LMFDB - Embedded newform 882.2.f.l.589.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (of order $3$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			589.1
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	882.589
Dual form			882.2.f.l.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.71053 + 0.272169i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.880438 + 1.52496i) q^{5} +(1.09097 + 1.34528i) q^{6} +1.00000 q^{8} +(2.85185 - 0.931107i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.71053 + 0.272169i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.880438 + 1.52496i) q^{5} +(1.09097 + 1.34528i) q^{6} +1.00000 q^{8} +(2.85185 - 0.931107i) q^{9} +1.76088 q^{10} +(-3.06238 - 5.30420i) q^{11} +(0.619562 - 1.61745i) q^{12} +(-0.380438 + 0.658939i) q^{13} +(1.09097 - 2.84813i) q^{15} +(-0.500000 - 0.866025i) q^{16} +6.84213 q^{17} +(-2.23229 - 2.00422i) q^{18} -1.94282 q^{19} +(-0.880438 - 1.52496i) q^{20} +(-3.06238 + 5.30420i) q^{22} +(0.210533 - 0.364654i) q^{23} +(-1.71053 + 0.272169i) q^{24} +(0.949657 + 1.64485i) q^{25} +0.760877 q^{26} +(-4.62476 + 2.36887i) q^{27} +(0.732287 + 1.26836i) q^{29} +(-3.01204 + 0.479256i) q^{30} +(-3.85185 + 6.67160i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.68194 + 8.23953i) q^{33} +(-3.42107 - 5.92546i) q^{34} +(-0.619562 + 2.93533i) q^{36} -2.88564 q^{37} +(0.971410 + 1.68253i) q^{38} +(0.471410 - 1.23068i) q^{39} +(-0.880438 + 1.52496i) q^{40} +(-3.47141 + 6.01266i) q^{41} +(4.33009 + 7.49994i) q^{43} +6.12476 q^{44} +(-1.09097 + 5.16875i) q^{45} -0.421067 q^{46} +(-0.830095 - 1.43777i) q^{47} +(1.09097 + 1.34528i) q^{48} +(0.949657 - 1.64485i) q^{50} +(-11.7037 + 1.86221i) q^{51} +(-0.380438 - 0.658939i) q^{52} +0.225450 q^{53} +(4.36389 + 2.82073i) q^{54} +10.7850 q^{55} +(3.32326 - 0.528775i) q^{57} +(0.732287 - 1.26836i) q^{58} +(-0.993163 + 1.72021i) q^{59} +(1.92107 + 2.36887i) q^{60} +(5.17511 + 8.96355i) q^{61} +7.70370 q^{62} +1.00000 q^{64} +(-0.669905 - 1.16031i) q^{65} +(3.79467 - 9.90650i) q^{66} +(-3.39248 + 5.87594i) q^{67} +(-3.42107 + 5.92546i) q^{68} +(-0.260877 + 0.681054i) q^{69} +10.7850 q^{71} +(2.85185 - 0.931107i) q^{72} -0.306707 q^{73} +(1.44282 + 2.49904i) q^{74} +(-2.07210 - 2.55511i) q^{75} +(0.971410 - 1.68253i) q^{76} +(-1.30150 + 0.207087i) q^{78} +(6.72257 + 11.6438i) q^{79} +1.76088 q^{80} +(7.26608 - 5.31075i) q^{81} +6.94282 q^{82} +(-1.56238 - 2.70612i) q^{83} +(-6.02408 + 10.4340i) q^{85} +(4.33009 - 7.49994i) q^{86} +(-1.59781 - 1.97026i) q^{87} +(-3.06238 - 5.30420i) q^{88} -2.60301 q^{89} +(5.02175 - 1.63957i) q^{90} +(0.210533 + 0.364654i) q^{92} +(4.77292 - 12.4603i) q^{93} +(-0.830095 + 1.43777i) q^{94} +(1.71053 - 2.96273i) q^{95} +(0.619562 - 1.61745i) q^{96} +(-1.81806 - 3.14897i) q^{97} +(-13.6722 - 12.2754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^8 + 8 * q^9	$ 6 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{8} + 8 q^{9} + 10 q^{10} - q^{11} + 4 q^{12} - 2 q^{13} - 2 q^{15} - 3 q^{16} + 8 q^{17} - 4 q^{18} + 6 q^{19} - 5 q^{20} - q^{22} - 7 q^{23} - 2 q^{24} - 2 q^{25} + 4 q^{26} + 7 q^{27} - 5 q^{29} + 7 q^{30} - 14 q^{31} - 3 q^{32} + 23 q^{33} - 4 q^{34} - 4 q^{36} + 18 q^{37} - 3 q^{38} - 6 q^{39} - 5 q^{40} - 12 q^{41} + 18 q^{43} + 2 q^{44} + 2 q^{45} + 14 q^{46} + 3 q^{47} - 2 q^{48} - 2 q^{50} - 52 q^{51} - 2 q^{52} - 18 q^{53} - 8 q^{54} + 14 q^{55} + 2 q^{57} - 5 q^{58} + 4 q^{59} - 5 q^{60} + 4 q^{61} + 28 q^{62} + 6 q^{64} - 12 q^{65} - 4 q^{66} + 5 q^{67} - 4 q^{68} - q^{69} + 14 q^{71} + 8 q^{72} + 50 q^{73} - 9 q^{74} - 19 q^{75} - 3 q^{76} + 9 q^{78} + 7 q^{79} + 10 q^{80} + 8 q^{81} + 24 q^{82} + 8 q^{83} + 14 q^{85} + 18 q^{86} - 11 q^{87} - q^{88} + 18 q^{89} + 29 q^{90} - 7 q^{92} + 3 q^{93} + 3 q^{94} + 2 q^{95} + 4 q^{96} - 28 q^{97} - 41 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^8 + 8 * q^9 + 10 * q^10 - q^11 + 4 * q^12 - 2 * q^13 - 2 * q^15 - 3 * q^16 + 8 * q^17 - 4 * q^18 + 6 * q^19 - 5 * q^20 - q^22 - 7 * q^23 - 2 * q^24 - 2 * q^25 + 4 * q^26 + 7 * q^27 - 5 * q^29 + 7 * q^30 - 14 * q^31 - 3 * q^32 + 23 * q^33 - 4 * q^34 - 4 * q^36 + 18 * q^37 - 3 * q^38 - 6 * q^39 - 5 * q^40 - 12 * q^41 + 18 * q^43 + 2 * q^44 + 2 * q^45 + 14 * q^46 + 3 * q^47 - 2 * q^48 - 2 * q^50 - 52 * q^51 - 2 * q^52 - 18 * q^53 - 8 * q^54 + 14 * q^55 + 2 * q^57 - 5 * q^58 + 4 * q^59 - 5 * q^60 + 4 * q^61 + 28 * q^62 + 6 * q^64 - 12 * q^65 - 4 * q^66 + 5 * q^67 - 4 * q^68 - q^69 + 14 * q^71 + 8 * q^72 + 50 * q^73 - 9 * q^74 - 19 * q^75 - 3 * q^76 + 9 * q^78 + 7 * q^79 + 10 * q^80 + 8 * q^81 + 24 * q^82 + 8 * q^83 + 14 * q^85 + 18 * q^86 - 11 * q^87 - q^88 + 18 * q^89 + 29 * q^90 - 7 * q^92 + 3 * q^93 + 3 * q^94 + 2 * q^95 + 4 * q^96 - 28 * q^97 - 41 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.71053	+	0.272169i	−0.987577	+	0.157137i
$3$	−1.71053	+	0.272169i	−0.987577	+	0.157137i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.880438	+	1.52496i	−0.393744	+	0.681985i	−0.992940	−	0.118618i	$-0.962154\pi$
$5$	−0.880438	+	1.52496i	−0.393744	+	0.681985i	0.599196	+	0.800602i	$0.295487\pi$
$6$	1.09097	+	1.34528i	0.445387	+	0.549209i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	2.85185	−	0.931107i	0.950616	−	0.310369i
$10$	1.76088			0.556838
$11$	−3.06238	−	5.30420i	−0.923343	−	1.59928i	−0.794205	−	0.607650i	$-0.792112\pi$
$11$	−3.06238	−	5.30420i	−0.923343	−	1.59928i	−0.129138	−	0.991627i	$-0.541221\pi$
$12$	0.619562	−	1.61745i	0.178852	−	0.466917i
$13$	−0.380438	+	0.658939i	−0.105515	+	0.182757i	−0.913948	−	0.405831i	$-0.866982\pi$
$13$	−0.380438	+	0.658939i	−0.105515	+	0.182757i	0.808434	+	0.588587i	$0.200316\pi$
$14$		0			0
$15$	1.09097	−	2.84813i	0.281688	−	0.735384i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.84213			1.65946			0.829731	−	0.558164i	$-0.188494\pi$
$17$	6.84213			1.65946			0.829731	+	0.558164i	$0.188494\pi$
$18$	−2.23229	−	2.00422i	−0.526155	−	0.472399i
$19$	−1.94282			−0.445713			−0.222857	−	0.974851i	$-0.571538\pi$
$19$	−1.94282			−0.445713			−0.222857	+	0.974851i	$0.571538\pi$
$20$	−0.880438	−	1.52496i	−0.196872	−	0.340992i
$21$		0			0
$22$	−3.06238	+	5.30420i	−0.652902	+	1.13086i
$23$	0.210533	−	0.364654i	0.0438992	−	0.0760357i	−0.843241	−	0.537536i	$-0.819355\pi$
$23$	0.210533	−	0.364654i	0.0438992	−	0.0760357i	0.887140	+	0.461500i	$0.152689\pi$
$24$	−1.71053	+	0.272169i	−0.349161	+	0.0555562i
$25$	0.949657	+	1.64485i	0.189931	+	0.328971i
$26$	0.760877			0.149220
$27$	−4.62476	+	2.36887i	−0.890036	+	0.455890i
$28$		0			0
$29$	0.732287	+	1.26836i	0.135982	+	0.235528i	0.925972	−	0.377592i	$-0.123248\pi$
$29$	0.732287	+	1.26836i	0.135982	+	0.235528i	−0.789990	+	0.613120i	$0.789914\pi$
$30$	−3.01204	+	0.479256i	−0.549920	+	0.0874997i
$31$	−3.85185	+	6.67160i	−0.691812	+	1.19825i	0.279431	+	0.960166i	$0.409854\pi$
$31$	−3.85185	+	6.67160i	−0.691812	+	1.19825i	−0.971243	+	0.238088i	$0.923479\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	6.68194	+	8.23953i	1.16318	+	1.43432i
$34$	−3.42107	−	5.92546i	−0.586708	−	1.01621i
$35$		0			0
$36$	−0.619562	+	2.93533i	−0.103260	+	0.489221i
$37$	−2.88564			−0.474396			−0.237198	−	0.971461i	$-0.576229\pi$
$37$	−2.88564			−0.474396			−0.237198	+	0.971461i	$0.576229\pi$
$38$	0.971410	+	1.68253i	0.157584	+	0.272943i
$39$	0.471410	−	1.23068i	0.0754860	−	0.197066i
$40$	−0.880438	+	1.52496i	−0.139210	+	0.241118i
$41$	−3.47141	+	6.01266i	−0.542143	+	0.939020i	0.456638	+	0.889653i	$0.349054\pi$
$41$	−3.47141	+	6.01266i	−0.542143	+	0.939020i	−0.998781	+	0.0493667i	$0.984280\pi$
$42$		0			0
$43$	4.33009	+	7.49994i	0.660333	+	1.14373i	0.980528	+	0.196379i	$0.0629183\pi$
$43$	4.33009	+	7.49994i	0.660333	+	1.14373i	−0.320195	+	0.947352i	$0.603748\pi$
$44$	6.12476			0.923343
$45$	−1.09097	+	5.16875i	−0.162632	+	0.770512i
$46$	−0.421067			−0.0620829
$47$	−0.830095	−	1.43777i	−0.121082	−	0.209720i	0.799113	−	0.601181i	$-0.205303\pi$
$47$	−0.830095	−	1.43777i	−0.121082	−	0.209720i	−0.920195	+	0.391461i	$0.871970\pi$
$48$	1.09097	+	1.34528i	0.157468	+	0.194175i
$49$		0			0
$50$	0.949657	−	1.64485i	0.134302	−	0.232617i
$51$	−11.7037	+	1.86221i	−1.63885	+	0.260762i
$52$	−0.380438	−	0.658939i	−0.0527573	−	0.0913783i
$53$	0.225450			0.0309680			0.0154840	−	0.999880i	$-0.495071\pi$
$53$	0.225450			0.0309680			0.0154840	+	0.999880i	$0.495071\pi$
$54$	4.36389	+	2.82073i	0.593850	+	0.383852i
$55$	10.7850			1.45424
$56$		0			0
$57$	3.32326	−	0.528775i	0.440176	−	0.0700379i
$58$	0.732287	−	1.26836i	0.0961540	−	0.166544i
$59$	−0.993163	+	1.72021i	−0.129299	+	0.223952i	−0.923405	−	0.383827i	$-0.874606\pi$
$59$	−0.993163	+	1.72021i	−0.129299	+	0.223952i	0.794106	+	0.607779i	$0.207939\pi$
$60$	1.92107	+	2.36887i	0.248009	+	0.305820i
$61$	5.17511	+	8.96355i	0.662605	+	1.14766i	0.979929	+	0.199348i	$0.0638823\pi$
$61$	5.17511	+	8.96355i	0.662605	+	1.14766i	−0.317324	+	0.948317i	$0.602784\pi$
$62$	7.70370			0.978370
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.669905	−	1.16031i	−0.0830915	−	0.143919i
$66$	3.79467	−	9.90650i	0.467091	−	1.21941i
$67$	−3.39248	+	5.87594i	−0.414457	+	0.717861i	−0.995371	−	0.0961042i	$-0.969362\pi$
$67$	−3.39248	+	5.87594i	−0.414457	+	0.717861i	0.580914	+	0.813965i	$0.302695\pi$
$68$	−3.42107	+	5.92546i	−0.414865	+	0.718568i
$69$	−0.260877	+	0.681054i	−0.0314059	+	0.0819893i
$70$		0			0
$71$	10.7850			1.27994			0.639969	−	0.768401i	$-0.278947\pi$
$71$	10.7850			1.27994			0.639969	+	0.768401i	$0.278947\pi$
$72$	2.85185	−	0.931107i	0.336094	−	0.109732i
$73$	−0.306707			−0.0358973			−0.0179487	−	0.999839i	$-0.505714\pi$
$73$	−0.306707			−0.0358973			−0.0179487	+	0.999839i	$0.505714\pi$
$74$	1.44282	+	2.49904i	0.167724	+	0.290507i
$75$	−2.07210	−	2.55511i	−0.239265	−	0.295039i
$76$	0.971410	−	1.68253i	0.111428	−	0.193000i
$77$		0			0
$78$	−1.30150	+	0.207087i	−0.147366	+	0.0234480i
$79$	6.72257	+	11.6438i	0.756348	+	1.31003i	0.944701	+	0.327932i	$0.106352\pi$
$79$	6.72257	+	11.6438i	0.756348	+	1.31003i	−0.188353	+	0.982101i	$0.560315\pi$
$80$	1.76088			0.196872
$81$	7.26608	−	5.31075i	0.807342	−	0.590084i
$82$	6.94282			0.766706
$83$	−1.56238	−	2.70612i	−0.171494	−	0.297036i	0.767449	−	0.641110i	$-0.221526\pi$
$83$	−1.56238	−	2.70612i	−0.171494	−	0.297036i	−0.938942	+	0.344075i	$0.888193\pi$
$84$		0			0
$85$	−6.02408	+	10.4340i	−0.653403	+	1.13173i
$86$	4.33009	−	7.49994i	0.466926	−	0.808740i
$87$	−1.59781	−	1.97026i	−0.171303	−	0.211234i
$88$	−3.06238	−	5.30420i	−0.326451	−	0.565430i
$89$	−2.60301			−0.275919			−0.137959	−	0.990438i	$-0.544054\pi$
$89$	−2.60301			−0.275919			−0.137959	+	0.990438i	$0.544054\pi$
$90$	5.02175	−	1.63957i	0.529339	−	0.172825i
$91$		0			0
$92$	0.210533	+	0.364654i	0.0219496	+	0.0380178i
$93$	4.77292	−	12.4603i	0.494928	−	1.29208i
$94$	−0.830095	+	1.43777i	−0.0856178	+	0.148294i
$95$	1.71053	−	2.96273i	0.175497	−	0.303970i
$96$	0.619562	−	1.61745i	0.0632337	−	0.165080i
$97$	−1.81806	−	3.14897i	−0.184596	−	0.319729i	0.758845	−	0.651272i	$-0.225764\pi$
$97$	−1.81806	−	3.14897i	−0.184596	−	0.319729i	−0.943440	+	0.331543i	$0.892431\pi$
$98$		0			0
$99$	−13.6722	−	12.2754i	−1.37411	−	1.23372i
$100$	−1.89931			−0.189931
$101$	4.00520	+	6.93721i	0.398532	+	0.690278i	0.993545	−	0.113438i	$-0.0361863\pi$
$101$	4.00520	+	6.93721i	0.398532	+	0.690278i	−0.595013	+	0.803716i	$0.702853\pi$
$102$	7.46457	+	9.20459i	0.739103	+	0.911390i
$103$	3.41423	−	5.91362i	0.336414	−	0.582686i	−0.647341	−	0.762200i	$-0.724119\pi$
$103$	3.41423	−	5.91362i	0.336414	−	0.582686i	0.983755	+	0.179514i	$0.0574525\pi$
$104$	−0.380438	+	0.658939i	−0.0373051	+	0.0646142i
$105$		0			0
$106$	−0.112725	−	0.195246i	−0.0109488	−	0.0189639i
$107$	−3.54583			−0.342788			−0.171394	−	0.985203i	$-0.554827\pi$
$107$	−3.54583			−0.342788			−0.171394	+	0.985203i	$0.554827\pi$
$108$	0.260877	−	5.18960i	0.0251029	−	0.499369i
$109$	−0.703697			−0.0674019			−0.0337010	−	0.999432i	$-0.510729\pi$
$109$	−0.703697			−0.0674019			−0.0337010	+	0.999432i	$0.510729\pi$
$110$	−5.39248	−	9.34004i	−0.514152	−	0.890538i
$111$	4.93598	−	0.785381i	0.468503	−	0.0745451i
$112$		0			0
$113$	4.25116	−	7.36323i	0.399916	−	0.692674i	−0.593799	−	0.804613i	$-0.702373\pi$
$113$	4.25116	−	7.36323i	0.399916	−	0.692674i	0.993715	+	0.111939i	$0.0357061\pi$
$114$	−2.11956	−	2.61364i	−0.198515	−	0.244790i
$115$	0.370723	+	0.642111i	0.0345701	+	0.0598772i
$116$	−1.46457			−0.135982
$117$	−0.471410	+	2.23342i	−0.0435819	+	0.206480i
$118$	1.98633			0.182856
$119$		0			0
$120$	1.09097	−	2.84813i	0.0995916	−	0.259997i
$121$	−13.2564	+	22.9607i	−1.20512	+	2.08734i
$122$	5.17511	−	8.96355i	0.468532	−	0.811521i
$123$	4.30150	−	11.2297i	0.387854	−	1.01254i
$124$	−3.85185	−	6.67160i	−0.345906	−	0.599127i
$125$	−12.1488			−1.08663
$126$		0			0
$127$	−18.9532			−1.68183			−0.840913	−	0.541170i	$-0.817982\pi$
$127$	−18.9532			−1.68183			−0.840913	+	0.541170i	$0.817982\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−9.44802	−	11.6504i	−0.831852	−	1.02576i
$130$	−0.669905	+	1.16031i	−0.0587546	+	0.101766i
$131$	3.64652	−	6.31595i	0.318598	−	0.551827i	−0.661598	−	0.749859i	$-0.730121\pi$
$131$	3.64652	−	6.31595i	0.318598	−	0.551827i	0.980196	+	0.198031i	$0.0634548\pi$
$132$	−10.4766	+	1.66697i	−0.911872	+	0.145091i
$133$		0			0
$134$	6.78495			0.586131
$135$	0.459372	−	9.13825i	0.0395364	−	0.786495i
$136$	6.84213			0.586708
$137$	4.09097	+	7.08577i	0.349515	+	0.605378i	0.986163	−	0.165776i	$-0.0530129\pi$
$137$	4.09097	+	7.08577i	0.349515	+	0.605378i	−0.636648	+	0.771154i	$0.719680\pi$
$138$	0.720248	−	0.114601i	0.0613116	−	0.00975550i
$139$	−6.23229	+	10.7946i	−0.528616	+	0.915589i	0.470828	+	0.882225i	$0.343955\pi$
$139$	−6.23229	+	10.7946i	−0.528616	+	0.915589i	−0.999443	+	0.0333640i	$0.989378\pi$
$140$		0			0
$141$	1.81122	+	2.23342i	0.152532	+	0.188088i
$142$	−5.39248	−	9.34004i	−0.452527	−	0.783799i
$143$	4.66019			0.389705
$144$	−2.23229	−	2.00422i	−0.186024	−	0.167018i
$145$	−2.57893			−0.214169
$146$	0.153353	+	0.265616i	0.0126916	+	0.0219825i
$147$		0			0
$148$	1.44282	−	2.49904i	0.118599	−	0.205420i
$149$	−4.41423	+	7.64567i	−0.361628	+	0.626358i	−0.988229	−	0.152982i	$-0.951112\pi$
$149$	−4.41423	+	7.64567i	−0.361628	+	0.626358i	0.626601	+	0.779340i	$0.284446\pi$
$150$	−1.17674	+	3.07204i	−0.0960805	+	0.250831i
$151$	7.49316	+	12.9785i	0.609785	+	1.05618i	0.991276	+	0.131806i	$0.0420775\pi$
$151$	7.49316	+	12.9785i	0.609785	+	1.05618i	−0.381491	+	0.924373i	$0.624589\pi$
$152$	−1.94282			−0.157584
$153$	19.5127	−	6.37076i	1.57751	−	0.515045i
$154$		0			0
$155$	−6.78263	−	11.7479i	−0.544794	−	0.943611i
$156$	0.830095	+	1.02359i	0.0664608	+	0.0819530i
$157$	−9.49028	+	16.4377i	−0.757407	+	1.31187i	0.186761	+	0.982405i	$0.440201\pi$
$157$	−9.49028	+	16.4377i	−0.757407	+	1.31187i	−0.944169	+	0.329462i	$0.893132\pi$
$158$	6.72257	−	11.6438i	0.534819	−	0.926334i
$159$	−0.385640	+	0.0613605i	−0.0305833	+	0.00486620i
$160$	−0.880438	−	1.52496i	−0.0696048	−	0.120559i
$161$		0			0
$162$	−8.23229	−	3.63723i	−0.646790	−	0.285768i
$163$	15.0377			1.17785			0.588924	−	0.808189i	$-0.299552\pi$
$163$	15.0377			1.17785			0.588924	+	0.808189i	$0.299552\pi$
$164$	−3.47141	−	6.01266i	−0.271072	−	0.469510i
$165$	−18.4480	+	2.93533i	−1.43618	+	0.228515i
$166$	−1.56238	+	2.70612i	−0.121264	+	0.210036i
$167$	0.572097	−	0.990901i	0.0442702	−	0.0766782i	−0.843041	−	0.537849i	$-0.819237\pi$
$167$	0.572097	−	0.990901i	0.0442702	−	0.0766782i	0.887311	+	0.461171i	$0.152570\pi$
$168$		0			0
$169$	6.21053	+	10.7570i	0.477733	+	0.827458i
$170$	12.0482			0.924051
$171$	−5.54063	+	1.80897i	−0.423702	+	0.138336i
$172$	−8.66019			−0.660333
$173$	−0.248838	−	0.431001i	−0.0189188	−	0.0327684i	0.856411	−	0.516295i	$-0.172689\pi$
$173$	−0.248838	−	0.431001i	−0.0189188	−	0.0327684i	−0.875330	+	0.483526i	$0.839356\pi$
$174$	−0.907394	+	2.36887i	−0.0687893	+	0.179584i
$175$		0			0
$176$	−3.06238	+	5.30420i	−0.230836	+	0.399819i
$177$	1.23065	−	3.21278i	0.0925015	−	0.241488i
$178$	1.30150	+	2.25427i	0.0975519	+	0.168965i
$179$	−8.82846			−0.659870			−0.329935	−	0.944004i	$-0.607027\pi$
$179$	−8.82846			−0.659870			−0.329935	+	0.944004i	$0.607027\pi$
$180$	−3.93078	−	3.52918i	−0.292983	−	0.263050i
$181$	1.32941			0.0988140			0.0494070	−	0.998779i	$-0.484267\pi$
$181$	1.32941			0.0988140			0.0494070	+	0.998779i	$0.484267\pi$
$182$		0			0
$183$	−11.2918	−	13.9239i	−0.834713	−	1.02929i
$184$	0.210533	−	0.364654i	0.0155207	−	0.0268827i
$185$	2.54063	−	4.40050i	0.186791	−	0.323531i
$186$	−13.1774	+	2.09671i	−0.966216	+	0.153738i
$187$	−20.9532	−	36.2920i	−1.53225	−	2.65394i
$188$	1.66019			0.121082
$189$		0			0
$190$	−3.42107			−0.248190
$191$	8.08414	+	14.0021i	0.584947	+	1.01316i	0.994882	+	0.101044i	$0.0322182\pi$
$191$	8.08414	+	14.0021i	0.584947	+	1.01316i	−0.409934	+	0.912115i	$0.634448\pi$
$192$	−1.71053	+	0.272169i	−0.123447	+	0.0196421i
$193$	7.08414	−	12.2701i	0.509927	−	0.883220i	−0.490007	−	0.871719i	$-0.663006\pi$
$193$	7.08414	−	12.2701i	0.509927	−	0.883220i	0.999934	−	0.0115011i	$-0.00366101\pi$
$194$	−1.81806	+	3.14897i	−0.130529	+	0.226083i
$195$	1.46169	+	1.80242i	0.104674	+	0.129074i
$196$		0			0
$197$	15.8421			1.12871			0.564353	−	0.825534i	$-0.309126\pi$
$197$	15.8421			1.12871			0.564353	+	0.825534i	$0.309126\pi$
$198$	−3.79467	+	17.9782i	−0.269675	+	1.27765i
$199$	8.94282			0.633940			0.316970	−	0.948436i	$-0.397335\pi$
$199$	8.94282			0.633940			0.316970	+	0.948436i	$0.397335\pi$
$200$	0.949657	+	1.64485i	0.0671509	+	0.116309i
$201$	4.20370	−	10.9743i	0.296506	−	0.774069i
$202$	4.00520	−	6.93721i	0.281805	−	0.488101i
$203$		0			0
$204$	4.23912	−	11.0668i	0.296798	−	0.774831i
$205$	−6.11273	−	10.5876i	−0.426931	−	0.739467i
$206$	−6.82846			−0.475761
$207$	0.260877	−	1.23597i	0.0181322	−	0.0859057i
$208$	0.760877			0.0527573
$209$	5.94966	+	10.3051i	0.411546	+	0.712819i
$210$		0			0
$211$	11.3856	−	19.7205i	0.783820	−	1.35762i	−0.145882	−	0.989302i	$-0.546602\pi$
$211$	11.3856	−	19.7205i	0.783820	−	1.35762i	0.929702	−	0.368314i	$-0.120065\pi$
$212$	−0.112725	+	0.195246i	−0.00774199	+	0.0134095i
$213$	−18.4480	+	2.93533i	−1.26404	+	0.201125i
$214$	1.77292	+	3.07078i	0.121194	+	0.209914i
$215$	−15.2495			−1.04001
$216$	−4.62476	+	2.36887i	−0.314675	+	0.161181i
$217$		0			0
$218$	0.351848	+	0.609419i	0.0238302	+	0.0412751i
$219$	0.524632	−	0.0834760i	0.0354514	−	0.00564078i
$220$	−5.39248	+	9.34004i	−0.363561	+	0.629706i
$221$	−2.60301	+	4.50855i	−0.175097	+	0.303278i
$222$	−3.14815	−	3.88200i	−0.211290	−	0.260543i
$223$	−6.44282	−	11.1593i	−0.431443	−	0.747281i	0.565555	−	0.824711i	$-0.308662\pi$
$223$	−6.44282	−	11.1593i	−0.431443	−	0.747281i	−0.996998	+	0.0774293i	$0.975329\pi$
$224$		0			0
$225$	4.23981	+	3.80664i	0.282654	+	0.253776i
$226$	−8.50232			−0.565566
$227$	−10.9984	−	19.0497i	−0.729987	−	1.26437i	−0.956888	−	0.290457i	$-0.906193\pi$
$227$	−10.9984	−	19.0497i	−0.729987	−	1.26437i	0.226901	−	0.973918i	$-0.427141\pi$
$228$	−1.20370	+	3.14241i	−0.0797168	+	0.208111i
$229$	1.89931	−	3.28971i	0.125510	−	0.217390i	−0.796422	−	0.604741i	$-0.793277\pi$
$229$	1.89931	−	3.28971i	0.125510	−	0.217390i	0.921932	+	0.387351i	$0.126610\pi$
$230$	0.370723	−	0.642111i	0.0244448	−	0.0423396i
$231$		0			0
$232$	0.732287	+	1.26836i	0.0480770	+	0.0832718i
$233$	6.67059			0.437005			0.218503	−	0.975836i	$-0.429883\pi$
$233$	6.67059			0.437005			0.218503	+	0.975836i	$0.429883\pi$
$234$	2.16991	−	0.708458i	0.141851	−	0.0463133i
$235$	2.92339			0.190701
$236$	−0.993163	−	1.72021i	−0.0646494	−	0.111976i
$237$	−14.6683	−	18.0875i	−0.952807	−	1.17491i
$238$		0			0
$239$	−7.82038	+	13.5453i	−0.505858	+	0.876172i	0.494119	+	0.869394i	$0.335491\pi$
$239$	−7.82038	+	13.5453i	−0.505858	+	0.876172i	−0.999977	+	0.00677786i	$0.997843\pi$
$240$	−3.01204	+	0.479256i	−0.194426	+	0.0309358i
$241$	−10.7060	−	18.5434i	−0.689635	−	1.19448i	−0.971956	−	0.235163i	$-0.924437\pi$
$241$	−10.7060	−	18.5434i	−0.689635	−	1.19448i	0.282320	−	0.959320i	$-0.408896\pi$
$242$	26.5127			1.70430
$243$	−10.9834	+	11.0618i	−0.704589	+	0.709616i
$244$	−10.3502			−0.662605
$245$		0			0
$246$	−11.8759	+	1.88962i	−0.757181	+	0.120478i
$247$	0.739123	−	1.28020i	0.0470293	−	0.0814571i
$248$	−3.85185	+	6.67160i	−0.244593	+	0.423647i
$249$	3.40903	+	4.20368i	0.216038	+	0.266398i
$250$	6.07442	+	10.5212i	0.384180	+	0.665419i
$251$	−23.6030			−1.48981			−0.744904	−	0.667171i	$-0.767505\pi$
$251$	−23.6030			−1.48981			−0.744904	+	0.667171i	$0.767505\pi$
$252$		0			0
$253$	−2.57893			−0.162136
$254$	9.47661	+	16.4140i	0.594616	+	1.02990i
$255$	7.46457	−	19.4873i	0.467450	−	1.22034i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.1300	+	17.5456i	−0.631890	+	1.09447i	0.355275	+	0.934762i	$0.384387\pi$
$257$	−10.1300	+	17.5456i	−0.631890	+	1.09447i	−0.987165	+	0.159704i	$0.948946\pi$
$258$	−5.36552	+	14.0074i	−0.334043	+	0.872064i
$259$		0			0
$260$	1.33981			0.0830915
$261$	3.26935	+	2.93533i	0.202368	+	0.181692i
$262$	−7.29303			−0.450565
$263$	11.2443	+	19.4757i	0.693355	+	1.20093i	0.970732	+	0.240165i	$0.0772014\pi$
$263$	11.2443	+	19.4757i	0.693355	+	1.20093i	−0.277377	+	0.960761i	$0.589465\pi$
$264$	6.68194	+	8.23953i	0.411245	+	0.507108i
$265$	−0.198495	+	0.343803i	−0.0121935	+	0.0211197i
$266$		0			0
$267$	4.45254	−	0.708458i	0.272491	−	0.0433569i
$268$	−3.39248	−	5.87594i	−0.207228	−	0.358930i
$269$	25.3412			1.54508			0.772540	−	0.634966i	$-0.218986\pi$
$269$	25.3412			1.54508			0.772540	+	0.634966i	$0.218986\pi$
$270$	−8.14364	+	4.17129i	−0.495606	+	0.253857i
$271$	13.7576			0.835715			0.417858	−	0.908513i	$-0.362781\pi$
$271$	13.7576			0.835715			0.417858	+	0.908513i	$0.362781\pi$
$272$	−3.42107	−	5.92546i	−0.207433	−	0.359284i
$273$		0			0
$274$	4.09097	−	7.08577i	0.247145	−	0.428067i
$275$	5.81642	−	10.0743i	0.350743	−	0.607505i
$276$	−0.459372	−	0.566453i	−0.0276509	−	0.0340965i
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	0.911112	−	0.412158i	$-0.135225\pi$
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	−0.812495	+	0.582968i	$0.801891\pi$
$278$	12.4646			0.747575
$279$	−4.77292	+	22.6129i	−0.285747	+	1.35380i
$280$		0			0
$281$	0.634479	+	1.09895i	0.0378498	+	0.0655578i	0.884330	−	0.466863i	$-0.154616\pi$
$281$	0.634479	+	1.09895i	0.0378498	+	0.0655578i	−0.846480	+	0.532421i	$0.821282\pi$
$282$	1.02859	−	2.68527i	0.0612516	−	0.159906i
$283$	4.09617	−	7.09478i	0.243492	−	0.421741i	−0.718214	−	0.695822i	$-0.755040\pi$
$283$	4.09617	−	7.09478i	0.243492	−	0.421741i	0.961707	+	0.274081i	$0.0883736\pi$
$284$	−5.39248	+	9.34004i	−0.319985	+	0.554230i
$285$	−2.11956	+	5.53340i	−0.125552	+	0.327771i
$286$	−2.33009	−	4.03584i	−0.137781	−	0.238644i
$287$		0			0
$288$	−0.619562	+	2.93533i	−0.0365080	+	0.172966i
$289$	29.8148			1.75381
$290$	1.28947	+	2.23342i	0.0757201	+	0.131151i
$291$	3.96690	+	4.89159i	0.232544	+	0.286750i
$292$	0.153353	−	0.265616i	0.00897433	−	0.0155440i
$293$	7.72545	−	13.3809i	0.451326	−	0.781719i	−0.547143	−	0.837039i	$-0.684285\pi$
$293$	7.72545	−	13.3809i	0.451326	−	0.781719i	0.998469	+	0.0553202i	$0.0176180\pi$
$294$		0			0
$295$	−1.74884	−	3.02908i	−0.101821	−	0.176360i
$296$	−2.88564			−0.167724
$297$	26.7278	+	17.2763i	1.55090	+	1.00247i
$298$	8.82846			0.511419
$299$	0.160190	+	0.277457i	0.00926402	+	0.0160458i
$300$	3.24884	−	0.516934i	0.187572	−	0.0298452i
$301$		0			0
$302$	7.49316	−	12.9785i	0.431183	−	0.746831i
$303$	−8.73912	−	10.7762i	−0.502050	−	0.619079i
$304$	0.971410	+	1.68253i	0.0557142	+	0.0964998i
$305$	−18.2255			−1.04359
$306$	−15.2736	−	13.7131i	−0.873134	−	0.783928i
$307$	4.89931			0.279619			0.139809	−	0.990178i	$-0.455351\pi$
$307$	4.89931			0.279619			0.139809	+	0.990178i	$0.455351\pi$
$308$		0			0
$309$	−4.23065	+	11.0447i	−0.240673	+	0.628310i
$310$	−6.78263	+	11.7479i	−0.385228	+	0.667234i
$311$	3.84501	−	6.65976i	0.218031	−	0.377640i	−0.736175	−	0.676791i	$-0.763370\pi$
$311$	3.84501	−	6.65976i	0.218031	−	0.377640i	0.954206	+	0.299151i	$0.0967034\pi$
$312$	0.471410	−	1.23068i	0.0266883	−	0.0696735i
$313$	0.861564	+	1.49227i	0.0486985	+	0.0843482i	0.889347	−	0.457233i	$-0.151159\pi$
$313$	0.861564	+	1.49227i	0.0486985	+	0.0843482i	−0.840649	+	0.541581i	$0.817826\pi$
$314$	18.9806			1.07114
$315$		0			0
$316$	−13.4451			−0.756348
$317$	−16.6014	−	28.7544i	−0.932426	−	1.61501i	−0.779161	−	0.626824i	$-0.784354\pi$
$317$	−16.6014	−	28.7544i	−0.932426	−	1.61501i	−0.153266	−	0.988185i	$-0.548979\pi$
$318$	0.245960	+	0.303294i	0.0137927	+	0.0170079i
$319$	4.48508	−	7.76839i	0.251116	−	0.434946i
$320$	−0.880438	+	1.52496i	−0.0492180	+	0.0852481i
$321$	6.06526	−	0.965064i	0.338530	−	0.0538646i
$322$		0			0
$323$	−13.2930			−0.739644
$324$	0.966208	+	8.94799i	0.0536782	+	0.497110i
$325$	−1.44514			−0.0801621
$326$	−7.51887	−	13.0231i	−0.416432	−	0.721281i
$327$	1.20370	−	0.191524i	0.0665646	−	0.0105913i
$328$	−3.47141	+	6.01266i	−0.191677	+	0.331994i
$329$		0			0
$330$	11.7661	+	14.5088i	0.647701	+	0.798683i
$331$	−1.44445	−	2.50187i	−0.0793944	−	0.137515i	0.823594	−	0.567179i	$-0.191965\pi$
$331$	−1.44445	−	2.50187i	−0.0793944	−	0.137515i	−0.902989	+	0.429664i	$0.858632\pi$
$332$	3.12476			0.171494
$333$	−8.22941	+	2.68684i	−0.450969	+	0.147238i
$334$	−1.14419			−0.0626075
$335$	−5.97373	−	10.3468i	−0.326380	−	0.565307i
$336$		0			0
$337$	−4.36156	+	7.55445i	−0.237590	+	0.411517i	−0.960022	−	0.279924i	$-0.909691\pi$
$337$	−4.36156	+	7.55445i	−0.237590	+	0.411517i	0.722433	+	0.691441i	$0.243024\pi$
$338$	6.21053	−	10.7570i	0.337808	−	0.585101i
$339$	−5.26771	+	13.7521i	−0.286103	+	0.746910i
$340$	−6.02408	−	10.4340i	−0.326701	−	0.565863i
$341$	47.1833			2.55512
$342$	4.33693	+	3.89384i	0.234514	+	0.210555i
$343$		0			0
$344$	4.33009	+	7.49994i	0.233463	+	0.404370i
$345$	−0.808897	−	0.997454i	−0.0435496	−	0.0537011i
$346$	−0.248838	+	0.431001i	−0.0133776	+	0.0231707i
$347$	−4.84733	+	8.39583i	−0.260219	+	0.450712i	−0.966300	−	0.257419i	$-0.917128\pi$
$347$	−4.84733	+	8.39583i	−0.260219	+	0.450712i	0.706081	+	0.708131i	$0.250461\pi$
$348$	2.50520	−	0.398611i	0.134293	−	0.0213678i
$349$	14.1992	+	24.5937i	0.760065	+	1.31647i	0.942817	+	0.333312i	$0.108166\pi$
$349$	14.1992	+	24.5937i	0.760065	+	1.31647i	−0.182752	+	0.983159i	$0.558500\pi$
$350$		0			0
$351$	0.198495	−	3.94865i	0.0105949	−	0.210763i
$352$	6.12476			0.326451
$353$	2.19686	+	3.80507i	0.116927	+	0.202524i	0.918548	−	0.395308i	$-0.129362\pi$
$353$	2.19686	+	3.80507i	0.116927	+	0.202524i	−0.801621	+	0.597832i	$0.796029\pi$
$354$	−3.39768	+	0.540616i	−0.180585	+	0.0287334i
$355$	−9.49549	+	16.4467i	−0.503968	+	0.872898i
$356$	1.30150	−	2.25427i	0.0689796	−	0.119476i
$357$		0			0
$358$	4.41423	+	7.64567i	0.233299	+	0.404086i
$359$	−32.1592			−1.69730			−0.848650	−	0.528955i	$-0.822584\pi$
$359$	−32.1592			−1.69730			−0.848650	+	0.528955i	$0.822584\pi$
$360$	−1.09097	+	5.16875i	−0.0574993	+	0.272417i
$361$	−15.2255			−0.801339
$362$	−0.664703	−	1.15130i	−0.0349360	−	0.0605110i
$363$	16.4263	−	42.8830i	0.862155	−	2.25077i
$364$		0			0
$365$	0.270036	−	0.467717i	0.0141343	−	0.0244814i
$366$	−6.41260	+	16.7409i	−0.335192	+	0.875063i
$367$	−17.3015	−	29.9671i	−0.903131	−	1.56427i	−0.823406	−	0.567452i	$-0.807929\pi$
$367$	−17.3015	−	29.9671i	−0.903131	−	1.56427i	−0.0797249	−	0.996817i	$-0.525404\pi$
$368$	−0.421067			−0.0219496
$369$	−4.30150	+	20.3794i	−0.223927	+	1.06091i
$370$	−5.08126			−0.264162
$371$		0			0
$372$	8.40451	+	10.3636i	0.435754	+	0.537330i
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	−0.972404	−	0.233303i	$-0.925047\pi$
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	0.688248	+	0.725475i	$0.258380\pi$
$374$	−20.9532	+	36.2920i	−1.08347	+	1.87662i
$375$	20.7810	−	3.30653i	1.07313	−	0.170749i
$376$	−0.830095	−	1.43777i	−0.0428089	−	0.0741472i
$377$	−1.11436			−0.0573925
$378$		0			0
$379$	33.9877			1.74583			0.872916	−	0.487871i	$-0.162226\pi$
$379$	33.9877			1.74583			0.872916	+	0.487871i	$0.162226\pi$
$380$	1.71053	+	2.96273i	0.0877485	+	0.151985i
$381$	32.4201	−	5.15847i	1.66093	−	0.264277i
$382$	8.08414	−	14.0021i	0.413620	−	0.716411i
$383$	10.5120	−	18.2074i	0.537140	−	0.930354i	−0.461916	−	0.886923i	$-0.652838\pi$
$383$	10.5120	−	18.2074i	0.537140	−	0.930354i	0.999056	−	0.0434304i	$-0.0138287\pi$
$384$	1.09097	+	1.34528i	0.0556734	+	0.0686511i
$385$		0			0
$386$	−14.1683			−0.721146
$387$	19.3320	+	17.3569i	0.982702	+	0.882302i
$388$	3.63611			0.184596
$389$	−6.86909	−	11.8976i	−0.348277	−	0.603233i	0.637667	−	0.770312i	$-0.279900\pi$
$389$	−6.86909	−	11.8976i	−0.348277	−	0.603233i	−0.985943	+	0.167080i	$0.946566\pi$
$390$	0.830095	−	2.16708i	0.0420335	−	0.109734i
$391$	1.44050	−	2.49501i	0.0728491	−	0.126178i
$392$		0			0
$393$	−4.51848	+	11.7961i	−0.227927	+	0.595035i
$394$	−7.92107	−	13.7197i	−0.399058	−	0.691188i
$395$	−23.6752			−1.19123
$396$	17.4669	−	5.70281i	0.877745	−	0.286577i
$397$	7.15787			0.359243			0.179622	−	0.983736i	$-0.442513\pi$
$397$	7.15787			0.359243			0.179622	+	0.983736i	$0.442513\pi$
$398$	−4.47141	−	7.74471i	−0.224132	−	0.388207i
$399$		0			0
$400$	0.949657	−	1.64485i	0.0474828	−	0.0822427i
$401$	4.63968	−	8.03616i	0.231695	−	0.401307i	−0.726612	−	0.687048i	$-0.758906\pi$
$401$	4.63968	−	8.03616i	0.231695	−	0.401307i	0.958307	+	0.285741i	$0.0922397\pi$
$402$	−11.6059	+	1.84665i	−0.578849	+	0.0921026i
$403$	−2.93078	−	5.07626i	−0.145993	−	0.252867i
$404$	−8.01040			−0.398532
$405$	1.70137	+	15.7563i	0.0845419	+	0.782937i
$406$		0			0
$407$	8.83693	+	15.3060i	0.438030	+	0.758691i
$408$	−11.7037	+	1.86221i	−0.579419	+	0.0921934i
$409$	−7.58414	+	13.1361i	−0.375011	+	0.649539i	−0.990329	−	0.138741i	$-0.955695\pi$
$409$	−7.58414	+	13.1361i	−0.375011	+	0.649539i	0.615317	+	0.788279i	$0.289028\pi$
$410$	−6.11273	+	10.5876i	−0.301886	+	0.522882i
$411$	−8.92627	−	11.0070i	−0.440300	−	0.542936i
$412$	3.41423	+	5.91362i	0.168207	+	0.291343i
$413$		0			0
$414$	−1.20082	+	0.392058i	−0.0590170	+	0.0192686i
$415$	5.50232			0.270098
$416$	−0.380438	−	0.658939i	−0.0186525	−	0.0323071i
$417$	7.72257	−	20.1608i	0.378176	−	0.987280i
$418$	5.94966	−	10.3051i	0.291007	−	0.504039i
$419$	−4.16827	+	7.21966i	−0.203633	+	0.352703i	−0.949696	−	0.313172i	$-0.898608\pi$
$419$	−4.16827	+	7.21966i	−0.203633	+	0.352703i	0.746063	+	0.665875i	$0.231942\pi$
$420$		0			0
$421$	−3.50232	−	6.06620i	−0.170693	−	0.295649i	0.767969	−	0.640486i	$-0.221267\pi$
$421$	−3.50232	−	6.06620i	−0.170693	−	0.295649i	−0.938662	+	0.344838i	$0.887934\pi$
$422$	−22.7713			−1.10849
$423$	−3.70602	−	3.32738i	−0.180193	−	0.161783i
$424$	0.225450			0.0109488
$425$	6.49768	+	11.2543i	0.315184	+	0.545914i
$426$	11.7661	+	14.5088i	0.570068	+	0.702953i
$427$		0			0
$428$	1.77292	−	3.07078i	0.0856971	−	0.148432i
$429$	−7.97141	+	1.26836i	−0.384863	+	0.0612369i
$430$	7.62476	+	13.2065i	0.367699	+	0.636873i
$431$	3.45090			0.166224			0.0831120	−	0.996540i	$-0.473514\pi$
$431$	3.45090			0.166224			0.0831120	+	0.996540i	$0.473514\pi$
$432$	4.36389	+	2.82073i	0.209958	+	0.135712i
$433$	28.2599			1.35809			0.679043	−	0.734099i	$-0.262395\pi$
$433$	28.2599			1.35809			0.679043	+	0.734099i	$0.262395\pi$
$434$		0			0
$435$	4.41135	−	0.701905i	0.211508	−	0.0336538i
$436$	0.351848	−	0.609419i	0.0168505	−	0.0291859i
$437$	−0.409028	+	0.708458i	−0.0195665	+	0.0338901i
$438$	−0.334608	−	0.412607i	−0.0159882	−	0.0197151i
$439$	14.4480	+	25.0247i	0.689566	+	1.19436i	0.971978	+	0.235071i	$0.0755322\pi$
$439$	14.4480	+	25.0247i	0.689566	+	1.19436i	−0.282412	+	0.959293i	$0.591134\pi$
$440$	10.7850			0.514152
$441$		0			0
$442$	5.20602			0.247625
$443$	6.88044	+	11.9173i	0.326899	+	0.566207i	0.981895	−	0.189426i	$-0.0606628\pi$
$443$	6.88044	+	11.9173i	0.326899	+	0.566207i	−0.654995	+	0.755633i	$0.727329\pi$
$444$	−1.78783	+	4.66738i	−0.0848467	+	0.221504i
$445$	2.29179	−	3.96950i	0.108641	−	0.188172i
$446$	−6.44282	+	11.1593i	−0.305076	+	0.528408i
$447$	5.46978	−	14.2796i	0.258711	−	0.675401i
$448$		0			0
$449$	−20.2003			−0.953309			−0.476655	−	0.879091i	$-0.658151\pi$
$449$	−20.2003			−0.953309			−0.476655	+	0.879091i	$0.658151\pi$
$450$	1.17674	−	5.57510i	0.0554721	−	0.262813i
$451$	42.5231			2.00234
$452$	4.25116	+	7.36323i	0.199958	+	0.346337i
$453$	−16.3497	−	20.1608i	−0.768174	−	0.947238i
$454$	−10.9984	+	19.0497i	−0.516179	+	0.894048i
$455$		0			0
$456$	3.32326	−	0.528775i	0.155626	−	0.0247621i
$457$	−10.0149	−	17.3463i	−0.468478	−	0.811428i	0.530873	−	0.847451i	$-0.321864\pi$
$457$	−10.0149	−	17.3463i	−0.468478	−	0.811428i	−0.999351	+	0.0360237i	$0.988531\pi$
$458$	−3.79863			−0.177498
$459$	−31.6432	+	16.2082i	−1.47698	+	0.756532i
$460$	−0.741446			−0.0345701
$461$	5.97661	+	10.3518i	0.278359	+	0.482131i	0.970977	−	0.239173i	$-0.0768763\pi$
$461$	5.97661	+	10.3518i	0.278359	+	0.482131i	−0.692618	+	0.721304i	$0.743543\pi$
$462$		0			0
$463$	6.64527	−	11.5100i	0.308832	−	0.534913i	−0.669275	−	0.743015i	$-0.733395\pi$
$463$	6.64527	−	11.5100i	0.308832	−	0.534913i	0.978107	+	0.208102i	$0.0667286\pi$
$464$	0.732287	−	1.26836i	0.0339956	−	0.0588820i
$465$	14.7993	+	18.2491i	0.686302	+	0.846281i
$466$	−3.33530	−	5.77690i	−0.154505	−	0.267610i
$467$	11.2301			0.519667			0.259833	−	0.965653i	$-0.416332\pi$
$467$	11.2301			0.519667			0.259833	+	0.965653i	$0.416332\pi$
$468$	−1.69850	−	1.52496i	−0.0785130	−	0.0704915i
$469$		0			0
$470$	−1.46169	−	2.53173i	−0.0674230	−	0.116780i
$471$	11.7596	−	30.7001i	0.541855	−	1.41459i
$472$	−0.993163	+	1.72021i	−0.0457141	+	0.0791791i
$473$	26.5208	−	45.9354i	1.21943	−	2.11211i
$474$	−8.33009	+	21.7468i	−0.382614	+	0.998866i
$475$	−1.84501	−	3.19565i	−0.0846550	−	0.146627i
$476$		0			0
$477$	0.642950	−	0.209918i	0.0294387	−	0.00961150i
$478$	15.6408			0.715392
$479$	16.3135	+	28.2559i	0.745385	+	1.29104i	0.950015	+	0.312205i	$0.101068\pi$
$479$	16.3135	+	28.2559i	0.745385	+	1.29104i	−0.204630	+	0.978839i	$0.565599\pi$
$480$	1.92107	+	2.36887i	0.0876843	+	0.108124i
$481$	1.09781	−	1.90146i	0.0500557	−	0.0866991i
$482$	−10.7060	+	18.5434i	−0.487646	+	0.844627i
$483$		0			0
$484$	−13.2564	−	22.9607i	−0.602562	−	1.04367i
$485$	6.40275			0.290734
$486$	15.0715	+	3.98104i	0.683659	+	0.180583i
$487$	−3.69794			−0.167570			−0.0837848	−	0.996484i	$-0.526701\pi$
$487$	−3.69794			−0.167570			−0.0837848	+	0.996484i	$0.526701\pi$
$488$	5.17511	+	8.96355i	0.234266	+	0.405761i
$489$	−25.7226	+	4.09280i	−1.16321	+	0.185083i
$490$		0			0
$491$	−18.7804	+	32.5287i	−0.847549	+	1.46800i	0.0358393	+	0.999358i	$0.488590\pi$
$491$	−18.7804	+	32.5287i	−0.847549	+	1.46800i	−0.883389	+	0.468641i	$0.844744\pi$
$492$	7.57442	+	9.34004i	0.341481	+	0.421082i
$493$	5.01040	+	8.67827i	0.225657	+	0.390850i
$494$	−1.47825			−0.0665095
$495$	30.7571	−	10.0419i	1.38243	−	0.451352i
$496$	7.70370			0.345906
$497$		0			0
$498$	1.93598	−	5.05415i	0.0867535	−	0.226482i
$499$	15.8977	−	27.5356i	0.711678	−	1.23266i	−0.252549	−	0.967584i	$-0.581269\pi$
$499$	15.8977	−	27.5356i	0.711678	−	1.23266i	0.964227	−	0.265078i	$-0.0853977\pi$
$500$	6.07442	−	10.5212i	0.271656	−	0.470523i
$501$	−0.708899	+	1.85068i	−0.0316713	+	0.0826821i
$502$	11.8015	+	20.4408i	0.526727	+	0.912318i
$503$	30.8252			1.37443			0.687214	−	0.726455i	$-0.258834\pi$
$503$	30.8252			1.37443			0.687214	+	0.726455i	$0.258834\pi$
$504$		0			0
$505$	−14.1053			−0.627679
$506$	1.28947	+	2.23342i	0.0573238	+	0.0992877i
$507$	−13.5510	−	16.7098i	−0.601822	−	0.742109i
$508$	9.47661	−	16.4140i	0.420457	−	0.728252i
$509$	−4.00808	+	6.94220i	−0.177655	+	0.307708i	−0.941077	−	0.338193i	$-0.890184\pi$
$509$	−4.00808	+	6.94220i	−0.177655	+	0.307708i	0.763422	+	0.645900i	$0.223518\pi$
$510$	−20.6088	+	3.27913i	−0.912572	+	0.145202i
$511$		0			0
$512$	1.00000			0.0441942
$513$	8.98508	−	4.60230i	0.396701	−	0.203196i
$514$	20.2599			0.893627
$515$	6.01204	+	10.4132i	0.264922	+	0.458858i
$516$	14.8135	−	2.35703i	0.652130	−	0.103763i
$517$	−5.08414	+	8.80598i	−0.223600	+	0.387287i
$518$		0			0
$519$	0.542951	+	0.669515i	0.0238329	+	0.0293885i
$520$	−0.669905	−	1.16031i	−0.0293773	−	0.0508829i
$521$	−29.7292			−1.30246			−0.651229	−	0.758881i	$-0.725746\pi$
$521$	−29.7292			−1.30246			−0.651229	+	0.758881i	$0.725746\pi$
$522$	0.907394	−	4.29900i	0.0397155	−	0.188162i
$523$	−26.9396			−1.17798			−0.588992	−	0.808139i	$-0.700475\pi$
$523$	−26.9396			−1.17798			−0.588992	+	0.808139i	$0.700475\pi$
$524$	3.64652	+	6.31595i	0.159299	+	0.275914i
$525$		0			0
$526$	11.2443	−	19.4757i	0.490276	−	0.849183i
$527$	−26.3549	+	45.6480i	−1.14804	+	1.98846i
$528$	3.79467	−	9.90650i	0.165142	−	0.431125i
$529$	11.4114	+	19.7650i	0.496146	+	0.859350i
$530$	0.396990			0.0172441
$531$	−1.23065	+	5.83052i	−0.0534057	+	0.253023i
$532$		0			0
$533$	−2.64132	−	4.57489i	−0.114408	−	0.198161i
$534$	−2.83981	−	3.50178i	−0.122891	−	0.151537i
$535$	3.12188	−	5.40726i	0.134971	−	0.233776i
$536$	−3.39248	+	5.87594i	−0.146533	+	0.253802i
$537$	15.1014	−	2.40283i	0.651672	−	0.103690i
$538$	−12.6706	−	21.9461i	−0.546268	−	0.946164i
$539$		0			0
$540$	7.68427	+	4.96695i	0.330678	+	0.213744i
$541$	−14.3114			−0.615293			−0.307647	−	0.951501i	$-0.599541\pi$
$541$	−14.3114			−0.615293			−0.307647	+	0.951501i	$0.599541\pi$
$542$	−6.87880	−	11.9144i	−0.295470	−	0.511769i
$543$	−2.27399	+	0.361823i	−0.0975864	+	0.0155273i
$544$	−3.42107	+	5.92546i	−0.146677	+	0.254052i
$545$	0.619562	−	1.07311i	0.0265391	−	0.0459671i
$546$		0			0
$547$	1.02463	+	1.77471i	0.0438101	+	0.0758813i	0.887099	−	0.461579i	$-0.152717\pi$
$547$	1.02463	+	1.77471i	0.0438101	+	0.0758813i	−0.843289	+	0.537461i	$0.819384\pi$
$548$	−8.18194			−0.349515
$549$	23.1046	+	20.7441i	0.986082	+	0.885337i
$550$	−11.6328			−0.496026
$551$	−1.42270	−	2.46419i	−0.0606091	−	0.104978i
$552$	−0.260877	+	0.681054i	−0.0111037	+	0.0289876i
$553$		0			0
$554$	1.64132	−	2.84284i	0.0697328	−	0.120781i
$555$	−3.14815	+	8.21868i	−0.133632	+	0.348863i
$556$	−6.23229	−	10.7946i	−0.264308	−	0.457795i
$557$	−17.6868			−0.749412			−0.374706	−	0.927144i	$-0.622256\pi$
$557$	−17.6868			−0.749412			−0.374706	+	0.927144i	$0.622256\pi$
$558$	21.9698	−	7.17297i	0.930055	−	0.303656i
$559$	−6.58934			−0.278699
$560$		0			0
$561$	45.7187	+	56.3759i	1.93025	+	2.38019i
$562$	0.634479	−	1.09895i	0.0267639	−	0.0463564i
$563$	−0.468531	+	0.811520i	−0.0197462	+	0.0342015i	−0.875730	−	0.482802i	$-0.839619\pi$
$563$	−0.468531	+	0.811520i	−0.0197462	+	0.0342015i	0.855983	+	0.517003i	$0.172952\pi$
$564$	−2.83981	+	0.451852i	−0.119578	+	0.0190264i
$565$	7.48577	+	12.9657i	0.314929	+	0.545473i
$566$	−8.19235			−0.344350
$567$		0			0
$568$	10.7850			0.452527
$569$	−11.7632	−	20.3745i	−0.493139	−	0.854142i	0.506830	−	0.862046i	$-0.330817\pi$
$569$	−11.7632	−	20.3745i	−0.493139	−	0.854142i	−0.999969	+	0.00790437i	$0.997484\pi$
$570$	5.85185	−	0.931107i	0.245107	−	0.0389998i
$571$	0.242002	−	0.419160i	0.0101275	−	0.0175413i	−0.860917	−	0.508745i	$-0.830110\pi$
$571$	0.242002	−	0.419160i	0.0101275	−	0.0175413i	0.871045	+	0.491204i	$0.163443\pi$
$572$	−2.33009	+	4.03584i	−0.0974262	+	0.168747i
$573$	−17.6391	−	21.7509i	−0.736885	−	0.908655i
$574$		0			0
$575$	0.799737			0.0333514
$576$	2.85185	−	0.931107i	0.118827	−	0.0387961i
$577$	4.46130			0.185727			0.0928633	−	0.995679i	$-0.470398\pi$
$577$	4.46130			0.185727			0.0928633	+	0.995679i	$0.470398\pi$
$578$	−14.9074	−	25.8204i	−0.620066	−	1.07399i
$579$	−8.77812	+	22.9165i	−0.364806	+	0.952376i
$580$	1.28947	−	2.23342i	0.0535422	−	0.0927378i
$581$		0			0
$582$	2.25280	−	5.88123i	0.0933814	−	0.243785i
$583$	−0.690415	−	1.19583i	−0.0285941	−	0.0495264i
$584$	−0.306707			−0.0126916
$585$	−2.99084	−	2.68527i	−0.123656	−	0.111022i
$586$	−15.4509			−0.638271
$587$	8.31518	+	14.4023i	0.343204	+	0.594447i	0.985026	−	0.172407i	$-0.0551544\pi$
$587$	8.31518	+	14.4023i	0.343204	+	0.594447i	−0.641822	+	0.766854i	$0.721821\pi$
$588$		0			0
$589$	7.48345	−	12.9617i	0.308350	−	0.534078i
$590$	−1.74884	+	3.02908i	−0.0719985	+	0.124705i
$591$	−27.0985	+	4.31173i	−1.11468	+	0.177361i
$592$	1.44282	+	2.49904i	0.0592995	+	0.102710i
$593$	−41.5264			−1.70528			−0.852642	−	0.522495i	$-0.825001\pi$
$593$	−41.5264			−1.70528			−0.852642	+	0.522495i	$0.825001\pi$
$594$	1.59781	−	31.7851i	0.0655589	−	1.30416i
$595$		0			0
$596$	−4.41423	−	7.64567i	−0.180814	−	0.313179i
$597$	−15.2970	+	2.43396i	−0.626064	+	0.0996152i
$598$	0.160190	−	0.277457i	0.00655065	−	0.0113461i
$599$	−7.53831	+	13.0567i	−0.308007	+	0.533483i	−0.977926	−	0.208950i	$-0.932995\pi$
$599$	−7.53831	+	13.0567i	−0.308007	+	0.533483i	0.669919	+	0.742434i	$0.266329\pi$
$600$	−2.07210	−	2.55511i	−0.0845930	−	0.104312i
$601$	−8.05555	−	13.9526i	−0.328593	−	0.569139i	0.653640	−	0.756805i	$-0.273241\pi$
$601$	−8.05555	−	13.9526i	−0.328593	−	0.569139i	−0.982233	+	0.187666i	$0.939908\pi$
$602$		0			0
$603$	−4.20370	+	19.9161i	−0.171188	+	0.811044i
$604$	−14.9863			−0.609785
$605$	−23.3428	−	40.4310i	−0.949021	−	1.64375i
$606$	−4.96294	+	12.9564i	−0.201606	+	0.526319i
$607$	−9.78659	+	16.9509i	−0.397225	+	0.688014i	−0.993382	−	0.114853i	$-0.963360\pi$
$607$	−9.78659	+	16.9509i	−0.397225	+	0.688014i	0.596157	+	0.802868i	$0.296694\pi$
$608$	0.971410	−	1.68253i	0.0393959	−	0.0682357i
$609$		0			0
$610$	9.11273	+	15.7837i	0.368963	+	0.639063i
$611$	1.26320			0.0511036
$612$	−4.23912	+	20.0839i	−0.171356	+	0.811843i
$613$	5.55159			0.224226			0.112113	−	0.993695i	$-0.464238\pi$
$613$	5.55159			0.224226			0.112113	+	0.993695i	$0.464238\pi$
$614$	−2.44966	−	4.24293i	−0.0988601	−	0.171231i
$615$	13.3376	+	16.4467i	0.537825	+	0.663194i
$616$		0			0
$617$	0.634479	−	1.09895i	0.0255431	−	0.0442420i	−0.852971	−	0.521958i	$-0.825202\pi$
$617$	0.634479	−	1.09895i	0.0255431	−	0.0442420i	0.878514	+	0.477716i	$0.158535\pi$
$618$	11.6803	−	1.85849i	0.469851	−	0.0747596i
$619$	−2.25116	−	3.89913i	−0.0904818	−	0.156719i	0.817232	−	0.576309i	$-0.195507\pi$
$619$	−2.25116	−	3.89913i	−0.0904818	−	0.156719i	−0.907714	+	0.419589i	$0.862174\pi$
$620$	13.5653			0.544794
$621$	−0.109846	+	2.18517i	−0.00440799	+	0.0876877i
$622$	−7.69002			−0.308342
$623$		0			0
$624$	−1.30150	+	0.207087i	−0.0521019	+	0.00829011i
$625$	5.94802	−	10.3023i	0.237921	−	0.412091i
$626$	0.861564	−	1.49227i	0.0344350	−	0.0596432i
$627$	−12.9818	−	16.0079i	−0.518444	−	0.639295i
$628$	−9.49028	−	16.4377i	−0.378704	−	0.655934i
$629$	−19.7439			−0.787242
$630$		0			0
$631$	−1.69905			−0.0676381			−0.0338191	−	0.999428i	$-0.510767\pi$
$631$	−1.69905			−0.0676381			−0.0338191	+	0.999428i	$0.510767\pi$
$632$	6.72257	+	11.6438i	0.267410	+	0.463167i
$633$	−14.1082	+	36.8314i	−0.560751	+	1.46392i
$634$	−16.6014	+	28.7544i	−0.659325	+	1.14198i
$635$	16.6871	−	28.9030i	0.662209	−	1.14698i
$636$	0.139680	−	0.364654i	0.00553868	−	0.0144595i
$637$		0			0
$638$	−8.97017			−0.355132
$639$	30.7571	−	10.0419i	1.21673	−	0.397253i
$640$	1.76088			0.0696048
$641$	0.474289	+	0.821492i	0.0187333	+	0.0324470i	0.875240	−	0.483689i	$-0.160703\pi$
$641$	0.474289	+	0.821492i	0.0187333	+	0.0324470i	−0.856507	+	0.516136i	$0.827370\pi$
$642$	−3.86840	−	4.77014i	−0.152674	−	0.188262i
$643$	−9.84897	+	17.0589i	−0.388405	+	0.672738i	−0.992235	−	0.124375i	$-0.960307\pi$
$643$	−9.84897	+	17.0589i	−0.388405	+	0.672738i	0.603830	+	0.797113i	$0.293641\pi$
$644$		0			0
$645$	26.0848	−	4.15044i	1.02709	−	0.163424i
$646$	6.64652	+	11.5121i	0.261504	+	0.452938i
$647$	−23.4542			−0.922079			−0.461039	−	0.887380i	$-0.652523\pi$
$647$	−23.4542			−0.922079			−0.461039	+	0.887380i	$0.652523\pi$
$648$	7.26608	−	5.31075i	0.285439	−	0.208626i
$649$	12.1658			0.477549
$650$	0.722572	+	1.25153i	0.0283416	+	0.0490891i
$651$		0			0
$652$	−7.51887	+	13.0231i	−0.294462	+	0.510023i
$653$	−11.3954	+	19.7373i	−0.445935	+	0.772382i	−0.998117	−	0.0613420i	$-0.980462\pi$
$653$	−11.3954	+	19.7373i	−0.445935	+	0.772382i	0.552182	+	0.833724i	$0.313795\pi$
$654$	−0.767713	−	0.946670i	−0.0300200	−	0.0370177i
$655$	6.42107	+	11.1216i	0.250892	+	0.434557i
$656$	6.94282			0.271072
$657$	−0.874681	+	0.285577i	−0.0341246	+	0.0111414i
$658$		0			0
$659$	−13.2398	−	22.9320i	−0.515750	−	0.893305i	−0.999833	−	0.0182828i	$-0.994180\pi$
$659$	−13.2398	−	22.9320i	−0.515750	−	0.893305i	0.484083	−	0.875022i	$-0.339153\pi$
$660$	6.68194	−	17.4441i	0.260094	−	0.679011i
$661$	13.3691	−	23.1559i	0.519997	−	0.900662i	−0.479732	−	0.877415i	$-0.659266\pi$
$661$	13.3691	−	23.1559i	0.519997	−	0.900662i	0.999730	−	0.0232469i	$-0.00740038\pi$
$662$	−1.44445	+	2.50187i	−0.0561403	+	0.0972379i
$663$	3.22545	−	8.42048i	0.125266	−	0.327024i
$664$	−1.56238	−	2.70612i	−0.0606322	−	0.105018i
$665$		0			0
$666$	6.44158	+	5.78346i	0.249606	+	0.224104i
$667$	0.616683			0.0238781
$668$	0.572097	+	0.990901i	0.0221351	+	0.0383391i
$669$	14.0579	+	17.3348i	0.543509	+	0.670202i
$670$	−5.97373	+	10.3468i	−0.230785	+	0.399732i
$671$	31.6963	−	54.8996i	1.22362	−	2.11938i
$672$		0			0
$673$	−10.3856	−	17.9885i	−0.400337	−	0.693404i	0.593429	−	0.804886i	$-0.297774\pi$
$673$	−10.3856	−	17.9885i	−0.400337	−	0.693404i	−0.993766	+	0.111482i	$0.964440\pi$
$674$	8.72313			0.336002
$675$	−8.28839	−	5.35744i	−0.319020	−	0.206208i
$676$	−12.4211			−0.477733
$677$	10.3490	+	17.9249i	0.397743	+	0.688911i	0.993447	−	0.114293i	$-0.0364602\pi$
$677$	10.3490	+	17.9249i	0.397743	+	0.688911i	−0.595704	+	0.803204i	$0.703127\pi$
$678$	14.5435	−	2.31407i	0.558540	−	0.0888712i
$679$		0			0
$680$	−6.02408	+	10.4340i	−0.231013	+	0.400126i
$681$	23.9978	+	29.5918i	0.919598	+	1.13396i
$682$	−23.5917	−	40.8620i	−0.903371	−	1.56469i
$683$	−28.5836			−1.09372			−0.546860	−	0.837224i	$-0.684177\pi$
$683$	−28.5836			−1.09372			−0.546860	+	0.837224i	$0.684177\pi$
$684$	1.20370	−	5.70281i	0.0460245	−	0.218052i
$685$	−14.4074			−0.550478
$686$		0			0
$687$	−2.35348	+	6.14409i	−0.0897910	+	0.234412i
$688$	4.33009	−	7.49994i	0.165083	−	0.285933i
$689$	−0.0857699	+	0.148558i	−0.00326757	+	0.00565960i
$690$	−0.459372	+	1.19925i	−0.0174880	+	0.0456548i
$691$	3.34897	+	5.80059i	0.127401	+	0.220665i	0.922669	−	0.385593i	$-0.126003\pi$
$691$	3.34897	+	5.80059i	0.127401	+	0.220665i	−0.795268	+	0.606258i	$0.792670\pi$
$692$	0.497677			0.0189188
$693$		0			0
$694$	9.69467			0.368005
$695$	−10.9743	−	19.0080i	−0.416278	−	0.721016i
$696$	−1.59781	−	1.97026i	−0.0605648	−	0.0746826i
$697$	−23.7518	+	41.1394i	−0.899665	+	1.55827i
$698$	14.1992	−	24.5937i	0.537447	−	0.930886i
$699$	−11.4103	+	1.81553i	−0.431576	+	0.0686695i
$700$		0			0
$701$	−25.1442			−0.949683			−0.474842	−	0.880071i	$-0.657495\pi$
$701$	−25.1442			−0.949683			−0.474842	+	0.880071i	$0.657495\pi$
$702$	−3.51887	+	1.80242i	−0.132811	+	0.0680280i
$703$	5.60628			0.211445
$704$	−3.06238	−	5.30420i	−0.115418	−	0.199910i
$705$	−5.00056	+	0.795655i	−0.188332	+	0.0299661i
$706$	2.19686	−	3.80507i	0.0826799	−	0.143206i
$707$		0			0
$708$	2.16703	+	2.67217i	0.0814418	+	0.100426i
$709$	−4.43310	−	7.67836i	−0.166489	−	0.288367i	0.770694	−	0.637205i	$-0.219910\pi$
$709$	−4.43310	−	7.67836i	−0.166489	−	0.288367i	−0.937183	+	0.348838i	$0.886576\pi$
$710$	18.9910			0.712719
$711$	30.0134	+	26.9470i	1.12559	+	1.01059i
$712$	−2.60301			−0.0975519
$713$	1.62188	+	2.80919i	0.0607401	+	0.105205i
$714$		0			0
$715$	−4.10301	+	7.10662i	−0.153444	+	0.265773i
$716$	4.41423	−	7.64567i	0.164968	−	0.285732i
$717$	9.69041	−	25.2981i	0.361895	−	0.944776i
$718$	16.0796	+	27.8507i	0.600086	+	1.03938i
$719$	−23.6030			−0.880244			−0.440122	−	0.897938i	$-0.645065\pi$
$719$	−23.6030			−0.880244			−0.440122	+	0.897938i	$0.645065\pi$
$720$	5.02175	−	1.63957i	0.187150	−	0.0611030i
$721$		0			0
$722$	7.61273	+	13.1856i	0.283316	+	0.490718i
$723$	23.3599	+	28.8052i	0.868765	+	1.07128i
$724$	−0.664703	+	1.15130i	−0.0247035	+	0.0427877i
$725$	−1.39084	+	2.40901i	−0.0516546	+	0.0894683i
$726$	−45.3509	+	7.21593i	−1.68313	+	0.267808i
$727$	3.25692	+	5.64115i	0.120792	+	0.209219i	0.920080	−	0.391730i	$-0.128123\pi$
$727$	3.25692	+	5.64115i	0.120792	+	0.209219i	−0.799288	+	0.600948i	$0.794790\pi$
$728$		0			0
$729$	15.7769	−	21.9110i	0.584329	−	0.811517i
$730$	−0.540073			−0.0199890
$731$	29.6271	+	51.3156i	1.09580	+	1.89798i
$732$	17.7044	−	2.81700i	0.654373	−	0.104119i
$733$	11.5991	−	20.0901i	0.428421	−	0.742047i	−0.568312	−	0.822813i	$-0.692403\pi$
$733$	11.5991	−	20.0901i	0.428421	−	0.742047i	0.996733	+	0.0807664i	$0.0257368\pi$
$734$	−17.3015	+	29.9671i	−0.638610	+	1.10611i
$735$		0			0
$736$	0.210533	+	0.364654i	0.00776036	+	0.0134413i
$737$	41.5562			1.53074
$738$	19.7999	−	6.46451i	0.728843	−	0.237962i
$739$	15.1568			0.557550			0.278775	−	0.960356i	$-0.410072\pi$
$739$	15.1568			0.557550			0.278775	+	0.960356i	$0.410072\pi$
$740$	2.54063	+	4.40050i	0.0933954	+	0.161765i
$741$	−0.915865	+	2.39099i	−0.0336451	+	0.0878352i
$742$		0			0
$743$	−5.21737	+	9.03675i	−0.191407	+	0.331526i	−0.945717	−	0.324992i	$-0.894638\pi$
$743$	−5.21737	+	9.03675i	−0.191407	+	0.331526i	0.754310	+	0.656518i	$0.227972\pi$
$744$	4.77292	−	12.4603i	0.174984	−	0.456818i
$745$	−7.77292	−	13.4631i	−0.284778	−	0.493249i
$746$	10.9759			0.401857
$747$	−6.97537	−	6.26271i	−0.255215	−	0.229141i
$748$	41.9064			1.53225
$749$		0			0
$750$	−13.2540	−	16.3436i	−0.483969	−	0.596784i
$751$	−20.1059	+	34.8244i	−0.733674	+	1.27076i	0.221628	+	0.975131i	$0.428863\pi$
$751$	−20.1059	+	34.8244i	−0.733674	+	1.27076i	−0.955303	+	0.295630i	$0.904470\pi$
$752$	−0.830095	+	1.43777i	−0.0302704	+	0.0524300i
$753$	40.3737	−	6.42400i	1.47130	−	0.234104i
$754$	0.557180	+	0.965064i	0.0202913	+	0.0351456i
$755$	−26.3891			−0.960397
$756$		0			0
$757$	−21.5206			−0.782181			−0.391091	−	0.920352i	$-0.627902\pi$
$757$	−21.5206			−0.782181			−0.391091	+	0.920352i	$0.627902\pi$
$758$	−16.9939	−	29.4342i	−0.617244	−	1.06910i
$759$	4.41135	−	0.701905i	0.160122	−	0.0254775i
$760$	1.71053	−	2.96273i	0.0620476	−	0.107470i
$761$	11.8313	−	20.4925i	0.428886	−	0.742852i	−0.567889	−	0.823105i	$-0.692240\pi$
$761$	11.8313	−	20.4925i	0.428886	−	0.742852i	0.996774	+	0.0802535i	$0.0255730\pi$
$762$	−20.6774	−	25.4974i	−0.749064	−	0.923674i
$763$		0			0
$764$	−16.1683			−0.584947
$765$	−7.46457	+	35.3653i	−0.269882	+	1.27863i
$766$	−21.0241			−0.759631
$767$	−0.755675	−	1.30887i	−0.0272858	−	0.0472605i
$768$	0.619562	−	1.61745i	0.0223565	−	0.0583647i
$769$	−5.62764	+	9.74736i	−0.202938	+	0.351499i	−0.949474	−	0.313846i	$-0.898382\pi$
$769$	−5.62764	+	9.74736i	−0.202938	+	0.351499i	0.746536	+	0.665345i	$0.231716\pi$
$770$		0			0
$771$	12.5523	−	32.7694i	0.452059	−	1.18016i
$772$	7.08414	+	12.2701i	0.254964	+	0.441610i
$773$	−0.277984			−0.00999839			−0.00499919	−	0.999988i	$-0.501591\pi$
$773$	−0.277984			−0.00999839			−0.00499919	+	0.999988i	$0.501591\pi$
$774$	5.36552	−	25.4205i	0.192860	−	0.913721i
$775$	−14.6317			−0.525587
$776$	−1.81806	−	3.14897i	−0.0652644	−	0.113041i
$777$		0			0
$778$	−6.86909	+	11.8976i	−0.246269	+	0.426550i
$779$	6.74433	−	11.6815i	0.241641	−	0.418534i
$780$	−2.29179	+	0.364654i	−0.0820592	+	0.0130567i
$781$	−33.0276	−	57.2056i	−1.18182	−	2.04698i
$782$	−2.88099			−0.103024
$783$	−6.39123	−	4.13116i	−0.228404	−	0.147636i
$784$		0			0
$785$	−16.7112	−	28.9447i	−0.596449	−	1.03308i
$786$	12.4750	−	1.98494i	0.444968	−	0.0708003i
$787$	14.6940	−	25.4507i	0.523784	−	0.907220i	−0.475833	−	0.879536i	$-0.657853\pi$
$787$	14.6940	−	25.4507i	0.523784	−	0.907220i	0.999617	−	0.0276845i	$-0.00881339\pi$
$788$	−7.92107	+	13.7197i	−0.282176	+	0.488744i
$789$	−24.5345	−	30.2536i	−0.873451	−	1.07705i
$790$	11.8376	+	20.5034i	0.421164	+	0.729477i
$791$		0			0
$792$	−13.6722	−	12.2754i	−0.485821	−	0.436186i
$793$	−7.87524			−0.279658
$794$	−3.57893	−	6.19889i	−0.127012	−	0.219991i
$795$	0.245960	−	0.642111i	0.00872330	−	0.0227733i
$796$	−4.47141	+	7.74471i	−0.158485	+	0.274504i
$797$	0.433105	−	0.750160i	0.0153414	−	0.0265720i	−0.858253	−	0.513227i	$-0.828450\pi$
$797$	0.433105	−	0.750160i	0.0153414	−	0.0265720i	0.873594	+	0.486655i	$0.161783\pi$
$798$		0			0
$799$	−5.67962	−	9.83739i	−0.200931	−	0.348022i
$800$	−1.89931			−0.0671509
$801$	−7.42339	+	2.42368i	−0.262293	+	0.0856366i
$802$	−9.27936			−0.327666
$803$	0.939253	+	1.62683i	0.0331455	+	0.0574097i
$804$	7.40219	+	9.12767i	0.261055	+	0.321908i
$805$		0			0
$806$	−2.93078	+	5.07626i	−0.103232	+	0.178804i
$807$	−43.3469	+	6.89708i	−1.52588	+	0.242789i
$808$	4.00520	+	6.93721i	0.140903	+	0.244050i
$809$	−19.3341			−0.679749			−0.339875	−	0.940471i	$-0.610385\pi$
$809$	−19.3341			−0.679749			−0.339875	+	0.940471i	$0.610385\pi$
$810$	12.7947	−	9.35158i	0.449559	−	0.328581i
$811$	−47.0391			−1.65177			−0.825884	−	0.563841i	$-0.809323\pi$
$811$	−47.0391			−1.65177			−0.825884	+	0.563841i	$0.809323\pi$
$812$		0			0
$813$	−23.5328	+	3.74439i	−0.825333	+	0.131321i
$814$	8.83693	−	15.3060i	0.309734	−	0.536476i
$815$	−13.2398	+	22.9320i	−0.463770	+	0.803274i
$816$	7.46457	+	9.20459i	0.261312	+	0.322225i
$817$	−8.41260	−	14.5710i	−0.294319	−	0.509776i
$818$	15.1683			0.530346
$819$		0			0
$820$	12.2255			0.426931
$821$	−0.705332	−	1.22167i	−0.0246162	−	0.0426366i	0.853455	−	0.521167i	$-0.174503\pi$
$821$	−0.705332	−	1.22167i	−0.0246162	−	0.0426366i	−0.878071	+	0.478530i	$0.841170\pi$
$822$	−5.06922	+	13.2339i	−0.176809	+	0.461585i
$823$	17.5196	−	30.3448i	0.610694	−	1.05775i	−0.380430	−	0.924810i	$-0.624224\pi$
$823$	17.5196	−	30.3448i	0.610694	−	1.05775i	0.991124	−	0.132943i	$-0.0424426\pi$
$824$	3.41423	−	5.91362i	0.118940	−	0.206011i
$825$	−7.20726	+	18.8155i	−0.250925	+	0.655073i
$826$		0			0
$827$	−18.5997			−0.646776			−0.323388	−	0.946266i	$-0.604822\pi$
$827$	−18.5997			−0.646776			−0.323388	+	0.946266i	$0.604822\pi$
$828$	0.939941	+	0.843910i	0.0326652	+	0.0293279i
$829$	−38.1696			−1.32569			−0.662843	−	0.748758i	$-0.730650\pi$
$829$	−38.1696			−1.32569			−0.662843	+	0.748758i	$0.730650\pi$
$830$	−2.75116	−	4.76515i	−0.0954942	−	0.165401i
$831$	−3.58126	−	4.41606i	−0.124232	−	0.153191i
$832$	−0.380438	+	0.658939i	−0.0131893	+	0.0228446i
$833$		0			0
$834$	−21.3211	+	3.39247i	−0.738288	+	0.117472i
$835$	1.00739	+	1.74485i	0.0348622	+	0.0603832i
$836$	−11.8993			−0.411546
$837$	2.00972	−	39.9791i	0.0694659	−	1.38188i
$838$	8.33654			0.287981
$839$	17.3691	+	30.0841i	0.599648	+	1.03862i	0.992873	+	0.119178i	$0.0380259\pi$
$839$	17.3691	+	30.0841i	0.599648	+	1.03862i	−0.393225	+	0.919442i	$0.628641\pi$
$840$		0			0
$841$	13.4275	−	23.2571i	0.463018	−	0.801970i
$842$	−3.50232	+	6.06620i	−0.120698	+	0.209055i
$843$	−1.38440	−	1.70710i	−0.0476811	−	0.0587958i
$844$	11.3856	+	19.7205i	0.391910	+	0.678808i
$845$	−21.8720			−0.752419
$846$	−1.02859	+	4.87320i	−0.0353637	+	0.167544i
$847$		0			0
$848$	−0.112725	−	0.195246i	−0.00387100	−	0.00670476i
$849$	−5.07566	+	13.2507i	−0.174196	+	0.454763i
$850$	6.49768	−	11.2543i	0.222868	−	0.386020i
$851$	−0.607523	+	1.05226i	−0.0208256	+	0.0360711i
$852$	6.68194	−	17.4441i	0.228920	−	0.597626i
$853$	−21.1586	−	36.6477i	−0.724455	−	1.25479i	−0.959198	−	0.282736i	$-0.908758\pi$
$853$	−21.1586	−	36.6477i	−0.724455	−	1.25479i	0.234743	−	0.972058i	$-0.424575\pi$
$854$		0			0
$855$	2.11956	−	10.0419i	0.0724875	−	0.343427i
$856$	−3.54583			−0.121194
$857$	−7.46169	−	12.9240i	−0.254887	−	0.441477i	0.709978	−	0.704224i	$-0.248705\pi$
$857$	−7.46169	−	12.9240i	−0.254887	−	0.441477i	−0.964865	+	0.262747i	$0.915371\pi$
$858$	5.08414	+	6.26926i	0.173570	+	0.214029i
$859$	−9.70658	+	16.8123i	−0.331184	+	0.573628i	−0.982744	−	0.184969i	$-0.940781\pi$
$859$	−9.70658	+	16.8123i	−0.331184	+	0.573628i	0.651560	+	0.758597i	$0.274115\pi$
$860$	7.62476	−	13.2065i	0.260002	−	0.450337i
$861$		0			0
$862$	−1.72545	−	2.98857i	−0.0587691	−	0.101791i
$863$	1.08453			0.0369177			0.0184588	−	0.999830i	$-0.494124\pi$
$863$	1.08453			0.0369177			0.0184588	+	0.999830i	$0.494124\pi$
$864$	0.260877	−	5.18960i	0.00887521	−	0.176554i
$865$	0.876348			0.0297967
$866$	−14.1300	−	24.4738i	−0.480156	−	0.831654i
$867$	−50.9992	+	8.11465i	−1.73202	+	0.275588i
$868$		0			0
$869$	41.1742	−	71.3157i	1.39674	−	2.41922i
$870$	−2.81354	−	3.46939i	−0.0953880	−	0.117623i
$871$	−2.58126	−	4.47087i	−0.0874625	−	0.151490i
$872$	−0.703697			−0.0238302
$873$	−8.11685	−	7.28757i	−0.274714	−	0.246647i
$874$	0.818057			0.0276712
$875$		0			0
$876$	−0.190024	+	0.496083i	−0.00642031	+	0.0167611i
$877$	14.2850	−	24.7423i	0.482369	−	0.835487i	−0.517427	−	0.855728i	$-0.673110\pi$
$877$	14.2850	−	24.7423i	0.482369	−	0.835487i	0.999795	+	0.0202407i	$0.00644326\pi$
$878$	14.4480	−	25.0247i	0.487597	−	0.844543i
$879$	−9.57279	+	24.9911i	−0.322882	+	0.842927i
$880$	−5.39248	−	9.34004i	−0.181780	−	0.314853i
$881$	45.9967			1.54967			0.774835	−	0.632164i	$-0.217833\pi$
$881$	45.9967			1.54967			0.774835	+	0.632164i	$0.217833\pi$
$882$		0			0
$883$	32.9384			1.10847			0.554233	−	0.832361i	$-0.313012\pi$
$883$	32.9384			1.10847			0.554233	+	0.832361i	$0.313012\pi$
$884$	−2.60301	−	4.50855i	−0.0875487	−	0.151639i
$885$	3.81587	+	4.70536i	0.128269	+	0.158169i
$886$	6.88044	−	11.9173i	0.231153	−	0.400368i
$887$	14.1699	−	24.5430i	0.475779	−	0.824073i	−0.523836	−	0.851819i	$-0.675500\pi$
$887$	14.1699	−	24.5430i	0.475779	−	0.824073i	0.999615	+	0.0277459i	$0.00883293\pi$
$888$	4.93598	−	0.785381i	0.165641	−	0.0263557i
$889$		0			0
$890$	−4.58358			−0.153642
$891$	−50.4208	−	22.2772i	−1.68916	−	0.746314i
$892$	12.8856			0.431443
$893$	1.61273	+	2.79332i	0.0539678	+	0.0934750i
$894$	−15.1014	+	2.40283i	−0.505066	+	0.0803627i
$895$	7.77292	−	13.4631i	0.259820	−	0.450021i
$896$		0			0
$897$	−0.349525	−	0.431001i	−0.0116703	−	0.0143907i
$898$	10.1001	+	17.4939i	0.337046	+	0.583780i
$899$	−11.2826			−0.376297
$900$	−5.41655	+	1.76846i	−0.180552	+	0.0589488i
$901$	1.54256			0.0513901
$902$	−21.2616	−	36.8261i	−0.707933	−	1.22618i
$903$		0			0
$904$	4.25116	−	7.36323i	0.141392	−	0.244897i
$905$	−1.17046	+	2.02730i	−0.0389074	+	0.0673896i
$906$	−9.28495	+	24.2396i	−0.308472	+	0.805308i
$907$	−3.97373	−	6.88271i	−0.131946	−	0.228537i	0.792481	−	0.609897i	$-0.208789\pi$
$907$	−3.97373	−	6.88271i	−0.131946	−	0.228537i	−0.924427	+	0.381360i	$0.875456\pi$
$908$	21.9967			0.729987
$909$	17.8815	+	16.0546i	0.593093	+	0.532498i
$910$		0			0
$911$	−4.00808	−	6.94220i	−0.132794	−	0.230005i	0.791959	−	0.610575i	$-0.209061\pi$
$911$	−4.00808	−	6.94220i	−0.132794	−	0.230005i	−0.924752	+	0.380569i	$0.875728\pi$
$912$	−2.11956	−	2.61364i	−0.0701857	−	0.0865462i
$913$	−9.56922	+	16.5744i	−0.316695	+	0.548532i
$914$	−10.0149	+	17.3463i	−0.331264	+	0.573766i
$915$	31.1752	−	4.96040i	1.03062	−	0.163986i
$916$	1.89931	+	3.28971i	0.0627551	+	0.108695i
$917$		0			0
$918$	29.8583	+	19.2998i	0.985471	+	0.636988i
$919$	24.0449			0.793168			0.396584	−	0.917999i	$-0.370196\pi$
$919$	24.0449			0.793168			0.396584	+	0.917999i	$0.370196\pi$
$920$	0.370723	+	0.642111i	0.0122224	+	0.0211698i
$921$	−8.38044	+	1.33344i	−0.276145	+	0.0439383i
$922$	5.97661	−	10.3518i	0.196829	−	0.340918i
$923$	−4.10301	+	7.10662i	−0.135052	+	0.233917i
$924$		0			0
$925$	−2.74037	−	4.74646i	−0.0901027	−	0.156062i
$926$	−13.2905			−0.436754
$927$	4.23065	−	20.0438i	0.138953	−	0.658324i
$928$	−1.46457			−0.0480770
$929$	−13.9331	−	24.1328i	−0.457130	−	0.791773i	0.541678	−	0.840586i	$-0.317789\pi$
$929$	−13.9331	−	24.1328i	−0.457130	−	0.791773i	−0.998808	+	0.0488134i	$0.984456\pi$
$930$	8.40451	−	21.9411i	0.275595	−	0.719478i
$931$		0			0
$932$	−3.33530	+	5.77690i	−0.109251	+	0.189229i
$933$	−4.76444	+	12.4382i	−0.155981	+	0.407209i
$934$	−5.61505	−	9.72555i	−0.183730	−	0.318230i
$935$	73.7921			2.41326
$936$	−0.471410	+	2.23342i	−0.0154085	+	0.0730017i
$937$	53.2211			1.73866			0.869328	−	0.494235i	$-0.164552\pi$
$937$	53.2211			1.73866			0.869328	+	0.494235i	$0.164552\pi$
$938$		0			0
$939$	−1.87988	−	2.31809i	−0.0613477	−	0.0756480i
$940$	−1.46169	+	2.53173i	−0.0476752	+	0.0825759i
$941$	15.0241	−	26.0225i	0.489771	−	0.848308i	−0.510160	−	0.860080i	$-0.670414\pi$
$941$	15.0241	−	26.0225i	0.489771	−	0.848308i	0.999931	+	0.0117715i	$0.00374709\pi$
$942$	−32.4669	+	5.16592i	−1.05783	+	0.168315i
$943$	1.46169	+	2.53173i	0.0475993	+	0.0824445i
$944$	1.98633			0.0646494
$945$		0			0
$946$	−53.0416			−1.72453
$947$	19.8445	+	34.3716i	0.644858	+	1.11693i	0.984334	+	0.176312i	$0.0564169\pi$
$947$	19.8445	+	34.3716i	0.644858	+	1.11693i	−0.339476	+	0.940615i	$0.610250\pi$
$948$	22.9984	−	3.65935i	0.746952	−	0.118850i
$949$	0.116683	−	0.202101i	0.00378769	−	0.00656047i
$950$	−1.84501	+	3.19565i	−0.0598601	+	0.103681i
$951$	36.2233	+	44.6670i	1.17462	+	1.44843i
$952$		0			0
$953$	23.0643			0.747126			0.373563	−	0.927605i	$-0.378136\pi$
$953$	23.0643			0.747126			0.373563	+	0.927605i	$0.378136\pi$
$954$	−0.503270	−	0.451852i	−0.0162940	−	0.0146292i
$955$	−28.4703			−0.921278
$956$	−7.82038	−	13.5453i	−0.252929	−	0.438086i
$957$	−5.55757	+	14.5088i	−0.179651	+	0.469003i
$958$	16.3135	−	28.2559i	0.527067	−	0.912906i
$959$		0			0
$960$	1.09097	−	2.84813i	0.0352110	−	0.0919230i
$961$	−14.1735	−	24.5492i	−0.457209	−	0.791909i
$962$	−2.19562			−0.0707895
$963$	−10.1122	+	3.30155i	−0.325860	+	0.106391i
$964$	21.4120			0.689635
$965$	12.4743	+	21.6061i	0.401562	+	0.695525i
$966$		0			0
$967$	15.2902	−	26.4833i	0.491698	−	0.851646i	−0.508256	−	0.861206i	$-0.669710\pi$
$967$	15.2902	−	26.4833i	0.491698	−	0.851646i	0.999954	+	0.00955967i	$0.00304298\pi$
$968$	−13.2564	+	22.9607i	−0.426076	+	0.737985i
$969$	22.7382	−	3.61795i	0.730455	−	0.116225i
$970$	−3.20137	−	5.54494i	−0.102790	−	0.178037i
$971$	−26.2060			−0.840991			−0.420496	−	0.907295i	$-0.638144\pi$
$971$	−26.2060			−0.840991			−0.420496	+	0.907295i	$0.638144\pi$
$972$	−4.08809	−	15.0429i	−0.131126	−	0.482500i
$973$		0			0
$974$	1.84897	+	3.20251i	0.0592448	+	0.102615i
$975$	2.47197	−	0.393323i	0.0791663	−	0.0125964i
$976$	5.17511	−	8.96355i	0.165651	−	0.286916i
$977$	−10.5270	+	18.2332i	−0.336787	+	0.583332i	−0.983826	−	0.179124i	$-0.942674\pi$
$977$	−10.5270	+	18.2332i	−0.336787	+	0.583332i	0.647039	+	0.762457i	$0.276007\pi$
$978$	16.4058	+	20.2300i	0.524598	+	0.646884i
$979$	7.97141	+	13.8069i	0.254767	+	0.441270i
$980$		0			0
$981$	−2.00684	+	0.655217i	−0.0640734	+	0.0209195i
$982$	37.5609			1.19862
$983$	9.76483	+	16.9132i	0.311450	+	0.539447i	0.978676	−	0.205408i	$-0.0658521\pi$
$983$	9.76483	+	16.9132i	0.311450	+	0.539447i	−0.667227	+	0.744855i	$0.732519\pi$
$984$	4.30150	−	11.2297i	0.137127	−	0.357989i
$985$	−13.9480	+	24.1587i	−0.444421	+	0.769760i
$986$	5.01040	−	8.67827i	0.159564	−	0.276373i
$987$		0			0
$988$	0.739123	+	1.28020i	0.0235146	+	0.0407286i
$989$	3.64652			0.115952
$990$	−24.0751	−	21.6154i	−0.765157	−	0.686983i
$991$	14.9967			0.476387			0.238193	−	0.971218i	$-0.423445\pi$
$991$	14.9967			0.476387			0.238193	+	0.971218i	$0.423445\pi$
$992$	−3.85185	−	6.67160i	−0.122296	−	0.211823i
$993$	3.15172	+	3.88640i	0.100017	+	0.123331i
$994$		0			0
$995$	−7.87360	+	13.6375i	−0.249610	+	0.432337i
$996$	−5.34501	+	0.850463i	−0.169363	+	0.0269479i
$997$	29.2821	+	50.7180i	0.927373	+	1.60626i	0.787700	+	0.616059i	$0.211272\pi$
$997$	29.2821	+	50.7180i	0.927373	+	1.60626i	0.139672	+	0.990198i	$0.455395\pi$
$998$	−31.7954			−1.00646
$999$	13.3454	−	6.83572i	0.422230	−	0.216273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.l.589.1		6
3.2	odd	2		2646.2.f.o.1765.2		6
7.2	even	3		126.2.h.c.67.2	yes	6
7.3	odd	6		882.2.e.p.373.1		6
7.4	even	3		126.2.e.d.121.3	yes	6
7.5	odd	6		882.2.h.o.67.2		6
7.6	odd	2		882.2.f.m.589.3		6
9.2	odd	6		2646.2.f.o.883.2		6
9.4	even	3		7938.2.a.cb.1.2		3
9.5	odd	6		7938.2.a.bu.1.2		3
9.7	even	3	inner	882.2.f.l.295.1		6
21.2	odd	6		378.2.h.d.361.2		6
21.5	even	6		2646.2.h.p.361.2		6
21.11	odd	6		378.2.e.c.37.2		6
21.17	even	6		2646.2.e.o.1549.2		6
21.20	even	2		2646.2.f.n.1765.2		6
28.11	odd	6		1008.2.q.h.625.1		6
28.23	odd	6		1008.2.t.g.193.2		6
63.2	odd	6		378.2.e.c.235.2		6
63.4	even	3		1134.2.g.k.163.2		6
63.11	odd	6		378.2.h.d.289.2		6
63.13	odd	6		7938.2.a.by.1.2		3
63.16	even	3		126.2.e.d.25.3	✓	6
63.20	even	6		2646.2.f.n.883.2		6
63.23	odd	6		1134.2.g.n.487.2		6
63.25	even	3		126.2.h.c.79.2	yes	6
63.32	odd	6		1134.2.g.n.163.2		6
63.34	odd	6		882.2.f.m.295.3		6
63.38	even	6		2646.2.h.p.667.2		6
63.41	even	6		7938.2.a.bx.1.2		3
63.47	even	6		2646.2.e.o.2125.2		6
63.52	odd	6		882.2.h.o.79.2		6
63.58	even	3		1134.2.g.k.487.2		6
63.61	odd	6		882.2.e.p.655.1		6
84.11	even	6		3024.2.q.h.2305.2		6
84.23	even	6		3024.2.t.g.1873.2		6
252.11	even	6		3024.2.t.g.289.2		6
252.79	odd	6		1008.2.q.h.529.1		6
252.151	odd	6		1008.2.t.g.961.2		6
252.191	even	6		3024.2.q.h.2881.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.3	✓	6	63.16	even	3
126.2.e.d.121.3	yes	6	7.4	even	3
126.2.h.c.67.2	yes	6	7.2	even	3
126.2.h.c.79.2	yes	6	63.25	even	3
378.2.e.c.37.2		6	21.11	odd	6
378.2.e.c.235.2		6	63.2	odd	6
378.2.h.d.289.2		6	63.11	odd	6
378.2.h.d.361.2		6	21.2	odd	6
882.2.e.p.373.1		6	7.3	odd	6
882.2.e.p.655.1		6	63.61	odd	6
882.2.f.l.295.1		6	9.7	even	3	inner
882.2.f.l.589.1		6	1.1	even	1	trivial
882.2.f.m.295.3		6	63.34	odd	6
882.2.f.m.589.3		6	7.6	odd	2
882.2.h.o.67.2		6	7.5	odd	6
882.2.h.o.79.2		6	63.52	odd	6
1008.2.q.h.529.1		6	252.79	odd	6
1008.2.q.h.625.1		6	28.11	odd	6
1008.2.t.g.193.2		6	28.23	odd	6
1008.2.t.g.961.2		6	252.151	odd	6
1134.2.g.k.163.2		6	63.4	even	3
1134.2.g.k.487.2		6	63.58	even	3
1134.2.g.n.163.2		6	63.32	odd	6
1134.2.g.n.487.2		6	63.23	odd	6
2646.2.e.o.1549.2		6	21.17	even	6
2646.2.e.o.2125.2		6	63.47	even	6
2646.2.f.n.883.2		6	63.20	even	6
2646.2.f.n.1765.2		6	21.20	even	2
2646.2.f.o.883.2		6	9.2	odd	6
2646.2.f.o.1765.2		6	3.2	odd	2
2646.2.h.p.361.2		6	21.5	even	6
2646.2.h.p.667.2		6	63.38	even	6
3024.2.q.h.2305.2		6	84.11	even	6
3024.2.q.h.2881.2		6	252.191	even	6
3024.2.t.g.289.2		6	252.11	even	6
3024.2.t.g.1873.2		6	84.23	even	6
7938.2.a.bu.1.2		3	9.5	odd	6
7938.2.a.bx.1.2		3	63.41	even	6
7938.2.a.by.1.2		3	63.13	odd	6
7938.2.a.cb.1.2		3	9.4	even	3

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.71053 + 0.272169i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.880438 + 1.52496i) q^{5} +(1.09097 + 1.34528i) q^{6} +1.00000 q^{8} +(2.85185 - 0.931107i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.71053 + 0.272169i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.880438 + 1.52496i) q^{5} +(1.09097 + 1.34528i) q^{6} +1.00000 q^{8} +(2.85185 - 0.931107i) q^{9} +1.76088 q^{10} +(-3.06238 - 5.30420i) q^{11} +(0.619562 - 1.61745i) q^{12} +(-0.380438 + 0.658939i) q^{13} +(1.09097 - 2.84813i) q^{15} +(-0.500000 - 0.866025i) q^{16} +6.84213 q^{17} +(-2.23229 - 2.00422i) q^{18} -1.94282 q^{19} +(-0.880438 - 1.52496i) q^{20} +(-3.06238 + 5.30420i) q^{22} +(0.210533 - 0.364654i) q^{23} +(-1.71053 + 0.272169i) q^{24} +(0.949657 + 1.64485i) q^{25} +0.760877 q^{26} +(-4.62476 + 2.36887i) q^{27} +(0.732287 + 1.26836i) q^{29} +(-3.01204 + 0.479256i) q^{30} +(-3.85185 + 6.67160i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.68194 + 8.23953i) q^{33} +(-3.42107 - 5.92546i) q^{34} +(-0.619562 + 2.93533i) q^{36} -2.88564 q^{37} +(0.971410 + 1.68253i) q^{38} +(0.471410 - 1.23068i) q^{39} +(-0.880438 + 1.52496i) q^{40} +(-3.47141 + 6.01266i) q^{41} +(4.33009 + 7.49994i) q^{43} +6.12476 q^{44} +(-1.09097 + 5.16875i) q^{45} -0.421067 q^{46} +(-0.830095 - 1.43777i) q^{47} +(1.09097 + 1.34528i) q^{48} +(0.949657 - 1.64485i) q^{50} +(-11.7037 + 1.86221i) q^{51} +(-0.380438 - 0.658939i) q^{52} +0.225450 q^{53} +(4.36389 + 2.82073i) q^{54} +10.7850 q^{55} +(3.32326 - 0.528775i) q^{57} +(0.732287 - 1.26836i) q^{58} +(-0.993163 + 1.72021i) q^{59} +(1.92107 + 2.36887i) q^{60} +(5.17511 + 8.96355i) q^{61} +7.70370 q^{62} +1.00000 q^{64} +(-0.669905 - 1.16031i) q^{65} +(3.79467 - 9.90650i) q^{66} +(-3.39248 + 5.87594i) q^{67} +(-3.42107 + 5.92546i) q^{68} +(-0.260877 + 0.681054i) q^{69} +10.7850 q^{71} +(2.85185 - 0.931107i) q^{72} -0.306707 q^{73} +(1.44282 + 2.49904i) q^{74} +(-2.07210 - 2.55511i) q^{75} +(0.971410 - 1.68253i) q^{76} +(-1.30150 + 0.207087i) q^{78} +(6.72257 + 11.6438i) q^{79} +1.76088 q^{80} +(7.26608 - 5.31075i) q^{81} +6.94282 q^{82} +(-1.56238 - 2.70612i) q^{83} +(-6.02408 + 10.4340i) q^{85} +(4.33009 - 7.49994i) q^{86} +(-1.59781 - 1.97026i) q^{87} +(-3.06238 - 5.30420i) q^{88} -2.60301 q^{89} +(5.02175 - 1.63957i) q^{90} +(0.210533 + 0.364654i) q^{92} +(4.77292 - 12.4603i) q^{93} +(-0.830095 + 1.43777i) q^{94} +(1.71053 - 2.96273i) q^{95} +(0.619562 - 1.61745i) q^{96} +(-1.81806 - 3.14897i) q^{97} +(-13.6722 - 12.2754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^8 + 8 * q^9	\( 6 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{8} + 8 q^{9} + 10 q^{10} - q^{11} + 4 q^{12} - 2 q^{13} - 2 q^{15} - 3 q^{16} + 8 q^{17} - 4 q^{18} + 6 q^{19} - 5 q^{20} - q^{22} - 7 q^{23} - 2 q^{24} - 2 q^{25} + 4 q^{26} + 7 q^{27} - 5 q^{29} + 7 q^{30} - 14 q^{31} - 3 q^{32} + 23 q^{33} - 4 q^{34} - 4 q^{36} + 18 q^{37} - 3 q^{38} - 6 q^{39} - 5 q^{40} - 12 q^{41} + 18 q^{43} + 2 q^{44} + 2 q^{45} + 14 q^{46} + 3 q^{47} - 2 q^{48} - 2 q^{50} - 52 q^{51} - 2 q^{52} - 18 q^{53} - 8 q^{54} + 14 q^{55} + 2 q^{57} - 5 q^{58} + 4 q^{59} - 5 q^{60} + 4 q^{61} + 28 q^{62} + 6 q^{64} - 12 q^{65} - 4 q^{66} + 5 q^{67} - 4 q^{68} - q^{69} + 14 q^{71} + 8 q^{72} + 50 q^{73} - 9 q^{74} - 19 q^{75} - 3 q^{76} + 9 q^{78} + 7 q^{79} + 10 q^{80} + 8 q^{81} + 24 q^{82} + 8 q^{83} + 14 q^{85} + 18 q^{86} - 11 q^{87} - q^{88} + 18 q^{89} + 29 q^{90} - 7 q^{92} + 3 q^{93} + 3 q^{94} + 2 q^{95} + 4 q^{96} - 28 q^{97} - 41 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^8 + 8 * q^9 + 10 * q^10 - q^11 + 4 * q^12 - 2 * q^13 - 2 * q^15 - 3 * q^16 + 8 * q^17 - 4 * q^18 + 6 * q^19 - 5 * q^20 - q^22 - 7 * q^23 - 2 * q^24 - 2 * q^25 + 4 * q^26 + 7 * q^27 - 5 * q^29 + 7 * q^30 - 14 * q^31 - 3 * q^32 + 23 * q^33 - 4 * q^34 - 4 * q^36 + 18 * q^37 - 3 * q^38 - 6 * q^39 - 5 * q^40 - 12 * q^41 + 18 * q^43 + 2 * q^44 + 2 * q^45 + 14 * q^46 + 3 * q^47 - 2 * q^48 - 2 * q^50 - 52 * q^51 - 2 * q^52 - 18 * q^53 - 8 * q^54 + 14 * q^55 + 2 * q^57 - 5 * q^58 + 4 * q^59 - 5 * q^60 + 4 * q^61 + 28 * q^62 + 6 * q^64 - 12 * q^65 - 4 * q^66 + 5 * q^67 - 4 * q^68 - q^69 + 14 * q^71 + 8 * q^72 + 50 * q^73 - 9 * q^74 - 19 * q^75 - 3 * q^76 + 9 * q^78 + 7 * q^79 + 10 * q^80 + 8 * q^81 + 24 * q^82 + 8 * q^83 + 14 * q^85 + 18 * q^86 - 11 * q^87 - q^88 + 18 * q^89 + 29 * q^90 - 7 * q^92 + 3 * q^93 + 3 * q^94 + 2 * q^95 + 4 * q^96 - 28 * q^97 - 41 * q^99

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