LMFDB - Embedded newform 882.2.h.o.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
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			67.2
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	882.67
Dual form			882.2.h.o.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.619562 + 1.61745i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.76088 q^{5} +(-1.09097 - 1.34528i) q^{6} +1.00000 q^{8} +(-2.23229 - 2.00422i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.619562 + 1.61745i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.76088 q^{5} +(-1.09097 - 1.34528i) q^{6} +1.00000 q^{8} +(-2.23229 - 2.00422i) q^{9} +(0.880438 - 1.52496i) q^{10} +6.12476 q^{11} +(1.71053 - 0.272169i) q^{12} +(0.380438 - 0.658939i) q^{13} +(1.09097 - 2.84813i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.42107 - 5.92546i) q^{17} +(2.85185 - 0.931107i) q^{18} +(-0.971410 - 1.68253i) q^{19} +(0.880438 + 1.52496i) q^{20} +(-3.06238 + 5.30420i) q^{22} -0.421067 q^{23} +(-0.619562 + 1.61745i) q^{24} -1.89931 q^{25} +(0.380438 + 0.658939i) q^{26} +(4.62476 - 2.36887i) q^{27} +(0.732287 + 1.26836i) q^{29} +(1.92107 + 2.36887i) q^{30} +(3.85185 + 6.67160i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.79467 + 9.90650i) q^{33} +(3.42107 + 5.92546i) q^{34} +(-0.619562 + 2.93533i) q^{36} +(1.44282 + 2.49904i) q^{37} +1.94282 q^{38} +(0.830095 + 1.02359i) q^{39} -1.76088 q^{40} +(3.47141 - 6.01266i) q^{41} +(4.33009 + 7.49994i) q^{43} +(-3.06238 - 5.30420i) q^{44} +(3.93078 + 3.52918i) q^{45} +(0.210533 - 0.364654i) q^{46} +(0.830095 - 1.43777i) q^{47} +(-1.09097 - 1.34528i) q^{48} +(0.949657 - 1.64485i) q^{50} +(7.46457 + 9.20459i) q^{51} -0.760877 q^{52} +(-0.112725 + 0.195246i) q^{53} +(-0.260877 + 5.18960i) q^{54} -10.7850 q^{55} +(3.32326 - 0.528775i) q^{57} -1.46457 q^{58} +(0.993163 + 1.72021i) q^{59} +(-3.01204 + 0.479256i) q^{60} +(-5.17511 + 8.96355i) q^{61} -7.70370 q^{62} +1.00000 q^{64} +(-0.669905 + 1.16031i) q^{65} +(-6.68194 - 8.23953i) q^{66} +(-3.39248 - 5.87594i) q^{67} -6.84213 q^{68} +(0.260877 - 0.681054i) q^{69} +10.7850 q^{71} +(-2.23229 - 2.00422i) q^{72} +(-0.153353 + 0.265616i) q^{73} -2.88564 q^{74} +(1.17674 - 3.07204i) q^{75} +(-0.971410 + 1.68253i) q^{76} +(-1.30150 + 0.207087i) q^{78} +(6.72257 - 11.6438i) q^{79} +(0.880438 - 1.52496i) q^{80} +(0.966208 + 8.94799i) q^{81} +(3.47141 + 6.01266i) q^{82} +(1.56238 + 2.70612i) q^{83} +(-6.02408 + 10.4340i) q^{85} -8.66019 q^{86} +(-2.50520 + 0.398611i) q^{87} +6.12476 q^{88} +(-1.30150 - 2.25427i) q^{89} +(-5.02175 + 1.63957i) q^{90} +(0.210533 + 0.364654i) q^{92} +(-13.1774 + 2.09671i) q^{93} +(0.830095 + 1.43777i) q^{94} +(1.71053 + 2.96273i) q^{95} +(1.71053 - 0.272169i) 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} - 4 q^{3} - 3 q^{4} - 10 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 - 10 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9	$ 6 q - 3 q^{2} - 4 q^{3} - 3 q^{4} - 10 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9} + 5 q^{10} + 2 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} - 3 q^{16} + 4 q^{17} + 8 q^{18} + 3 q^{19} + 5 q^{20} - q^{22} + 14 q^{23} - 4 q^{24} + 4 q^{25} + 2 q^{26} - 7 q^{27} - 5 q^{29} - 5 q^{30} + 14 q^{31} - 3 q^{32} + 4 q^{33} + 4 q^{34} - 4 q^{36} - 9 q^{37} - 6 q^{38} - 3 q^{39} - 10 q^{40} + 12 q^{41} + 18 q^{43} - q^{44} + 31 q^{45} - 7 q^{46} - 3 q^{47} + 2 q^{48} - 2 q^{50} + 26 q^{51} - 4 q^{52} + 9 q^{53} - q^{54} - 14 q^{55} + 2 q^{57} + 10 q^{58} - 4 q^{59} + 7 q^{60} - 4 q^{61} - 28 q^{62} + 6 q^{64} - 12 q^{65} - 23 q^{66} + 5 q^{67} - 8 q^{68} + q^{69} + 14 q^{71} - 4 q^{72} + 25 q^{73} + 18 q^{74} + 25 q^{75} + 3 q^{76} + 9 q^{78} + 7 q^{79} + 5 q^{80} + 32 q^{81} + 12 q^{82} - 8 q^{83} + 14 q^{85} - 36 q^{86} + 20 q^{87} + 2 q^{88} + 9 q^{89} - 29 q^{90} - 7 q^{92} - 3 q^{93} - 3 q^{94} + 2 q^{95} + 2 q^{96} + 28 q^{97} - 41 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 - 10 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9 + 5 * q^10 + 2 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 - 3 * q^16 + 4 * q^17 + 8 * q^18 + 3 * q^19 + 5 * q^20 - q^22 + 14 * q^23 - 4 * q^24 + 4 * q^25 + 2 * q^26 - 7 * q^27 - 5 * q^29 - 5 * q^30 + 14 * q^31 - 3 * q^32 + 4 * q^33 + 4 * q^34 - 4 * q^36 - 9 * q^37 - 6 * q^38 - 3 * q^39 - 10 * q^40 + 12 * q^41 + 18 * q^43 - q^44 + 31 * q^45 - 7 * q^46 - 3 * q^47 + 2 * q^48 - 2 * q^50 + 26 * q^51 - 4 * q^52 + 9 * q^53 - q^54 - 14 * q^55 + 2 * q^57 + 10 * q^58 - 4 * q^59 + 7 * q^60 - 4 * q^61 - 28 * q^62 + 6 * q^64 - 12 * q^65 - 23 * q^66 + 5 * q^67 - 8 * q^68 + q^69 + 14 * q^71 - 4 * q^72 + 25 * q^73 + 18 * q^74 + 25 * q^75 + 3 * q^76 + 9 * q^78 + 7 * q^79 + 5 * q^80 + 32 * q^81 + 12 * q^82 - 8 * q^83 + 14 * q^85 - 36 * q^86 + 20 * q^87 + 2 * q^88 + 9 * q^89 - 29 * q^90 - 7 * q^92 - 3 * q^93 - 3 * q^94 + 2 * q^95 + 2 * q^96 + 28 * q^97 - 41 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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
$3$	−0.619562	+	1.61745i	−0.357704	+	0.933835i
$3$	−0.619562	+	1.61745i	−0.357704	+	0.933835i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.76088			−0.787488			−0.393744	−	0.919220i	$-0.628820\pi$
$5$	−1.76088			−0.787488			−0.393744	+	0.919220i	$0.628820\pi$
$6$	−1.09097	−	1.34528i	−0.445387	−	0.549209i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−2.23229	−	2.00422i	−0.744096	−	0.668073i
$10$	0.880438	−	1.52496i	0.278419	−	0.482236i
$11$	6.12476			1.84669			0.923343	−	0.383977i	$-0.125446\pi$
$11$	6.12476			1.84669			0.923343	+	0.383977i	$0.125446\pi$
$12$	1.71053	−	0.272169i	0.493788	−	0.0785683i
$13$	0.380438	−	0.658939i	0.105515	−	0.182757i	−0.808434	−	0.588587i	$-0.799684\pi$
$13$	0.380438	−	0.658939i	0.105515	−	0.182757i	0.913948	+	0.405831i	$0.133018\pi$
$14$		0			0
$15$	1.09097	−	2.84813i	0.281688	−	0.735384i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.42107	−	5.92546i	0.829731	−	1.43714i	−0.0685191	−	0.997650i	$-0.521827\pi$
$17$	3.42107	−	5.92546i	0.829731	−	1.43714i	0.898250	−	0.439486i	$-0.144839\pi$
$18$	2.85185	−	0.931107i	0.672187	−	0.219464i
$19$	−0.971410	−	1.68253i	−0.222857	−	0.385999i	0.732818	−	0.680425i	$-0.238205\pi$
$19$	−0.971410	−	1.68253i	−0.222857	−	0.385999i	−0.955674	+	0.294426i	$0.904872\pi$
$20$	0.880438	+	1.52496i	0.196872	+	0.340992i
$21$		0			0
$22$	−3.06238	+	5.30420i	−0.652902	+	1.13086i
$23$	−0.421067			−0.0877985			−0.0438992	−	0.999036i	$-0.513978\pi$
$23$	−0.421067			−0.0877985			−0.0438992	+	0.999036i	$0.513978\pi$
$24$	−0.619562	+	1.61745i	−0.126467	+	0.330161i
$25$	−1.89931			−0.379863
$26$	0.380438	+	0.658939i	0.0746101	+	0.129228i
$27$	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	$0.789914\pi$
$30$	1.92107	+	2.36887i	0.350737	+	0.432495i
$31$	3.85185	+	6.67160i	0.691812	+	1.19825i	0.971243	+	0.238088i	$0.0765208\pi$
$31$	3.85185	+	6.67160i	0.691812	+	1.19825i	−0.279431	+	0.960166i	$0.590146\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−3.79467	+	9.90650i	−0.660567	+	1.72450i
$34$	3.42107	+	5.92546i	0.586708	+	1.01621i
$35$		0			0
$36$	−0.619562	+	2.93533i	−0.103260	+	0.489221i
$37$	1.44282	+	2.49904i	0.237198	+	0.410839i	0.959909	−	0.280311i	$-0.0904376\pi$
$37$	1.44282	+	2.49904i	0.237198	+	0.410839i	−0.722711	+	0.691150i	$0.757104\pi$
$38$	1.94282			0.315167
$39$	0.830095	+	1.02359i	0.132922	+	0.163906i
$40$	−1.76088			−0.278419
$41$	3.47141	−	6.01266i	0.542143	−	0.939020i	−0.456638	−	0.889653i	$-0.650946\pi$
$41$	3.47141	−	6.01266i	0.542143	−	0.939020i	0.998781	−	0.0493667i	$-0.0157203\pi$
$42$		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	$0.603748\pi$
$44$	−3.06238	−	5.30420i	−0.461671	−	0.799638i
$45$	3.93078	+	3.52918i	0.585966	+	0.526100i
$46$	0.210533	−	0.364654i	0.0310414	−	0.0537654i
$47$	0.830095	−	1.43777i	0.121082	−	0.209720i	−0.799113	−	0.601181i	$-0.794697\pi$
$47$	0.830095	−	1.43777i	0.121082	−	0.209720i	0.920195	+	0.391461i	$0.128030\pi$
$48$	−1.09097	−	1.34528i	−0.157468	−	0.194175i
$49$		0			0
$50$	0.949657	−	1.64485i	0.134302	−	0.232617i
$51$	7.46457	+	9.20459i	1.04525	+	1.28890i
$52$	−0.760877			−0.105515
$53$	−0.112725	+	0.195246i	−0.0154840	+	0.0268190i	−0.873664	−	0.486531i	$-0.838262\pi$
$53$	−0.112725	+	0.195246i	−0.0154840	+	0.0268190i	0.858180	+	0.513350i	$0.171596\pi$
$54$	−0.260877	+	5.18960i	−0.0355008	+	0.706215i
$55$	−10.7850			−1.45424
$56$		0			0
$57$	3.32326	−	0.528775i	0.440176	−	0.0700379i
$58$	−1.46457			−0.192308
$59$	0.993163	+	1.72021i	0.129299	+	0.223952i	0.923405	−	0.383827i	$-0.125394\pi$
$59$	0.993163	+	1.72021i	0.129299	+	0.223952i	−0.794106	+	0.607779i	$0.792061\pi$
$60$	−3.01204	+	0.479256i	−0.388852	+	0.0618716i
$61$	−5.17511	+	8.96355i	−0.662605	+	1.14766i	0.317324	+	0.948317i	$0.397216\pi$
$61$	−5.17511	+	8.96355i	−0.662605	+	1.14766i	−0.979929	+	0.199348i	$0.936118\pi$
$62$	−7.70370			−0.978370
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.669905	+	1.16031i	−0.0830915	+	0.143919i
$66$	−6.68194	−	8.23953i	−0.822490	−	1.01422i
$67$	−3.39248	−	5.87594i	−0.414457	−	0.717861i	0.580914	−	0.813965i	$-0.302695\pi$
$67$	−3.39248	−	5.87594i	−0.414457	−	0.717861i	−0.995371	+	0.0961042i	$0.969362\pi$
$68$	−6.84213			−0.829731
$69$	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	$0.278947\pi$
$72$	−2.23229	−	2.00422i	−0.263078	−	0.236200i
$73$	−0.153353	+	0.265616i	−0.0179487	+	0.0310880i	−0.874860	−	0.484375i	$-0.839047\pi$
$73$	−0.153353	+	0.265616i	−0.0179487	+	0.0310880i	0.856912	+	0.515463i	$0.172380\pi$
$74$	−2.88564			−0.335449
$75$	1.17674	−	3.07204i	0.135878	−	0.354729i
$76$	−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	−0.188353	−	0.982101i	$-0.560315\pi$
$79$	6.72257	−	11.6438i	0.756348	−	1.31003i	0.944701	−	0.327932i	$-0.106352\pi$
$80$	0.880438	−	1.52496i	0.0984360	−	0.170496i
$81$	0.966208	+	8.94799i	0.107356	+	0.994221i
$82$	3.47141	+	6.01266i	0.383353	+	0.663987i
$83$	1.56238	+	2.70612i	0.171494	+	0.297036i	0.938942	−	0.344075i	$-0.111807\pi$
$83$	1.56238	+	2.70612i	0.171494	+	0.297036i	−0.767449	+	0.641110i	$0.778474\pi$
$84$		0			0
$85$	−6.02408	+	10.4340i	−0.653403	+	1.13173i
$86$	−8.66019			−0.933852
$87$	−2.50520	+	0.398611i	−0.268586	+	0.0427356i
$88$	6.12476			0.652902
$89$	−1.30150	−	2.25427i	−0.137959	−	0.238952i	0.788765	−	0.614695i	$-0.210721\pi$
$89$	−1.30150	−	2.25427i	−0.137959	−	0.238952i	−0.926724	+	0.375743i	$0.877388\pi$
$90$	−5.02175	+	1.63957i	−0.529339	+	0.172825i
$91$		0			0
$92$	0.210533	+	0.364654i	0.0219496	+	0.0380178i
$93$	−13.1774	+	2.09671i	−1.36644	+	0.217418i
$94$	0.830095	+	1.43777i	0.0856178	+	0.148294i
$95$	1.71053	+	2.96273i	0.175497	+	0.303970i
$96$	1.71053	−	0.272169i	0.174581	−	0.0277781i
$97$	1.81806	+	3.14897i	0.184596	+	0.319729i	0.943440	−	0.331543i	$-0.107569\pi$
$97$	1.81806	+	3.14897i	0.184596	+	0.319729i	−0.758845	+	0.651272i	$0.774236\pi$
$98$		0			0
$99$	−13.6722	−	12.2754i	−1.37411	−	1.23372i
$100$	0.949657	+	1.64485i	0.0949657	+	0.164485i
$101$	8.01040			0.797065			0.398532	−	0.917154i	$-0.369520\pi$
$101$	8.01040			0.797065			0.398532	+	0.917154i	$0.369520\pi$
$102$	−11.7037	+	1.86221i	−1.15884	+	0.184387i
$103$	6.82846			0.672828			0.336414	−	0.941714i	$-0.390786\pi$
$103$	6.82846			0.672828			0.336414	+	0.941714i	$0.390786\pi$
$104$	0.380438	−	0.658939i	0.0373051	−	0.0646142i
$105$		0			0
$106$	−0.112725	−	0.195246i	−0.0109488	−	0.0189639i
$107$	1.77292	+	3.07078i	0.171394	+	0.296863i	0.938908	−	0.344170i	$-0.111840\pi$
$107$	1.77292	+	3.07078i	0.171394	+	0.296863i	−0.767513	+	0.641033i	$0.778506\pi$
$108$	−4.36389	−	2.82073i	−0.419915	−	0.271424i
$109$	0.351848	−	0.609419i	0.0337010	−	0.0583718i	−0.848683	−	0.528902i	$-0.822604\pi$
$109$	0.351848	−	0.609419i	0.0337010	−	0.0583718i	0.882384	+	0.470530i	$0.155937\pi$
$110$	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	$0.0357061\pi$
$114$	−1.20370	+	3.14241i	−0.112737	+	0.294314i
$115$	0.741446			0.0691402
$116$	0.732287	−	1.26836i	0.0679911	−	0.117764i
$117$	−2.16991	+	0.708458i	−0.200608	+	0.0654970i
$118$	−1.98633			−0.182856
$119$		0			0
$120$	1.09097	−	2.84813i	0.0995916	−	0.259997i
$121$	26.5127			2.41025
$122$	−5.17511	−	8.96355i	−0.468532	−	0.811521i
$123$	7.57442	+	9.34004i	0.682962	+	0.842163i
$124$	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
$129$	−14.8135	+	2.35703i	−1.30426	+	0.207525i
$130$	−0.669905	−	1.16031i	−0.0587546	−	0.101766i
$131$	7.29303			0.637195			0.318598	−	0.947890i	$-0.396788\pi$
$131$	7.29303			0.637195			0.318598	+	0.947890i	$0.396788\pi$
$132$	10.4766	−	1.66697i	0.911872	−	0.145091i
$133$		0			0
$134$	6.78495			0.586131
$135$	−8.14364	+	4.17129i	−0.700893	+	0.359008i
$136$	3.42107	−	5.92546i	0.293354	−	0.508104i
$137$	−8.18194			−0.699031			−0.349515	−	0.936931i	$-0.613654\pi$
$137$	−8.18194			−0.699031			−0.349515	+	0.936931i	$0.613654\pi$
$138$	0.459372	+	0.566453i	0.0391043	+	0.0482197i
$139$	6.23229	−	10.7946i	0.528616	−	0.915589i	−0.470828	−	0.882225i	$-0.656045\pi$
$139$	6.23229	−	10.7946i	0.528616	−	0.915589i	0.999443	−	0.0333640i	$-0.0106220\pi$
$140$		0			0
$141$	1.81122	+	2.23342i	0.152532	+	0.188088i
$142$	−5.39248	+	9.34004i	−0.452527	+	0.783799i
$143$	2.33009	−	4.03584i	0.194852	−	0.337494i
$144$	2.85185	−	0.931107i	0.237654	−	0.0775923i
$145$	−1.28947	−	2.23342i	−0.107084	−	0.185476i
$146$	−0.153353	−	0.265616i	−0.0126916	−	0.0219825i
$147$		0			0
$148$	1.44282	−	2.49904i	0.118599	−	0.205420i
$149$	8.82846			0.723256			0.361628	−	0.932323i	$-0.382221\pi$
$149$	8.82846			0.723256			0.361628	+	0.932323i	$0.382221\pi$
$150$	2.07210	+	2.55511i	0.169186	+	0.208624i
$151$	−14.9863			−1.21957			−0.609785	−	0.792567i	$-0.708744\pi$
$151$	−14.9863			−1.21957			−0.609785	+	0.792567i	$0.708744\pi$
$152$	−0.971410	−	1.68253i	−0.0787918	−	0.136471i
$153$	−19.5127	+	6.37076i	−1.57751	+	0.515045i
$154$		0			0
$155$	−6.78263	−	11.7479i	−0.544794	−	0.943611i
$156$	0.471410	−	1.23068i	0.0377430	−	0.0985332i
$157$	9.49028	+	16.4377i	0.757407	+	1.31187i	0.944169	+	0.329462i	$0.106868\pi$
$157$	9.49028	+	16.4377i	0.757407	+	1.31187i	−0.186761	+	0.982405i	$0.559799\pi$
$158$	6.72257	+	11.6438i	0.534819	+	0.926334i
$159$	−0.245960	−	0.303294i	−0.0195059	−	0.0240528i
$160$	0.880438	+	1.52496i	0.0696048	+	0.120559i
$161$		0			0
$162$	−8.23229	−	3.63723i	−0.646790	−	0.285768i
$163$	−7.51887	−	13.0231i	−0.588924	−	1.02005i	−0.994374	−	0.105929i	$-0.966219\pi$
$163$	−7.51887	−	13.0231i	−0.588924	−	1.02005i	0.405450	−	0.914117i	$-0.367115\pi$
$164$	−6.94282			−0.542143
$165$	6.68194	−	17.4441i	0.520189	−	1.35802i
$166$	−3.12476			−0.242529
$167$	−0.572097	+	0.990901i	−0.0442702	+	0.0766782i	−0.887311	−	0.461171i	$-0.847430\pi$
$167$	−0.572097	+	0.990901i	−0.0442702	+	0.0766782i	0.843041	+	0.537849i	$0.180763\pi$
$168$		0			0
$169$	6.21053	+	10.7570i	0.477733	+	0.827458i
$170$	−6.02408	−	10.4340i	−0.462026	−	0.800252i
$171$	−1.20370	+	5.70281i	−0.0920490	+	0.436105i
$172$	4.33009	−	7.49994i	0.330167	−	0.571865i
$173$	0.248838	−	0.431001i	0.0189188	−	0.0327684i	−0.856411	−	0.516295i	$-0.827311\pi$
$173$	0.248838	−	0.431001i	0.0189188	−	0.0327684i	0.875330	+	0.483526i	$0.160644\pi$
$174$	0.907394	−	2.36887i	0.0687893	−	0.179584i
$175$		0			0
$176$	−3.06238	+	5.30420i	−0.230836	+	0.399819i
$177$	−3.39768	+	0.540616i	−0.255385	+	0.0406352i
$178$	2.60301			0.195104
$179$	4.41423	−	7.64567i	0.329935	−	0.571464i	−0.652564	−	0.757734i	$-0.726306\pi$
$179$	4.41423	−	7.64567i	0.329935	−	0.571464i	0.982499	+	0.186270i	$0.0596398\pi$
$180$	1.09097	−	5.16875i	0.0813162	−	0.385256i
$181$	−1.32941			−0.0988140			−0.0494070	−	0.998779i	$-0.515733\pi$
$181$	−1.32941			−0.0988140			−0.0494070	+	0.998779i	$0.515733\pi$
$182$		0			0
$183$	−11.2918	−	13.9239i	−0.834713	−	1.02929i
$184$	−0.421067			−0.0310414
$185$	−2.54063	−	4.40050i	−0.186791	−	0.323531i
$186$	4.77292	−	12.4603i	0.349967	−	0.913637i
$187$	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	−0.409934	−	0.912115i	$-0.634448\pi$
$191$	8.08414	−	14.0021i	0.584947	−	1.01316i	0.994882	−	0.101044i	$-0.0322182\pi$
$192$	−0.619562	+	1.61745i	−0.0447130	+	0.116729i
$193$	7.08414	+	12.2701i	0.509927	+	0.883220i	0.999934	+	0.0115011i	$0.00366101\pi$
$193$	7.08414	+	12.2701i	0.509927	+	0.883220i	−0.490007	+	0.871719i	$0.663006\pi$
$194$	−3.63611			−0.261058
$195$	−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	$0.309126\pi$
$198$	17.4669	−	5.70281i	1.24132	−	0.405281i
$199$	4.47141	−	7.74471i	0.316970	−	0.549008i	−0.662884	−	0.748722i	$-0.730668\pi$
$199$	4.47141	−	7.74471i	0.316970	−	0.549008i	0.979854	+	0.199714i	$0.0640013\pi$
$200$	−1.89931			−0.134302
$201$	11.6059	−	1.84665i	0.818616	−	0.130253i
$202$	−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
$206$	−3.41423	+	5.91362i	−0.237881	+	0.412021i
$207$	0.939941	+	0.843910i	0.0653304	+	0.0586558i
$208$	0.380438	+	0.658939i	0.0263787	+	0.0456892i
$209$	−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	$-0.120065\pi$
$212$	0.225450			0.0154840
$213$	−6.68194	+	17.4441i	−0.457839	+	1.19525i
$214$	−3.54583			−0.242388
$215$	−7.62476	−	13.2065i	−0.520005	−	0.900674i
$216$	4.62476	−	2.36887i	0.314675	−	0.161181i
$217$		0			0
$218$	0.351848	+	0.609419i	0.0238302	+	0.0412751i
$219$	−0.334608	−	0.412607i	−0.0226107	−	0.0278814i
$220$	5.39248	+	9.34004i	0.363561	+	0.629706i
$221$	−2.60301	−	4.50855i	−0.175097	−	0.303278i
$222$	1.78783	−	4.66738i	0.119991	−	0.313254i
$223$	6.44282	+	11.1593i	0.431443	+	0.747281i	0.996998	−	0.0774293i	$-0.0246712\pi$
$223$	6.44282	+	11.1593i	0.431443	+	0.747281i	−0.565555	+	0.824711i	$0.691338\pi$
$224$		0			0
$225$	4.23981	+	3.80664i	0.282654	+	0.253776i
$226$	4.25116	+	7.36323i	0.282783	+	0.489795i
$227$	−21.9967			−1.45997			−0.729987	−	0.683461i	$-0.760474\pi$
$227$	−21.9967			−1.45997			−0.729987	+	0.683461i	$0.760474\pi$
$228$	−2.11956	−	2.61364i	−0.140371	−	0.173092i
$229$	3.79863			0.251020			0.125510	−	0.992092i	$-0.459943\pi$
$229$	3.79863			0.251020			0.125510	+	0.992092i	$0.459943\pi$
$230$	−0.370723	+	0.642111i	−0.0244448	+	0.0423396i
$231$		0			0
$232$	0.732287	+	1.26836i	0.0480770	+	0.0832718i
$233$	−3.33530	−	5.77690i	−0.218503	−	0.378458i	0.735848	−	0.677147i	$-0.236784\pi$
$233$	−3.33530	−	5.77690i	−0.218503	−	0.378458i	−0.954350	+	0.298689i	$0.903451\pi$
$234$	0.471410	−	2.23342i	0.0308170	−	0.146003i
$235$	−1.46169	+	2.53173i	−0.0953505	+	0.165152i
$236$	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	$0.997843\pi$
$240$	1.92107	+	2.36887i	0.124004	+	0.152910i
$241$	−21.4120			−1.37927			−0.689635	−	0.724157i	$-0.742229\pi$
$241$	−21.4120			−1.37927			−0.689635	+	0.724157i	$0.742229\pi$
$242$	−13.2564	+	22.9607i	−0.852151	+	1.47597i
$243$	−15.0715	−	3.98104i	−0.966840	−	0.255384i
$244$	10.3502			0.662605
$245$		0			0
$246$	−11.8759	+	1.88962i	−0.757181	+	0.120478i
$247$	−1.47825			−0.0940586
$248$	3.85185	+	6.67160i	0.244593	+	0.423647i
$249$	−5.34501	+	0.850463i	−0.338726	+	0.0538959i
$250$	−6.07442	+	10.5212i	−0.384180	+	0.665419i
$251$	23.6030			1.48981			0.744904	−	0.667171i	$-0.232495\pi$
$251$	23.6030			1.48981			0.744904	+	0.667171i	$0.232495\pi$
$252$		0			0
$253$	−2.57893			−0.162136
$254$	9.47661	−	16.4140i	0.594616	−	1.02990i
$255$	−13.1442	−	16.2082i	−0.823121	−	1.01499i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−20.2599			−1.26378			−0.631890	−	0.775058i	$-0.717721\pi$
$257$	−20.2599			−1.26378			−0.631890	+	0.775058i	$0.717721\pi$
$258$	5.36552	−	14.0074i	0.334043	−	0.872064i
$259$		0			0
$260$	1.33981			0.0830915
$261$	0.907394	−	4.29900i	0.0561663	−	0.266102i
$262$	−3.64652	+	6.31595i	−0.225283	+	0.390201i
$263$	−22.4887			−1.38671			−0.693355	−	0.720596i	$-0.743868\pi$
$263$	−22.4887			−1.38671			−0.693355	+	0.720596i	$0.743868\pi$
$264$	−3.79467	+	9.90650i	−0.233546	+	0.609703i
$265$	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
$269$	12.6706	−	21.9461i	0.772540	−	1.33808i	−0.163627	−	0.986522i	$-0.552319\pi$
$269$	12.6706	−	21.9461i	0.772540	−	1.33808i	0.936167	−	0.351556i	$-0.114347\pi$
$270$	0.459372	−	9.13825i	0.0279565	−	0.556136i
$271$	6.87880	+	11.9144i	0.417858	+	0.723751i	0.995724	−	0.0923810i	$-0.0294478\pi$
$271$	6.87880	+	11.9144i	0.417858	+	0.723751i	−0.577866	+	0.816132i	$0.696114\pi$
$272$	3.42107	+	5.92546i	0.207433	+	0.359284i
$273$		0			0
$274$	4.09097	−	7.08577i	0.247145	−	0.428067i
$275$	−11.6328			−0.701487
$276$	−0.720248	+	0.114601i	−0.0433539	+	0.00689818i
$277$	−3.28263			−0.197234			−0.0986171	−	0.995125i	$-0.531442\pi$
$277$	−3.28263			−0.197234			−0.0986171	+	0.995125i	$0.531442\pi$
$278$	6.23229	+	10.7946i	0.373788	+	0.647419i
$279$	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	$0.821282\pi$
$282$	−2.83981	+	0.451852i	−0.169108	+	0.0269074i
$283$	−4.09617	−	7.09478i	−0.243492	−	0.421741i	0.718214	−	0.695822i	$-0.244960\pi$
$283$	−4.09617	−	7.09478i	−0.243492	−	0.421741i	−0.961707	+	0.274081i	$0.911626\pi$
$284$	−5.39248	−	9.34004i	−0.319985	−	0.554230i
$285$	−5.85185	+	0.931107i	−0.346634	+	0.0551540i
$286$	2.33009	+	4.03584i	0.137781	+	0.238644i
$287$		0			0
$288$	−0.619562	+	2.93533i	−0.0365080	+	0.172966i
$289$	−14.9074	−	25.8204i	−0.876906	−	1.51884i
$290$	2.57893			0.151440
$291$	−6.21969	+	0.989636i	−0.364605	+	0.0580135i
$292$	0.306707			0.0179487
$293$	−7.72545	+	13.3809i	−0.451326	+	0.781719i	−0.998469	−	0.0553202i	$-0.982382\pi$
$293$	−7.72545	+	13.3809i	−0.451326	+	0.781719i	0.547143	+	0.837039i	$0.315715\pi$
$294$		0			0
$295$	−1.74884	−	3.02908i	−0.101821	−	0.176360i
$296$	1.44282	+	2.49904i	0.0838622	+	0.145254i
$297$	28.3256	−	14.5088i	1.64362	−	0.841886i
$298$	−4.41423	+	7.64567i	−0.255709	+	0.442902i
$299$	−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
$303$	−4.96294	+	12.9564i	−0.285113	+	0.744327i
$304$	1.94282			0.111428
$305$	9.11273	−	15.7837i	0.521793	−	0.903772i
$306$	4.23912	−	20.0839i	0.242335	−	1.14812i
$307$	−4.89931			−0.279619			−0.139809	−	0.990178i	$-0.544649\pi$
$307$	−4.89931			−0.279619			−0.139809	+	0.990178i	$0.544649\pi$
$308$		0			0
$309$	−4.23065	+	11.0447i	−0.240673	+	0.628310i
$310$	13.5653			0.770455
$311$	−3.84501	−	6.65976i	−0.218031	−	0.377640i	0.736175	−	0.676791i	$-0.236630\pi$
$311$	−3.84501	−	6.65976i	−0.218031	−	0.377640i	−0.954206	+	0.299151i	$0.903297\pi$
$312$	0.830095	+	1.02359i	0.0469949	+	0.0579495i
$313$	−0.861564	+	1.49227i	−0.0486985	+	0.0843482i	−0.889347	−	0.457233i	$-0.848841\pi$
$313$	−0.861564	+	1.49227i	−0.0486985	+	0.0843482i	0.840649	+	0.541581i	$0.182174\pi$
$314$	−18.9806			−1.07114
$315$		0			0
$316$	−13.4451			−0.756348
$317$	−16.6014	+	28.7544i	−0.932426	+	1.61501i	−0.153266	+	0.988185i	$0.548979\pi$
$317$	−16.6014	+	28.7544i	−0.932426	+	1.61501i	−0.779161	+	0.626824i	$0.784354\pi$
$318$	0.385640	−	0.0613605i	0.0216256	−	0.00344093i
$319$	4.48508	+	7.76839i	0.251116	+	0.434946i
$320$	−1.76088			−0.0984360
$321$	−6.06526	+	0.965064i	−0.338530	+	0.0538646i
$322$		0			0
$323$	−13.2930			−0.739644
$324$	7.26608	−	5.31075i	0.403671	−	0.295042i
$325$	−0.722572	+	1.25153i	−0.0400811	+	0.0694224i
$326$	15.0377			0.832864
$327$	0.767713	+	0.946670i	0.0424546	+	0.0523510i
$328$	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	−0.902989	−	0.429664i	$-0.858632\pi$
$331$	−1.44445	+	2.50187i	−0.0793944	+	0.137515i	0.823594	+	0.567179i	$0.191965\pi$
$332$	1.56238	−	2.70612i	0.0857468	−	0.148518i
$333$	1.78783	−	8.47030i	0.0979726	−	0.464169i
$334$	−0.572097	−	0.990901i	−0.0313037	−	0.0542197i
$335$	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	$0.243024\pi$
$338$	−12.4211			−0.675617
$339$	9.27579	+	11.4380i	0.503792	+	0.621228i
$340$	12.0482			0.653403
$341$	23.5917	+	40.8620i	1.27756	+	2.21280i
$342$	−4.33693	−	3.89384i	−0.234514	−	0.210555i
$343$		0			0
$344$	4.33009	+	7.49994i	0.233463	+	0.404370i
$345$	−0.459372	+	1.19925i	−0.0247317	+	0.0645656i
$346$	0.248838	+	0.431001i	0.0133776	+	0.0231707i
$347$	−4.84733	−	8.39583i	−0.260219	−	0.450712i	0.706081	−	0.708131i	$-0.250461\pi$
$347$	−4.84733	−	8.39583i	−0.260219	−	0.450712i	−0.966300	+	0.257419i	$0.917128\pi$
$348$	1.59781	+	1.97026i	0.0856515	+	0.105617i
$349$	−14.1992	−	24.5937i	−0.760065	−	1.31647i	−0.942817	−	0.333312i	$-0.891834\pi$
$349$	−14.1992	−	24.5937i	−0.760065	−	1.31647i	0.182752	−	0.983159i	$-0.441500\pi$
$350$		0			0
$351$	0.198495	−	3.94865i	0.0105949	−	0.210763i
$352$	−3.06238	−	5.30420i	−0.163225	−	0.282715i
$353$	4.39372			0.233854			0.116927	−	0.993141i	$-0.462696\pi$
$353$	4.39372			0.233854			0.116927	+	0.993141i	$0.462696\pi$
$354$	1.23065	−	3.21278i	0.0654084	−	0.170758i
$355$	−18.9910			−1.00794
$356$	−1.30150	+	2.25427i	−0.0689796	+	0.119476i
$357$		0			0
$358$	4.41423	+	7.64567i	0.233299	+	0.404086i
$359$	16.0796	+	27.8507i	0.848650	+	1.46990i	0.882413	+	0.470475i	$0.155917\pi$
$359$	16.0796	+	27.8507i	0.848650	+	1.46990i	−0.0337633	+	0.999430i	$0.510749\pi$
$360$	3.93078	+	3.52918i	0.207170	+	0.186004i
$361$	7.61273	−	13.1856i	0.400670	−	0.693980i
$362$	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
$366$	17.7044	−	2.81700i	0.925423	−	0.147247i
$367$	−34.6030			−1.80626			−0.903131	−	0.429365i	$-0.858738\pi$
$367$	−34.6030			−1.80626			−0.903131	+	0.429365i	$0.858738\pi$
$368$	0.210533	−	0.364654i	0.0109748	−	0.0190089i
$369$	−19.7999	+	6.46451i	−1.03074	+	0.336529i
$370$	5.08126			0.264162
$371$		0			0
$372$	8.40451	+	10.3636i	0.435754	+	0.537330i
$373$	10.9759			0.568312			0.284156	−	0.958778i	$-0.408287\pi$
$373$	10.9759			0.568312			0.284156	+	0.958778i	$0.408287\pi$
$374$	20.9532	+	36.2920i	1.08347	+	1.87662i
$375$	−7.52696	+	19.6501i	−0.388690	+	1.01473i
$376$	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
$381$	11.7427	−	30.6559i	0.601596	−	1.57055i
$382$	8.08414	+	14.0021i	0.413620	+	0.716411i
$383$	21.0241			1.07428			0.537140	−	0.843493i	$-0.319505\pi$
$383$	21.0241			1.07428			0.537140	+	0.843493i	$0.319505\pi$
$384$	−1.09097	−	1.34528i	−0.0556734	−	0.0686511i
$385$		0			0
$386$	−14.1683			−0.721146
$387$	5.36552	−	25.4205i	0.272745	−	1.29220i
$388$	1.81806	−	3.14897i	0.0922978	−	0.159865i
$389$	13.7382			0.696553			0.348277	−	0.937392i	$-0.386767\pi$
$389$	13.7382			0.696553			0.348277	+	0.937392i	$0.386767\pi$
$390$	2.29179	−	0.364654i	0.116049	−	0.0184650i
$391$	−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
$395$	−11.8376	+	20.5034i	−0.595615	+	1.03164i
$396$	−3.79467	+	17.9782i	−0.190689	+	0.903438i
$397$	3.57893	+	6.19889i	0.179622	+	0.311114i	0.941751	−	0.336311i	$-0.109179\pi$
$397$	3.57893	+	6.19889i	0.179622	+	0.311114i	−0.762129	+	0.647425i	$0.775846\pi$
$398$	4.47141	+	7.74471i	0.224132	+	0.388207i
$399$		0			0
$400$	0.949657	−	1.64485i	0.0474828	−	0.0822427i
$401$	−9.27936			−0.463389			−0.231695	−	0.972789i	$-0.574427\pi$
$401$	−9.27936			−0.463389			−0.231695	+	0.972789i	$0.574427\pi$
$402$	−4.20370	+	10.9743i	−0.209661	+	0.547349i
$403$	5.86156			0.291985
$404$	−4.00520	−	6.93721i	−0.199266	−	0.345139i
$405$	−1.70137	−	15.7563i	−0.0845419	−	0.782937i
$406$		0			0
$407$	8.83693	+	15.3060i	0.438030	+	0.758691i
$408$	7.46457	+	9.20459i	0.369551	+	0.455695i
$409$	7.58414	+	13.1361i	0.375011	+	0.649539i	0.990329	−	0.138741i	$-0.0443055\pi$
$409$	7.58414	+	13.1361i	0.375011	+	0.649539i	−0.615317	+	0.788279i	$0.710972\pi$
$410$	−6.11273	−	10.5876i	−0.301886	−	0.522882i
$411$	5.06922	−	13.2339i	0.250046	−	0.652779i
$412$	−3.41423	−	5.91362i	−0.168207	−	0.291343i
$413$		0			0
$414$	−1.20082	+	0.392058i	−0.0590170	+	0.0192686i
$415$	−2.75116	−	4.76515i	−0.135049	−	0.233912i
$416$	−0.760877			−0.0373051
$417$	13.5985	+	16.7684i	0.665921	+	0.821150i
$418$	11.8993			0.582014
$419$	4.16827	−	7.21966i	0.203633	−	0.352703i	−0.746063	−	0.665875i	$-0.768058\pi$
$419$	4.16827	−	7.21966i	0.203633	−	0.352703i	0.949696	+	0.313172i	$0.101392\pi$
$420$		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	$0.887934\pi$
$422$	11.3856	+	19.7205i	0.554244	+	0.959979i
$423$	−4.73461	+	1.54581i	−0.230205	+	0.0751601i
$424$	−0.112725	+	0.195246i	−0.00547442	+	0.00948197i
$425$	−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
$429$	5.08414	+	6.26926i	0.245464	+	0.302683i
$430$	15.2495			0.735397
$431$	−1.72545	+	2.98857i	−0.0831120	+	0.143954i	−0.904585	−	0.426293i	$-0.859819\pi$
$431$	−1.72545	+	2.98857i	−0.0831120	+	0.143954i	0.821473	+	0.570247i	$0.193153\pi$
$432$	−0.260877	+	5.18960i	−0.0125514	+	0.249685i
$433$	−28.2599			−1.35809			−0.679043	−	0.734099i	$-0.737605\pi$
$433$	−28.2599			−1.35809			−0.679043	+	0.734099i	$0.737605\pi$
$434$		0			0
$435$	4.41135	−	0.701905i	0.211508	−	0.0336538i
$436$	−0.703697			−0.0337010
$437$	0.409028	+	0.708458i	0.0195665	+	0.0338901i
$438$	0.524632	−	0.0834760i	0.0250679	−	0.00398864i
$439$	−14.4480	+	25.0247i	−0.689566	+	1.19436i	0.282412	+	0.959293i	$0.408866\pi$
$439$	−14.4480	+	25.0247i	−0.689566	+	1.19436i	−0.971978	+	0.235071i	$0.924468\pi$
$440$	−10.7850			−0.514152
$441$		0			0
$442$	5.20602			0.247625
$443$	6.88044	−	11.9173i	0.326899	−	0.566207i	−0.654995	−	0.755633i	$-0.727329\pi$
$443$	6.88044	−	11.9173i	0.326899	−	0.566207i	0.981895	+	0.189426i	$0.0606628\pi$
$444$	3.14815	+	3.88200i	0.149405	+	0.184231i
$445$	2.29179	+	3.96950i	0.108641	+	0.188172i
$446$	−12.8856			−0.610153
$447$	−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	$0.658151\pi$
$450$	−5.41655	+	1.76846i	−0.255339	+	0.0833662i
$451$	21.2616	−	36.8261i	1.00117	−	1.73407i
$452$	−8.50232			−0.399916
$453$	9.28495	−	24.2396i	0.436245	−	1.13888i
$454$	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	−0.999351	−	0.0360237i	$-0.988531\pi$
$457$	−10.0149	+	17.3463i	−0.468478	+	0.811428i	0.530873	+	0.847451i	$0.321864\pi$
$458$	−1.89931	+	3.28971i	−0.0887491	+	0.153718i
$459$	1.78495	−	35.5079i	0.0833145	−	1.65737i
$460$	−0.370723	−	0.642111i	−0.0172851	−	0.0299386i
$461$	−5.97661	−	10.3518i	−0.278359	−	0.482131i	0.692618	−	0.721304i	$-0.256457\pi$
$461$	−5.97661	−	10.3518i	−0.278359	−	0.482131i	−0.970977	+	0.239173i	$0.923124\pi$
$462$		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	$0.0667286\pi$
$464$	−1.46457			−0.0679911
$465$	23.2038	−	3.69204i	1.07605	−	0.171214i
$466$	6.67059			0.309009
$467$	5.61505	+	9.72555i	0.259833	+	0.450045i	0.966197	−	0.257804i	$-0.0829990\pi$
$467$	5.61505	+	9.72555i	0.259833	+	0.450045i	−0.706364	+	0.707849i	$0.749666\pi$
$468$	1.69850	+	1.52496i	0.0785130	+	0.0704915i
$469$		0			0
$470$	−1.46169	−	2.53173i	−0.0674230	−	0.116780i
$471$	−32.4669	+	5.16592i	−1.49600	+	0.238033i
$472$	0.993163	+	1.72021i	0.0457141	+	0.0791791i
$473$	26.5208	+	45.9354i	1.21943	+	2.11211i
$474$	−22.9984	+	3.65935i	−1.05635	+	0.168079i
$475$	1.84501	+	3.19565i	0.0846550	+	0.146627i
$476$		0			0
$477$	0.642950	−	0.209918i	0.0294387	−	0.00961150i
$478$	−7.82038	−	13.5453i	−0.357696	−	0.619547i
$479$	32.6271			1.49077			0.745385	−	0.666634i	$-0.232266\pi$
$479$	32.6271			1.49077			0.745385	+	0.666634i	$0.232266\pi$
$480$	−3.01204	+	0.479256i	−0.137480	+	0.0218749i
$481$	2.19562			0.100111
$482$	10.7060	−	18.5434i	0.487646	−	0.844627i
$483$		0			0
$484$	−13.2564	−	22.9607i	−0.602562	−	1.04367i
$485$	−3.20137	−	5.54494i	−0.145367	−	0.251783i
$486$	10.9834	−	11.0618i	0.498219	−	0.501774i
$487$	1.84897	−	3.20251i	0.0837848	−	0.145120i	−0.821088	−	0.570802i	$-0.806632\pi$
$487$	1.84897	−	3.20251i	0.0837848	−	0.145120i	0.904873	+	0.425682i	$0.139966\pi$
$488$	−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	$0.844744\pi$
$492$	4.30150	−	11.2297i	0.193927	−	0.506272i
$493$	10.0208			0.451314
$494$	0.739123	−	1.28020i	0.0332547	−	0.0575989i
$495$	24.0751	+	21.6154i	1.08210	+	0.971541i
$496$	−7.70370			−0.345906
$497$		0			0
$498$	1.93598	−	5.05415i	0.0867535	−	0.226482i
$499$	−31.7954			−1.42336			−0.711678	−	0.702506i	$-0.752064\pi$
$499$	−31.7954			−1.42336			−0.711678	+	0.702506i	$0.752064\pi$
$500$	−6.07442	−	10.5212i	−0.271656	−	0.470523i
$501$	−1.24828	−	1.53926i	−0.0557692	−	0.0687692i
$502$	−11.8015	+	20.4408i	−0.526727	+	0.912318i
$503$	−30.8252			−1.37443			−0.687214	−	0.726455i	$-0.741166\pi$
$503$	−30.8252			−1.37443			−0.687214	+	0.726455i	$0.741166\pi$
$504$		0			0
$505$	−14.1053			−0.627679
$506$	1.28947	−	2.23342i	0.0573238	−	0.0992877i
$507$	−21.2466	+	3.38063i	−0.943597	+	0.150139i
$508$	9.47661	+	16.4140i	0.420457	+	0.728252i
$509$	−8.01616			−0.355310			−0.177655	−	0.984093i	$-0.556851\pi$
$509$	−8.01616			−0.355310			−0.177655	+	0.984093i	$0.556851\pi$
$510$	20.6088	−	3.27913i	0.912572	−	0.145202i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−8.47825	−	5.48016i	−0.374324	−	0.241955i
$514$	10.1300	−	17.5456i	0.446814	−	0.773904i
$515$	−12.0241			−0.529844
$516$	9.44802	+	11.6504i	0.415926	+	0.512880i
$517$	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
$521$	−14.8646	+	25.7462i	−0.651229	+	1.12796i	0.331596	+	0.943421i	$0.392413\pi$
$521$	−14.8646	+	25.7462i	−0.651229	+	1.12796i	−0.982825	+	0.184540i	$0.940920\pi$
$522$	3.26935	+	2.93533i	0.143095	+	0.128476i
$523$	−13.4698	−	23.3303i	−0.588992	−	1.02016i	−0.994365	−	0.106013i	$-0.966192\pi$
$523$	−13.4698	−	23.3303i	−0.588992	−	1.02016i	0.405373	−	0.914152i	$-0.367142\pi$
$524$	−3.64652	−	6.31595i	−0.159299	−	0.275914i
$525$		0			0
$526$	11.2443	−	19.4757i	0.490276	−	0.849183i
$527$	52.7097			2.29607
$528$	−6.68194	−	8.23953i	−0.290794	−	0.358579i
$529$	−22.8227			−0.992291
$530$	0.198495	+	0.343803i	0.00862207	+	0.0149339i
$531$	1.23065	−	5.83052i	0.0534057	−	0.253023i
$532$		0			0
$533$	−2.64132	−	4.57489i	−0.114408	−	0.198161i
$534$	−1.61273	+	4.21024i	−0.0697894	+	0.182195i
$535$	−3.12188	−	5.40726i	−0.134971	−	0.233776i
$536$	−3.39248	−	5.87594i	−0.146533	−	0.253802i
$537$	9.63160	+	11.8768i	0.415634	+	0.512520i
$538$	12.6706	+	21.9461i	0.546268	+	0.946164i
$539$		0			0
$540$	7.68427	+	4.96695i	0.330678	+	0.213744i
$541$	7.15568	+	12.3940i	0.307647	+	0.532859i	0.977847	−	0.209321i	$-0.0671252\pi$
$541$	7.15568	+	12.3940i	0.307647	+	0.532859i	−0.670201	+	0.742180i	$0.733792\pi$
$542$	−13.7576			−0.590940
$543$	0.823649	−	2.15025i	0.0353462	−	0.0922760i
$544$	−6.84213			−0.293354
$545$	−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	$0.819384\pi$
$548$	4.09097	+	7.08577i	0.174758	+	0.302689i
$549$	29.5172	−	9.63716i	1.25977	−	0.411304i
$550$	5.81642	−	10.0743i	0.248013	−	0.429571i
$551$	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
$555$	8.69166	−	1.38296i	0.368940	−	0.0587033i
$556$	−12.4646			−0.528616
$557$	8.84338	−	15.3172i	0.374706	−	0.649010i	−0.615577	−	0.788077i	$-0.711077\pi$
$557$	8.84338	−	15.3172i	0.374706	−	0.649010i	0.990283	+	0.139067i	$0.0444103\pi$
$558$	17.1969	+	15.4399i	0.728001	+	0.653623i
$559$	6.58934			0.278699
$560$		0			0
$561$	45.7187	+	56.3759i	1.93025	+	2.38019i
$562$	−1.26896			−0.0535277
$563$	0.468531	+	0.811520i	0.0197462	+	0.0342015i	0.875730	−	0.482802i	$-0.160381\pi$
$563$	0.468531	+	0.811520i	0.0197462	+	0.0342015i	−0.855983	+	0.517003i	$0.827048\pi$
$564$	1.02859	−	2.68527i	0.0433115	−	0.113070i
$565$	−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	−0.999969	−	0.00790437i	$-0.997484\pi$
$569$	−11.7632	+	20.3745i	−0.493139	+	0.854142i	0.506830	+	0.862046i	$0.330817\pi$
$570$	2.11956	−	5.53340i	0.0887787	−	0.231769i
$571$	0.242002	+	0.419160i	0.0101275	+	0.0175413i	0.871045	−	0.491204i	$-0.163443\pi$
$571$	0.242002	+	0.419160i	0.0101275	+	0.0175413i	−0.860917	+	0.508745i	$0.830110\pi$
$572$	−4.66019			−0.194852
$573$	17.6391	+	21.7509i	0.736885	+	0.908655i
$574$		0			0
$575$	0.799737			0.0333514
$576$	−2.23229	−	2.00422i	−0.0930119	−	0.0835091i
$577$	2.23065	−	3.86360i	0.0928633	−	0.160844i	−0.815852	−	0.578261i	$-0.803731\pi$
$577$	2.23065	−	3.86360i	0.0928633	−	0.160844i	0.908715	+	0.417417i	$0.137065\pi$
$578$	29.8148			1.24013
$579$	−24.2353	+	3.85616i	−1.00718	+	0.160257i
$580$	−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
$584$	−0.153353	+	0.265616i	−0.00634581	+	0.0109913i
$585$	3.82094	−	1.24751i	0.157976	−	0.0515781i
$586$	−7.72545	−	13.3809i	−0.319135	−	0.552759i
$587$	−8.31518	−	14.4023i	−0.343204	−	0.594447i	0.641822	−	0.766854i	$-0.278179\pi$
$587$	−8.31518	−	14.4023i	−0.343204	−	0.594447i	−0.985026	+	0.172407i	$0.944846\pi$
$588$		0			0
$589$	7.48345	−	12.9617i	0.308350	−	0.534078i
$590$	3.49768			0.143997
$591$	−9.81518	+	25.6239i	−0.403742	+	1.05402i
$592$	−2.88564			−0.118599
$593$	−20.7632	−	35.9629i	−0.852642	−	1.47682i	−0.878815	−	0.477163i	$-0.841665\pi$
$593$	−20.7632	−	35.9629i	−0.852642	−	1.47682i	0.0261726	−	0.999657i	$-0.491668\pi$
$594$	−1.59781	+	31.7851i	−0.0655589	+	1.30416i
$595$		0			0
$596$	−4.41423	−	7.64567i	−0.180814	−	0.313179i
$597$	9.75636	+	12.0306i	0.399301	+	0.492380i
$598$	−0.160190	−	0.277457i	−0.00655065	−	0.0113461i
$599$	−7.53831	−	13.0567i	−0.308007	−	0.533483i	0.669919	−	0.742434i	$-0.266329\pi$
$599$	−7.53831	−	13.0567i	−0.308007	−	0.533483i	−0.977926	+	0.208950i	$0.932995\pi$
$600$	1.17674	−	3.07204i	0.0480403	−	0.125416i
$601$	8.05555	+	13.9526i	0.328593	+	0.569139i	0.982233	−	0.187666i	$-0.0600924\pi$
$601$	8.05555	+	13.9526i	0.328593	+	0.569139i	−0.653640	+	0.756805i	$0.726759\pi$
$602$		0			0
$603$	−4.20370	+	19.9161i	−0.171188	+	0.811044i
$604$	7.49316	+	12.9785i	0.304892	+	0.528089i
$605$	−46.6856			−1.89804
$606$	−8.73912	−	10.7762i	−0.355003	−	0.437755i
$607$	−19.5732			−0.794451			−0.397225	−	0.917721i	$-0.630027\pi$
$607$	−19.5732			−0.794451			−0.397225	+	0.917721i	$0.630027\pi$
$608$	−0.971410	+	1.68253i	−0.0393959	+	0.0682357i
$609$		0			0
$610$	9.11273	+	15.7837i	0.368963	+	0.639063i
$611$	−0.631600	−	1.09396i	−0.0255518	−	0.0442570i
$612$	15.2736	+	13.7131i	0.617399	+	0.554321i
$613$	−2.77579	+	4.80782i	−0.112113	+	0.194186i	−0.916622	−	0.399755i	$-0.869095\pi$
$613$	−2.77579	+	4.80782i	−0.112113	+	0.194186i	0.804509	+	0.593941i	$0.202429\pi$
$614$	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	$0.158535\pi$
$618$	−7.44966	−	9.18620i	−0.299669	−	0.369523i
$619$	−4.50232			−0.180964			−0.0904818	−	0.995898i	$-0.528841\pi$
$619$	−4.50232			−0.180964			−0.0904818	+	0.995898i	$0.528841\pi$
$620$	−6.78263	+	11.7479i	−0.272397	+	0.471805i
$621$	−1.94733	+	0.997454i	−0.0781438	+	0.0400264i
$622$	7.69002			0.308342
$623$		0			0
$624$	−1.30150	+	0.207087i	−0.0521019	+	0.00829011i
$625$	−11.8960			−0.475842
$626$	−0.861564	−	1.49227i	−0.0344350	−	0.0596432i
$627$	20.3542	−	3.23862i	0.812867	−	0.129338i
$628$	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
$633$	24.8428	+	30.6338i	0.987414	+	1.21758i
$634$	−16.6014	−	28.7544i	−0.659325	−	1.14198i
$635$	33.3743			1.32442
$636$	−0.139680	+	0.364654i	−0.00553868	+	0.0144595i
$637$		0			0
$638$	−8.97017			−0.355132
$639$	−24.0751	−	21.6154i	−0.952397	−	0.855093i
$640$	0.880438	−	1.52496i	0.0348024	−	0.0602795i
$641$	−0.948577			−0.0374666			−0.0187333	−	0.999825i	$-0.505963\pi$
$641$	−0.948577			−0.0374666			−0.0187333	+	0.999825i	$0.505963\pi$
$642$	2.19686	−	5.73520i	0.0867032	−	0.226350i
$643$	9.84897	−	17.0589i	0.388405	−	0.672738i	−0.603830	−	0.797113i	$-0.706359\pi$
$643$	9.84897	−	17.0589i	0.388405	−	0.672738i	0.992235	+	0.124375i	$0.0396927\pi$
$644$		0			0
$645$	26.0848	−	4.15044i	1.02709	−	0.163424i
$646$	6.64652	−	11.5121i	0.261504	−	0.452938i
$647$	−11.7271	+	20.3119i	−0.461039	+	0.798543i	−0.999013	−	0.0444181i	$-0.985857\pi$
$647$	−11.7271	+	20.3119i	−0.461039	+	0.798543i	0.537974	+	0.842962i	$0.319190\pi$
$648$	0.966208	+	8.94799i	0.0379562	+	0.351510i
$649$	6.08289	+	10.5359i	0.238774	+	0.413569i
$650$	−0.722572	−	1.25153i	−0.0283416	−	0.0490891i
$651$		0			0
$652$	−7.51887	+	13.0231i	−0.294462	+	0.510023i
$653$	22.7907			0.891869			0.445935	−	0.895065i	$-0.352871\pi$
$653$	22.7907			0.891869			0.445935	+	0.895065i	$0.352871\pi$
$654$	−1.20370	+	0.191524i	−0.0470683	+	0.00748919i
$655$	−12.8421			−0.501784
$656$	3.47141	+	6.01266i	0.135536	+	0.234755i
$657$	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	$-0.339153\pi$
$660$	−18.4480	+	2.93533i	−0.718088	+	0.114257i
$661$	−13.3691	−	23.1559i	−0.519997	−	0.900662i	−0.999730	−	0.0232469i	$-0.992600\pi$
$661$	−13.3691	−	23.1559i	−0.519997	−	0.900662i	0.479732	−	0.877415i	$-0.340734\pi$
$662$	−1.44445	−	2.50187i	−0.0561403	−	0.0972379i
$663$	8.90507	−	1.41692i	0.345844	−	0.0550284i
$664$	1.56238	+	2.70612i	0.0606322	+	0.105018i
$665$		0			0
$666$	6.44158	+	5.78346i	0.249606	+	0.224104i
$667$	−0.308342	−	0.534063i	−0.0119390	−	0.0206790i
$668$	1.14419			0.0442702
$669$	−22.0413	+	3.50707i	−0.852167	+	0.135591i
$670$	−11.9475			−0.461571
$671$	−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	$0.964440\pi$
$674$	−4.36156	−	7.55445i	−0.168001	−	0.290987i
$675$	−8.78387	+	4.49923i	−0.338091	+	0.173176i
$676$	6.21053	−	10.7570i	0.238867	−	0.413729i
$677$	−10.3490	+	17.9249i	−0.397743	+	0.688911i	−0.993447	−	0.114293i	$-0.963540\pi$
$677$	−10.3490	+	17.9249i	−0.397743	+	0.688911i	0.595704	+	0.803204i	$0.296873\pi$
$678$	−14.5435	+	2.31407i	−0.558540	+	0.0888712i
$679$		0			0
$680$	−6.02408	+	10.4340i	−0.231013	+	0.400126i
$681$	13.6283	−	35.5786i	0.522239	−	1.36338i
$682$	−47.1833			−1.80674
$683$	14.2918	−	24.7541i	0.546860	−	0.947190i	−0.451627	−	0.892207i	$-0.649156\pi$
$683$	14.2918	−	24.7541i	0.546860	−	0.947190i	0.998487	−	0.0549828i	$-0.0175104\pi$
$684$	5.54063	−	1.80897i	0.211851	−	0.0691678i
$685$	14.4074			0.550478
$686$		0			0
$687$	−2.35348	+	6.14409i	−0.0897910	+	0.234412i
$688$	−8.66019			−0.330167
$689$	0.0857699	+	0.148558i	0.00326757	+	0.00565960i
$690$	−0.808897	−	0.997454i	−0.0307942	−	0.0379724i
$691$	−3.34897	+	5.80059i	−0.127401	+	0.220665i	−0.922669	−	0.385593i	$-0.873997\pi$
$691$	−3.34897	+	5.80059i	−0.127401	+	0.220665i	0.795268	+	0.606258i	$0.207330\pi$
$692$	−0.497677			−0.0189188
$693$		0			0
$694$	9.69467			0.368005
$695$	−10.9743	+	19.0080i	−0.416278	+	0.721016i
$696$	−2.50520	+	0.398611i	−0.0949594	+	0.0151093i
$697$	−23.7518	−	41.1394i	−0.899665	−	1.55827i
$698$	28.3984			1.07489
$699$	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	$0.657495\pi$
$702$	3.32038	+	2.14622i	0.125320	+	0.0810040i
$703$	2.80314	−	4.85518i	0.105722	−	0.183117i
$704$	6.12476			0.230836
$705$	−3.18934	−	3.93278i	−0.120117	−	0.148117i
$706$	−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	−0.937183	−	0.348838i	$-0.886576\pi$
$709$	−4.43310	+	7.67836i	−0.166489	+	0.288367i	0.770694	+	0.637205i	$0.219910\pi$
$710$	9.49549	−	16.4467i	0.356359	−	0.617232i
$711$	−38.3435	+	12.5189i	−1.43799	+	0.469494i
$712$	−1.30150	−	2.25427i	−0.0487760	−	0.0844824i
$713$	−1.62188	−	2.80919i	−0.0607401	−	0.105205i
$714$		0			0
$715$	−4.10301	+	7.10662i	−0.153444	+	0.265773i
$716$	−8.82846			−0.329935
$717$	−17.0636	−	21.0412i	−0.637253	−	0.785799i
$718$	−32.1592			−1.20017
$719$	−11.8015	−	20.4408i	−0.440122	−	0.762313i	0.557576	−	0.830126i	$-0.311731\pi$
$719$	−11.8015	−	20.4408i	−0.440122	−	0.762313i	−0.997698	+	0.0678123i	$0.978398\pi$
$720$	−5.02175	+	1.63957i	−0.187150	+	0.0611030i
$721$		0			0
$722$	7.61273	+	13.1856i	0.283316	+	0.490718i
$723$	13.2661	−	34.6329i	0.493371	−	1.28801i
$724$	0.664703	+	1.15130i	0.0247035	+	0.0427877i
$725$	−1.39084	−	2.40901i	−0.0516546	−	0.0894683i
$726$	−28.9246	−	35.6671i	−1.07349	−	1.32373i
$727$	−3.25692	−	5.64115i	−0.120792	−	0.209219i	0.799288	−	0.600948i	$-0.205210\pi$
$727$	−3.25692	−	5.64115i	−0.120792	−	0.209219i	−0.920080	+	0.391730i	$0.871877\pi$
$728$		0			0
$729$	15.7769	−	21.9110i	0.584329	−	0.811517i
$730$	0.270036	+	0.467717i	0.00999449	+	0.0173110i
$731$	59.2542			2.19159
$732$	−6.41260	+	16.7409i	−0.237016	+	0.618763i
$733$	23.1981			0.856842			0.428421	−	0.903579i	$-0.359070\pi$
$733$	23.1981			0.856842			0.428421	+	0.903579i	$0.359070\pi$
$734$	17.3015	−	29.9671i	0.638610	−	1.10611i
$735$		0			0
$736$	0.210533	+	0.364654i	0.00776036	+	0.0134413i
$737$	−20.7781	−	35.9888i	−0.765372	−	1.32566i
$738$	4.30150	−	20.3794i	0.158341	−	0.750178i
$739$	−7.57838	+	13.1261i	−0.278775	+	0.482853i	−0.971081	−	0.238752i	$-0.923262\pi$
$739$	−7.57838	+	13.1261i	−0.278775	+	0.482853i	0.692305	+	0.721605i	$0.256595\pi$
$740$	−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	$0.227972\pi$
$744$	−13.1774	+	2.09671i	−0.483108	+	0.0768689i
$745$	−15.5458			−0.569555
$746$	−5.48796	+	9.50543i	−0.200929	+	0.348018i
$747$	1.93598	−	9.17220i	0.0708339	−	0.335593i
$748$	−41.9064			−1.53225
$749$		0			0
$750$	−13.2540	−	16.3436i	−0.483969	−	0.596784i
$751$	40.2118			1.46735			0.733674	−	0.679501i	$-0.237804\pi$
$751$	40.2118			1.46735			0.733674	+	0.679501i	$0.237804\pi$
$752$	0.830095	+	1.43777i	0.0302704	+	0.0524300i
$753$	−14.6235	+	38.1767i	−0.532911	+	1.39124i
$754$	−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
$759$	1.59781	−	4.17129i	0.0579968	−	0.151408i
$760$	1.71053	+	2.96273i	0.0620476	+	0.107470i
$761$	23.6627			0.857771			0.428886	−	0.903359i	$-0.358906\pi$
$761$	23.6627			0.857771			0.428886	+	0.903359i	$0.358906\pi$
$762$	20.6774	+	25.4974i	0.749064	+	0.923674i
$763$		0			0
$764$	−16.1683			−0.584947
$765$	34.3595	−	11.2181i	1.24227	−	0.405592i
$766$	−10.5120	+	18.2074i	−0.379815	+	0.657860i
$767$	1.51135			0.0545717
$768$	1.71053	−	0.272169i	0.0617236	−	0.00982104i
$769$	5.62764	−	9.74736i	0.202938	−	0.351499i	−0.746536	−	0.665345i	$-0.768284\pi$
$769$	5.62764	−	9.74736i	0.202938	−	0.351499i	0.949474	+	0.313846i	$0.101618\pi$
$770$		0			0
$771$	12.5523	−	32.7694i	0.452059	−	1.18016i
$772$	7.08414	−	12.2701i	0.254964	−	0.441610i
$773$	−0.138992	+	0.240741i	−0.00499919	+	0.00865886i	−0.868514	−	0.495664i	$-0.834925\pi$
$773$	−0.138992	+	0.240741i	−0.00499919	+	0.00865886i	0.863515	+	0.504323i	$0.168258\pi$
$774$	19.3320	+	17.3569i	0.694875	+	0.623882i
$775$	−7.31587	−	12.6715i	−0.262794	−	0.455172i
$776$	1.81806	+	3.14897i	0.0652644	+	0.113041i
$777$		0			0
$778$	−6.86909	+	11.8976i	−0.246269	+	0.426550i
$779$	−13.4887			−0.483281
$780$	−0.830095	+	2.16708i	−0.0297222	+	0.0775937i
$781$	66.0553			2.36364
$782$	−1.44050	−	2.49501i	−0.0515121	−	0.0892215i
$783$	6.39123	+	4.13116i	0.228404	+	0.147636i
$784$		0			0
$785$	−16.7112	−	28.9447i	−0.596449	−	1.03308i
$786$	−7.95649	−	9.81118i	−0.283799	−	0.349953i
$787$	−14.6940	−	25.4507i	−0.523784	−	0.907220i	−0.999617	−	0.0276845i	$-0.991187\pi$
$787$	−14.6940	−	25.4507i	−0.523784	−	0.907220i	0.475833	−	0.879536i	$-0.342147\pi$
$788$	−7.92107	−	13.7197i	−0.282176	−	0.488744i
$789$	13.9331	−	36.3743i	0.496032	−	1.29496i
$790$	−11.8376	−	20.5034i	−0.421164	−	0.729477i
$791$		0			0
$792$	−13.6722	−	12.2754i	−0.485821	−	0.436186i
$793$	3.93762	+	6.82015i	0.139829	+	0.242191i
$794$	−7.15787			−0.254023
$795$	0.433105	+	0.534063i	0.0153606	+	0.0189413i
$796$	−8.94282			−0.316970
$797$	−0.433105	+	0.750160i	−0.0153414	+	0.0265720i	−0.873594	−	0.486655i	$-0.838217\pi$
$797$	−0.433105	+	0.750160i	−0.0153414	+	0.0265720i	0.858253	+	0.513227i	$0.171550\pi$
$798$		0			0
$799$	−5.67962	−	9.83739i	−0.200931	−	0.348022i
$800$	0.949657	+	1.64485i	0.0335754	+	0.0581544i
$801$	−1.61273	+	7.64068i	−0.0569828	+	0.269970i
$802$	4.63968	−	8.03616i	0.163833	−	0.283767i
$803$	−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
$807$	27.6465	+	34.0910i	0.973203	+	1.20006i
$808$	8.01040			0.281805
$809$	9.66703	−	16.7438i	0.339875	−	0.588680i	−0.644534	−	0.764575i	$-0.722949\pi$
$809$	9.66703	−	16.7438i	0.339875	−	0.588680i	0.984409	+	0.175895i	$0.0562820\pi$
$810$	14.4960	+	6.40472i	0.509339	+	0.225039i
$811$	47.0391			1.65177			0.825884	−	0.563841i	$-0.190677\pi$
$811$	47.0391			1.65177			0.825884	+	0.563841i	$0.190677\pi$
$812$		0			0
$813$	−23.5328	+	3.74439i	−0.825333	+	0.131321i
$814$	−17.6739			−0.619469
$815$	13.2398	+	22.9320i	0.463770	+	0.803274i
$816$	−11.7037	+	1.86221i	−0.409711	+	0.0651905i
$817$	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	−0.878071	−	0.478530i	$-0.841170\pi$
$821$	−0.705332	+	1.22167i	−0.0246162	+	0.0426366i	0.853455	+	0.521167i	$0.174503\pi$
$822$	8.92627	+	11.0070i	0.311339	+	0.383914i
$823$	17.5196	+	30.3448i	0.610694	+	1.05775i	0.991124	+	0.132943i	$0.0424426\pi$
$823$	17.5196	+	30.3448i	0.610694	+	1.05775i	−0.380430	+	0.924810i	$0.624224\pi$
$824$	6.82846			0.237881
$825$	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	$0.604822\pi$
$828$	0.260877	−	1.23597i	0.00906609	−	0.0429529i
$829$	−19.0848	+	33.0559i	−0.662843	+	1.14808i	0.317022	+	0.948418i	$0.397317\pi$
$829$	−19.0848	+	33.0559i	−0.662843	+	1.14808i	−0.979865	+	0.199660i	$0.936016\pi$
$830$	5.50232			0.190988
$831$	2.03379	−	5.30949i	0.0705515	−	0.184184i
$832$	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
$836$	−5.94966	+	10.3051i	−0.205773	+	0.356410i
$837$	33.6181	+	21.7300i	1.16201	+	0.751099i
$838$	4.16827	+	7.21966i	0.143991	+	0.249399i
$839$	−17.3691	−	30.0841i	−0.599648	−	1.03862i	−0.992873	−	0.119178i	$-0.961974\pi$
$839$	−17.3691	−	30.0841i	−0.599648	−	1.03862i	0.393225	−	0.919442i	$-0.371359\pi$
$840$		0			0
$841$	13.4275	−	23.2571i	0.463018	−	0.801970i
$842$	7.00465			0.241396
$843$	−2.17059	+	0.345370i	−0.0747592	+	0.0118952i
$844$	−22.7713			−0.783820
$845$	−10.9360	−	18.9417i	−0.376209	−	0.651614i
$846$	1.02859	−	4.87320i	0.0353637	−	0.167544i
$847$		0			0
$848$	−0.112725	−	0.195246i	−0.00387100	−	0.00670476i
$849$	14.0133	−	2.22970i	0.480935	−	0.0765231i
$850$	−6.49768	−	11.2543i	−0.222868	−	0.386020i
$851$	−0.607523	−	1.05226i	−0.0208256	−	0.0360711i
$852$	18.4480	−	2.93533i	0.632019	−	0.100563i
$853$	21.1586	+	36.6477i	0.724455	+	1.25479i	0.959198	+	0.282736i	$0.0912419\pi$
$853$	21.1586	+	36.6477i	0.724455	+	1.25479i	−0.234743	+	0.972058i	$0.575425\pi$
$854$		0			0
$855$	2.11956	−	10.0419i	0.0724875	−	0.343427i
$856$	1.77292	+	3.07078i	0.0605970	+	0.104957i
$857$	−14.9234			−0.509773			−0.254887	−	0.966971i	$-0.582038\pi$
$857$	−14.9234			−0.509773			−0.254887	+	0.966971i	$0.582038\pi$
$858$	−7.97141	+	1.26836i	−0.272139	+	0.0433010i
$859$	−19.4132			−0.662368			−0.331184	−	0.943566i	$-0.607448\pi$
$859$	−19.4132			−0.662368			−0.331184	+	0.943566i	$0.607448\pi$
$860$	−7.62476	+	13.2065i	−0.260002	+	0.450337i
$861$		0			0
$862$	−1.72545	−	2.98857i	−0.0587691	−	0.101791i
$863$	−0.542263	−	0.939227i	−0.0184588	−	0.0319717i	0.856648	−	0.515901i	$-0.172543\pi$
$863$	−0.542263	−	0.939227i	−0.0184588	−	0.0319717i	−0.875107	+	0.483929i	$0.839209\pi$
$864$	−4.36389	−	2.82073i	−0.148462	−	0.0959630i
$865$	−0.438174	+	0.758939i	−0.0148984	+	0.0258047i
$866$	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
$870$	−1.59781	+	4.17129i	−0.0541708	+	0.141420i
$871$	−5.16251			−0.174925
$872$	0.351848	−	0.609419i	0.0119151	−	0.0206375i
$873$	2.25280	−	10.6732i	0.0762456	−	0.361232i
$874$	−0.818057			−0.0276712
$875$		0			0
$876$	−0.190024	+	0.496083i	−0.00642031	+	0.0167611i
$877$	−28.5699			−0.964737			−0.482369	−	0.875968i	$-0.660223\pi$
$877$	−28.5699			−0.964737			−0.482369	+	0.875968i	$0.660223\pi$
$878$	−14.4480	−	25.0247i	−0.487597	−	0.844543i
$879$	−16.8565	−	20.7858i	−0.568555	−	0.701088i
$880$	5.39248	−	9.34004i	0.181780	−	0.314853i
$881$	−45.9967			−1.54967			−0.774835	−	0.632164i	$-0.782167\pi$
$881$	−45.9967			−1.54967			−0.774835	+	0.632164i	$0.782167\pi$
$882$		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
$885$	5.98289	−	0.951958i	0.201113	−	0.0319997i
$886$	6.88044	+	11.9173i	0.231153	+	0.400368i
$887$	28.3398			0.951558			0.475779	−	0.879565i	$-0.342166\pi$
$887$	28.3398			0.951558			0.475779	+	0.879565i	$0.342166\pi$
$888$	−4.93598	+	0.785381i	−0.165641	+	0.0263557i
$889$		0			0
$890$	−4.58358			−0.153642
$891$	5.91780	+	54.8043i	0.198254	+	1.83601i
$892$	6.44282	−	11.1593i	0.215722	−	0.373641i
$893$	−3.22545			−0.107936
$894$	−9.63160	−	11.8768i	−0.322129	−	0.397218i
$895$	−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
$899$	−5.64132	+	9.77104i	−0.188148	+	0.325883i
$900$	1.17674	−	5.57510i	0.0392247	−	0.185837i
$901$	0.771280	+	1.33590i	0.0256951	+	0.0445052i
$902$	21.2616	+	36.8261i	0.707933	+	1.22618i
$903$		0			0
$904$	4.25116	−	7.36323i	0.141392	−	0.244897i
$905$	2.34092			0.0778149
$906$	16.3497	+	20.1608i	0.543181	+	0.669798i
$907$	7.94747			0.263891			0.131946	−	0.991257i	$-0.457878\pi$
$907$	7.94747			0.263891			0.131946	+	0.991257i	$0.457878\pi$
$908$	10.9984	+	19.0497i	0.364994	+	0.632187i
$909$	−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	$0.875728\pi$
$912$	−1.20370	+	3.14241i	−0.0398584	+	0.104056i
$913$	9.56922	+	16.5744i	0.316695	+	0.548532i
$914$	−10.0149	−	17.3463i	−0.331264	−	0.573766i
$915$	19.8834	+	24.5184i	0.657327	+	0.810552i
$916$	−1.89931	−	3.28971i	−0.0627551	−	0.108695i
$917$		0			0
$918$	29.8583	+	19.2998i	0.985471	+	0.636988i
$919$	−12.0224	−	20.8235i	−0.396584	−	0.686903i	0.596718	−	0.802451i	$-0.296471\pi$
$919$	−12.0224	−	20.8235i	−0.396584	−	0.686903i	−0.993302	+	0.115548i	$0.963138\pi$
$920$	0.741446			0.0244448
$921$	3.03543	−	7.92439i	0.100021	−	0.261118i
$922$	11.9532			0.393658
$923$	4.10301	−	7.10662i	0.135052	−	0.233917i
$924$		0			0
$925$	−2.74037	−	4.74646i	−0.0901027	−	0.156062i
$926$	6.64527	+	11.5100i	0.218377	+	0.378240i
$927$	−15.2431	−	13.6857i	−0.500648	−	0.449498i
$928$	0.732287	−	1.26836i	0.0240385	−	0.0416359i
$929$	13.9331	−	24.1328i	0.457130	−	0.791773i	−0.541678	−	0.840586i	$-0.682211\pi$
$929$	13.9331	−	24.1328i	0.457130	−	0.791773i	0.998808	+	0.0488134i	$0.0155440\pi$
$930$	−8.40451	+	21.9411i	−0.275595	+	0.719478i
$931$		0			0
$932$	−3.33530	+	5.77690i	−0.109251	+	0.189229i
$933$	13.1540	−	2.09298i	0.430644	−	0.0685212i
$934$	−11.2301			−0.367460
$935$	−36.8960	+	63.9058i	−1.20663	+	2.08994i
$936$	−2.16991	+	0.708458i	−0.0709256	+	0.0231567i
$937$	−53.2211			−1.73866			−0.869328	−	0.494235i	$-0.835448\pi$
$937$	−53.2211			−1.73866			−0.869328	+	0.494235i	$0.835448\pi$
$938$		0			0
$939$	−1.87988	−	2.31809i	−0.0613477	−	0.0756480i
$940$	2.92339			0.0953505
$941$	−15.0241	−	26.0225i	−0.489771	−	0.848308i	0.510160	−	0.860080i	$-0.329586\pi$
$941$	−15.0241	−	26.0225i	−0.489771	−	0.848308i	−0.999931	+	0.0117715i	$0.996253\pi$
$942$	11.7596	−	30.7001i	0.383150	−	1.00026i
$943$	−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	−0.339476	−	0.940615i	$-0.610250\pi$
$947$	19.8445	−	34.3716i	0.644858	−	1.11693i	0.984334	−	0.176312i	$-0.0564169\pi$
$948$	8.33009	−	21.7468i	0.270549	−	0.706305i
$949$	0.116683	+	0.202101i	0.00378769	+	0.00656047i
$950$	−3.69002			−0.119720
$951$	−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	$0.378136\pi$
$954$	−0.139680	+	0.661770i	−0.00452232	+	0.0214256i
$955$	−14.2352	+	24.6560i	−0.460639	+	0.797850i
$956$	15.6408			0.505858
$957$	−15.3438	+	2.44140i	−0.495994	+	0.0789192i
$958$	−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
$962$	−1.09781	+	1.90146i	−0.0353948	+	0.0613055i
$963$	2.19686	−	10.4082i	0.0707928	−	0.335399i
$964$	10.7060	+	18.5434i	0.344818	+	0.597242i
$965$	−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	$0.00304298\pi$
$968$	26.5127			0.852151
$969$	8.23585	−	21.5008i	0.264574	−	0.690706i
$970$	6.40275			0.205580
$971$	−13.1030	−	22.6951i	−0.420496	−	0.728320i	0.575492	−	0.817807i	$-0.304810\pi$
$971$	−13.1030	−	22.6951i	−0.420496	−	0.728320i	−0.995988	+	0.0894874i	$0.971477\pi$
$972$	4.08809	+	15.0429i	0.131126	+	0.482500i
$973$		0			0
$974$	1.84897	+	3.20251i	0.0592448	+	0.102615i
$975$	−1.57661	−	1.94412i	−0.0504919	−	0.0622618i
$976$	−5.17511	−	8.96355i	−0.165651	−	0.286916i
$977$	−10.5270	−	18.2332i	−0.336787	−	0.583332i	0.647039	−	0.762457i	$-0.276007\pi$
$977$	−10.5270	−	18.2332i	−0.336787	−	0.583332i	−0.983826	+	0.179124i	$0.942674\pi$
$978$	−9.31681	+	24.3228i	−0.297919	+	0.777757i
$979$	−7.97141	−	13.8069i	−0.254767	−	0.441270i
$980$		0			0
$981$	−2.00684	+	0.655217i	−0.0640734	+	0.0209195i
$982$	−18.7804	−	32.5287i	−0.599308	−	1.03803i
$983$	19.5297			0.622900			0.311450	−	0.950263i	$-0.399185\pi$
$983$	19.5297			0.622900			0.311450	+	0.950263i	$0.399185\pi$
$984$	7.57442	+	9.34004i	0.241464	+	0.297750i
$985$	−27.8960			−0.888842
$986$	−5.01040	+	8.67827i	−0.159564	+	0.276373i
$987$		0			0
$988$	0.739123	+	1.28020i	0.0235146	+	0.0407286i
$989$	−1.82326	−	3.15798i	−0.0579762	−	0.100418i
$990$	−30.7571	+	10.0419i	−0.977523	+	0.319154i
$991$	−7.49837	+	12.9875i	−0.238193	+	0.412563i	−0.960196	−	0.279327i	$-0.909889\pi$
$991$	−7.49837	+	12.9875i	−0.238193	+	0.412563i	0.722003	+	0.691890i	$0.243222\pi$
$992$	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
$996$	3.40903	+	4.20368i	0.108019	+	0.133199i
$997$	58.5641			1.85475			0.927373	−	0.374139i	$-0.122062\pi$
$997$	58.5641			1.85475			0.927373	+	0.374139i	$0.122062\pi$
$998$	15.8977	−	27.5356i	0.503232	−	0.871624i
$999$	12.5926	+	8.13960i	0.398412	+	0.257526i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.3	✓	6	63.34	odd	6
126.2.e.d.121.3	yes	6	7.5	odd	6
126.2.h.c.67.2	yes	6	7.6	odd	2
126.2.h.c.79.2	yes	6	63.61	odd	6
378.2.e.c.37.2		6	21.5	even	6
378.2.e.c.235.2		6	63.20	even	6
378.2.h.d.289.2		6	63.47	even	6
378.2.h.d.361.2		6	21.20	even	2
882.2.e.p.373.1		6	7.2	even	3
882.2.e.p.655.1		6	9.7	even	3
882.2.f.l.295.1		6	63.52	odd	6
882.2.f.l.589.1		6	7.3	odd	6
882.2.f.m.295.3		6	63.25	even	3
882.2.f.m.589.3		6	7.4	even	3
882.2.h.o.67.2		6	1.1	even	1	trivial
882.2.h.o.79.2		6	63.16	even	3	inner
1008.2.q.h.529.1		6	252.223	even	6
1008.2.q.h.625.1		6	28.19	even	6
1008.2.t.g.193.2		6	28.27	even	2
1008.2.t.g.961.2		6	252.187	even	6
1134.2.g.k.163.2		6	63.40	odd	6
1134.2.g.k.487.2		6	63.13	odd	6
1134.2.g.n.163.2		6	63.5	even	6
1134.2.g.n.487.2		6	63.41	even	6
2646.2.e.o.1549.2		6	21.2	odd	6
2646.2.e.o.2125.2		6	9.2	odd	6
2646.2.f.n.883.2		6	63.11	odd	6
2646.2.f.n.1765.2		6	21.11	odd	6
2646.2.f.o.883.2		6	63.38	even	6
2646.2.f.o.1765.2		6	21.17	even	6
2646.2.h.p.361.2		6	3.2	odd	2
2646.2.h.p.667.2		6	63.2	odd	6
3024.2.q.h.2305.2		6	84.47	odd	6
3024.2.q.h.2881.2		6	252.83	odd	6
3024.2.t.g.289.2		6	252.47	odd	6
3024.2.t.g.1873.2		6	84.83	odd	2
7938.2.a.bu.1.2		3	63.59	even	6
7938.2.a.bx.1.2		3	63.32	odd	6
7938.2.a.by.1.2		3	63.4	even	3
7938.2.a.cb.1.2		3	63.31	odd	6

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.619562 + 1.61745i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.76088 q^{5} +(-1.09097 - 1.34528i) q^{6} +1.00000 q^{8} +(-2.23229 - 2.00422i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.619562 + 1.61745i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.76088 q^{5} +(-1.09097 - 1.34528i) q^{6} +1.00000 q^{8} +(-2.23229 - 2.00422i) q^{9} +(0.880438 - 1.52496i) q^{10} +6.12476 q^{11} +(1.71053 - 0.272169i) q^{12} +(0.380438 - 0.658939i) q^{13} +(1.09097 - 2.84813i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.42107 - 5.92546i) q^{17} +(2.85185 - 0.931107i) q^{18} +(-0.971410 - 1.68253i) q^{19} +(0.880438 + 1.52496i) q^{20} +(-3.06238 + 5.30420i) q^{22} -0.421067 q^{23} +(-0.619562 + 1.61745i) q^{24} -1.89931 q^{25} +(0.380438 + 0.658939i) q^{26} +(4.62476 - 2.36887i) q^{27} +(0.732287 + 1.26836i) q^{29} +(1.92107 + 2.36887i) q^{30} +(3.85185 + 6.67160i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.79467 + 9.90650i) q^{33} +(3.42107 + 5.92546i) q^{34} +(-0.619562 + 2.93533i) q^{36} +(1.44282 + 2.49904i) q^{37} +1.94282 q^{38} +(0.830095 + 1.02359i) q^{39} -1.76088 q^{40} +(3.47141 - 6.01266i) q^{41} +(4.33009 + 7.49994i) q^{43} +(-3.06238 - 5.30420i) q^{44} +(3.93078 + 3.52918i) q^{45} +(0.210533 - 0.364654i) q^{46} +(0.830095 - 1.43777i) q^{47} +(-1.09097 - 1.34528i) q^{48} +(0.949657 - 1.64485i) q^{50} +(7.46457 + 9.20459i) q^{51} -0.760877 q^{52} +(-0.112725 + 0.195246i) q^{53} +(-0.260877 + 5.18960i) q^{54} -10.7850 q^{55} +(3.32326 - 0.528775i) q^{57} -1.46457 q^{58} +(0.993163 + 1.72021i) q^{59} +(-3.01204 + 0.479256i) q^{60} +(-5.17511 + 8.96355i) q^{61} -7.70370 q^{62} +1.00000 q^{64} +(-0.669905 + 1.16031i) q^{65} +(-6.68194 - 8.23953i) q^{66} +(-3.39248 - 5.87594i) q^{67} -6.84213 q^{68} +(0.260877 - 0.681054i) q^{69} +10.7850 q^{71} +(-2.23229 - 2.00422i) q^{72} +(-0.153353 + 0.265616i) q^{73} -2.88564 q^{74} +(1.17674 - 3.07204i) q^{75} +(-0.971410 + 1.68253i) q^{76} +(-1.30150 + 0.207087i) q^{78} +(6.72257 - 11.6438i) q^{79} +(0.880438 - 1.52496i) q^{80} +(0.966208 + 8.94799i) q^{81} +(3.47141 + 6.01266i) q^{82} +(1.56238 + 2.70612i) q^{83} +(-6.02408 + 10.4340i) q^{85} -8.66019 q^{86} +(-2.50520 + 0.398611i) q^{87} +6.12476 q^{88} +(-1.30150 - 2.25427i) q^{89} +(-5.02175 + 1.63957i) q^{90} +(0.210533 + 0.364654i) q^{92} +(-13.1774 + 2.09671i) q^{93} +(0.830095 + 1.43777i) q^{94} +(1.71053 + 2.96273i) q^{95} +(1.71053 - 0.272169i) q^{96} +(1.81806 + 3.14897i) q^{97} +(-13.6722 - 12.2754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 4 q^{3} - 3 q^{4} - 10 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 - 10 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9	\( 6 q - 3 q^{2} - 4 q^{3} - 3 q^{4} - 10 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9} + 5 q^{10} + 2 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} - 3 q^{16} + 4 q^{17} + 8 q^{18} + 3 q^{19} + 5 q^{20} - q^{22} + 14 q^{23} - 4 q^{24} + 4 q^{25} + 2 q^{26} - 7 q^{27} - 5 q^{29} - 5 q^{30} + 14 q^{31} - 3 q^{32} + 4 q^{33} + 4 q^{34} - 4 q^{36} - 9 q^{37} - 6 q^{38} - 3 q^{39} - 10 q^{40} + 12 q^{41} + 18 q^{43} - q^{44} + 31 q^{45} - 7 q^{46} - 3 q^{47} + 2 q^{48} - 2 q^{50} + 26 q^{51} - 4 q^{52} + 9 q^{53} - q^{54} - 14 q^{55} + 2 q^{57} + 10 q^{58} - 4 q^{59} + 7 q^{60} - 4 q^{61} - 28 q^{62} + 6 q^{64} - 12 q^{65} - 23 q^{66} + 5 q^{67} - 8 q^{68} + q^{69} + 14 q^{71} - 4 q^{72} + 25 q^{73} + 18 q^{74} + 25 q^{75} + 3 q^{76} + 9 q^{78} + 7 q^{79} + 5 q^{80} + 32 q^{81} + 12 q^{82} - 8 q^{83} + 14 q^{85} - 36 q^{86} + 20 q^{87} + 2 q^{88} + 9 q^{89} - 29 q^{90} - 7 q^{92} - 3 q^{93} - 3 q^{94} + 2 q^{95} + 2 q^{96} + 28 q^{97} - 41 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 4 * q^3 - 3 * q^4 - 10 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9 + 5 * q^10 + 2 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 - 3 * q^16 + 4 * q^17 + 8 * q^18 + 3 * q^19 + 5 * q^20 - q^22 + 14 * q^23 - 4 * q^24 + 4 * q^25 + 2 * q^26 - 7 * q^27 - 5 * q^29 - 5 * q^30 + 14 * q^31 - 3 * q^32 + 4 * q^33 + 4 * q^34 - 4 * q^36 - 9 * q^37 - 6 * q^38 - 3 * q^39 - 10 * q^40 + 12 * q^41 + 18 * q^43 - q^44 + 31 * q^45 - 7 * q^46 - 3 * q^47 + 2 * q^48 - 2 * q^50 + 26 * q^51 - 4 * q^52 + 9 * q^53 - q^54 - 14 * q^55 + 2 * q^57 + 10 * q^58 - 4 * q^59 + 7 * q^60 - 4 * q^61 - 28 * q^62 + 6 * q^64 - 12 * q^65 - 23 * q^66 + 5 * q^67 - 8 * q^68 + q^69 + 14 * q^71 - 4 * q^72 + 25 * q^73 + 18 * q^74 + 25 * q^75 + 3 * q^76 + 9 * q^78 + 7 * q^79 + 5 * q^80 + 32 * q^81 + 12 * q^82 - 8 * q^83 + 14 * q^85 - 36 * q^86 + 20 * q^87 + 2 * q^88 + 9 * q^89 - 29 * q^90 - 7 * q^92 - 3 * q^93 - 3 * q^94 + 2 * q^95 + 2 * q^96 + 28 * q^97 - 41 * q^99

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