89350 - 4.55732i) q^{76} +4.02052 q^{77} +(-7.01651 - 11.7213i) q^{78} -5.01179 q^{79} +(-0.00192867 + 0.00111352i) q^{80} +(4.07871 + 7.06453i) q^{81} +(5.51461 - 9.55158i) q^{82} -3.24122i q^{83} +(-13.8749 - 8.01071i) q^{84} +(-6.73737 - 3.88982i) q^{85} +12.0412i q^{86} +(-0.183597 + 0.317999i) q^{87} +(-1.90251 - 3.29525i) q^{88} +(7.80700 - 4.50737i) q^{89} +0.689709 q^{90} +(-5.53669 - 9.24923i) q^{91} -11.1319 q^{92} +(-1.43390 + 0.827863i) q^{93} +(-7.62367 - 13.2046i) q^{94} +(1.64133 - 2.84287i) q^{95} -9.36258i q^{96} +(4.13384 + 2.38668i) q^{97} +(-3.84206 - 2.21821i) q^{98} +0.347719i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) $ 68 * q + 32 * q^4 - 34 * q^9	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.98176	+	1.14417i	−1.40132	+	0.809050i	−0.994528	−	0.104473i	$-0.966685\pi$
$2$	−1.98176	+	1.14417i	−1.40132	+	0.809050i	−0.406788	+	0.913523i	$0.633351\pi$
$3$	0.827863	+	1.43390i	0.477967	+	0.827863i	0.999681	−	0.0252576i	$-0.00804059\pi$
$3$	0.827863	+	1.43390i	0.477967	+	0.827863i	−0.521714	+	0.853120i	$0.674707\pi$
$4$	1.61825	−	2.80289i	0.809124	−	1.40144i
$5$		−	1.16564i		−	0.521288i	−0.965435	−	0.260644i	$-0.916065\pi$
$5$		−	1.16564i		−	0.521288i	0.965435	−	0.260644i	$-0.0839349\pi$
$6$	−3.28125	−	1.89443i	−1.33956	−	0.773398i
$7$	−2.58921	−	1.49488i	−0.978631	−	0.565013i	−0.0767746	−	0.997048i	$-0.524462\pi$
$7$	−2.58921	−	1.49488i	−0.978631	−	0.565013i	−0.901857	+	0.432036i	$0.857796\pi$
$8$			2.82952i			1.00039i
$9$	0.129286	−	0.223931i	0.0430955	−	0.0746436i
$10$	1.33368	+	2.31001i	0.421748	+	0.730489i
$11$	−1.16460	+	0.672380i	−0.351139	+	0.202730i	−0.665187	−	0.746677i	$-0.731648\pi$
$11$	−1.16460	+	0.672380i	−0.351139	+	0.202730i	0.314048	+	0.949407i	$0.398315\pi$
$12$	5.35875			1.54694
$13$	3.15059	+	1.75322i	0.873816	+	0.486256i
$13$	3.15059	+	1.75322i	0.873816	+	0.486256i
$14$	6.84160			1.82849
$15$	1.67141	−	0.964986i	0.431555	−	0.249158i
$16$	−0.000955288	−	0.00165461i	−0.000238822	−	0.000413652i
$17$	3.33708	−	5.77999i	0.809361	−	1.40185i	−0.103946	−	0.994583i	$-0.533147\pi$
$17$	3.33708	−	5.77999i	0.809361	−	1.40185i	0.913307	−	0.407272i	$-0.133520\pi$
$18$			0.591702i			0.139466i
$19$	2.43890	+	1.40810i	0.559523	+	0.323041i	0.752954	−	0.658073i	$-0.228628\pi$
$19$	2.43890	+	1.40810i	0.559523	+	0.323041i	−0.193431	+	0.981114i	$0.561962\pi$
$20$	−3.26714	−	1.88629i	−0.730556	−	0.421787i
$21$		−	4.95023i		−	1.08023i
$22$	1.53863	−	2.66499i	0.328038	−	0.568178i
$23$	−1.71975	−	2.97870i	−0.358593	−	0.621102i	0.629133	−	0.777298i	$-0.283410\pi$
$23$	−1.71975	−	2.97870i	−0.358593	−	0.621102i	−0.987726	+	0.156196i	$0.950077\pi$
$24$	−4.05725	+	2.34245i	−0.828183	+	0.478151i
$25$	3.64129			0.728259
$26$	−8.24969	+	0.130344i	−1.61790	+	0.0255625i
$27$	5.39530			1.03833
$28$	−8.37998	+	4.83818i	−1.58367	+	0.914331i
$29$	0.110886	+	0.192060i	0.0205910	+	0.0356647i	0.876137	−	0.482062i	$-0.160112\pi$
$29$	0.110886	+	0.192060i	0.0205910	+	0.0356647i	−0.855546	+	0.517726i	$0.826779\pi$
$30$	−2.20822	+	3.82474i	−0.403163	+	0.698299i
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$	−4.89709	−	2.82733i	−0.865691	−	0.499807i
$33$	−1.92825	−	1.11328i	−0.335666	−	0.193797i
$34$			15.2727i			2.61925i
$35$	−1.74249	+	3.01808i	−0.294535	+	0.510149i
$36$	−0.418435	−	0.724751i	−0.0697392	−	0.120792i
$37$	9.86577	−	5.69600i	1.62192	−	0.936417i	0.635517	−	0.772087i	$-0.280787\pi$
$37$	9.86577	−	5.69600i	1.62192	−	0.936417i	0.986405	−	0.164330i	$-0.0525462\pi$
$38$	−6.44443			−1.04542
$39$	0.0943101	+	5.96906i	0.0151017	+	0.955814i
$40$	3.29819			0.521489
$41$	−4.17402	+	2.40987i	−0.651873	+	0.376359i	−0.789173	−	0.614170i	$-0.789491\pi$
$41$	−4.17402	+	2.40987i	−0.651873	+	0.376359i	0.137301	+	0.990529i	$0.456157\pi$
$42$	5.66391	+	9.81018i	0.873960	+	1.51374i
$43$	2.63099	−	4.55700i	0.401222	−	0.694936i	−0.592652	−	0.805459i	$-0.701919\pi$
$43$	2.63099	−	4.55700i	0.401222	−	0.694936i	0.993874	+	0.110522i	$0.0352524\pi$
$44$			4.35231i			0.656135i
$45$	−0.261022	−	0.150701i	−0.0389108	−	0.0224652i
$46$	6.81627	+	3.93538i	1.00500	+	0.580240i
$47$			6.66306i			0.971908i	0.873984	+	0.485954i	$0.161528\pi$
$47$			6.66306i			0.971908i	−0.873984	+	0.485954i	$0.838472\pi$
$48$	0.00158169	−	0.00273958i	0.000228298	−	0.000395424i
$49$	0.969355	+	1.67897i	0.138479	+	0.239853i
$50$	−7.21617	+	4.16626i	−1.02052	+	0.589198i
$51$	11.0506			1.54739
$52$	10.0125	−	5.99360i	1.38849	−	0.831163i
$53$	4.26104			0.585299			0.292650	−	0.956220i	$-0.405463\pi$
$53$	4.26104			0.585299			0.292650	+	0.956220i	$0.405463\pi$
$54$	−10.6922	+	6.17314i	−1.45502	+	0.840058i
$55$	0.783750	+	1.35750i	0.105681	+	0.183045i
$56$	4.22980	−	7.32623i	0.565231	−	0.979009i
$57$			4.66286i			0.617611i
$58$	−0.439499	−	0.253745i	−0.0577091	−	0.0333184i
$59$	−1.92911	−	1.11377i	−0.251149	−	0.145001i	0.369141	−	0.929373i	$-0.379652\pi$
$59$	−1.92911	−	1.11377i	−0.251149	−	0.145001i	−0.620290	+	0.784372i	$0.712985\pi$
$60$		−	6.24635i		−	0.806400i
$61$	−7.53621	+	13.0531i	−0.964913	+	1.67128i	−0.255065	+	0.966924i	$0.582097\pi$
$61$	−7.53621	+	13.0531i	−0.964913	+	1.67128i	−0.709848	+	0.704354i	$0.751237\pi$
$62$	−1.14417	−	1.98176i	−0.145310	−	0.251684i
$63$	−0.669501	+	0.386536i	−0.0843492	+	0.0486990i
$64$	12.9436			1.61795
$65$	2.04362	−	3.67244i	0.253480	−	0.455510i
$66$	5.09511			0.627165
$67$	4.16970	−	2.40738i	0.509410	−	0.294108i	−0.223181	−	0.974777i	$-0.571644\pi$
$67$	4.16970	−	2.40738i	0.509410	−	0.294108i	0.732591	+	0.680669i	$0.238311\pi$
$68$	−10.8004	−	18.7069i	−1.30975	−	2.26855i
$69$	2.84744	−	4.93191i	0.342791	−	0.593732i
$70$		−	7.97481i		−	0.953173i
$71$	−9.09887	−	5.25324i	−1.07984	−	0.623444i	−0.148985	−	0.988839i	$-0.547601\pi$
$71$	−9.09887	−	5.25324i	−1.07984	−	0.623444i	−0.930853	+	0.365395i	$0.880934\pi$
$72$	0.633616	+	0.365819i	0.0746724	+	0.0431121i
$73$		−	13.9653i		−	1.63451i	−0.576274	−	0.817257i	$-0.695494\pi$
$73$		−	13.9653i		−	1.63451i	0.576274	−	0.817257i	$-0.304506\pi$
$74$	−13.0344	+	22.5762i	−1.51522	+	2.62443i
$75$	3.01449	+	5.22125i	0.348084	+	0.602898i
$76$	7.89350	−	4.55732i	0.905447	−	0.522760i
$77$	4.02052			0.458181
$78$	−7.01651	−	11.7213i	−0.794464	−	1.32718i
$79$	−5.01179			−0.563871			−0.281935	−	0.959433i	$-0.590976\pi$
$79$	−5.01179			−0.563871			−0.281935	+	0.959433i	$0.590976\pi$
$80$	−0.00192867	+	0.00111352i	−0.000215632	+	0.000124495i
$81$	4.07871	+	7.06453i	0.453190	+	0.784948i
$82$	5.51461	−	9.55158i	0.608986	−	1.05480i
$83$		−	3.24122i		−	0.355770i	−0.984051	−	0.177885i	$-0.943075\pi$
$83$		−	3.24122i		−	0.355770i	0.984051	−	0.177885i	$-0.0569254\pi$
$84$	−13.8749	−	8.01071i	−1.51388	−	0.874040i
$85$	−6.73737	−	3.88982i	−0.730770	−	0.421910i
$86$			12.0412i			1.29843i
$87$	−0.183597	+	0.317999i	−0.0196837	+	0.0340931i
$88$	−1.90251	−	3.29525i	−0.202809	−	0.351275i
$89$	7.80700	−	4.50737i	0.827540	−	0.477781i	−0.0254695	−	0.999676i	$-0.508108\pi$
$89$	7.80700	−	4.50737i	0.827540	−	0.477781i	0.853010	+	0.521895i	$0.174775\pi$
$90$	0.689709			0.0727017
$91$	−5.53669	−	9.24923i	−0.580403	−	0.969583i
$92$	−11.1319			−1.16058
$93$	−1.43390	+	0.827863i	−0.148689	+	0.0858454i
$94$	−7.62367	−	13.2046i	−0.786322	−	1.36195i
$95$	1.64133	−	2.84287i	0.168397	−	0.291673i
$96$		−	9.36258i		−	0.955564i
$97$	4.13384	+	2.38668i	0.419728	+	0.242330i	0.694961	−	0.719047i	$-0.255422\pi$
$97$	4.13384	+	2.38668i	0.419728	+	0.242330i	−0.275233	+	0.961378i	$0.588755\pi$
$98$	−3.84206	−	2.21821i	−0.388106	−	0.224073i
$99$			0.347719i			0.0349470i
$100$	5.89251	−	10.2061i	0.589251	−	1.02061i
$101$	−1.79500	−	3.10902i	−0.178609	−	0.309359i	0.762795	−	0.646640i	$-0.223826\pi$
$101$	−1.79500	−	3.10902i	−0.178609	−	0.309359i	−0.941404	+	0.337280i	$0.890493\pi$
$102$	−21.8996	+	12.6437i	−2.16838	+	1.25192i
$103$	−11.0519			−1.08897			−0.544486	−	0.838770i	$-0.683275\pi$
$103$	−11.0519			−1.08897			−0.544486	+	0.838770i	$0.683275\pi$
$104$	−4.96078	+	8.91466i	−0.486444	+	0.874154i
$105$	−5.77017			−0.563111
$106$	−8.44436	+	4.87535i	−0.820189	+	0.473536i
$107$	−4.63608	−	8.02992i	−0.448186	−	0.776282i	0.550082	−	0.835111i	$-0.314597\pi$
$107$	−4.63608	−	8.02992i	−0.448186	−	0.776282i	−0.998268	+	0.0588293i	$0.981263\pi$
$108$	8.73094	−	15.1224i	0.840135	−	1.45516i
$109$		−	2.45675i		−	0.235314i	−0.993054	−	0.117657i	$-0.962462\pi$
$109$		−	2.45675i		−	0.235314i	0.993054	−	0.117657i	$-0.0375384\pi$
$110$	−3.10641	−	1.79349i	−0.296184	−	0.171002i
$111$	16.3350	+	9.43102i	1.55045	+	0.895153i
$112$			0.00571218i			0.000539750i
$113$	−0.0875022	+	0.151558i	−0.00823152	+	0.0142574i	−0.870112	−	0.492854i	$-0.835954\pi$
$113$	−0.0875022	+	0.151558i	−0.00823152	+	0.0142574i	0.861880	+	0.507112i	$0.169287\pi$
$114$	−5.33510	−	9.24067i	−0.499678	−	0.865468i
$115$	−3.47208	+	2.00460i	−0.323773	+	0.186930i
$116$	0.717765			0.0666428
$117$	0.799929	−	0.478846i	0.0739534	−	0.0442693i
$118$	5.09738			0.469252
$119$	−17.2808	+	9.97710i	−1.58413	+	0.914599i
$120$	2.73045	+	4.72927i	0.249255	+	0.431722i
$121$	−4.59581	+	7.96018i	−0.417801	+	0.723652i
$122$		−	34.4908i		−	3.12265i
$123$	−6.91104	−	3.99009i	−0.623147	−	0.359774i
$124$	2.80289	+	1.61825i	0.251707	+	0.145323i
$125$		−	10.0726i		−	0.900921i
$126$	0.884526	−	1.53204i	0.0787999	−	0.136485i
$127$	10.3318	+	17.8952i	0.916800	+	1.58794i	0.804244	+	0.594299i	$0.202570\pi$
$127$	10.3318	+	17.8952i	0.916800	+	1.58794i	0.112556	+	0.993645i	$0.464096\pi$
$128$	−15.8570	+	9.15502i	−1.40157	+	0.809198i
$129$	8.71238			0.767083
$130$	0.151933	+	9.61614i	0.0133254	+	0.843391i
$131$	−1.18334			−0.103389			−0.0516945	−	0.998663i	$-0.516462\pi$
$131$	−1.18334			−0.103389			−0.0516945	+	0.998663i	$0.516462\pi$
$132$	−6.24078	+	3.60312i	−0.543190	+	0.313611i
$133$	−4.20990	−	7.29176i	−0.365044	−	0.632275i
$134$	−5.50890	+	9.54169i	−0.475896	+	0.824276i
$135$		−	6.28896i		−	0.541267i
$136$	16.3546	+	9.44234i	1.40240	+	0.809674i
$137$	9.36968	+	5.40959i	0.800506	+	0.462172i	0.843648	−	0.536897i	$-0.180404\pi$
$137$	9.36968	+	5.40959i	0.800506	+	0.462172i	−0.0431422	+	0.999069i	$0.513737\pi$
$138$			13.0318i			1.10934i
$139$	2.95199	−	5.11300i	0.250385	−	0.433679i	−0.713247	−	0.700913i	$-0.752776\pi$
$139$	2.95199	−	5.11300i	0.250385	−	0.433679i	0.963632	+	0.267234i	$0.0861095\pi$
$140$	5.63956	+	9.76800i	0.476630	+	0.825547i
$141$	−9.55417	+	5.51610i	−0.804606	+	0.464540i
$142$	24.0424			2.01759
$143$	−4.84800	+	0.0765976i	−0.405410	+	0.00640541i
$144$	−0.000494023	0		−4.11686e−5	0
$145$	0.223873	−	0.129253i	0.0185916	−	0.0107339i
$146$	15.9787	+	27.6758i	1.32240	+	2.29047i
$147$	−1.60499	+	2.77992i	−0.132377	+	0.229284i
$148$		−	36.8702i		−	3.03071i
$149$	14.3445	+	8.28178i	1.17514	+	0.678470i	0.954886	−	0.296972i	$-0.0959768\pi$
$149$	14.3445	+	8.28178i	1.17514	+	0.678470i	0.220258	+	0.975442i	$0.429310\pi$
$150$	−11.9480	−	6.89818i	−0.975550	−	0.563234i
$151$		−	13.4220i		−	1.09227i	−0.837697	−	0.546135i	$-0.816099\pi$
$151$		−	13.4220i		−	1.09227i	0.837697	−	0.546135i	$-0.183901\pi$
$152$	−3.98425	+	6.90093i	−0.323166	+	0.559739i
$153$	−0.862879	−	1.49455i	−0.0697596	−	0.120827i
$154$	−7.96771	+	4.60016i	−0.642056	+	0.370691i
$155$	1.16564			0.0936261
$156$	16.8832	+	9.39507i	1.35174	+	0.752208i
$157$	3.88582			0.310122			0.155061	−	0.987905i	$-0.450443\pi$
$157$	3.88582			0.310122			0.155061	+	0.987905i	$0.450443\pi$
$158$	9.93217	−	5.73434i	0.790161	−	0.456200i
$159$	3.52756	+	6.10991i	0.279754	+	0.484547i
$160$	−3.29564	+	5.70822i	−0.260543	+	0.451274i
$161$			10.2833i			0.810439i
$162$	−16.1660	−	9.33347i	−1.27012	−	0.733307i
$163$	15.3333	+	8.85266i	1.20099	+	0.693394i	0.960776	−	0.277326i	$-0.0894480\pi$
$163$	15.3333	+	8.85266i	1.20099	+	0.693394i	0.240217	+	0.970719i	$0.422781\pi$
$164$			15.5991i			1.21808i
$165$	−1.29768	+	2.24764i	−0.101024	+	0.174979i
$166$	3.70850	+	6.42331i	0.287835	+	0.498546i
$167$	−0.849295	+	0.490341i	−0.0657204	+	0.0379437i	−0.532500	−	0.846430i	$-0.678747\pi$
$167$	−0.849295	+	0.490341i	−0.0657204	+	0.0379437i	0.466780	+	0.884374i	$0.345414\pi$
$168$	14.0068			1.08065
$169$	6.85243	+	11.0474i	0.527110	+	0.849797i
$170$	17.8025			1.36539
$171$	0.630634	−	0.364097i	0.0482258	−	0.0278432i
$172$	−8.51518	−	14.7487i	−0.649276	−	1.12458i
$173$	4.72774	−	8.18868i	0.359443	−	0.622574i	−0.628425	−	0.777870i	$-0.716300\pi$
$173$	4.72774	−	8.18868i	0.359443	−	0.622574i	0.987868	+	0.155297i	$0.0496334\pi$
$174$		−	0.840265i		−	0.0637003i
$175$	−9.42809	−	5.44331i	−0.712697	−	0.411476i
$176$	0.00222505	+	0.00128463i	0.000167719	+	9.68329e-5i
$177$		−	3.68820i		−	0.277222i
$178$	−10.3144	+	17.8651i	−0.773097	+	1.33904i
$179$	−4.11732	−	7.13140i	−0.307743	−	0.533026i	0.670125	−	0.742248i	$-0.266240\pi$
$179$	−4.11732	−	7.13140i	−0.307743	−	0.533026i	−0.977868	+	0.209222i	$0.932907\pi$
$180$	−0.844795	+	0.487743i	−0.0629673	+	0.0363542i
$181$	−5.36382			−0.398689			−0.199345	−	0.979929i	$-0.563881\pi$
$181$	−5.36382			−0.398689			−0.199345	+	0.979929i	$0.563881\pi$
$182$	21.5551	+	11.9948i	1.59777	+	0.889117i
$183$	−24.9558			−1.84479
$184$	8.42829	−	4.86607i	0.621342	−	0.358732i
$185$	−6.63946	−	11.4999i	−0.488143	−	0.845489i
$186$	1.89443	−	3.28125i	0.138906	−	0.240593i
$187$			8.97515i			0.656328i
$188$	18.6758	+	10.7825i	1.36207	+	0.786394i
$189$	−13.9696	−	8.06535i	−1.01614	−	0.586668i
$190$			7.51186i			0.544967i
$191$	−7.55804	+	13.0909i	−0.546881	+	0.947225i	0.451605	+	0.892218i	$0.350852\pi$
$191$	−7.55804	+	13.0909i	−0.546881	+	0.947225i	−0.998486	+	0.0550074i	$0.982482\pi$
$192$	10.7155	+	18.5599i	0.773327	+	1.33944i
$193$	−7.60965	+	4.39343i	−0.547754	+	0.316246i	−0.748216	−	0.663455i	$-0.769089\pi$
$193$	−7.60965	+	4.39343i	−0.547754	+	0.316246i	0.200461	+	0.979702i	$0.435756\pi$
$194$	−10.9230			−0.784229
$195$	6.95775	−	0.109931i	0.498255	−	0.00787234i
$196$	6.27463			0.448188
$197$	−18.8837	+	10.9025i	−1.34541	+	0.776770i	−0.987595	−	0.157024i	$-0.949810\pi$
$197$	−18.8837	+	10.9025i	−1.34541	+	0.776770i	−0.357811	+	0.933794i	$0.616477\pi$
$198$	−0.397849	−	0.689095i	−0.0282739	−	0.0489718i
$199$	5.82778	−	10.0940i	0.413121	−	0.715546i	−0.582109	−	0.813111i	$-0.697772\pi$
$199$	5.82778	−	10.0940i	0.413121	−	0.715546i	0.995229	+	0.0975653i	$0.0311055\pi$
$200$			10.3031i			0.728540i
$201$	6.90388	+	3.98596i	0.486962	+	0.281148i
$202$	7.11450	+	4.10756i	0.500574	+	0.289007i
$203$		−	0.663048i		−	0.0465368i
$204$	17.8826	−	30.9735i	1.25203	−	2.16858i
$205$	2.80903	+	4.86539i	0.196191	+	0.339814i
$206$	21.9021	−	12.6452i	1.52599	−	0.881033i
$207$	−0.889363			−0.0618150
$208$	−0.000108826	−	0.00688782i	−7.54575e−6	−	0.000477584i
$209$	−3.78712			−0.261961
$210$	11.4351	−	6.60205i	0.789096	−	0.455585i
$211$	0.0302017	+	0.0523110i	0.00207917	+	0.00360124i	0.867063	−	0.498198i	$-0.166005\pi$
$211$	0.0302017	+	0.0523110i	0.00207917	+	0.00360124i	−0.864984	+	0.501800i	$0.832672\pi$
$212$	6.89542	−	11.9432i	0.473580	−	0.820264i
$213$		−	17.3958i		−	1.19194i
$214$	18.3752	+	10.6089i	1.25610	+	0.725210i
$215$	−5.31180	−	3.06677i	−0.362262	−	0.209152i
$216$			15.2661i			1.03873i
$217$	1.49488	−	2.58921i	0.101479	−	0.175767i
$218$	2.81094	+	4.86869i	0.190381	+	0.329750i
$219$	20.0248	−	11.5613i	1.35315	−	0.781243i
$220$	5.07321			0.342036
$221$	20.6474	−	12.3597i	1.38889	−	0.831406i
$222$	−43.1627			−2.89689
$223$	−16.5603	+	9.56112i	−1.10896	+	0.640260i	−0.938560	−	0.345115i	$-0.887840\pi$
$223$	−16.5603	+	9.56112i	−1.10896	+	0.640260i	−0.170402	+	0.985375i	$0.554507\pi$
$224$	8.45307	+	14.6411i	0.564795	+	0.978253i
$225$	0.470770	−	0.815397i	0.0313847	−	0.0543598i
$226$		−	0.400470i		−	0.0266388i
$227$	−1.21674	−	0.702483i	−0.0807576	−	0.0466254i	0.459077	−	0.888396i	$-0.348180\pi$
$227$	−1.21674	−	0.702483i	−0.0807576	−	0.0466254i	−0.539835	+	0.841771i	$0.681513\pi$
$228$	13.0695	+	7.54566i	0.865547	+	0.499724i
$229$			3.13334i			0.207057i	0.994626	+	0.103529i	$0.0330133\pi$
$229$			3.13334i			0.207057i	−0.994626	+	0.103529i	$0.966987\pi$
$230$	4.58721	−	7.94529i	0.302472	−	0.523897i
$231$	3.32844	+	5.76503i	0.218995	+	0.379311i
$232$	−0.543439	+	0.313755i	−0.0356785	+	0.0205990i
$233$	−6.45119			−0.422632			−0.211316	−	0.977418i	$-0.567775\pi$
$233$	−6.45119			−0.422632			−0.211316	+	0.977418i	$0.567775\pi$
$234$	−1.03739	+	1.86421i	−0.0678160	+	0.121867i
$235$	7.76670			0.506644
$236$	−6.24356	+	3.60472i	−0.406421	+	0.234647i
$237$	−4.14908	−	7.18641i	−0.269511	−	0.466808i
$238$	22.8310	−	39.5444i	1.47991	−	2.56328i
$239$			16.2114i			1.04863i	0.851524	+	0.524315i	$0.175679\pi$
$239$			16.2114i			1.04863i	−0.851524	+	0.524315i	$0.824321\pi$
$240$	−0.00319335	−	0.00184368i	−0.000206130	−	0.000119009i
$241$	3.17424	+	1.83265i	0.204471	+	0.118051i	0.598739	−	0.800944i	$-0.295669\pi$
$241$	3.17424	+	1.83265i	0.204471	+	0.118051i	−0.394268	+	0.918995i	$0.629002\pi$
$242$		−	21.0335i		−	1.35209i
$243$	1.33973	−	2.32048i	0.0859436	−	0.148859i
$244$	24.3909	+	42.2463i	1.56147	+	2.70454i
$245$	1.95707	−	1.12991i	0.125033	−	0.0721876i
$246$	18.2614			1.16430
$247$	5.21527	+	8.71229i	0.331840	+	0.554350i
$248$	−2.82952			−0.179675
$249$	4.64758	−	2.68328i	0.294528	−	0.170046i
$250$	11.5248	+	19.9615i	0.728890	+	1.26247i
$251$	−15.4041	+	26.6808i	−0.972301	+	1.68407i	−0.283731	+	0.958904i	$0.591572\pi$
$251$	−15.4041	+	26.6808i	−0.972301	+	1.68407i	−0.688569	+	0.725171i	$0.741761\pi$
$252$			2.50205i			0.157614i
$253$	4.00564	+	2.31265i	0.251832	+	0.145395i
$254$	−40.9503	−	23.6427i	−2.56945	−	1.48347i
$255$		−	12.8810i		−	0.806636i
$256$	8.00618	−	13.8671i	0.500386	−	0.866695i
$257$	−2.53629	−	4.39299i	−0.158210	−	0.274027i	0.776014	−	0.630716i	$-0.217239\pi$
$257$	−2.53629	−	4.39299i	−0.158210	−	0.274027i	−0.934223	+	0.356689i	$0.883905\pi$
$258$	−17.2658	+	9.96844i	−1.07492	+	0.620608i
$259$	−34.0595			−2.11635
$260$	−6.98635	−	11.6709i	−0.433275	−	0.723801i
$261$	0.0573443			0.00354952
$262$	2.34510	−	1.35394i	0.144880	−	0.0836468i
$263$	−5.47171	−	9.47729i	−0.337400	−	0.584395i	0.646543	−	0.762878i	$-0.276214\pi$
$263$	−5.47171	−	9.47729i	−0.337400	−	0.584395i	−0.983943	+	0.178483i	$0.942881\pi$
$264$	3.15004	−	5.45603i	0.193872	−	0.335795i
$265$		−	4.96682i		−	0.305109i
$266$	16.6860	+	9.63367i	1.02308	+	0.590678i
$267$	12.9262	+	7.46297i	0.791074	+	0.456727i
$268$		−	15.5829i		−	0.951879i
$269$	−1.75681	+	3.04289i	−0.107115	+	0.185528i	−0.914600	−	0.404359i	$-0.867495\pi$
$269$	−1.75681	+	3.04289i	−0.107115	+	0.185528i	0.807485	+	0.589888i	$0.200828\pi$
$270$	7.19563	+	12.4632i	0.437912	+	0.758486i
$271$	−16.9716	+	9.79854i	−1.03095	+	0.595219i	−0.917257	−	0.398297i	$-0.869601\pi$
$271$	−16.9716	+	9.79854i	−1.03095	+	0.595219i	−0.113693	+	0.993516i	$0.536268\pi$
$272$	−0.0127515			−0.000773173
$273$	8.67886	−	15.5962i	0.525268	−	0.943922i
$274$	−24.7579			−1.49568
$275$	−4.24064	+	2.44833i	−0.255720	+	0.147640i
$276$	−9.21572	−	15.9621i	−0.554721	−	0.960805i
$277$	−5.42456	+	9.39562i	−0.325930	+	0.564528i	−0.981700	−	0.190433i	$-0.939011\pi$
$277$	−5.42456	+	9.39562i	−0.325930	+	0.564528i	0.655770	+	0.754961i	$0.272344\pi$
$278$			13.5103i			0.810295i
$279$	0.223931	+	0.129286i	0.0134064	+	0.00774018i
$280$	−8.53972	−	4.93041i	−0.510346	−	0.294648i
$281$		−	5.18454i		−	0.309284i	−0.987971	−	0.154642i	$-0.950578\pi$
$281$		−	5.18454i		−	0.309284i	0.987971	−	0.154642i	$-0.0494224\pi$
$282$	12.6227	−	21.8632i	0.751672	−	1.30193i
$283$	8.55608	+	14.8196i	0.508606	+	0.880932i	0.999950	+	0.00996632i	$0.00317243\pi$
$283$	8.55608	+	14.8196i	0.508606	+	0.880932i	−0.491344	+	0.870966i	$0.663494\pi$
$284$	−29.4485	+	17.0021i	−1.74744	+	1.00889i
$285$	5.43520			0.321953
$286$	9.51993	−	5.69873i	0.562925	−	0.336973i
$287$	14.4099			0.850591
$288$	−1.26625	+	0.731072i	−0.0746147	+	0.0430788i
$289$	−13.7722	−	23.8542i	−0.810131	−	1.40319i
$290$	−0.295774	+	0.512296i	−0.0173685	+	0.0300831i
$291$			7.90336i			0.463303i
$292$	−39.1431	−	22.5993i	−2.29068	−	1.32252i
$293$	−15.7413	−	9.08826i	−0.919618	−	0.530942i	−0.0361048	−	0.999348i	$-0.511495\pi$
$293$	−15.7413	−	9.08826i	−0.919618	−	0.530942i	−0.883513	+	0.468406i	$0.844828\pi$
$294$		−	7.34550i		−	0.428398i
$295$	−1.29825	+	2.24864i	−0.0755872	+	0.130921i
$296$	16.1170	+	27.9154i	0.936779	+	1.62255i
$297$	−6.28335	+	3.62769i	−0.364597	+	0.210500i
$298$	−37.9030			−2.19566
$299$	−0.195914	−	12.3998i	−0.0113300	−	0.717097i
$300$	19.5128			1.12657
$301$	−13.6244	+	7.86604i	−0.785296	+	0.453391i
$302$	15.3571	+	26.5992i	0.883701	+	1.53061i
$303$	2.97202	−	5.14769i	0.170738	−	0.295727i
$304$		−	0.00538057i		−	0.000308597i
$305$	15.2152	+	8.78448i	0.871218	+	0.502998i
$306$	3.42004	+	1.97456i	0.195510	+	0.112878i
$307$			2.69825i			0.153998i	0.997031	+	0.0769988i	$0.0245338\pi$
$307$			2.69825i			0.153998i	−0.997031	+	0.0769988i	$0.975466\pi$
$308$	6.50620	−	11.2691i	0.370725	−	0.642115i
$309$	−9.14943	−	15.8473i	−0.520493	−	0.901520i
$310$	−2.31001	+	1.33368i	−0.131200	+	0.0757482i
$311$	32.1030			1.82039			0.910197	−	0.414176i	$-0.135930\pi$
$311$	32.1030			1.82039			0.910197	+	0.414176i	$0.135930\pi$
$312$	−16.8896	+	0.266852i	−0.956184	+	0.0151075i
$313$	−27.5752			−1.55864			−0.779320	−	0.626626i	$-0.784435\pi$
$313$	−27.5752			−1.55864			−0.779320	+	0.626626i	$0.784435\pi$
$314$	−7.70075	+	4.44603i	−0.434579	+	0.250904i
$315$	0.450561	+	0.780394i	0.0253862	+	0.0439702i
$316$	−8.11032	+	14.0475i	−0.456241	+	0.790233i
$317$			31.8275i			1.78761i	0.448456	+	0.893805i	$0.351974\pi$
$317$			31.8275i			1.78761i	−0.448456	+	0.893805i	$0.648026\pi$
$318$	−13.9815	−	8.07225i	−0.784046	−	0.452669i
$319$	−0.258275	−	0.149115i	−0.0144606	−	0.00834886i
$320$		−	15.0875i		−	0.843419i
$321$	7.67607	−	13.2953i	0.428436	−	0.742074i
$322$	−11.7659	−	20.3791i	−0.655686	−	1.13568i
$323$	16.2776	−	9.39790i	0.905712	−	0.522913i
$324$	26.4015			1.46675
$325$	11.4722	+	6.38400i	0.636364	+	0.354120i
$326$	−40.5158			−2.24396
$327$	3.52274	−	2.03385i	0.194808	−	0.112472i
$328$	−6.81878	−	11.8105i	−0.376504	−	0.652125i
$329$	9.96051	−	17.2521i	0.549140	−	0.951139i
$330$		−	5.93904i		−	0.326933i
$331$	14.0536	+	8.11386i	0.772456	+	0.445978i	0.833750	−	0.552142i	$-0.186189\pi$
$331$	14.0536	+	8.11386i	0.772456	+	0.445978i	−0.0612938	+	0.998120i	$0.519523\pi$
$332$	−9.08476	−	5.24509i	−0.498591	−	0.287862i
$333$		−	2.94566i		−	0.161421i
$334$	1.12207	−	1.94348i	0.0613967	−	0.106342i
$335$	−2.80612	−	4.86035i	−0.153315	−	0.265549i
$336$	−0.00819069	+	0.00472890i	−0.000446839	+	0.000257983i
$337$	−35.8683			−1.95387			−0.976936	−	0.213533i	$-0.931503\pi$
$337$	−35.8683			−1.95387			−0.976936	+	0.213533i	$0.931503\pi$
$338$	−26.2199	−	14.0529i	−1.42618	−	0.764376i
$339$	−0.289759			−0.0157376
$340$	−21.8055	+	12.5894i	−1.18257	+	0.682755i
$341$	−0.672380	−	1.16460i	−0.0364114	−	0.0630664i
$342$	−0.833177	+	1.44311i	−0.0450531	+	0.0780342i
$343$			15.1321i			0.817056i
$344$	12.8941	+	7.44443i	0.695205	+	0.401377i
$345$	−5.74881	−	3.31907i	−0.309505	−	0.178693i
$346$			21.6373i			1.16323i
$347$	−11.9179	+	20.6423i	−0.639784	+	1.10814i	0.345695	+	0.938347i	$0.387643\pi$
$347$	−11.9179	+	20.6423i	−0.639784	+	1.10814i	−0.985480	+	0.169792i	$0.945690\pi$
$348$	0.594211	+	1.02920i	0.0318531	+	0.0551711i
$349$	−30.5271	+	17.6248i	−1.63408	+	0.943435i	−0.651260	+	0.758855i	$0.725759\pi$
$349$	−30.5271	+	17.6248i	−1.63408	+	0.943435i	−0.982817	+	0.184580i	$0.940907\pi$
$350$	24.9123			1.33162
$351$	16.9984	+	9.45916i	0.907307	+	0.504893i
$352$	7.60417			0.405304
$353$	18.3030	−	10.5672i	0.974171	−	0.562438i	0.0736655	−	0.997283i	$-0.476530\pi$
$353$	18.3030	−	10.5672i	0.974171	−	0.562438i	0.900505	+	0.434845i	$0.143197\pi$
$354$	4.21993	+	7.30913i	0.224287	+	0.388476i
$355$	−6.12336	+	10.6060i	−0.324994	+	0.562906i
$356$		−	29.1762i		−	1.54633i
$357$	−28.6123	−	16.5193i	−1.51433	−	0.874296i
$358$	16.3191	+	9.42182i	0.862490	+	0.497959i
$359$		−	12.7307i		−	0.671901i	−0.941880	−	0.335950i	$-0.890943\pi$
$359$		−	12.7307i		−	0.671901i	0.941880	−	0.335950i	$-0.109057\pi$
$360$	0.426411	−	0.738566i	0.0224738	−	0.0389258i
$361$	−5.53450	−	9.58603i	−0.291289	−	0.504528i
$362$	10.6298	−	6.13712i	0.558690	−	0.322560i
$363$	−15.2188			−0.798780
$364$	−34.8843	+	0.551166i	−1.82843	+	0.0288889i
$365$	−16.2784			−0.852052
$366$	49.4564	−	28.5537i	2.58513	−	1.49252i
$367$	−10.8245	−	18.7485i	−0.565033	−	0.978665i	−0.997047	−	0.0767983i	$-0.975530\pi$
$367$	−10.8245	−	18.7485i	−0.565033	−	0.978665i	0.432014	−	0.901867i	$-0.357803\pi$
$368$	−0.00328572	+	0.00569103i	−0.000171280	+	0.000296665i
$369$			1.24626i			0.0648775i
$370$	26.3156	+	15.1933i	1.36809	+	0.789864i
$371$	−11.0328	−	6.36976i	−0.572792	−	0.330702i
$372$			5.35875i			0.277838i
$373$	14.1255	−	24.4661i	0.731391	−	1.26681i	−0.224898	−	0.974382i	$-0.572205\pi$
$373$	14.1255	−	24.4661i	0.731391	−	1.26681i	0.956289	−	0.292424i	$-0.0944618\pi$
$374$	−10.2691	−	17.7866i	−0.531002	−	0.919723i
$375$	14.4431	−	8.33873i	0.745839	−	0.430610i
$376$	−18.8533			−0.972283
$377$	0.0126322	+	0.799512i	0.000650589	+	0.0411769i
$378$	36.9125			1.89857
$379$	25.5614	−	14.7579i	1.31300	−	0.758061i	0.330408	−	0.943838i	$-0.392814\pi$
$379$	25.5614	−	14.7579i	1.31300	−	0.758061i	0.982592	+	0.185777i	$0.0594802\pi$
$380$	−5.31217	−	9.20095i	−0.272508	−	0.471999i
$381$	−17.1066	+	29.6296i	−0.876400	+	1.51797i
$382$		−	34.5907i		−	1.76982i
$383$	24.8170	+	14.3281i	1.26809	+	0.732130i	0.974626	−	0.223841i	$-0.0718595\pi$
$383$	24.8170	+	14.3281i	1.26809	+	0.732130i	0.293461	+	0.955971i	$0.405193\pi$
$384$	−26.2548	−	15.1582i	−1.33981	−	0.773539i
$385$		−	4.68646i		−	0.238844i
$386$	10.0537	−	17.4135i	0.511718	−	0.886321i
$387$	−0.680302	−	1.17832i	−0.0345817	−	0.0598972i
$388$	13.3792	−	7.72446i	0.679224	−	0.392150i
$389$	21.4851			1.08934			0.544669	−	0.838651i	$-0.316655\pi$
$389$	21.4851			1.08934			0.544669	+	0.838651i	$0.316655\pi$
$390$	−13.6628	+	8.17870i	−0.691843	+	0.414145i
$391$	−22.9558			−1.16093
$392$	−4.75069	+	2.74281i	−0.239946	+	0.138533i
$393$	−0.979643	−	1.69679i	−0.0494165	−	0.0855918i
$394$	24.9486	−	43.2122i	1.25689	−	2.17700i
$395$			5.84192i			0.293939i
$396$	0.974616	+	0.562695i	0.0489763	+	0.0282765i
$397$	−6.01423	−	3.47232i	−0.301846	−	0.174271i	0.341426	−	0.939909i	$-0.389090\pi$
$397$	−6.01423	−	3.47232i	−0.301846	−	0.174271i	−0.643272	+	0.765638i	$0.722423\pi$
$398$			26.6719i			1.33694i
$399$	6.97043	−	12.0731i	0.348958	−	0.604413i
$400$	−0.00347848	−	0.00602491i	−0.000173924	−	0.000301246i
$401$	29.7572	−	17.1803i	1.48600	−	0.857944i	0.486129	−	0.873887i	$-0.338408\pi$
$401$	29.7572	−	17.1803i	1.48600	−	0.857944i	0.999873	+	0.0159430i	$0.00507503\pi$
$402$	−18.2424			−0.909850
$403$	−1.75322	+	3.15059i	−0.0873342	+	0.156942i
$404$	−11.6190			−0.578066
$405$	8.23467	−	4.75429i	0.409184	−	0.236243i
$406$	0.758639	+	1.31400i	0.0376506	+	0.0652128i
$407$	−7.65976	+	13.2671i	−0.379680	+	0.657625i
$408$			31.2678i			1.54799i
$409$	18.2613	+	10.5432i	0.902962	+	0.521326i	0.878160	−	0.478367i	$-0.158771\pi$
$409$	18.2613	+	10.5432i	0.902962	+	0.521326i	0.0248023	+	0.999692i	$0.492104\pi$
$410$	−11.1337	−	6.42802i	−0.549852	−	0.317457i
$411$			17.9136i			0.883612i
$412$	−17.8847	+	30.9771i	−0.881114	+	1.52613i
$413$	3.32992	+	5.76759i	0.163855	+	0.283805i
$414$	1.76250	−	1.01758i	0.0866223	−	0.0500114i
$415$	−3.77808			−0.185458
$416$	−10.4718	−	17.4934i	−0.513420	−	0.857687i
$417$	9.77538			0.478702
$418$	7.50516	−	4.33311i	0.367089	−	0.211939i
$419$	20.2471	+	35.0690i	0.989135	+	1.71323i	0.621880	+	0.783112i	$0.286369\pi$
$419$	20.2471	+	35.0690i	0.989135	+	1.71323i	0.367255	+	0.930120i	$0.380298\pi$
$420$	−9.33756	+	16.1731i	−0.455626	+	0.789168i
$421$			8.67865i			0.422971i	0.977381	+	0.211486i	$0.0678302\pi$
$421$			8.67865i			0.422971i	−0.977381	+	0.211486i	$0.932170\pi$
$422$	−0.119705	−	0.0691118i	−0.00582716	−	0.00336431i
$423$	1.49206	+	0.861444i	0.0725466	+	0.0418848i
$424$			12.0567i			0.585525i
$425$	12.1513	−	21.0467i	0.589424	−	1.02091i
$426$	19.9038	+	34.4744i	0.964341	+	1.67029i
$427$	39.0257	−	22.5315i	1.88859	−	1.09038i
$428$	−30.0093			−1.45055
$429$	−4.12331	−	6.88813i	−0.199075	−	0.332562i
$430$	14.0356			0.676858
$431$	−1.59055	+	0.918303i	−0.0766140	+	0.0442331i	−0.537818	−	0.843061i	$-0.680751\pi$
$431$	−1.59055	+	0.918303i	−0.0766140	+	0.0442331i	0.461204	+	0.887294i	$0.347418\pi$
$432$	−0.00515407	−	0.00892711i	−0.000247975	−	0.000429506i
$433$	−8.18383	+	14.1748i	−0.393290	+	0.681198i	−0.992881	−	0.119108i	$-0.961996\pi$
$433$	−8.18383	+	14.1748i	−0.393290	+	0.681198i	0.599591	+	0.800306i	$0.295330\pi$
$434$			6.84160i			0.328407i
$435$	0.370671	+	0.214007i	0.0177723	+	0.0102609i
$436$	−6.88600	−	3.97563i	−0.329780	−	0.190398i
$437$		−	9.68635i		−	0.463361i
$438$	−26.4563	+	45.8236i	−1.26413	+	2.18954i
$439$	−10.4651	−	18.1260i	−0.499471	−	0.865109i	0.500529	−	0.865720i	$-0.333139\pi$
$439$	−10.4651	−	18.1260i	−0.499471	−	0.865109i	−1.00000		0.000611071i	$0.999805\pi$
$440$	−3.84106	+	2.21764i	−0.183115	+	0.105722i
$441$	0.501298			0.0238713
$442$	−26.7765	+	48.1182i	−1.27363	+	2.28875i
$443$	−8.09774			−0.384735			−0.192368	−	0.981323i	$-0.561617\pi$
$443$	−8.09774			−0.384735			−0.192368	+	0.981323i	$0.561617\pi$
$444$	52.8682	−	30.5234i	2.50901	−	1.44858i
$445$	−5.25395	−	9.10012i	−0.249061	−	0.431387i
$446$	21.8791	−	37.8957i	1.03600	−	1.79441i
$447$			27.4247i			1.29714i
$448$	−33.5138	−	19.3492i	−1.58338	−	0.914164i
$449$	−7.84837	−	4.53126i	−0.370387	−	0.213843i	0.303240	−	0.952914i	$-0.401932\pi$
$449$	−7.84837	−	4.53126i	−0.370387	−	0.213843i	−0.673628	+	0.739071i	$0.735265\pi$
$450$			2.15456i			0.101567i
$451$	3.24070	−	5.61306i	0.152599	−	0.264309i
$452$	0.283201	+	0.490518i	0.0133206	+	0.0230720i
$453$	19.2459	−	11.1116i	0.904249	−	0.522069i
$454$	3.21504			0.150889
$455$	−10.7812	+	6.45376i	−0.505432	+	0.302557i
$456$	−13.1937			−0.617850
$457$	−8.70469	+	5.02566i	−0.407188	+	0.235090i	−0.689581	−	0.724209i	$-0.742205\pi$
$457$	−8.70469	+	5.02566i	−0.407188	+	0.235090i	0.282393	+	0.959299i	$0.408872\pi$
$458$	−3.58507	−	6.20953i	−0.167519	−	0.290152i
$459$	18.0046	−	31.1848i	0.840381	−	1.45558i
$460$			12.9758i			0.604999i
$461$	5.23441	+	3.02209i	0.243791	+	0.140753i	0.616918	−	0.787028i	$-0.288381\pi$
$461$	5.23441	+	3.02209i	0.243791	+	0.140753i	−0.373127	+	0.927780i	$0.621714\pi$
$462$	−13.1923	−	7.61660i	−0.613763	−	0.354356i
$463$			31.6378i			1.47034i	0.677885	+	0.735168i	$0.262897\pi$
$463$			31.6378i			1.47034i	−0.677885	+	0.735168i	$0.737103\pi$
$464$	0.000211856	0	0.000366946i	9.83519e−6	0	1.70350e-5i
$465$	0.964986	+	1.67141i	0.0447502	+	0.0775096i
$466$	12.7847	−	7.38126i	0.592241	−	0.341930i
$467$	36.2253			1.67631			0.838154	−	0.545433i	$-0.183635\pi$
$467$	36.2253			1.67631			0.838154	+	0.545433i	$0.183635\pi$
$468$	−0.0476681	−	3.01700i	−0.00220346	−	0.139461i
$469$	−14.3950			−0.664699
$470$	−15.3917	+	8.88642i	−0.709968	+	0.409900i
$471$	3.21692	+	5.57187i	0.148228	+	0.256738i
$472$	3.15144	−	5.45846i	0.145057	−	0.251246i
$473$			7.07609i			0.325359i
$474$	16.4449	+	9.49449i	0.755341	+	0.436097i
$475$	8.88077	+	5.12731i	0.407478	+	0.235257i
$476$			64.5817i			2.96010i
$477$	0.550895	−	0.954178i	0.0252237	−	0.0436888i
$478$	−18.5486	−	32.1272i	−0.848394	−	1.46946i
$479$	−18.8047	+	10.8569i	−0.859210	+	0.496065i	−0.863748	−	0.503925i	$-0.831889\pi$
$479$	−18.8047	+	10.8569i	−0.859210	+	0.496065i	0.00453787	+	0.999990i	$0.498556\pi$
$480$	−10.9134			−0.498124
$481$	41.0693	−	0.648889i	1.87260	−	0.0295868i
$482$	−8.38745			−0.382038
$483$	−14.7453	+	8.51318i	−0.670932	+	0.387363i
$484$	14.8743	+	25.7631i	0.676105	+	1.17105i
$485$	2.78199	−	4.81855i	0.126324	−	0.218799i
$486$			6.13150i			0.278131i
$487$	10.4259	+	6.01937i	0.472440	+	0.272764i	0.717261	−	0.696805i	$-0.245396\pi$
$487$	10.4259	+	6.01937i	0.472440	+	0.272764i	−0.244820	+	0.969568i	$0.578729\pi$
$488$	−36.9340	−	21.3239i	−1.67192	−	0.965286i
$489$			29.3151i			1.32568i
$490$	−2.58563	+	4.47844i	−0.116807	+	0.202315i
$491$	−1.96290	−	3.39985i	−0.0885846	−	0.153433i	0.818328	−	0.574751i	$-0.194901\pi$
$491$	−1.96290	−	3.39985i	−0.0885846	−	0.153433i	−0.906913	+	0.421318i	$0.861568\pi$
$492$	−22.3675	+	12.9139i	−1.00841	+	0.582204i
$493$	1.48014			0.0666624
$494$	−20.3037	−	11.2985i	−0.913509	−	0.508344i
$495$	0.405313			0.0182175
$496$	0.00165461		0.000955288i	7.42941e−5		4.28937e-5i
$497$	15.7060	+	27.2035i	0.704508	+	1.22024i
$498$	−6.14026	+	10.6352i	−0.275152	+	0.476576i
$499$		−	4.56322i		−	0.204278i	−0.994770	−	0.102139i	$-0.967431\pi$
$499$		−	4.56322i		−	0.204278i	0.994770	−	0.102139i	$-0.0325686\pi$
$500$	−28.2324	−	16.3000i	−1.26259	−	0.728956i
$501$	−1.40620	−	0.811870i	−0.0628244	−	0.0362717i
$502$		−	70.4998i		−	3.14656i
$503$	−19.6124	+	33.9697i	−0.874474	+	1.51463i	−0.0171522	+	0.999853i	$0.505460\pi$
$503$	−19.6124	+	33.9697i	−0.874474	+	1.51463i	−0.857322	+	0.514781i	$0.827873\pi$
$504$	−1.09371	−	1.89437i	−0.0487178	−	0.0843817i
$505$	−3.62399	+	2.09231i	−0.161265	+	0.0931066i
$506$	−10.5843			−0.470528
$507$	−10.1680	+	18.9714i	−0.451575	+	0.842549i
$508$	66.8777			2.96722
$509$	−28.4849	+	16.4457i	−1.26257	+	0.728945i	−0.973571	−	0.228385i	$-0.926656\pi$
$509$	−28.4849	+	16.4457i	−1.26257	+	0.728945i	−0.288998	+	0.957330i	$0.593322\pi$
$510$	14.7380	+	25.5270i	0.652609	+	1.13035i
$511$	−20.8765	+	36.1591i	−0.923521	+	1.59959i
$512$			0.0216157i			0.000955288i
$513$	13.1586	+	7.59714i	0.580967	+	0.335422i
$514$	10.0526	+	5.80390i	0.443403	+	0.255999i
$515$			12.8824i			0.567668i
$516$	14.0988	−	24.4198i	0.620665	−	1.07502i
$517$	−4.48011	−	7.75978i	−0.197035	−	0.341275i
$518$	67.4976	−	38.9698i	2.96568	−	1.71223i
$519$	15.6557			0.687207
$520$	10.3912	+	5.78246i	0.455686	+	0.253578i
$521$	−8.31125			−0.364122			−0.182061	−	0.983287i	$-0.558277\pi$
$521$	−8.31125			−0.364122			−0.182061	+	0.983287i	$0.558277\pi$
$522$	−0.113643	+	0.0656116i	−0.00497400	+	0.00287174i
$523$	0.0865411	+	0.149894i	0.00378418	+	0.00655439i	0.867911	−	0.496719i	$-0.165462\pi$
$523$	0.0865411	+	0.149894i	0.00378418	+	0.00655439i	−0.864127	+	0.503274i	$0.832129\pi$
$524$	−1.91494	+	3.31677i	−0.0836544	+	0.144894i
$525$		−	18.0253i		−	0.786687i
$526$	21.6872	+	12.5211i	0.945609	+	0.545947i
$527$	5.77999	+	3.33708i	0.251781	+	0.145366i
$528$			0.00425400i			0.000185132i
$529$	5.58490	−	9.67334i	0.242822	−	0.420580i
$530$	5.68289	+	9.84305i	0.246849	+	0.427555i
$531$	−0.498816	+	0.287991i	−0.0216468	+	0.0124978i
$532$	−27.2506			−1.18146
$533$	−17.3757	+	0.274533i	−0.752624	+	0.0118913i
$534$	−34.1556			−1.47806
$535$	−9.35996	+	5.40397i	−0.404666	+	0.233634i
$536$	6.81172	+	11.7983i	0.294222	+	0.509607i
$537$	6.81715	−	11.8076i	0.294182	−	0.509538i
$538$		−	8.04037i		−	0.346645i
$539$	−2.25782	−	1.30355i	−0.0972510	−	0.0561479i
$540$	−17.6272	−	10.1771i	−0.758555	−	0.437952i
$541$		−	35.6501i		−	1.53272i	−0.642413	−	0.766359i	$-0.722066\pi$
$541$		−	35.6501i		−	1.53272i	0.642413	−	0.766359i	$-0.277934\pi$
$542$	22.4224	−	38.8367i	0.963124	−	1.66818i
$543$	−4.44050	−	7.69118i	−0.190560	−	0.330060i
$544$	−32.6840	+	18.8701i	−1.40131	+	0.809048i
$545$	−2.86368			−0.122667
$546$	0.645232	+	40.8379i	0.0276134	+	1.74770i
$547$	−29.6538			−1.26791			−0.633953	−	0.773371i	$-0.718569\pi$
$547$	−29.6538			−1.26791			−0.633953	+	0.773371i	$0.718569\pi$
$548$	30.3249	−	17.5081i	1.29542	−	0.747909i
$549$	1.94866	+	3.37518i	0.0831668	+	0.144049i
$550$	5.60262	−	9.70402i	0.238896	−	0.413781i
$551$			0.624556i			0.0266070i
$552$	13.9549	+	8.05688i	0.593961	+	0.342924i
$553$	12.9766	+	7.49205i	0.551821	+	0.318594i
$554$		−	24.8265i		−	1.05478i
$555$	10.9931	−	19.0407i	0.466632	−	0.808231i
$556$	−9.55411	−	16.5482i	−0.405185	−	0.701800i
$557$	−7.74827	+	4.47347i	−0.328305	+	0.189547i	−0.655088	−	0.755552i	$-0.727369\pi$
$557$	−7.74827	+	4.47347i	−0.328305	+	0.189547i	0.326783	+	0.945099i	$0.394035\pi$
$558$	−0.591702			−0.0250488
$559$	16.2786	−	9.74454i	0.688511	−	0.412150i
$560$	0.00665832			0.000281365
$561$	−12.8695	+	7.43019i	−0.543350	+	0.313703i
$562$	5.93200	+	10.2745i	0.250226	+	0.433404i
$563$	−5.71183	+	9.89317i	−0.240725	+	0.416948i	−0.960921	−	0.276823i	$-0.910718\pi$
$563$	−5.71183	+	9.89317i	−0.240725	+	0.416948i	0.720196	+	0.693770i	$0.244052\pi$
$564$			35.7057i			1.50348i
$565$	0.176662	+	0.101996i	0.00743222	+	0.00429099i
$566$	−33.9122	−	19.5792i	−1.42544	−	0.822976i
$567$		−	24.3888i		−	1.02423i
$568$	14.8641	−	25.7454i	0.623685	−	1.08025i
$569$	−7.00352	−	12.1304i	−0.293603	−	0.508535i	0.681056	−	0.732231i	$-0.261521\pi$
$569$	−7.00352	−	12.1304i	−0.293603	−	0.508535i	−0.974659	+	0.223696i	$0.928188\pi$
$570$	−10.7713	+	6.21879i	−0.451158	+	0.260476i
$571$	36.2259			1.51601			0.758004	−	0.652250i	$-0.226175\pi$
$571$	36.2259			1.51601			0.758004	+	0.652250i	$0.226175\pi$
$572$	−7.63057	+	13.7123i	−0.319050	+	0.573342i
$573$	−25.0281			−1.04556
$574$	−28.5570	+	16.4874i	−1.19195	+	0.688170i
$575$	−6.26212	−	10.8463i	−0.261149	−	0.452323i
$576$	1.67343	−	2.89847i	0.0697264	−	0.120770i
$577$		−	34.5709i		−	1.43920i	−0.694387	−	0.719602i	$-0.744324\pi$
$577$		−	34.5709i		−	1.43920i	0.694387	−	0.719602i	$-0.255676\pi$
$578$	54.5865	+	31.5155i	2.27050	+	1.31087i
$579$	−12.5995	−	7.27432i	−0.523617	−	0.302310i
$580$		−	0.836652i		−	0.0347401i
$581$	−4.84524	+	8.39220i	−0.201014	+	0.348167i
$582$	−9.04278	−	15.6626i	−0.374835	−	0.649234i
$583$	−4.96240	+	2.86504i	−0.205521	+	0.118658i
$584$	39.5151			1.63514
$585$	−0.558160	−	0.932425i	−0.0230771	−	0.0385510i
$586$	41.5940			1.71823
$587$	6.53643	−	3.77381i	0.269787	−	0.155762i	−0.359004	−	0.933336i	$-0.616883\pi$
$587$	6.53643	−	3.77381i	0.269787	−	0.155762i	0.628791	+	0.777574i	$0.283550\pi$
$588$	5.19453	+	8.99719i	0.214219	+	0.371038i
$589$	−1.40810	+	2.43890i	−0.0580198	+	0.100493i
$590$		−	5.94169i		−	0.244615i
$591$	−31.2662	−	18.0515i	−1.28612	−	0.742541i
$592$	−0.0188493	−	0.0108826i	−0.000774701	−	0.000447274i
$593$			26.2214i			1.07678i	0.842695	+	0.538391i	$0.180968\pi$
$593$			26.2214i			1.07678i	−0.842695	+	0.538391i	$0.819032\pi$
$594$	8.30139	−	14.3784i	0.340610	−	0.589954i
$595$	11.6297	+	20.1432i	0.476770	+	0.825789i
$596$	46.4258	−	26.8039i	1.90167	−	1.09793i
$597$	19.2984			0.789832
$598$	14.5757	+	24.3492i	0.596044	+	0.995712i
$599$	−7.99098			−0.326503			−0.163251	−	0.986585i	$-0.552198\pi$
$599$	−7.99098			−0.326503			−0.163251	+	0.986585i	$0.552198\pi$
$600$	−14.7736	+	8.52956i	−0.603131	+	0.348218i
$601$	5.55772	+	9.62625i	0.226704	+	0.392663i	0.956829	−	0.290650i	$-0.0938717\pi$
$601$	5.55772	+	9.62625i	0.226704	+	0.392663i	−0.730125	+	0.683313i	$0.760538\pi$
$602$	18.0002	−	31.1772i	0.733632	−	1.27069i
$603$		−	1.24497i		−	0.0506989i
$604$	−37.6204	−	21.7202i	−1.53075	−	0.883781i
$605$	9.27866	+	5.35704i	0.377231	+	0.217795i
$606$			13.6020i			0.552543i
$607$	12.0145	−	20.8097i	0.487652	−	0.844638i	−0.512247	−	0.858838i	$-0.671187\pi$
$607$	12.0145	−	20.8097i	0.487652	−	0.844638i	0.999899	+	0.0142002i	$0.00452023\pi$
$608$	−7.96235	−	13.7912i	−0.322916	−	0.559307i
$609$	0.950744	−	0.548913i	0.0385261	−	0.0222431i
$610$	−40.2037			−1.62780
$611$	−11.6818	+	20.9926i	−0.472596	+	0.849269i
$612$	−5.58541			−0.225777
$613$	−6.83888	+	3.94843i	−0.276220	+	0.159476i	−0.631711	−	0.775204i	$-0.717647\pi$
$613$	−6.83888	+	3.94843i	−0.276220	+	0.159476i	0.355491	+	0.934680i	$0.384314\pi$
$614$	−3.08726	−	5.34729i	−0.124592	−	0.215799i
$615$	−4.65099	+	8.05575i	−0.187546	+	0.324839i
$616$			11.3761i			0.458358i
$617$	38.0117	+	21.9461i	1.53030	+	0.883516i	0.999348	+	0.0361115i	$0.0114972\pi$
$617$	38.0117	+	21.9461i	1.53030	+	0.883516i	0.530947	+	0.847405i	$0.321836\pi$
$618$	36.2639	+	20.9370i	1.45875	+	0.842209i
$619$		−	24.5974i		−	0.988653i	−0.869276	−	0.494326i	$-0.835415\pi$
$619$		−	24.5974i		−	0.988653i	0.869276	−	0.494326i	$-0.164585\pi$
$620$	1.88629	−	3.26714i	0.0757551	−	0.131212i
$621$	−9.27858	−	16.0710i	−0.372337	−	0.644906i
$622$	−63.6204	+	36.7313i	−2.55095	+	1.47279i
$623$	−26.9520			−1.07981
$624$	0.00978635	−	0.00585822i	0.000391768	−	0.000234516i
$625$	6.46549			0.258620
$626$	54.6474	−	31.5507i	2.18415	−	1.26102i
$627$	−3.13522	−	5.43035i	−0.125208	−	0.216867i
$628$	6.28821	−	10.8915i	0.250927	−	0.434618i
$629$		−	76.0321i		−	3.03160i
$630$	−1.78581	−	1.03104i	−0.0711482	−	0.0410774i
$631$	18.7540	+	10.8276i	0.746583	+	0.431040i	0.824458	−	0.565923i	$-0.191480\pi$
$631$	18.7540	+	10.8276i	0.746583	+	0.431040i	−0.0778749	+	0.996963i	$0.524813\pi$
$632$		−	14.1810i		−	0.564089i
$633$	−0.0500058	+	0.0866126i	−0.00198755	+	0.00344254i
$634$	−36.4160	−	63.0744i	−1.44627	−	2.50501i
$635$	20.8593	−	12.0431i	0.827776	−	0.477917i
$636$	22.8339			0.905421
$637$	0.110429	+	6.98925i	0.00437535	+	0.276924i
$638$	0.682453			0.0270186
$639$	−2.35272	+	1.35834i	−0.0930722	+	0.0537353i
$640$	10.6714	+	18.4834i	0.421825	+	0.730622i
$641$	−9.16018	+	15.8659i	−0.361806	+	0.626666i	−0.988258	−	0.152794i	$-0.951173\pi$
$641$	−9.16018	+	15.8659i	−0.361806	+	0.626666i	0.626453	+	0.779460i	$0.284506\pi$
$642$			35.1309i			1.38651i
$643$	−30.3463	−	17.5204i	−1.19674	−	0.690938i	−0.236913	−	0.971531i	$-0.576136\pi$
$643$	−30.3463	−	17.5204i	−1.19674	−	0.690938i	−0.959827	+	0.280593i	$0.909469\pi$
$644$	28.8230	+	16.6410i	1.13578	+	0.655746i
$645$		−	10.1555i		−	0.399871i
$646$	−21.5056	+	37.2488i	−0.846126	+	1.46553i
$647$	−7.54305	−	13.0649i	−0.296548	−	0.513636i	0.678796	−	0.734327i	$-0.262502\pi$
$647$	−7.54305	−	13.0649i	−0.296548	−	0.513636i	−0.975344	+	0.220691i	$0.929169\pi$
$648$	−19.9892	+	11.5408i	−0.785252	+	0.453365i
$649$	2.99551			0.117584
$650$	−30.0396	+	0.474620i	−1.17825	+	0.0186161i
$651$	4.95023			0.194015
$652$	49.6260	−	28.6516i	1.94350	−	1.12208i
$653$	0.340523	+	0.589803i	0.0133257	+	0.0230808i	0.872611	−	0.488415i	$-0.162425\pi$
$653$	0.340523	+	0.589803i	0.0133257	+	0.0230808i	−0.859286	+	0.511496i	$0.829092\pi$
$654$	−4.65415	+	8.06122i	−0.181992	+	0.315219i
$655$			1.37934i			0.0538954i
$656$	0.00797479	+	0.00460425i	0.000311363	+	0.000179766i
$657$	−3.12726	−	1.80552i	−0.122006	−	0.0704401i
$658$			45.5860i			1.77713i
$659$	−10.3238	+	17.8813i	−0.402158	+	0.696558i	−0.993986	−	0.109506i	$-0.965073\pi$
$659$	−10.3238	+	17.8813i	−0.402158	+	0.696558i	0.591828	+	0.806064i	$0.298406\pi$
$660$	4.19992	+	7.27447i	0.163482	+	0.283159i
$661$	−22.0214	+	12.7141i	−0.856535	+	0.494521i	−0.862850	−	0.505459i	$-0.831323\pi$
$661$	−22.0214	+	12.7141i	−0.856535	+	0.494521i	0.00631539	+	0.999980i	$0.497990\pi$
$662$	−37.1345			−1.44327
$663$	34.8158	+	19.3741i	1.35214	+	0.752429i
$664$	9.17108			0.355907
$665$	−8.49953	+	4.90721i	−0.329598	+	0.190293i
$666$	3.37034	+	5.83760i	0.130598	+	0.226202i
$667$	0.381393	−	0.660593i	0.0147676	−	0.0255783i
$668$			3.17397i			0.122805i
$669$	−27.4194	−	15.8306i	−1.06009	−	0.612046i
$670$	11.1221	+	6.42136i	0.429685	+	0.248079i
$671$		−	20.2688i		−	0.782468i
$672$	−13.9960	+	24.2417i	−0.539906	+	0.935145i
$673$	−7.53163	−	13.0452i	−0.290323	−	0.502854i	0.683563	−	0.729892i	$-0.260429\pi$
$673$	−7.53163	−	13.0452i	−0.290323	−	0.502854i	−0.973886	+	0.227037i	$0.927096\pi$
$674$	71.0824	−	41.0394i	2.73799	−	1.58078i
$675$	19.6459			0.756170
$676$	42.0534	−	1.32921i	1.61744	−	0.0511233i
$677$	13.4298			0.516150			0.258075	−	0.966125i	$-0.416912\pi$
$677$	13.4298			0.516150			0.258075	+	0.966125i	$0.416912\pi$
$678$	0.574233	−	0.331534i	0.0220533	−	0.0127325i
$679$	−7.13561	−	12.3592i	−0.273839	−	0.474304i
$680$	11.0063	−	19.0635i	0.422073	−	0.731052i
$681$		−	2.32624i		−	0.0891416i
$682$	2.66499	+	1.53863i	0.102048	+	0.0589173i
$683$	−19.2876	−	11.1357i	−0.738020	−	0.426096i	0.0833292	−	0.996522i	$-0.473445\pi$
$683$	−19.2876	−	11.1357i	−0.738020	−	0.426096i	−0.821349	+	0.570426i	$0.806778\pi$
$684$		−	2.35680i		−	0.0901144i
$685$	6.30561	−	10.9216i	0.240925	−	0.417294i
$686$	−17.3137	−	29.9881i	−0.661039	−	1.14495i
$687$	−4.49290	+	2.59398i	−0.171415	+	0.0989664i
$688$	−0.0100534			−0.000383282
$689$	13.4248	+	7.47055i	0.511444	+	0.284605i
$690$	15.1903			0.578286
$691$	15.6005	−	9.00694i	0.593470	−	0.342640i	−0.172998	−	0.984922i	$-0.555346\pi$
$691$	15.6005	−	9.00694i	0.593470	−	0.342640i	0.766468	+	0.642282i	$0.222012\pi$
$692$	−15.3013	−	26.5026i	−0.581668	−	1.00748i
$693$	0.519799	−	0.900318i	0.0197455	−	0.0342003i
$694$		−	54.5442i		−	2.07047i
$695$	−5.95990	−	3.44095i	−0.226072	−	0.130523i
$696$	−0.899786	−	0.519492i	−0.0341063	−	0.0196913i
$697$			32.1678i			1.21844i
$698$	40.3316	−	69.8563i	1.52657	−	2.64410i
$699$	−5.34070	−	9.25037i	−0.202004	−	0.349881i
$700$	−30.5140	+	17.6172i	−1.15332	+	0.665869i
$701$	−12.1690			−0.459617			−0.229809	−	0.973236i	$-0.573810\pi$
$701$	−12.1690			−0.459617			−0.229809	+	0.973236i	$0.573810\pi$
$702$	−44.5096	+	0.703244i	−1.67991	+	0.0265422i
$703$	32.0822			1.21000
$704$	−15.0741	+	8.70303i	−0.568126	+	0.328008i
$705$	6.42976	+	11.1367i	0.242159	+	0.419432i
$706$	−24.1814	+	41.8835i	−0.910080	+	1.57631i
$707$			10.7332i			0.403665i
$708$	−10.3376	−	5.96843i	−0.388512	−	0.224307i
$709$	−17.8614	−	10.3123i	−0.670800	−	0.387287i	0.125579	−	0.992084i	$-0.459921\pi$
$709$	−17.8614	−	10.3123i	−0.670800	−	0.387287i	−0.796380	+	0.604797i	$0.793254\pi$
$710$		−	28.0246i		−	1.05175i
$711$	−0.647957	+	1.12229i	−0.0243003	+	0.0420893i
$712$	12.7537	+	22.0901i	0.477965	+	0.827860i
$713$	2.97870	−	1.71975i	0.111553	−	0.0644052i
$714$	75.6037			2.82940
$715$	0.0892848	+	5.65100i	0.00333906	+	0.211335i
$716$	−26.6514			−0.996008
$717$	−23.2456	+	13.4208i	−0.868122	+	0.501210i
$718$	14.5661	+	25.2292i	0.543601	+	0.941545i
$719$	−14.6427	+	25.3618i	−0.546079	+	0.945837i	0.452459	+	0.891785i	$0.350547\pi$
$719$	−14.6427	+	25.3618i	−0.546079	+	0.945837i	−0.998538	+	0.0540515i	$0.982786\pi$
$720$		0	0.000575851i		0	2.14607e-5i
$721$	28.6157	+	16.5213i	1.06570	+	0.615284i
$722$	21.9361	+	12.6648i	0.816377	+	0.471335i
$723$			6.06873i			0.225699i
$724$	−8.67998	+	15.0342i	−0.322589	+	0.558741i
$725$	0.403769	+	0.699349i	0.0149956	+	0.0259732i
$726$	30.1600	−	17.4129i	1.11934	−	0.646253i
$727$	4.82505			0.178951			0.0894756	−	0.995989i	$-0.471481\pi$
$727$	4.82505			0.178951			0.0894756	+	0.995989i	$0.471481\pi$
$728$	26.1709	−	15.6662i	0.969958	−	0.580627i
$729$	28.9087			1.07069
$730$	32.2599	−	18.6253i	1.19399	−	0.689353i
$731$	−17.5596	−	30.4142i	−0.649467	−	1.12491i
$732$	−40.3847	+	69.9483i	−1.49266	+	2.58536i
$733$		−	5.74059i		−	0.212033i	−0.994364	−	0.106017i	$-0.966190\pi$
$733$		−	5.74059i		−	0.212033i	0.994364	−	0.106017i	$-0.0338097\pi$
$734$	42.9030	+	24.7701i	1.58358	+	0.914279i
$735$	3.24037	+	1.87083i	0.119523	+	0.0690066i
$736$			19.4493i			0.716909i
$737$	−3.23735	+	5.60725i	−0.119249	+	0.206546i
$738$	−1.42593	−	2.46978i	−0.0524891	−	0.0909138i
$739$	0.304004	−	0.175517i	0.0111830	−	0.00645648i	−0.494398	−	0.869236i	$-0.664611\pi$
$739$	0.304004	−	0.175517i	0.0111830	−	0.00645648i	0.505581	+	0.862779i	$0.331278\pi$
$740$	−42.9772			−1.57987
$741$	−8.17503	+	14.6908i	−0.300317	+	0.539679i
$742$	29.1524			1.07022
$743$	43.3990	−	25.0564i	1.59216	−	0.919231i	0.599219	−	0.800585i	$-0.295478\pi$
$743$	43.3990	−	25.0564i	1.59216	−	0.919231i	0.992937	−	0.118646i	$-0.0378554\pi$
$744$	−2.34245	−	4.05725i	−0.0858785	−	0.148746i
$745$	9.65353	−	16.7204i	0.353678	−	0.612589i
$746$			64.6479i			2.36693i
$747$	−0.725808	−	0.419045i	−0.0265559	−	0.0153321i
$748$	25.1563	+	14.5240i	0.919807	+	0.531051i
$749$			27.7216i			1.01292i
$750$	−19.0818	+	33.0507i	−0.696770	+	1.20684i
$751$	−10.1842	−	17.6395i	−0.371625	−	0.643674i	0.618191	−	0.786028i	$-0.287866\pi$
$751$	−10.1842	−	17.6395i	−0.371625	−	0.643674i	−0.989816	+	0.142355i	$0.954533\pi$
$752$	0.0110248	−	0.00636514i	0.000402031	−	0.000232113i
$753$	−51.0101			−1.85891
$754$	−0.939811	−	1.56999i	−0.0342259	−	0.0571755i
$755$	−15.6452			−0.569387
$756$	−45.2125	+	26.1035i	−1.64436	+	0.949374i
$757$	4.56723	+	7.91068i	0.165999	+	0.287519i	0.937010	−	0.349304i	$-0.113582\pi$
$757$	4.56723	+	7.91068i	0.165999	+	0.287519i	−0.771011	+	0.636822i	$0.780249\pi$
$758$	−33.7710	+	58.4931i	−1.22662	+	2.12457i
$759$			7.65824i			0.277977i
$760$	8.04397	+	4.64419i	0.291785	+	0.168462i
$761$	27.6201	+	15.9465i	1.00123	+	0.578058i	0.908611	−	0.417643i	$-0.137144\pi$
$761$	27.6201	+	15.9465i	1.00123	+	0.578058i	0.0926156	+	0.995702i	$0.470477\pi$
$762$		−	78.2916i		−	2.83621i
$763$	−3.67256	+	6.36106i	−0.132956	+	0.230286i
$764$	24.4616	+	42.3687i	0.884989	+	1.53285i
$765$	−1.74210	+	1.00580i	−0.0629858	+	0.0363649i
$766$	−65.5750			−2.36932
$767$	−4.12515	−	6.89120i	−0.148950	−	0.248827i
$768$	26.5121			0.956672
$769$	−28.5537	+	16.4855i	−1.02967	+	0.594482i	−0.916891	−	0.399138i	$-0.869310\pi$
$769$	−28.5537	+	16.4855i	−1.02967	+	0.594482i	−0.112782	+	0.993620i	$0.535976\pi$
$770$	5.36211	+	9.28744i	0.193237	+	0.334696i
$771$	4.19940	−	7.27358i	0.151238	−	0.261952i
$772$			28.4386i			1.02353i
$773$	−14.5948	−	8.42632i	−0.524939	−	0.303074i	0.214014	−	0.976831i	$-0.431346\pi$
$773$	−14.5948	−	8.42632i	−0.524939	−	0.303074i	−0.738953	+	0.673757i	$0.764680\pi$
$774$	2.69639	+	1.55676i	0.0969197	+	0.0559566i
$775$			3.64129i			0.130799i
$776$	−6.75315	+	11.6968i	−0.242424	+	0.419890i
$777$	−28.1966	−	48.8379i	−1.01155	−	1.75205i
$778$	−42.5783	+	24.5826i	−1.52651	+	0.881329i
$779$	−13.5734			−0.486317
$780$	10.9512	−	19.6797i	0.392117	−	0.704645i
$781$	14.1287			0.505564
$782$	45.4929	−	26.2653i	1.62682	−	0.939247i
$783$	0.598264	+	1.03622i	0.0213802	+	0.0370316i
$784$	0.00185203	−	0.00320780i	6.61438e−5	−	0.000114564i
$785$		−	4.52944i		−	0.161663i
$786$	3.88283	+	2.24176i	0.138496	+	0.0799608i
$787$	27.8310	+	16.0682i	0.992067	+	0.572770i	0.905892	−	0.423510i	$-0.139202\pi$
$787$	27.8310	+	16.0682i	0.992067	+	0.572770i	0.0861756	+	0.996280i	$0.472535\pi$
$788$			70.5717i			2.51401i
$789$	9.05966	−	15.6918i	0.322532	−	0.558642i
$790$	−6.68415	−	11.5773i	−0.237811	−	0.411901i
$791$	0.453124	−	0.261611i	0.0161112	−	0.00930183i
$792$	−0.983877			−0.0349605
$793$	−46.6285	+	27.9123i	−1.65583	+	0.991195i
$794$	15.8917			0.563975
$795$	7.12193	−	4.11185i	0.252589	−	0.145832i
$796$	−18.8616	−	32.6692i	−0.668531	−	1.15793i
$797$	9.16399	−	15.8725i	0.324605	−	0.562233i	−0.656827	−	0.754041i	$-0.728102\pi$
$797$	9.16399	−	15.8725i	0.324605	−	0.562233i	0.981432	+	0.191808i	$0.0614352\pi$
$798$			31.9014i			1.12930i
$799$	38.5125	+	22.2352i	1.36247	+	0.786624i
$800$	−17.8317	−	10.2952i	−0.630447	−	0.363989i
$801$		−	2.33097i		−	0.0823607i
$802$	−39.3144	+	68.0945i	−1.38824	+	2.40450i
$803$	9.38998	+	16.2639i	0.331365	+	0.573941i
$804$	22.3444	−	12.9005i	0.788025	−	0.454967i
$805$	11.9866			0.422472
$806$	−0.130344	−	8.24969i	−0.00459116	−	0.290583i
$807$	−5.81761			−0.204789
$808$	8.79704	−	5.07898i	0.309479	−	0.178678i
$809$	25.3257	+	43.8654i	0.890404	+	1.54222i	0.839392	+	0.543527i	$0.182911\pi$
$809$	25.3257	+	43.8654i	0.890404	+	1.54222i	0.0510120	+	0.998698i	$0.483755\pi$
$810$	−10.8794	+	18.8437i	−0.382264	+	0.662101i
$811$			15.5125i			0.544716i	0.962196	+	0.272358i	$0.0878035\pi$
$811$			15.5125i			0.544716i	−0.962196	+	0.272358i	$0.912197\pi$
$812$	−1.85845	−	1.07298i	−0.0652187	−	0.0376541i
$813$	−28.1003	−	16.2237i	−0.985520	−	0.568990i
$814$		−	35.0563i		−	1.22872i
$815$	10.3190	−	17.8730i	0.361458	−	0.626063i
$816$	−0.0105565	−	0.0182844i	−0.000369551	−	0.000640081i
$817$	12.8334	−	7.40939i	0.448986	−	0.259222i
$818$	−48.2526			−1.68711
$819$	−2.78701	+	0.0440342i	−0.0973859	+	0.00153868i
$820$	18.1828			0.634973
$821$	6.23630	−	3.60053i	0.217648	−	0.125659i	−0.387213	−	0.921990i	$-0.626562\pi$
$821$	6.23630	−	3.60053i	0.217648	−	0.125659i	0.604861	+	0.796331i	$0.293229\pi$
$822$	−20.4962	−	35.5004i	−0.714886	−	1.23822i
$823$	−17.4515	+	30.2269i	−0.608321	+	1.05364i	0.383196	+	0.923667i	$0.374823\pi$
$823$	−17.4515	+	30.2269i	−0.608321	+	1.05364i	−0.991517	+	0.129976i	$0.958510\pi$
$824$		−	31.2715i		−	1.08939i
$825$	−7.02133	−	4.05377i	−0.244451	−	0.141134i
$826$	−13.1982	−	7.61999i	−0.459224	−	0.265133i
$827$		−	15.2492i		−	0.530267i	−0.964212	−	0.265134i	$-0.914584\pi$
$827$		−	15.2492i		−	0.530267i	0.964212	−	0.265134i	$-0.0854161\pi$
$828$	−1.43921	+	2.49278i	−0.0500160	+	0.0866302i
$829$	7.29608	+	12.6372i	0.253403	+	0.438907i	0.964461	−	0.264227i	$-0.0851167\pi$
$829$	7.29608	+	12.6372i	0.253403	+	0.438907i	−0.711057	+	0.703134i	$0.751783\pi$
$830$	7.48724	−	4.32276i	0.259886	−	0.150045i
$831$	−17.9632			−0.623136
$832$	40.7800	+	22.6930i	1.41379	+	0.786739i
$833$	12.9393			0.448319
$834$	−19.3725	+	11.1847i	−0.670813	+	0.387294i
$835$	0.571559	+	0.989969i	0.0197796	+	0.0342593i
$836$	−6.12850	+	10.6149i	−0.211958	+	0.367123i
$837$			5.39530i			0.186489i
$838$	−80.2498	−	46.3322i	−2.77218	−	1.60052i
$839$	7.25814	+	4.19049i	0.250579	+	0.144672i	0.620029	−	0.784579i	$-0.287121\pi$
$839$	7.25814	+	4.19049i	0.250579	+	0.144672i	−0.369450	+	0.929250i	$0.620454\pi$
$840$		−	16.3268i		−	0.563328i
$841$	14.4754	−	25.0721i	0.499152	−	0.864557i
$842$	−9.92984	−	17.1990i	−0.342205	−	0.592716i
$843$	7.43412	−	4.29209i	0.256045	−	0.147827i
$844$	0.195496			0.00672924
$845$	12.8772	−	7.98743i	0.442989	−	0.274776i
$846$	−3.94255			−0.135548
$847$	23.7991	−	13.7404i	0.817746	−	0.472126i
$848$	−0.00407052	−	0.00705035i	−0.000139782	−	0.000242110i
$849$	−14.1665	+	24.5371i	−0.486194	+	0.842112i
$850$			55.6126i			1.90750i
$851$	−33.9334	−	19.5914i	−1.16322	−	0.671586i
$852$	−48.7586	−	28.1508i	−1.67044	−	0.964429i
$853$		−	11.9819i		−	0.410253i	−0.978735	−	0.205127i	$-0.934239\pi$
$853$		−	11.9819i		−	0.410253i	0.978735	−	0.205127i	$-0.0657606\pi$
$854$	−51.5598	+	89.3041i	−1.76434	+	3.05592i
$855$	−0.424404	−	0.735090i	−0.0145143	−	0.0251395i
$856$	22.7208	−	13.1179i	0.776581	−	0.448360i
$857$	47.7544			1.63126			0.815630	−	0.578574i	$-0.196391\pi$
$857$	47.7544			1.63126			0.815630	+	0.578574i	$0.196391\pi$
$858$	16.0526	+	8.93286i	0.548027	+	0.304963i
$859$	−27.3365			−0.932710			−0.466355	−	0.884598i	$-0.654433\pi$
$859$	−27.3365			−0.932710			−0.466355	+	0.884598i	$0.654433\pi$
$860$	−17.1916	+	9.92559i	−0.586230	+	0.338460i
$861$	11.9294	+	20.6624i	0.406554	+	0.704172i
$862$	2.10139	−	3.63971i	0.0715736	−	0.123969i
$863$		−	39.1219i		−	1.33173i	−0.746074	−	0.665863i	$-0.768063\pi$
$863$		−	39.1219i		−	1.33173i	0.746074	−	0.665863i	$-0.231937\pi$
$864$	−26.4213	−	15.2543i	−0.898870	−	0.518963i
$865$	−9.54501	−	5.51082i	−0.324540	−	0.187373i
$866$		−	37.4548i		−	1.27276i
$867$	22.8030	−	39.4960i	0.774431	−	1.34135i
$868$	−4.83818	−	8.37998i	−0.164219	−	0.284435i
$869$	5.83672	−	3.36983i	0.197997	−	0.114314i
$870$	−0.979442			−0.0332062
$871$	17.3577	−	0.274248i	0.588143	−	0.00929255i
$872$	6.95143			0.235405
$873$	1.06890	−	0.617130i	0.0361768	−	0.0208867i
$874$	11.0828	+	19.1960i	0.374882	+	0.649315i
$875$	−15.0574	+	26.0801i	−0.509032	+	0.881669i
$876$		−	74.8364i		−	2.52849i
$877$	−18.0910	−	10.4448i	−0.610890	−	0.352698i	0.162424	−	0.986721i	$-0.448069\pi$
$877$	−18.0910	−	10.4448i	−0.610890	−	0.352698i	−0.773314	+	0.634024i	$0.781402\pi$
$878$	41.4785	+	23.9476i	1.39983	+	0.808194i
$879$		−	30.0953i		−	1.01509i
$880$	0.00149741	−	0.00259360i	5.04778e−5	−	8.74302e-5i
$881$	−3.25288	−	5.63416i	−0.109592	−	0.189820i	0.806013	−	0.591898i	$-0.201621\pi$
$881$	−3.25288	−	5.63416i	−0.109592	−	0.189820i	−0.915605	+	0.402079i	$0.868288\pi$
$882$	−0.993452	+	0.573570i	−0.0334513	+	0.0193131i
$883$	−10.5474			−0.354948			−0.177474	−	0.984126i	$-0.556793\pi$
$883$	−10.5474			−0.354948			−0.177474	+	0.984126i	$0.556793\pi$
$884$	−1.23039	−	77.8734i	−0.0413824	−	2.61917i
$885$	−4.29910			−0.144513
$886$	16.0478	−	9.26519i	0.539136	−	0.311270i
$887$	−23.0050	−	39.8457i	−0.772431	−	1.33789i	−0.936227	−	0.351395i	$-0.885707\pi$
$887$	−23.0050	−	39.8457i	−0.772431	−	1.33789i	0.163797	−	0.986494i	$-0.447626\pi$
$888$	−26.6853	+	46.2202i	−0.895499	+	1.55105i
$889$		−	61.7794i		−	2.07202i
$890$	20.8241	+	12.0228i	0.698027	+	0.403006i
$891$	−9.50011	−	5.48489i	−0.318266	−	0.183751i
$892$			61.8890i			2.07220i
$893$	−9.38227	+	16.2506i	−0.313966	+	0.543805i
$894$	−31.3785	−	54.3492i	−1.04945	−	1.81771i
$895$	−8.31262	+	4.79929i	−0.277860	+	0.160423i
$896$	54.7428			1.82883
$897$	17.6178	−	10.5462i	0.588242	−	0.352128i
$898$	20.7381			0.692040
$899$	−0.192060	+	0.110886i	−0.00640558	+	0.00369826i
$900$	−1.52364	−	2.63903i	−0.0507881	−	0.0879677i
$901$	14.2194	−	24.6288i	0.473718	−	0.820504i
$902$			14.8316i			0.493840i
$903$	−22.5582	−	13.0240i	−0.750691	−	0.433412i
$904$	−0.428837	−	0.247589i	−0.0142629	−	0.00823470i
$905$			6.25226i			0.207832i
$906$	−25.4271	+	44.0411i	−0.844759	+	1.46317i
$907$	−29.3569	−	50.8477i	−0.974781	−	1.68837i	−0.680657	−	0.732602i	$-0.738305\pi$
$907$	−29.3569	−	50.8477i	−0.974781	−	1.68837i	−0.294124	−	0.955767i	$-0.595028\pi$
$908$	−3.93796	+	2.27358i	−0.130686	+	0.0754514i
$909$	−0.928274			−0.0307889
$910$	13.9816	−	25.1254i	0.463486	−	0.832898i
$911$	37.5292			1.24340			0.621700	−	0.783256i	$-0.286442\pi$
$911$	37.5292			1.24340			0.621700	+	0.783256i	$0.286442\pi$
$912$	0.00771520	−	0.00445437i	0.000255476	−	0.000147499i
$913$	2.17933	+	3.77471i	0.0721253	+	0.124925i
$914$	11.5004	−	19.9193i	0.380400	−	0.658871i
$915$			29.0894i			0.961665i
$916$	8.78240	+	5.07052i	0.290179	+	0.167535i
$917$	3.06392	+	1.76896i	0.101180	+	0.0584161i
$918$			82.4011i			2.71964i
$919$	−7.10814	+	12.3117i	−0.234476	+	0.406124i	−0.959120	−	0.282999i	$-0.908671\pi$
$919$	−7.10814	+	12.3117i	−0.234476	+	0.406124i	0.724644	+	0.689123i	$0.242004\pi$
$920$	−5.67207	−	9.82431i	−0.187003	−	0.323898i
$921$	−3.86903	+	2.23378i	−0.127489	+	0.0736057i
$922$	−13.8311			−0.455503
$923$	−19.4567	−	32.5031i	−0.640426	−	1.06985i
$924$	21.5450			0.708777
$925$	35.9242	−	20.7408i	1.18118	−	0.681954i
$926$	−36.1990	−	62.6986i	−1.18957	−	2.06040i
$927$	−1.42886	+	2.47485i	−0.0469298	+	0.0812848i
$928$		−	1.25405i		−	0.0411662i
$929$	31.8850	+	18.4088i	1.04611	+	0.603973i	0.921558	−	0.388240i	$-0.126917\pi$
$929$	31.8850	+	18.4088i	1.04611	+	0.603973i	0.124553	+	0.992213i	$0.460250\pi$
$930$	−3.82474	−	2.20822i	−0.125418	−	0.0724102i
$931$			5.45980i			0.178938i
$932$	−10.4396	+	18.0820i	−0.341961	+	0.592295i
$933$	26.5769	+	46.0325i	0.870088	+	1.50704i
$934$	−71.7899	+	41.4479i	−2.34904	+	1.35622i
$935$	10.4618			0.342136
$936$	1.35490	+	2.26341i	0.0442864	+	0.0739820i
$937$	14.1542			0.462398			0.231199	−	0.972907i	$-0.425735\pi$
$937$	14.1542			0.462398			0.231199	+	0.972907i	$0.425735\pi$
$938$	28.5274	−	16.4703i	0.931454	−	0.537775i
$939$	−22.8285	−	39.5400i	−0.744978	−	1.29034i
$940$	12.5684	−	21.7692i	0.409938	−	0.710033i
$941$		−	42.0386i		−	1.37042i	−0.728346	−	0.685210i	$-0.759710\pi$
$941$		−	42.0386i		−	1.37042i	0.728346	−	0.685210i	$-0.240290\pi$
$942$	−12.7503	−	7.36141i	−0.415428	−	0.239848i
$943$	14.3566	+	8.28877i	0.467514	+	0.269919i
$944$			0.00425589i			0.000138518i
$945$	−9.40126	+	16.2835i	−0.305823	+	0.529701i
$946$	−8.09625	−	14.0231i	−0.263232	−	0.455931i
$947$	−13.6226	+	7.86501i	−0.442675	+	0.255579i	−0.704732	−	0.709474i	$-0.748933\pi$
$947$	−13.6226	+	7.86501i	−0.442675	+	0.255579i	0.262057	+	0.965053i	$0.415599\pi$
$948$	−26.8569			−0.872273
$949$	24.4842	−	43.9989i	0.794792	−	1.42826i
$950$	−23.4661			−0.761340
$951$	−45.6374	+	26.3488i	−1.47990	+	0.854418i
$952$	−28.2304	−	48.8965i	−0.914953	−	1.58474i
$953$	4.98311	−	8.63101i	0.161419	−	0.279586i	−0.773959	−	0.633236i	$-0.781726\pi$
$953$	4.98311	−	8.63101i	0.161419	−	0.279586i	0.935378	+	0.353650i	$0.115060\pi$
$954$			2.52127i			0.0816291i
$955$	15.2592	+	8.80992i	0.493777	+	0.285082i
$956$	45.4388	+	26.2341i	1.46960	+	0.848472i
$957$		−	0.493788i		−	0.0159619i
$958$	24.8443	−	43.0316i	0.802683	−	1.39029i
$959$	−16.1734	−	28.0132i	−0.522267	−	0.904592i
$960$	21.6340	−	12.4904i	0.698235	−	0.403126i
$961$	−1.00000			−0.0322581
$962$	−80.6471	+	48.2762i	−2.60017	+	1.55649i
$963$	−2.39753			−0.0772592
$964$	10.2734	−	5.93136i	0.330885	−	0.191036i
$965$	5.12114	+	8.87007i	0.164855	+	0.285538i
$966$	19.4810	−	33.7421i	0.626792	−	1.08564i
$967$		−	23.4245i		−	0.753282i	−0.926359	−	0.376641i	$-0.877079\pi$
$967$		−	23.4245i		−	0.753282i	0.926359	−	0.376641i	$-0.122921\pi$
$968$	−22.5235	−	13.0039i	−0.723932	−	0.417962i
$969$	26.9513	+	15.5603i	0.865801	+	0.499870i
$970$			12.7323i			0.408809i
$971$	−23.2109	+	40.2025i	−0.744874	+	1.29016i	0.205380	+	0.978682i	$0.434157\pi$
$971$	−23.2109	+	40.2025i	−0.744874	+	1.29016i	−0.950254	+	0.311477i	$0.899176\pi$
$972$	−4.33602	−	7.51021i	−0.139078	−	0.240890i
$973$	−15.2867	+	8.82577i	−0.490069	+	0.282941i
$974$	−27.5487			−0.882718
$975$	0.343411	+	21.7351i	0.0109980	+	0.696080i
$976$	0.0287970			0.000921770
$977$	4.05911	−	2.34353i	0.129862	−	0.0749761i	−0.433661	−	0.901076i	$-0.642779\pi$
$977$	4.05911	−	2.34353i	0.129862	−	0.0749761i	0.563524	+	0.826100i	$0.309445\pi$
$978$	−33.5415	−	58.0956i	−1.07254	−	1.85769i
$979$	−6.06134	+	10.4985i	−0.193721	+	0.335535i
$980$		−	7.31393i		−	0.233635i
$981$	−0.550142	−	0.317625i	−0.0175647	−	0.0101410i
$982$	7.78001	+	4.49179i	0.248270	+	0.143339i
$983$			12.3743i			0.394679i	0.980335	+	0.197339i	$0.0632301\pi$
$983$			12.3743i			0.394679i	−0.980335	+	0.197339i	$0.936770\pi$
$984$	11.2900	−	19.5549i	0.359913	−	0.623388i
$985$	12.7083	+	22.0115i	0.404921	+	0.701344i
$986$	−2.93329	+	1.69354i	−0.0934150	+	0.0539332i
$987$	32.9837			1.04988
$988$	32.8592	−	0.519169i	1.04539	−	0.0165170i
$989$	−18.0986			−0.575501
$990$	−0.803233	+	0.463747i	−0.0255284	+	0.0147388i
$991$	−1.68797	−	2.92365i	−0.0536201	−	0.0928727i	0.837970	−	0.545717i	$-0.183743\pi$
$991$	−1.68797	−	2.92365i	−0.0536201	−	0.0928727i	−0.891590	+	0.452844i	$0.850409\pi$
$992$	2.82733	−	4.89709i	0.0897679	−	0.155483i
$993$			26.8686i			0.852650i
$994$	−62.2508	−	35.9405i	−1.97448	−	1.13996i
$995$	−11.7659	−	6.79307i	−0.373005	−	0.215355i
$996$		−	17.3689i		−	0.550353i
$997$	5.32742	−	9.22736i	0.168721	−	0.292233i	−0.769249	−	0.638949i	$-0.779370\pi$
$997$	5.32742	−	9.22736i	0.168721	−	0.292233i	0.937970	+	0.346715i	$0.112703\pi$
$998$	5.22109	+	9.04320i	0.165271	+	0.286257i
$999$	53.2288	−	30.7317i	1.68408	−	0.972307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.5	✓	68
13.2	odd	12		5239.2.a.q.1.6		34
13.4	even	6	inner	403.2.r.a.342.5	yes	68
13.11	odd	12		5239.2.a.r.1.29		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.5	✓	68	1.1	even	1	trivial
403.2.r.a.342.5	yes	68	13.4	even	6	inner
5239.2.a.q.1.6		34	13.2	odd	12
5239.2.a.r.1.29		34	13.11	odd	12

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98176 + 1.14417i) q^{2} +(0.827863 + 1.43390i) q^{3} +(1.61825 - 2.80289i) q^{4} -1.16564i q^{5} +(-3.28125 - 1.89443i) q^{6} +(-2.58921 - 1.49488i) q^{7} +2.82952i q^{8} +(0.129286 - 0.223931i) q^{9} +O(q^{10})\)	\(q+(-1.98176 + 1.14417i) q^{2} +(0.827863 + 1.43390i) q^{3} +(1.61825 - 2.80289i) q^{4} -1.16564i q^{5} +(-3.28125 - 1.89443i) q^{6} +(-2.58921 - 1.49488i) q^{7} +2.82952i q^{8} +(0.129286 - 0.223931i) q^{9} +(1.33368 + 2.31001i) q^{10} +(-1.16460 + 0.672380i) q^{11} +5.35875 q^{12} +(3.15059 + 1.75322i) q^{13} +6.84160 q^{14} +(1.67141 - 0.964986i) q^{15} +(-0.000955288 - 0.00165461i) q^{16} +(3.33708 - 5.77999i) q^{17} +0.591702i q^{18} +(2.43890 + 1.40810i) q^{19} +(-3.26714 - 1.88629i) q^{20} -4.95023i q^{21} +(1.53863 - 2.66499i) q^{22} +(-1.71975 - 2.97870i) q^{23} +(-4.05725 + 2.34245i) q^{24} +3.64129 q^{25} +(-8.24969 + 0.130344i) q^{26} +5.39530 q^{27} +(-8.37998 + 4.83818i) q^{28} +(0.110886 + 0.192060i) q^{29} +(-2.20822 + 3.82474i) q^{30} +1.00000i q^{31} +(-4.89709 - 2.82733i) q^{32} +(-1.92825 - 1.11328i) q^{33} +15.2727i q^{34} +(-1.74249 + 3.01808i) q^{35} +(-0.418435 - 0.724751i) q^{36} +(9.86577 - 5.69600i) q^{37} -6.44443 q^{38} +(0.0943101 + 5.96906i) q^{39} +3.29819 q^{40} +(-4.17402 + 2.40987i) q^{41} +(5.66391 + 9.81018i) q^{42} +(2.63099 - 4.55700i) q^{43} +4.35231i q^{44} +(-0.261022 - 0.150701i) q^{45} +(6.81627 + 3.93538i) q^{46} +6.66306i q^{47} +(0.00158169 - 0.00273958i) q^{48} +(0.969355 + 1.67897i) q^{49} +(-7.21617 + 4.16626i) q^{50} +11.0506 q^{51} +(10.0125 - 5.99360i) q^{52} +4.26104 q^{53} +(-10.6922 + 6.17314i) q^{54} +(0.783750 + 1.35750i) q^{55} +(4.22980 - 7.32623i) q^{56} +4.66286i q^{57} +(-0.439499 - 0.253745i) q^{58} +(-1.92911 - 1.11377i) q^{59} -6.24635i q^{60} +(-7.53621 + 13.0531i) q^{61} +(-1.14417 - 1.98176i) q^{62} +(-0.669501 + 0.386536i) q^{63} +12.9436 q^{64} +(2.04362 - 3.67244i) q^{65} +5.09511 q^{66} +(4.16970 - 2.40738i) q^{67} +(-10.8004 - 18.7069i) q^{68} +(2.84744 - 4.93191i) q^{69} -7.97481i q^{70} +(-9.09887 - 5.25324i) q^{71} +(0.633616 + 0.365819i) q^{72} -13.9653i q^{73} +(-13.0344 + 22.5762i) q^{74} +(3.01449 + 5.22125i) q^{75} +(7.89350 - 4.55732i) q^{76} +4.02052 q^{77} +(-7.01651 - 11.7213i) q^{78} -5.01179 q^{79} +(-0.00192867 + 0.00111352i) q^{80} +(4.07871 + 7.06453i) q^{81} +(5.51461 - 9.55158i) q^{82} -3.24122i q^{83} +(-13.8749 - 8.01071i) q^{84} +(-6.73737 - 3.88982i) q^{85} +12.0412i q^{86} +(-0.183597 + 0.317999i) q^{87} +(-1.90251 - 3.29525i) q^{88} +(7.80700 - 4.50737i) q^{89} +0.689709 q^{90} +(-5.53669 - 9.24923i) q^{91} -11.1319 q^{92} +(-1.43390 + 0.827863i) q^{93} +(-7.62367 - 13.2046i) q^{94} +(1.64133 - 2.84287i) q^{95} -9.36258i q^{96} +(4.13384 + 2.38668i) q^{97} +(-3.84206 - 2.21821i) q^{98} +0.347719i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) \) 68 * q + 32 * q^4 - 34 * q^9	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

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