LMFDB - Embedded newform 1134.2.g.k.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(163,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("1134.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.g (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:	$9.05503558921$
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:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1134.163
Dual form			1134.2.g.k.487.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.880438 + 1.52496i) q^{5} +(2.56238 + 0.658939i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.880438 + 1.52496i) q^{5} +(2.56238 + 0.658939i) q^{7} +1.00000 q^{8} +(-0.880438 - 1.52496i) q^{10} +(-3.06238 - 5.30420i) q^{11} +0.760877 q^{13} +(-1.85185 + 1.88962i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.42107 - 5.92546i) q^{17} +(0.971410 - 1.68253i) q^{19} +1.76088 q^{20} +6.12476 q^{22} +(0.210533 - 0.364654i) q^{23} +(0.949657 + 1.64485i) q^{25} +(-0.380438 + 0.658939i) q^{26} +(-0.710533 - 2.54856i) q^{28} -1.46457 q^{29} +(-3.85185 - 6.67160i) q^{31} +(-0.500000 - 0.866025i) q^{32} +6.84213 q^{34} +(-3.26088 + 3.32738i) q^{35} +(1.44282 - 2.49904i) q^{37} +(0.971410 + 1.68253i) q^{38} +(-0.880438 + 1.52496i) q^{40} +6.94282 q^{41} -8.66019 q^{43} +(-3.06238 + 5.30420i) q^{44} +(0.210533 + 0.364654i) q^{46} +(-0.830095 + 1.43777i) q^{47} +(6.13160 + 3.37690i) q^{49} -1.89931 q^{50} +(-0.380438 - 0.658939i) q^{52} +(-0.112725 - 0.195246i) q^{53} +10.7850 q^{55} +(2.56238 + 0.658939i) q^{56} +(0.732287 - 1.26836i) q^{58} +(-0.993163 - 1.72021i) q^{59} +(5.17511 - 8.96355i) q^{61} +7.70370 q^{62} +1.00000 q^{64} +(-0.669905 + 1.16031i) q^{65} +(-3.39248 - 5.87594i) q^{67} +(-3.42107 + 5.92546i) q^{68} +(-1.25116 - 4.48769i) q^{70} +10.7850 q^{71} +(0.153353 + 0.265616i) q^{73} +(1.44282 + 2.49904i) q^{74} -1.94282 q^{76} +(-4.35185 - 15.6093i) q^{77} +(6.72257 - 11.6438i) q^{79} +(-0.880438 - 1.52496i) q^{80} +(-3.47141 + 6.01266i) q^{82} +3.12476 q^{83} +12.0482 q^{85} +(4.33009 - 7.49994i) q^{86} +(-3.06238 - 5.30420i) q^{88} +(1.30150 - 2.25427i) q^{89} +(1.94966 + 0.501371i) q^{91} -0.421067 q^{92} +(-0.830095 - 1.43777i) q^{94} +(1.71053 + 2.96273i) q^{95} +3.63611 q^{97} +(-5.99028 + 3.62167i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8} - 5 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 3 q^{16} - 4 q^{17} - 3 q^{19} + 10 q^{20} + 2 q^{22} - 7 q^{23} - 2 q^{25} - 2 q^{26} + 4 q^{28} + 10 q^{29} - 14 q^{31} - 3 q^{32} + 8 q^{34} - 19 q^{35} - 9 q^{37} - 3 q^{38} - 5 q^{40} + 24 q^{41} - 36 q^{43} - q^{44} - 7 q^{46} + 3 q^{47} + 12 q^{49} + 4 q^{50} - 2 q^{52} + 9 q^{53} + 14 q^{55} - 2 q^{56} - 5 q^{58} + 4 q^{59} + 4 q^{61} + 28 q^{62} + 6 q^{64} - 12 q^{65} + 5 q^{67} - 4 q^{68} + 17 q^{70} + 14 q^{71} - 25 q^{73} - 9 q^{74} + 6 q^{76} - 17 q^{77} + 7 q^{79} - 5 q^{80} - 12 q^{82} - 16 q^{83} - 28 q^{85} + 18 q^{86} - q^{88} - 9 q^{89} + 4 q^{91} + 14 q^{92} + 3 q^{94} + 2 q^{95} + 56 q^{97} - 12 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8 - 5 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 3 * q^16 - 4 * q^17 - 3 * q^19 + 10 * q^20 + 2 * q^22 - 7 * q^23 - 2 * q^25 - 2 * q^26 + 4 * q^28 + 10 * q^29 - 14 * q^31 - 3 * q^32 + 8 * q^34 - 19 * q^35 - 9 * q^37 - 3 * q^38 - 5 * q^40 + 24 * q^41 - 36 * q^43 - q^44 - 7 * q^46 + 3 * q^47 + 12 * q^49 + 4 * q^50 - 2 * q^52 + 9 * q^53 + 14 * q^55 - 2 * q^56 - 5 * q^58 + 4 * q^59 + 4 * q^61 + 28 * q^62 + 6 * q^64 - 12 * q^65 + 5 * q^67 - 4 * q^68 + 17 * q^70 + 14 * q^71 - 25 * q^73 - 9 * q^74 + 6 * q^76 - 17 * q^77 + 7 * q^79 - 5 * q^80 - 12 * q^82 - 16 * q^83 - 28 * q^85 + 18 * q^86 - q^88 - 9 * q^89 + 4 * q^91 + 14 * q^92 + 3 * q^94 + 2 * q^95 + 56 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−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	$0.295487\pi$
$6$		0			0
$7$	2.56238	+	0.658939i	0.968489	+	0.249055i
$7$	2.56238	+	0.658939i	0.968489	+	0.249055i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.880438	−	1.52496i	−0.278419	−	0.482236i
$11$	−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			0
$13$	0.760877			0.211029			0.105515	−	0.994418i	$-0.466351\pi$
$13$	0.760877			0.211029			0.105515	+	0.994418i	$0.466351\pi$
$14$	−1.85185	+	1.88962i	−0.494927	+	0.505022i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.42107	−	5.92546i	−0.829731	−	1.43714i	−0.898250	−	0.439486i	$-0.855161\pi$
$17$	−3.42107	−	5.92546i	−0.829731	−	1.43714i	0.0685191	−	0.997650i	$-0.478173\pi$
$18$		0			0
$19$	0.971410	−	1.68253i	0.222857	−	0.385999i	−0.732818	−	0.680425i	$-0.761795\pi$
$19$	0.971410	−	1.68253i	0.222857	−	0.385999i	0.955674	+	0.294426i	$0.0951285\pi$
$20$	1.76088			0.393744
$21$		0			0
$22$	6.12476			1.30580
$23$	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	$0.152689\pi$
$24$		0			0
$25$	0.949657	+	1.64485i	0.189931	+	0.328971i
$26$	−0.380438	+	0.658939i	−0.0746101	+	0.129228i
$27$		0			0
$28$	−0.710533	−	2.54856i	−0.134278	−	0.481632i
$29$	−1.46457			−0.271964			−0.135982	−	0.990711i	$-0.543419\pi$
$29$	−1.46457			−0.271964			−0.135982	+	0.990711i	$0.543419\pi$
$30$		0			0
$31$	−3.85185	−	6.67160i	−0.691812	−	1.19825i	−0.971243	−	0.238088i	$-0.923479\pi$
$31$	−3.85185	−	6.67160i	−0.691812	−	1.19825i	0.279431	−	0.960166i	$-0.409854\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	6.84213			1.17342
$35$	−3.26088	+	3.32738i	−0.551189	+	0.562431i
$36$		0			0
$37$	1.44282	−	2.49904i	0.237198	−	0.410839i	−0.722711	−	0.691150i	$-0.757104\pi$
$37$	1.44282	−	2.49904i	0.237198	−	0.410839i	0.959909	+	0.280311i	$0.0904376\pi$
$38$	0.971410	+	1.68253i	0.157584	+	0.272943i
$39$		0			0
$40$	−0.880438	+	1.52496i	−0.139210	+	0.241118i
$41$	6.94282			1.08429			0.542143	−	0.840286i	$-0.317613\pi$
$41$	6.94282			1.08429			0.542143	+	0.840286i	$0.317613\pi$
$42$		0			0
$43$	−8.66019			−1.32067			−0.660333	−	0.750973i	$-0.729585\pi$
$43$	−8.66019			−1.32067			−0.660333	+	0.750973i	$0.729585\pi$
$44$	−3.06238	+	5.30420i	−0.461671	+	0.799638i
$45$		0			0
$46$	0.210533	+	0.364654i	0.0310414	+	0.0537654i
$47$	−0.830095	+	1.43777i	−0.121082	+	0.209720i	−0.920195	−	0.391461i	$-0.871970\pi$
$47$	−0.830095	+	1.43777i	−0.121082	+	0.209720i	0.799113	+	0.601181i	$0.205303\pi$
$48$		0			0
$49$	6.13160	+	3.37690i	0.875943	+	0.482415i
$50$	−1.89931			−0.268603
$51$		0			0
$52$	−0.380438	−	0.658939i	−0.0527573	−	0.0913783i
$53$	−0.112725	−	0.195246i	−0.0154840	−	0.0268190i	0.858180	−	0.513350i	$-0.171596\pi$
$53$	−0.112725	−	0.195246i	−0.0154840	−	0.0268190i	−0.873664	+	0.486531i	$0.838262\pi$
$54$		0			0
$55$	10.7850			1.45424
$56$	2.56238	+	0.658939i	0.342413	+	0.0880544i
$57$		0			0
$58$	0.732287	−	1.26836i	0.0961540	−	0.166544i
$59$	−0.993163	−	1.72021i	−0.129299	−	0.223952i	0.794106	−	0.607779i	$-0.207939\pi$
$59$	−0.993163	−	1.72021i	−0.129299	−	0.223952i	−0.923405	+	0.383827i	$0.874606\pi$
$60$		0			0
$61$	5.17511	−	8.96355i	0.662605	−	1.14766i	−0.317324	−	0.948317i	$-0.602784\pi$
$61$	5.17511	−	8.96355i	0.662605	−	1.14766i	0.979929	−	0.199348i	$-0.0638823\pi$
$62$	7.70370			0.978370
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.669905	+	1.16031i	−0.0830915	+	0.143919i
$66$		0			0
$67$	−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	$0.969362\pi$
$68$	−3.42107	+	5.92546i	−0.414865	+	0.718568i
$69$		0			0
$70$	−1.25116	−	4.48769i	−0.149542	−	0.536382i
$71$	10.7850			1.27994			0.639969	−	0.768401i	$-0.278947\pi$
$71$	10.7850			1.27994			0.639969	+	0.768401i	$0.278947\pi$
$72$		0			0
$73$	0.153353	+	0.265616i	0.0179487	+	0.0310880i	0.874860	−	0.484375i	$-0.160953\pi$
$73$	0.153353	+	0.265616i	0.0179487	+	0.0310880i	−0.856912	+	0.515463i	$0.827620\pi$
$74$	1.44282	+	2.49904i	0.167724	+	0.290507i
$75$		0			0
$76$	−1.94282			−0.222857
$77$	−4.35185	−	15.6093i	−0.495939	−	1.77885i
$78$		0			0
$79$	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			0
$82$	−3.47141	+	6.01266i	−0.383353	+	0.663987i
$83$	3.12476			0.342987			0.171494	−	0.985185i	$-0.445141\pi$
$83$	3.12476			0.342987			0.171494	+	0.985185i	$0.445141\pi$
$84$		0			0
$85$	12.0482			1.30681
$86$	4.33009	−	7.49994i	0.466926	−	0.808740i
$87$		0			0
$88$	−3.06238	−	5.30420i	−0.326451	−	0.565430i
$89$	1.30150	−	2.25427i	0.137959	−	0.238952i	−0.788765	−	0.614695i	$-0.789279\pi$
$89$	1.30150	−	2.25427i	0.137959	−	0.238952i	0.926724	+	0.375743i	$0.122612\pi$
$90$		0			0
$91$	1.94966	+	0.501371i	0.204380	+	0.0525580i
$92$	−0.421067			−0.0438992
$93$		0			0
$94$	−0.830095	−	1.43777i	−0.0856178	−	0.148294i
$95$	1.71053	+	2.96273i	0.175497	+	0.303970i
$96$		0			0
$97$	3.63611			0.369191			0.184596	−	0.982815i	$-0.440902\pi$
$97$	3.63611			0.369191			0.184596	+	0.982815i	$0.440902\pi$
$98$	−5.99028	+	3.62167i	−0.605110	+	0.365844i
$99$		0			0
$100$	0.949657	−	1.64485i	0.0949657	−	0.164485i
$101$	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	$0.702853\pi$
$102$		0			0
$103$	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	$0.0574525\pi$
$104$	0.760877			0.0746101
$105$		0			0
$106$	0.225450			0.0218977
$107$	1.77292	−	3.07078i	0.171394	−	0.296863i	−0.767513	−	0.641033i	$-0.778506\pi$
$107$	1.77292	−	3.07078i	0.171394	−	0.296863i	0.938908	+	0.344170i	$0.111840\pi$
$108$		0			0
$109$	0.351848	+	0.609419i	0.0337010	+	0.0583718i	0.882384	−	0.470530i	$-0.155937\pi$
$109$	0.351848	+	0.609419i	0.0337010	+	0.0583718i	−0.848683	+	0.528902i	$0.822604\pi$
$110$	−5.39248	+	9.34004i	−0.514152	+	0.890538i
$111$		0			0
$112$	−1.85185	+	1.88962i	−0.174983	+	0.178552i
$113$	−8.50232			−0.799831			−0.399916	−	0.916552i	$-0.630961\pi$
$113$	−8.50232			−0.799831			−0.399916	+	0.916552i	$0.630961\pi$
$114$		0			0
$115$	0.370723	+	0.642111i	0.0345701	+	0.0598772i
$116$	0.732287	+	1.26836i	0.0679911	+	0.117764i
$117$		0			0
$118$	1.98633			0.182856
$119$	−4.86156	−	17.4376i	−0.445659	−	1.59850i
$120$		0			0
$121$	−13.2564	+	22.9607i	−1.20512	+	2.08734i
$122$	5.17511	+	8.96355i	0.468532	+	0.811521i
$123$		0			0
$124$	−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
$129$		0			0
$130$	−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	$0.0634548\pi$
$132$		0			0
$133$	3.59781	−	3.67119i	0.311970	−	0.318332i
$134$	6.78495			0.586131
$135$		0			0
$136$	−3.42107	−	5.92546i	−0.293354	−	0.508104i
$137$	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			0
$139$	12.4646			1.05723			0.528616	−	0.848861i	$-0.322711\pi$
$139$	12.4646			1.05723			0.528616	+	0.848861i	$0.322711\pi$
$140$	4.51204	+	1.16031i	0.381337	+	0.0980641i
$141$		0			0
$142$	−5.39248	+	9.34004i	−0.452527	+	0.783799i
$143$	−2.33009	−	4.03584i	−0.194852	−	0.337494i
$144$		0			0
$145$	1.28947	−	2.23342i	0.107084	−	0.185476i
$146$	−0.306707			−0.0253832
$147$		0			0
$148$	−2.88564			−0.237198
$149$	−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	$0.284446\pi$
$150$		0			0
$151$	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	$0.624589\pi$
$152$	0.971410	−	1.68253i	0.0787918	−	0.136471i
$153$		0			0
$154$	15.6940	+	4.03584i	1.26466	+	0.325217i
$155$	13.5653			1.08959
$156$		0			0
$157$	−9.49028	−	16.4377i	−0.757407	−	1.31187i	−0.944169	−	0.329462i	$-0.893132\pi$
$157$	−9.49028	−	16.4377i	−0.757407	−	1.31187i	0.186761	−	0.982405i	$-0.440201\pi$
$158$	6.72257	+	11.6438i	0.534819	+	0.926334i
$159$		0			0
$160$	1.76088			0.139210
$161$	0.779752	−	0.795655i	0.0614530	−	0.0627064i
$162$		0			0
$163$	−7.51887	+	13.0231i	−0.588924	+	1.02005i	0.405450	+	0.914117i	$0.367115\pi$
$163$	−7.51887	+	13.0231i	−0.588924	+	1.02005i	−0.994374	+	0.105929i	$0.966219\pi$
$164$	−3.47141	−	6.01266i	−0.271072	−	0.469510i
$165$		0			0
$166$	−1.56238	+	2.70612i	−0.121264	+	0.210036i
$167$	−1.14419			−0.0885404			−0.0442702	−	0.999020i	$-0.514096\pi$
$167$	−1.14419			−0.0885404			−0.0442702	+	0.999020i	$0.514096\pi$
$168$		0			0
$169$	−12.4211			−0.955467
$170$	−6.02408	+	10.4340i	−0.462026	+	0.800252i
$171$		0			0
$172$	4.33009	+	7.49994i	0.330167	+	0.571865i
$173$	−0.248838	+	0.431001i	−0.0189188	+	0.0327684i	−0.875330	−	0.483526i	$-0.839356\pi$
$173$	−0.248838	+	0.431001i	−0.0189188	+	0.0327684i	0.856411	+	0.516295i	$0.172689\pi$
$174$		0			0
$175$	1.34953	+	4.84051i	0.102015	+	0.365908i
$176$	6.12476			0.461671
$177$		0			0
$178$	1.30150	+	2.25427i	0.0975519	+	0.168965i
$179$	4.41423	+	7.64567i	0.329935	+	0.571464i	0.982499	−	0.186270i	$-0.0596398\pi$
$179$	4.41423	+	7.64567i	0.329935	+	0.571464i	−0.652564	+	0.757734i	$0.726306\pi$
$180$		0			0
$181$	1.32941			0.0988140			0.0494070	−	0.998779i	$-0.484267\pi$
$181$	1.32941			0.0988140			0.0494070	+	0.998779i	$0.484267\pi$
$182$	−1.40903	+	1.43777i	−0.104444	+	0.106574i
$183$		0			0
$184$	0.210533	−	0.364654i	0.0155207	−	0.0268827i
$185$	2.54063	+	4.40050i	0.186791	+	0.323531i
$186$		0			0
$187$	−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			0
$193$	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	$0.663006\pi$
$194$	−1.81806	+	3.14897i	−0.130529	+	0.226083i
$195$		0			0
$196$	−0.141315	−	6.99857i	−0.0100939	−	0.499898i
$197$	15.8421			1.12871			0.564353	−	0.825534i	$-0.309126\pi$
$197$	15.8421			1.12871			0.564353	+	0.825534i	$0.309126\pi$
$198$		0			0
$199$	−4.47141	−	7.74471i	−0.316970	−	0.549008i	0.662884	−	0.748722i	$-0.269332\pi$
$199$	−4.47141	−	7.74471i	−0.316970	−	0.549008i	−0.979854	+	0.199714i	$0.935999\pi$
$200$	0.949657	+	1.64485i	0.0671509	+	0.116309i
$201$		0			0
$202$	−8.01040			−0.563610
$203$	−3.75280	−	0.965064i	−0.263395	−	0.0677342i
$204$		0			0
$205$	−6.11273	+	10.5876i	−0.426931	+	0.739467i
$206$	3.41423	+	5.91362i	0.237881	+	0.412021i
$207$		0			0
$208$	−0.380438	+	0.658939i	−0.0263787	+	0.0456892i
$209$	−11.8993			−0.823093
$210$		0			0
$211$	−22.7713			−1.56764			−0.783820	−	0.620988i	$-0.786731\pi$
$211$	−22.7713			−1.56764			−0.783820	+	0.620988i	$0.786731\pi$
$212$	−0.112725	+	0.195246i	−0.00774199	+	0.0134095i
$213$		0			0
$214$	1.77292	+	3.07078i	0.121194	+	0.209914i
$215$	7.62476	−	13.2065i	0.520005	−	0.900674i
$216$		0			0
$217$	−5.47373	−	19.6333i	−0.371581	−	1.33280i
$218$	−0.703697			−0.0476604
$219$		0			0
$220$	−5.39248	−	9.34004i	−0.363561	−	0.629706i
$221$	−2.60301	−	4.50855i	−0.175097	−	0.303278i
$222$		0			0
$223$	12.8856			0.862886			0.431443	−	0.902140i	$-0.358005\pi$
$223$	12.8856			0.862886			0.431443	+	0.902140i	$0.358005\pi$
$224$	−0.710533	−	2.54856i	−0.0474745	−	0.170283i
$225$		0			0
$226$	4.25116	−	7.36323i	0.282783	−	0.489795i
$227$	−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	$-0.427141\pi$
$228$		0			0
$229$	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	$0.126610\pi$
$230$	−0.741446			−0.0488895
$231$		0			0
$232$	−1.46457			−0.0961540
$233$	−3.33530	+	5.77690i	−0.218503	+	0.378458i	−0.954350	−	0.298689i	$-0.903451\pi$
$233$	−3.33530	+	5.77690i	−0.218503	+	0.378458i	0.735848	+	0.677147i	$0.236784\pi$
$234$		0			0
$235$	−1.46169	−	2.53173i	−0.0953505	−	0.165152i
$236$	−0.993163	+	1.72021i	−0.0646494	+	0.111976i
$237$		0			0
$238$	17.5322	+	4.50855i	1.13644	+	0.292246i
$239$	15.6408			1.01172			0.505858	−	0.862617i	$-0.331176\pi$
$239$	15.6408			1.01172			0.505858	+	0.862617i	$0.331176\pi$
$240$		0			0
$241$	−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	$-0.408896\pi$
$242$	−13.2564	−	22.9607i	−0.852151	−	1.47597i
$243$		0			0
$244$	−10.3502			−0.662605
$245$	−10.5482	+	6.37731i	−0.673897	+	0.407432i
$246$		0			0
$247$	0.739123	−	1.28020i	0.0470293	−	0.0814571i
$248$	−3.85185	−	6.67160i	−0.244593	−	0.423647i
$249$		0			0
$250$	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
$255$		0			0
$256$	−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	$0.948946\pi$
$258$		0			0
$259$	5.34377	−	5.45276i	0.332046	−	0.338818i
$260$	1.33981			0.0830915
$261$		0			0
$262$	3.64652	+	6.31595i	0.225283	+	0.390201i
$263$	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	$0.589465\pi$
$264$		0			0
$265$	0.396990			0.0243869
$266$	1.38044	+	4.95139i	0.0846401	+	0.303589i
$267$		0			0
$268$	−3.39248	+	5.87594i	−0.207228	+	0.358930i
$269$	−12.6706	−	21.9461i	−0.772540	−	1.33808i	−0.936167	−	0.351556i	$-0.885653\pi$
$269$	−12.6706	−	21.9461i	−0.772540	−	1.33808i	0.163627	−	0.986522i	$-0.447681\pi$
$270$		0			0
$271$	−6.87880	+	11.9144i	−0.417858	+	0.723751i	−0.995724	−	0.0923810i	$-0.970552\pi$
$271$	−6.87880	+	11.9144i	−0.417858	+	0.723751i	0.577866	+	0.816132i	$0.303886\pi$
$272$	6.84213			0.414865
$273$		0			0
$274$	−8.18194			−0.494289
$275$	5.81642	−	10.0743i	0.350743	−	0.607505i
$276$		0			0
$277$	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	$0.801891\pi$
$278$	−6.23229	+	10.7946i	−0.373788	+	0.647419i
$279$		0			0
$280$	−3.26088	+	3.32738i	−0.194875	+	0.198849i
$281$	−1.26896			−0.0756996			−0.0378498	−	0.999283i	$-0.512051\pi$
$281$	−1.26896			−0.0756996			−0.0378498	+	0.999283i	$0.512051\pi$
$282$		0			0
$283$	4.09617	+	7.09478i	0.243492	+	0.421741i	0.961707	−	0.274081i	$-0.0883736\pi$
$283$	4.09617	+	7.09478i	0.243492	+	0.421741i	−0.718214	+	0.695822i	$0.755040\pi$
$284$	−5.39248	−	9.34004i	−0.319985	−	0.554230i
$285$		0			0
$286$	4.66019			0.275563
$287$	17.7902	+	4.57489i	1.05012	+	0.270047i
$288$		0			0
$289$	−14.9074	+	25.8204i	−0.876906	+	1.51884i
$290$	1.28947	+	2.23342i	0.0757201	+	0.131151i
$291$		0			0
$292$	0.153353	−	0.265616i	0.00897433	−	0.0155440i
$293$	−15.4509			−0.902651			−0.451326	−	0.892359i	$-0.649049\pi$
$293$	−15.4509			−0.902651			−0.451326	+	0.892359i	$0.649049\pi$
$294$		0			0
$295$	3.49768			0.203643
$296$	1.44282	−	2.49904i	0.0838622	−	0.145254i
$297$		0			0
$298$	−4.41423	−	7.64567i	−0.255709	−	0.442902i
$299$	0.160190	−	0.277457i	0.00926402	−	0.0160458i
$300$		0			0
$301$	−22.1907	−	5.70653i	−1.27905	−	0.328919i
$302$	−14.9863			−0.862366
$303$		0			0
$304$	0.971410	+	1.68253i	0.0557142	+	0.0964998i
$305$	9.11273	+	15.7837i	0.521793	+	0.903772i
$306$		0			0
$307$	4.89931			0.279619			0.139809	−	0.990178i	$-0.455351\pi$
$307$	4.89931			0.279619			0.139809	+	0.990178i	$0.455351\pi$
$308$	−11.3421	+	11.5735i	−0.646278	+	0.659459i
$309$		0			0
$310$	−6.78263	+	11.7479i	−0.385228	+	0.667234i
$311$	3.84501	+	6.65976i	0.218031	+	0.377640i	0.954206	−	0.299151i	$-0.0967034\pi$
$311$	3.84501	+	6.65976i	0.218031	+	0.377640i	−0.736175	+	0.676791i	$0.763370\pi$
$312$		0			0
$313$	0.861564	−	1.49227i	0.0486985	−	0.0843482i	−0.840649	−	0.541581i	$-0.817826\pi$
$313$	0.861564	−	1.49227i	0.0486985	−	0.0843482i	0.889347	+	0.457233i	$0.151159\pi$
$314$	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			0
$319$	4.48508	+	7.76839i	0.251116	+	0.434946i
$320$	−0.880438	+	1.52496i	−0.0492180	+	0.0852481i
$321$		0			0
$322$	0.299182	+	1.07311i	0.0166728	+	0.0598022i
$323$	−13.2930			−0.739644
$324$		0			0
$325$	0.722572	+	1.25153i	0.0400811	+	0.0694224i
$326$	−7.51887	−	13.0231i	−0.416432	−	0.721281i
$327$		0			0
$328$	6.94282			0.383353
$329$	−3.07442	+	3.13713i	−0.169498	+	0.172955i
$330$		0			0
$331$	−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
$333$		0			0
$334$	0.572097	−	0.990901i	0.0313037	−	0.0542197i
$335$	11.9475			0.652760
$336$		0			0
$337$	8.72313			0.475179			0.237590	−	0.971366i	$-0.423643\pi$
$337$	8.72313			0.475179			0.237590	+	0.971366i	$0.423643\pi$
$338$	6.21053	−	10.7570i	0.337808	−	0.585101i
$339$		0			0
$340$	−6.02408	−	10.4340i	−0.326701	−	0.565863i
$341$	−23.5917	+	40.8620i	−1.27756	+	2.21280i
$342$		0			0
$343$	13.4863	+	12.6933i	0.728193	+	0.685372i
$344$	−8.66019			−0.466926
$345$		0			0
$346$	−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	$0.917128\pi$
$348$		0			0
$349$	−28.3984			−1.52013			−0.760065	−	0.649847i	$-0.774833\pi$
$349$	−28.3984			−1.52013			−0.760065	+	0.649847i	$0.774833\pi$
$350$	−4.86677	−	1.25153i	−0.260140	−	0.0668971i
$351$		0			0
$352$	−3.06238	+	5.30420i	−0.163225	+	0.282715i
$353$	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	$0.796029\pi$
$354$		0			0
$355$	−9.49549	+	16.4467i	−0.503968	+	0.872898i
$356$	−2.60301			−0.137959
$357$		0			0
$358$	−8.82846			−0.466599
$359$	16.0796	−	27.8507i	0.848650	−	1.46990i	−0.0337633	−	0.999430i	$-0.510749\pi$
$359$	16.0796	−	27.8507i	0.848650	−	1.46990i	0.882413	−	0.470475i	$-0.155917\pi$
$360$		0			0
$361$	7.61273	+	13.1856i	0.400670	+	0.693980i
$362$	−0.664703	+	1.15130i	−0.0349360	+	0.0605110i
$363$		0			0
$364$	−0.540628	−	1.93914i	−0.0283366	−	0.101638i
$365$	−0.540073			−0.0282687
$366$		0			0
$367$	−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	$-0.525404\pi$
$368$	0.210533	+	0.364654i	0.0109748	+	0.0190089i
$369$		0			0
$370$	−5.08126			−0.264162
$371$	−0.160190	−	0.574573i	−0.00831664	−	0.0298303i
$372$		0			0
$373$	−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
$375$		0			0
$376$	−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
$381$		0			0
$382$	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	$-0.0138287\pi$
$384$		0			0
$385$	27.6352	+	7.10662i	1.40842	+	0.362187i
$386$	−14.1683			−0.721146
$387$		0			0
$388$	−1.81806	−	3.14897i	−0.0922978	−	0.159865i
$389$	−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			0
$391$	−2.88099			−0.145698
$392$	6.13160	+	3.37690i	0.309693	+	0.170559i
$393$		0			0
$394$	−7.92107	+	13.7197i	−0.399058	+	0.691188i
$395$	11.8376	+	20.5034i	0.595615	+	1.03164i
$396$		0			0
$397$	−3.57893	+	6.19889i	−0.179622	+	0.311114i	−0.941751	−	0.336311i	$-0.890821\pi$
$397$	−3.57893	+	6.19889i	−0.179622	+	0.311114i	0.762129	+	0.647425i	$0.224154\pi$
$398$	8.94282			0.448263
$399$		0			0
$400$	−1.89931			−0.0949657
$401$	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	$0.0922397\pi$
$402$		0			0
$403$	−2.93078	−	5.07626i	−0.145993	−	0.252867i
$404$	4.00520	−	6.93721i	0.199266	−	0.345139i
$405$		0			0
$406$	2.71217	−	2.76748i	0.134603	−	0.137348i
$407$	−17.6739			−0.876061
$408$		0			0
$409$	−7.58414	−	13.1361i	−0.375011	−	0.649539i	0.615317	−	0.788279i	$-0.289028\pi$
$409$	−7.58414	−	13.1361i	−0.375011	−	0.649539i	−0.990329	+	0.138741i	$0.955695\pi$
$410$	−6.11273	−	10.5876i	−0.301886	−	0.522882i
$411$		0			0
$412$	−6.82846			−0.336414
$413$	−1.41135	−	5.06227i	−0.0694481	−	0.249098i
$414$		0			0
$415$	−2.75116	+	4.76515i	−0.135049	+	0.233912i
$416$	−0.380438	−	0.658939i	−0.0186525	−	0.0323071i
$417$		0			0
$418$	5.94966	−	10.3051i	0.291007	−	0.504039i
$419$	8.33654			0.407267			0.203633	−	0.979047i	$-0.434725\pi$
$419$	8.33654			0.407267			0.203633	+	0.979047i	$0.434725\pi$
$420$		0			0
$421$	7.00465			0.341386			0.170693	−	0.985324i	$-0.445399\pi$
$421$	7.00465			0.341386			0.170693	+	0.985324i	$0.445399\pi$
$422$	11.3856	−	19.7205i	0.554244	−	0.959979i
$423$		0			0
$424$	−0.112725	−	0.195246i	−0.00547442	−	0.00948197i
$425$	6.49768	−	11.2543i	0.315184	−	0.545914i
$426$		0			0
$427$	19.1670	−	19.5580i	0.927557	−	0.946476i
$428$	−3.54583			−0.171394
$429$		0			0
$430$	7.62476	+	13.2065i	0.367699	+	0.636873i
$431$	−1.72545	−	2.98857i	−0.0831120	−	0.143954i	0.821473	−	0.570247i	$-0.193153\pi$
$431$	−1.72545	−	2.98857i	−0.0831120	−	0.143954i	−0.904585	+	0.426293i	$0.859819\pi$
$432$		0			0
$433$	28.2599			1.35809			0.679043	−	0.734099i	$-0.262395\pi$
$433$	28.2599			1.35809			0.679043	+	0.734099i	$0.262395\pi$
$434$	19.7398	+	5.07626i	0.947541	+	0.243668i
$435$		0			0
$436$	0.351848	−	0.609419i	0.0168505	−	0.0291859i
$437$	−0.409028	−	0.708458i	−0.0195665	−	0.0338901i
$438$		0			0
$439$	14.4480	−	25.0247i	0.689566	−	1.19436i	−0.282412	−	0.959293i	$-0.591134\pi$
$439$	14.4480	−	25.0247i	0.689566	−	1.19436i	0.971978	−	0.235071i	$-0.0755322\pi$
$440$	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	$0.0606628\pi$
$444$		0			0
$445$	2.29179	+	3.96950i	0.108641	+	0.188172i
$446$	−6.44282	+	11.1593i	−0.305076	+	0.528408i
$447$		0			0
$448$	2.56238	+	0.658939i	0.121061	+	0.0311319i
$449$	−20.2003			−0.953309			−0.476655	−	0.879091i	$-0.658151\pi$
$449$	−20.2003			−0.953309			−0.476655	+	0.879091i	$0.658151\pi$
$450$		0			0
$451$	−21.2616	−	36.8261i	−1.00117	−	1.73407i
$452$	4.25116	+	7.36323i	0.199958	+	0.346337i
$453$		0			0
$454$	21.9967			1.03236
$455$	−2.48113	+	2.53173i	−0.116317	+	0.118689i
$456$		0			0
$457$	−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
$459$		0			0
$460$	0.370723	−	0.642111i	0.0172851	−	0.0299386i
$461$	−11.9532			−0.556717			−0.278359	−	0.960477i	$-0.589790\pi$
$461$	−11.9532			−0.556717			−0.278359	+	0.960477i	$0.589790\pi$
$462$		0			0
$463$	−13.2905			−0.617664			−0.308832	−	0.951117i	$-0.599938\pi$
$463$	−13.2905			−0.617664			−0.308832	+	0.951117i	$0.599938\pi$
$464$	0.732287	−	1.26836i	0.0339956	−	0.0588820i
$465$		0			0
$466$	−3.33530	−	5.77690i	−0.154505	−	0.267610i
$467$	−5.61505	+	9.72555i	−0.259833	+	0.450045i	−0.966197	−	0.257804i	$-0.917001\pi$
$467$	−5.61505	+	9.72555i	−0.259833	+	0.450045i	0.706364	+	0.707849i	$0.250334\pi$
$468$		0			0
$469$	−4.82094	−	17.2918i	−0.222610	−	0.798463i
$470$	2.92339			0.134846
$471$		0			0
$472$	−0.993163	−	1.72021i	−0.0457141	−	0.0791791i
$473$	26.5208	+	45.9354i	1.21943	+	2.11211i
$474$		0			0
$475$	3.69002			0.169310
$476$	−12.6706	+	12.9290i	−0.580756	+	0.592601i
$477$		0			0
$478$	−7.82038	+	13.5453i	−0.357696	+	0.619547i
$479$	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	$0.565599\pi$
$480$		0			0
$481$	1.09781	−	1.90146i	0.0500557	−	0.0866991i
$482$	21.4120			0.975292
$483$		0			0
$484$	26.5127			1.20512
$485$	−3.20137	+	5.54494i	−0.145367	+	0.251783i
$486$		0			0
$487$	1.84897	+	3.20251i	0.0837848	+	0.145120i	0.904873	−	0.425682i	$-0.139966\pi$
$487$	1.84897	+	3.20251i	0.0837848	+	0.145120i	−0.821088	+	0.570802i	$0.806632\pi$
$488$	5.17511	−	8.96355i	0.234266	−	0.405761i
$489$		0			0
$490$	−0.248838	−	12.3236i	−0.0112414	−	0.556725i
$491$	37.5609			1.69510			0.847549	−	0.530717i	$-0.178077\pi$
$491$	37.5609			1.69510			0.847549	+	0.530717i	$0.178077\pi$
$492$		0			0
$493$	5.01040	+	8.67827i	0.225657	+	0.390850i
$494$	0.739123	+	1.28020i	0.0332547	+	0.0575989i
$495$		0			0
$496$	7.70370			0.345906
$497$	27.6352	+	7.10662i	1.23961	+	0.318776i
$498$		0			0
$499$	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			0
$502$	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
$507$		0			0
$508$	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	$0.223518\pi$
$510$		0			0
$511$	0.217925	+	0.781660i	0.00964045	+	0.0345786i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−10.1300	−	17.5456i	−0.446814	−	0.773904i
$515$	6.01204	+	10.4132i	0.264922	+	0.458858i
$516$		0			0
$517$	10.1683			0.447200
$518$	2.05034	+	7.35422i	0.0900869	+	0.323126i
$519$		0			0
$520$	−0.669905	+	1.16031i	−0.0293773	+	0.0508829i
$521$	14.8646	+	25.7462i	0.651229	+	1.12796i	0.982825	+	0.184540i	$0.0590795\pi$
$521$	14.8646	+	25.7462i	0.651229	+	1.12796i	−0.331596	+	0.943421i	$0.607587\pi$
$522$		0			0
$523$	13.4698	−	23.3303i	0.588992	−	1.02016i	−0.405373	−	0.914152i	$-0.632858\pi$
$523$	13.4698	−	23.3303i	0.588992	−	1.02016i	0.994365	−	0.106013i	$-0.0338084\pi$
$524$	−7.29303			−0.318598
$525$		0			0
$526$	−22.4887			−0.980552
$527$	−26.3549	+	45.6480i	−1.14804	+	1.98846i
$528$		0			0
$529$	11.4114	+	19.7650i	0.496146	+	0.859350i
$530$	−0.198495	+	0.343803i	−0.00862207	+	0.0149339i
$531$		0			0
$532$	−4.97825	−	1.28020i	−0.215834	−	0.0555037i
$533$	5.28263			0.228816
$534$		0			0
$535$	3.12188	+	5.40726i	0.134971	+	0.233776i
$536$	−3.39248	−	5.87594i	−0.146533	−	0.253802i
$537$		0			0
$538$	25.3412			1.09254
$539$	−0.865521	−	42.8646i	−0.0372806	−	1.84631i
$540$		0			0
$541$	7.15568	−	12.3940i	0.307647	−	0.532859i	−0.670201	−	0.742180i	$-0.733792\pi$
$541$	7.15568	−	12.3940i	0.307647	−	0.532859i	0.977847	+	0.209321i	$0.0671252\pi$
$542$	−6.87880	−	11.9144i	−0.295470	−	0.511769i
$543$		0			0
$544$	−3.42107	+	5.92546i	−0.146677	+	0.254052i
$545$	−1.23912			−0.0530782
$546$		0			0
$547$	−2.04926			−0.0876202			−0.0438101	−	0.999040i	$-0.513950\pi$
$547$	−2.04926			−0.0876202			−0.0438101	+	0.999040i	$0.513950\pi$
$548$	4.09097	−	7.08577i	0.174758	−	0.302689i
$549$		0			0
$550$	5.81642	+	10.0743i	0.248013	+	0.429571i
$551$	−1.42270	+	2.46419i	−0.0606091	+	0.104978i
$552$		0			0
$553$	24.8984	−	25.4062i	1.05879	−	1.08038i
$554$	−3.28263			−0.139466
$555$		0			0
$556$	−6.23229	−	10.7946i	−0.264308	−	0.457795i
$557$	8.84338	+	15.3172i	0.374706	+	0.649010i	0.990283	−	0.139067i	$-0.0444103\pi$
$557$	8.84338	+	15.3172i	0.374706	+	0.649010i	−0.615577	+	0.788077i	$0.711077\pi$
$558$		0			0
$559$	−6.58934			−0.278699
$560$	−1.25116	−	4.48769i	−0.0528712	−	0.189640i
$561$		0			0
$562$	0.634479	−	1.09895i	0.0267639	−	0.0463564i
$563$	−0.468531	−	0.811520i	−0.0197462	−	0.0342015i	0.855983	−	0.517003i	$-0.172952\pi$
$563$	−0.468531	−	0.811520i	−0.0197462	−	0.0342015i	−0.875730	+	0.482802i	$0.839619\pi$
$564$		0			0
$565$	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	$0.330817\pi$
$570$		0			0
$571$	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	$0.830110\pi$
$572$	−2.33009	+	4.03584i	−0.0974262	+	0.168747i
$573$		0			0
$574$	−12.8571	+	13.1193i	−0.536643	+	0.547588i
$575$	0.799737			0.0333514
$576$		0			0
$577$	−2.23065	−	3.86360i	−0.0928633	−	0.160844i	0.815852	−	0.578261i	$-0.196269\pi$
$577$	−2.23065	−	3.86360i	−0.0928633	−	0.160844i	−0.908715	+	0.417417i	$0.862935\pi$
$578$	−14.9074	−	25.8204i	−0.620066	−	1.07399i
$579$		0			0
$580$	−2.57893			−0.107084
$581$	8.00684	+	2.05903i	0.332180	+	0.0854228i
$582$		0			0
$583$	−0.690415	+	1.19583i	−0.0285941	+	0.0495264i
$584$	0.153353	+	0.265616i	0.00634581	+	0.0109913i
$585$		0			0
$586$	7.72545	−	13.3809i	0.319135	−	0.552759i
$587$	−16.6304			−0.686408			−0.343204	−	0.939261i	$-0.611512\pi$
$587$	−16.6304			−0.686408			−0.343204	+	0.939261i	$0.611512\pi$
$588$		0			0
$589$	−14.9669			−0.616700
$590$	−1.74884	+	3.02908i	−0.0719985	+	0.124705i
$591$		0			0
$592$	1.44282	+	2.49904i	0.0592995	+	0.102710i
$593$	20.7632	−	35.9629i	0.852642	−	1.47682i	−0.0261726	−	0.999657i	$-0.508332\pi$
$593$	20.7632	−	35.9629i	0.852642	−	1.47682i	0.878815	−	0.477163i	$-0.158335\pi$
$594$		0			0
$595$	30.8720	+	7.93899i	1.26563	+	0.325467i
$596$	8.82846			0.361628
$597$		0			0
$598$	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	$0.932995\pi$
$600$		0			0
$601$	16.1111			0.657185			0.328593	−	0.944472i	$-0.393426\pi$
$601$	16.1111			0.657185			0.328593	+	0.944472i	$0.393426\pi$
$602$	16.0374	−	16.3645i	0.653634	−	0.666965i
$603$		0			0
$604$	7.49316	−	12.9785i	0.304892	−	0.528089i
$605$	−23.3428	−	40.4310i	−0.949021	−	1.64375i
$606$		0			0
$607$	−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	$0.296694\pi$
$608$	−1.94282			−0.0787918
$609$		0			0
$610$	−18.2255			−0.737927
$611$	−0.631600	+	1.09396i	−0.0255518	+	0.0442570i
$612$		0			0
$613$	−2.77579	−	4.80782i	−0.112113	−	0.194186i	0.804509	−	0.593941i	$-0.202429\pi$
$613$	−2.77579	−	4.80782i	−0.112113	−	0.194186i	−0.916622	+	0.399755i	$0.869095\pi$
$614$	−2.44966	+	4.24293i	−0.0988601	+	0.171231i
$615$		0			0
$616$	−4.35185	−	15.6093i	−0.175341	−	0.628917i
$617$	−1.26896			−0.0510863			−0.0255431	−	0.999674i	$-0.508132\pi$
$617$	−1.26896			−0.0510863			−0.0255431	+	0.999674i	$0.508132\pi$
$618$		0			0
$619$	−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	$0.862174\pi$
$620$	−6.78263	−	11.7479i	−0.272397	−	0.471805i
$621$		0			0
$622$	−7.69002			−0.308342
$623$	4.82038	−	4.91870i	0.193124	−	0.197063i
$624$		0			0
$625$	5.94802	−	10.3023i	0.237921	−	0.412091i
$626$	0.861564	+	1.49227i	0.0344350	+	0.0596432i
$627$		0			0
$628$	−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
$633$		0			0
$634$	−16.6014	−	28.7544i	−0.659325	−	1.14198i
$635$	16.6871	−	28.9030i	0.662209	−	1.14698i
$636$		0			0
$637$	4.66539	+	2.56941i	0.184850	+	0.101804i
$638$	−8.97017			−0.355132
$639$		0			0
$640$	−0.880438	−	1.52496i	−0.0348024	−	0.0602795i
$641$	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	$0.827370\pi$
$642$		0			0
$643$	19.6979			0.776811			0.388405	−	0.921489i	$-0.373026\pi$
$643$	19.6979			0.776811			0.388405	+	0.921489i	$0.373026\pi$
$644$	−1.07893	−	0.277457i	−0.0425159	−	0.0109333i
$645$		0			0
$646$	6.64652	−	11.5121i	0.261504	−	0.452938i
$647$	11.7271	+	20.3119i	0.461039	+	0.798543i	0.999013	−	0.0444181i	$-0.0141434\pi$
$647$	11.7271	+	20.3119i	0.461039	+	0.798543i	−0.537974	+	0.842962i	$0.680810\pi$
$648$		0			0
$649$	−6.08289	+	10.5359i	−0.238774	+	0.413569i
$650$	−1.44514			−0.0566832
$651$		0			0
$652$	15.0377			0.588924
$653$	−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			0
$655$	6.42107	+	11.1216i	0.250892	+	0.434557i
$656$	−3.47141	+	6.01266i	−0.135536	+	0.234755i
$657$		0			0
$658$	−1.17962	−	4.23109i	−0.0459864	−	0.164945i
$659$	26.4796			1.03150			0.515750	−	0.856739i	$-0.327513\pi$
$659$	26.4796			1.03150			0.515750	+	0.856739i	$0.327513\pi$
$660$		0			0
$661$	13.3691	+	23.1559i	0.519997	+	0.900662i	0.999730	+	0.0232469i	$0.00740038\pi$
$661$	13.3691	+	23.1559i	0.519997	+	0.900662i	−0.479732	+	0.877415i	$0.659266\pi$
$662$	−1.44445	−	2.50187i	−0.0561403	−	0.0972379i
$663$		0			0
$664$	3.12476			0.121264
$665$	2.43078	+	8.71878i	0.0942617	+	0.338100i
$666$		0			0
$667$	−0.308342	+	0.534063i	−0.0119390	+	0.0206790i
$668$	0.572097	+	0.990901i	0.0221351	+	0.0383391i
$669$		0			0
$670$	−5.97373	+	10.3468i	−0.230785	+	0.399732i
$671$	−63.3926			−2.44724
$672$		0			0
$673$	20.7713			0.800674			0.400337	−	0.916368i	$-0.368893\pi$
$673$	20.7713			0.800674			0.400337	+	0.916368i	$0.368893\pi$
$674$	−4.36156	+	7.55445i	−0.168001	+	0.290987i
$675$		0			0
$676$	6.21053	+	10.7570i	0.238867	+	0.413729i
$677$	10.3490	−	17.9249i	0.397743	−	0.688911i	−0.595704	−	0.803204i	$-0.703127\pi$
$677$	10.3490	−	17.9249i	0.397743	−	0.688911i	0.993447	+	0.114293i	$0.0364602\pi$
$678$		0			0
$679$	9.31711	+	2.39598i	0.357558	+	0.0919491i
$680$	12.0482			0.462026
$681$		0			0
$682$	−23.5917	−	40.8620i	−0.903371	−	1.56469i
$683$	14.2918	+	24.7541i	0.546860	+	0.947190i	0.998487	+	0.0549828i	$0.0175104\pi$
$683$	14.2918	+	24.7541i	0.546860	+	0.947190i	−0.451627	+	0.892207i	$0.649156\pi$
$684$		0			0
$685$	−14.4074			−0.550478
$686$	−17.7359	+	5.33287i	−0.677158	+	0.203610i
$687$		0			0
$688$	4.33009	−	7.49994i	0.165083	−	0.285933i
$689$	−0.0857699	−	0.148558i	−0.00326757	−	0.00565960i
$690$		0			0
$691$	3.34897	−	5.80059i	0.127401	−	0.220665i	−0.795268	−	0.606258i	$-0.792670\pi$
$691$	3.34897	−	5.80059i	0.127401	−	0.220665i	0.922669	+	0.385593i	$0.126003\pi$
$692$	0.497677			0.0189188
$693$		0			0
$694$	9.69467			0.368005
$695$	−10.9743	+	19.0080i	−0.416278	+	0.721016i
$696$		0			0
$697$	−23.7518	−	41.1394i	−0.899665	−	1.55827i
$698$	14.1992	−	24.5937i	0.537447	−	0.930886i
$699$		0			0
$700$	3.51724	−	3.58898i	0.132939	−	0.135651i
$701$	−25.1442			−0.949683			−0.474842	−	0.880071i	$-0.657495\pi$
$701$	−25.1442			−0.949683			−0.474842	+	0.880071i	$0.657495\pi$
$702$		0			0
$703$	−2.80314	−	4.85518i	−0.105722	−	0.183117i
$704$	−3.06238	−	5.30420i	−0.115418	−	0.199910i
$705$		0			0
$706$	−4.39372			−0.165360
$707$	5.69166	+	20.4150i	0.214057	+	0.767784i
$708$		0			0
$709$	−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
$711$		0			0
$712$	1.30150	−	2.25427i	0.0487760	−	0.0844824i
$713$	−3.24377			−0.121480
$714$		0			0
$715$	8.20602			0.306888
$716$	4.41423	−	7.64567i	0.164968	−	0.285732i
$717$		0			0
$718$	16.0796	+	27.8507i	0.600086	+	1.03938i
$719$	11.8015	−	20.4408i	0.440122	−	0.762313i	−0.557576	−	0.830126i	$-0.688269\pi$
$719$	11.8015	−	20.4408i	0.440122	−	0.762313i	0.997698	+	0.0678123i	$0.0216019\pi$
$720$		0			0
$721$	12.6453	−	12.9032i	0.470935	−	0.480540i
$722$	−15.2255			−0.566633
$723$		0			0
$724$	−0.664703	−	1.15130i	−0.0247035	−	0.0427877i
$725$	−1.39084	−	2.40901i	−0.0516546	−	0.0894683i
$726$		0			0
$727$	−6.51384			−0.241585			−0.120792	−	0.992678i	$-0.538544\pi$
$727$	−6.51384			−0.241585			−0.120792	+	0.992678i	$0.538544\pi$
$728$	1.94966	+	0.501371i	0.0722591	+	0.0185820i
$729$		0			0
$730$	0.270036	−	0.467717i	0.00999449	−	0.0173110i
$731$	29.6271	+	51.3156i	1.09580	+	1.89798i
$732$		0			0
$733$	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	$0.0257368\pi$
$734$	34.6030			1.27722
$735$		0			0
$736$	−0.421067			−0.0155207
$737$	−20.7781	+	35.9888i	−0.765372	+	1.32566i
$738$		0			0
$739$	−7.57838	−	13.1261i	−0.278775	−	0.482853i	0.692305	−	0.721605i	$-0.256595\pi$
$739$	−7.57838	−	13.1261i	−0.278775	−	0.482853i	−0.971081	+	0.238752i	$0.923262\pi$
$740$	2.54063	−	4.40050i	0.0933954	−	0.161765i
$741$		0			0
$742$	0.577690	+	0.148558i	0.0212076	+	0.00545373i
$743$	10.4347			0.382813			0.191407	−	0.981511i	$-0.438695\pi$
$743$	10.4347			0.382813			0.191407	+	0.981511i	$0.438695\pi$
$744$		0			0
$745$	−7.77292	−	13.4631i	−0.284778	−	0.493249i
$746$	−5.48796	−	9.50543i	−0.200929	−	0.348018i
$747$		0			0
$748$	41.9064			1.53225
$749$	6.56634	−	6.70027i	0.239929	−	0.244822i
$750$		0			0
$751$	−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
$753$		0			0
$754$	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
$759$		0			0
$760$	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	$0.0255730\pi$
$762$		0			0
$763$	0.500000	+	1.79341i	0.0181012	+	0.0649258i
$764$	−16.1683			−0.584947
$765$		0			0
$766$	10.5120	+	18.2074i	0.379815	+	0.657860i
$767$	−0.755675	−	1.30887i	−0.0272858	−	0.0472605i
$768$		0			0
$769$	11.2553			0.405876			0.202938	−	0.979192i	$-0.434951\pi$
$769$	11.2553			0.405876			0.202938	+	0.979192i	$0.434951\pi$
$770$	−19.9721	+	20.3794i	−0.719744	+	0.734424i
$771$		0			0
$772$	7.08414	−	12.2701i	0.254964	−	0.441610i
$773$	0.138992	+	0.240741i	0.00499919	+	0.00865886i	0.868514	−	0.495664i	$-0.165075\pi$
$773$	0.138992	+	0.240741i	0.00499919	+	0.00865886i	−0.863515	+	0.504323i	$0.831742\pi$
$774$		0			0
$775$	7.31587	−	12.6715i	0.262794	−	0.455172i
$776$	3.63611			0.130529
$777$		0			0
$778$	13.7382			0.492538
$779$	6.74433	−	11.6815i	0.241641	−	0.418534i
$780$		0			0
$781$	−33.0276	−	57.2056i	−1.18182	−	2.04698i
$782$	1.44050	−	2.49501i	0.0515121	−	0.0892215i
$783$		0			0
$784$	−5.99028	+	3.62167i	−0.213939	+	0.129345i
$785$	33.4224			1.19290
$786$		0			0
$787$	14.6940	+	25.4507i	0.523784	+	0.907220i	0.999617	+	0.0276845i	$0.00881339\pi$
$787$	14.6940	+	25.4507i	0.523784	+	0.907220i	−0.475833	+	0.879536i	$0.657853\pi$
$788$	−7.92107	−	13.7197i	−0.282176	−	0.488744i
$789$		0			0
$790$	−23.6752			−0.842327
$791$	−21.7862	−	5.60251i	−0.774628	−	0.199202i
$792$		0			0
$793$	3.93762	−	6.82015i	0.139829	−	0.242191i
$794$	−3.57893	−	6.19889i	−0.127012	−	0.219991i
$795$		0			0
$796$	−4.47141	+	7.74471i	−0.158485	+	0.274504i
$797$	−0.866210			−0.0306827			−0.0153414	−	0.999882i	$-0.504883\pi$
$797$	−0.866210			−0.0306827			−0.0153414	+	0.999882i	$0.504883\pi$
$798$		0			0
$799$	11.3592			0.401861
$800$	0.949657	−	1.64485i	0.0335754	−	0.0581544i
$801$		0			0
$802$	4.63968	+	8.03616i	0.163833	+	0.283767i
$803$	0.939253	−	1.62683i	0.0331455	−	0.0574097i
$804$		0			0
$805$	0.526822	+	1.88962i	0.0185680	+	0.0666003i
$806$	5.86156			0.206465
$807$		0			0
$808$	4.00520	+	6.93721i	0.140903	+	0.244050i
$809$	9.66703	+	16.7438i	0.339875	+	0.588680i	0.984409	−	0.175895i	$-0.0562820\pi$
$809$	9.66703	+	16.7438i	0.339875	+	0.588680i	−0.644534	+	0.764575i	$0.722949\pi$
$810$		0			0
$811$	−47.0391			−1.65177			−0.825884	−	0.563841i	$-0.809323\pi$
$811$	−47.0391			−1.65177			−0.825884	+	0.563841i	$0.809323\pi$
$812$	1.04063	+	3.73255i	0.0365189	+	0.130987i
$813$		0			0
$814$	8.83693	−	15.3060i	0.309734	−	0.536476i
$815$	−13.2398	−	22.9320i	−0.463770	−	0.803274i
$816$		0			0
$817$	−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	$0.174503\pi$
$822$		0			0
$823$	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	$0.624224\pi$
$824$	3.41423	−	5.91362i	0.118940	−	0.206011i
$825$		0			0
$826$	5.08973	+	1.30887i	0.177094	+	0.0455413i
$827$	−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			0
$829$	19.0848	+	33.0559i	0.662843	+	1.14808i	0.979865	+	0.199660i	$0.0639838\pi$
$829$	19.0848	+	33.0559i	0.662843	+	1.14808i	−0.317022	+	0.948418i	$0.602683\pi$
$830$	−2.75116	−	4.76515i	−0.0954942	−	0.165401i
$831$		0			0
$832$	0.760877			0.0263787
$833$	−0.966897	−	47.8852i	−0.0335010	−	1.65912i
$834$		0			0
$835$	1.00739	−	1.74485i	0.0348622	−	0.0603832i
$836$	5.94966	+	10.3051i	0.205773	+	0.356410i
$837$		0			0
$838$	−4.16827	+	7.21966i	−0.143991	+	0.249399i
$839$	−34.7382			−1.19930			−0.599648	−	0.800264i	$-0.704693\pi$
$839$	−34.7382			−1.19930			−0.599648	+	0.800264i	$0.704693\pi$
$840$		0			0
$841$	−26.8550			−0.926035
$842$	−3.50232	+	6.06620i	−0.120698	+	0.209055i
$843$		0			0
$844$	11.3856	+	19.7205i	0.391910	+	0.678808i
$845$	10.9360	−	18.9417i	0.376209	−	0.651614i
$846$		0			0
$847$	−49.0976	+	50.0989i	−1.68701	+	1.72142i
$848$	0.225450			0.00774199
$849$		0			0
$850$	6.49768	+	11.2543i	0.222868	+	0.386020i
$851$	−0.607523	−	1.05226i	−0.0208256	−	0.0360711i
$852$		0			0
$853$	42.3171			1.44891			0.724455	−	0.689322i	$-0.242091\pi$
$853$	42.3171			1.44891			0.724455	+	0.689322i	$0.242091\pi$
$854$	7.35417	+	26.3781i	0.251655	+	0.902640i
$855$		0			0
$856$	1.77292	−	3.07078i	0.0605970	−	0.104957i
$857$	−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	$0.915371\pi$
$858$		0			0
$859$	−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	$0.274115\pi$
$860$	−15.2495			−0.520005
$861$		0			0
$862$	3.45090			0.117538
$863$	−0.542263	+	0.939227i	−0.0184588	+	0.0319717i	−0.875107	−	0.483929i	$-0.839209\pi$
$863$	−0.542263	+	0.939227i	−0.0184588	+	0.0319717i	0.856648	+	0.515901i	$0.172543\pi$
$864$		0			0
$865$	−0.438174	−	0.758939i	−0.0148984	−	0.0258047i
$866$	−14.1300	+	24.4738i	−0.480156	+	0.831654i
$867$		0			0
$868$	−14.2661	+	14.5570i	−0.484222	+	0.494098i
$869$	−82.3483			−2.79348
$870$		0			0
$871$	−2.58126	−	4.47087i	−0.0874625	−	0.151490i
$872$	0.351848	+	0.609419i	0.0119151	+	0.0206375i
$873$		0			0
$874$	0.818057			0.0276712
$875$	−31.1300	−	8.00534i	−1.05238	−	0.270630i
$876$		0			0
$877$	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
$879$		0			0
$880$	−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
$885$		0			0
$886$	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	$0.00883293\pi$
$888$		0			0
$889$	−48.5654	−	12.4890i	−1.62883	−	0.418868i
$890$	−4.58358			−0.153642
$891$		0			0
$892$	−6.44282	−	11.1593i	−0.215722	−	0.373641i
$893$	1.61273	+	2.79332i	0.0539678	+	0.0934750i
$894$		0			0
$895$	−15.5458			−0.519640
$896$	−1.85185	+	1.88962i	−0.0618659	+	0.0631277i
$897$		0			0
$898$	10.1001	−	17.4939i	0.337046	−	0.583780i
$899$	5.64132	+	9.77104i	0.188148	+	0.325883i
$900$		0			0
$901$	−0.771280	+	1.33590i	−0.0256951	+	0.0445052i
$902$	42.5231			1.41587
$903$		0			0
$904$	−8.50232			−0.282783
$905$	−1.17046	+	2.02730i	−0.0389074	+	0.0673896i
$906$		0			0
$907$	−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	$0.875456\pi$
$908$	−10.9984	+	19.0497i	−0.364994	+	0.632187i
$909$		0			0
$910$	−0.951980	−	3.41458i	−0.0315578	−	0.113192i
$911$	8.01616			0.265587			0.132794	−	0.991144i	$-0.457605\pi$
$911$	8.01616			0.265587			0.132794	+	0.991144i	$0.457605\pi$
$912$		0			0
$913$	−9.56922	−	16.5744i	−0.316695	−	0.548532i
$914$	−10.0149	−	17.3463i	−0.331264	−	0.573766i
$915$		0			0
$916$	−3.79863			−0.125510
$917$	13.5056	−	13.7811i	0.445994	−	0.455090i
$918$		0			0
$919$	−12.0224	+	20.8235i	−0.396584	+	0.686903i	−0.993302	−	0.115548i	$-0.963138\pi$
$919$	−12.0224	+	20.8235i	−0.396584	+	0.686903i	0.596718	+	0.802451i	$0.296471\pi$
$920$	0.370723	+	0.642111i	0.0122224	+	0.0211698i
$921$		0			0
$922$	5.97661	−	10.3518i	0.196829	−	0.340918i
$923$	8.20602			0.270104
$924$		0			0
$925$	5.48073			0.180205
$926$	6.64527	−	11.5100i	0.218377	−	0.378240i
$927$		0			0
$928$	0.732287	+	1.26836i	0.0240385	+	0.0416359i
$929$	−13.9331	+	24.1328i	−0.457130	+	0.791773i	−0.998808	−	0.0488134i	$-0.984456\pi$
$929$	−13.9331	+	24.1328i	−0.457130	+	0.791773i	0.541678	+	0.840586i	$0.317789\pi$
$930$		0			0
$931$	11.6380	−	7.03625i	0.381422	−	0.230604i
$932$	6.67059			0.218503
$933$		0			0
$934$	−5.61505	−	9.72555i	−0.183730	−	0.318230i
$935$	−36.8960	−	63.9058i	−1.20663	−	2.08994i
$936$		0			0
$937$	53.2211			1.73866			0.869328	−	0.494235i	$-0.164552\pi$
$937$	53.2211			1.73866			0.869328	+	0.494235i	$0.164552\pi$
$938$	17.3856	+	4.47087i	0.567661	+	0.145979i
$939$		0			0
$940$	−1.46169	+	2.53173i	−0.0476752	+	0.0825759i
$941$	15.0241	+	26.0225i	0.489771	+	0.848308i	0.999931	−	0.0117715i	$-0.00374709\pi$
$941$	15.0241	+	26.0225i	0.489771	+	0.848308i	−0.510160	+	0.860080i	$0.670414\pi$
$942$		0			0
$943$	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	$-0.0564169\pi$
$948$		0			0
$949$	0.116683	+	0.202101i	0.00378769	+	0.00656047i
$950$	−1.84501	+	3.19565i	−0.0598601	+	0.103681i
$951$		0			0
$952$	−4.86156	−	17.4376i	−0.157564	−	0.565155i
$953$	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			0
$955$	14.2352	+	24.6560i	0.460639	+	0.797850i
$956$	−7.82038	−	13.5453i	−0.252929	−	0.438086i
$957$		0			0
$958$	−32.6271			−1.05413
$959$	5.81354	+	20.8521i	0.187729	+	0.673351i
$960$		0			0
$961$	−14.1735	+	24.5492i	−0.457209	+	0.791909i
$962$	1.09781	+	1.90146i	0.0353948	+	0.0613055i
$963$		0			0
$964$	−10.7060	+	18.5434i	−0.344818	+	0.597242i
$965$	−24.9486			−0.803123
$966$		0			0
$967$	−30.5803			−0.983396			−0.491698	−	0.870766i	$-0.663624\pi$
$967$	−30.5803			−0.983396			−0.491698	+	0.870766i	$0.663624\pi$
$968$	−13.2564	+	22.9607i	−0.426076	+	0.737985i
$969$		0			0
$970$	−3.20137	−	5.54494i	−0.102790	−	0.178037i
$971$	13.1030	−	22.6951i	0.420496	−	0.728320i	−0.575492	−	0.817807i	$-0.695190\pi$
$971$	13.1030	−	22.6951i	0.420496	−	0.728320i	0.995988	+	0.0894874i	$0.0285229\pi$
$972$		0			0
$973$	31.9390	+	8.21339i	1.02392	+	0.263309i
$974$	−3.69794			−0.118490
$975$		0			0
$976$	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	$0.942674\pi$
$978$		0			0
$979$	−15.9428			−0.509535
$980$	10.7970	+	5.94631i	0.344897	+	0.189948i
$981$		0			0
$982$	−18.7804	+	32.5287i	−0.599308	+	1.03803i
$983$	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	$0.732519\pi$
$984$		0			0
$985$	−13.9480	+	24.1587i	−0.444421	+	0.769760i
$986$	−10.0208			−0.319128
$987$		0			0
$988$	−1.47825			−0.0470293
$989$	−1.82326	+	3.15798i	−0.0579762	+	0.100418i
$990$		0			0
$991$	−7.49837	−	12.9875i	−0.238193	−	0.412563i	0.722003	−	0.691890i	$-0.243222\pi$
$991$	−7.49837	−	12.9875i	−0.238193	−	0.412563i	−0.960196	+	0.279327i	$0.909889\pi$
$992$	−3.85185	+	6.67160i	−0.122296	+	0.211823i
$993$		0			0
$994$	−19.9721	+	20.3794i	−0.633476	+	0.646397i
$995$	15.7472			0.499220
$996$		0			0
$997$	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	$0.455395\pi$
$998$	15.8977	+	27.5356i	0.503232	+	0.871624i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.3	✓	6	63.4	even	3
126.2.e.d.121.3	yes	6	9.7	even	3
126.2.h.c.67.2	yes	6	63.25	even	3
126.2.h.c.79.2	yes	6	9.4	even	3
378.2.e.c.37.2		6	9.2	odd	6
378.2.e.c.235.2		6	63.32	odd	6
378.2.h.d.289.2		6	9.5	odd	6
378.2.h.d.361.2		6	63.11	odd	6
882.2.e.p.373.1		6	63.34	odd	6
882.2.e.p.655.1		6	63.31	odd	6
882.2.f.l.295.1		6	63.58	even	3
882.2.f.l.589.1		6	63.16	even	3
882.2.f.m.295.3		6	63.40	odd	6
882.2.f.m.589.3		6	63.61	odd	6
882.2.h.o.67.2		6	63.52	odd	6
882.2.h.o.79.2		6	63.13	odd	6
1008.2.q.h.529.1		6	252.67	odd	6
1008.2.q.h.625.1		6	36.7	odd	6
1008.2.t.g.193.2		6	252.151	odd	6
1008.2.t.g.961.2		6	36.31	odd	6
1134.2.g.k.163.2		6	1.1	even	1	trivial
1134.2.g.k.487.2		6	7.4	even	3	inner
1134.2.g.n.163.2		6	3.2	odd	2
1134.2.g.n.487.2		6	21.11	odd	6
2646.2.e.o.1549.2		6	63.20	even	6
2646.2.e.o.2125.2		6	63.59	even	6
2646.2.f.n.883.2		6	63.5	even	6
2646.2.f.n.1765.2		6	63.47	even	6
2646.2.f.o.883.2		6	63.23	odd	6
2646.2.f.o.1765.2		6	63.2	odd	6
2646.2.h.p.361.2		6	63.38	even	6
2646.2.h.p.667.2		6	63.41	even	6
3024.2.q.h.2305.2		6	36.11	even	6
3024.2.q.h.2881.2		6	252.95	even	6
3024.2.t.g.289.2		6	36.23	even	6
3024.2.t.g.1873.2		6	252.11	even	6
7938.2.a.bu.1.2		3	21.2	odd	6
7938.2.a.bx.1.2		3	21.5	even	6
7938.2.a.by.1.2		3	7.5	odd	6
7938.2.a.cb.1.2		3	7.2	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.880438 + 1.52496i) q^{5} +(2.56238 + 0.658939i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.880438 + 1.52496i) q^{5} +(2.56238 + 0.658939i) q^{7} +1.00000 q^{8} +(-0.880438 - 1.52496i) q^{10} +(-3.06238 - 5.30420i) q^{11} +0.760877 q^{13} +(-1.85185 + 1.88962i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.42107 - 5.92546i) q^{17} +(0.971410 - 1.68253i) q^{19} +1.76088 q^{20} +6.12476 q^{22} +(0.210533 - 0.364654i) q^{23} +(0.949657 + 1.64485i) q^{25} +(-0.380438 + 0.658939i) q^{26} +(-0.710533 - 2.54856i) q^{28} -1.46457 q^{29} +(-3.85185 - 6.67160i) q^{31} +(-0.500000 - 0.866025i) q^{32} +6.84213 q^{34} +(-3.26088 + 3.32738i) q^{35} +(1.44282 - 2.49904i) q^{37} +(0.971410 + 1.68253i) q^{38} +(-0.880438 + 1.52496i) q^{40} +6.94282 q^{41} -8.66019 q^{43} +(-3.06238 + 5.30420i) q^{44} +(0.210533 + 0.364654i) q^{46} +(-0.830095 + 1.43777i) q^{47} +(6.13160 + 3.37690i) q^{49} -1.89931 q^{50} +(-0.380438 - 0.658939i) q^{52} +(-0.112725 - 0.195246i) q^{53} +10.7850 q^{55} +(2.56238 + 0.658939i) q^{56} +(0.732287 - 1.26836i) q^{58} +(-0.993163 - 1.72021i) q^{59} +(5.17511 - 8.96355i) q^{61} +7.70370 q^{62} +1.00000 q^{64} +(-0.669905 + 1.16031i) q^{65} +(-3.39248 - 5.87594i) q^{67} +(-3.42107 + 5.92546i) q^{68} +(-1.25116 - 4.48769i) q^{70} +10.7850 q^{71} +(0.153353 + 0.265616i) q^{73} +(1.44282 + 2.49904i) q^{74} -1.94282 q^{76} +(-4.35185 - 15.6093i) q^{77} +(6.72257 - 11.6438i) q^{79} +(-0.880438 - 1.52496i) q^{80} +(-3.47141 + 6.01266i) q^{82} +3.12476 q^{83} +12.0482 q^{85} +(4.33009 - 7.49994i) q^{86} +(-3.06238 - 5.30420i) q^{88} +(1.30150 - 2.25427i) q^{89} +(1.94966 + 0.501371i) q^{91} -0.421067 q^{92} +(-0.830095 - 1.43777i) q^{94} +(1.71053 + 2.96273i) q^{95} +3.63611 q^{97} +(-5.99028 + 3.62167i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8} - 5 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 3 q^{16} - 4 q^{17} - 3 q^{19} + 10 q^{20} + 2 q^{22} - 7 q^{23} - 2 q^{25} - 2 q^{26} + 4 q^{28} + 10 q^{29} - 14 q^{31} - 3 q^{32} + 8 q^{34} - 19 q^{35} - 9 q^{37} - 3 q^{38} - 5 q^{40} + 24 q^{41} - 36 q^{43} - q^{44} - 7 q^{46} + 3 q^{47} + 12 q^{49} + 4 q^{50} - 2 q^{52} + 9 q^{53} + 14 q^{55} - 2 q^{56} - 5 q^{58} + 4 q^{59} + 4 q^{61} + 28 q^{62} + 6 q^{64} - 12 q^{65} + 5 q^{67} - 4 q^{68} + 17 q^{70} + 14 q^{71} - 25 q^{73} - 9 q^{74} + 6 q^{76} - 17 q^{77} + 7 q^{79} - 5 q^{80} - 12 q^{82} - 16 q^{83} - 28 q^{85} + 18 q^{86} - q^{88} - 9 q^{89} + 4 q^{91} + 14 q^{92} + 3 q^{94} + 2 q^{95} + 56 q^{97} - 12 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8 - 5 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 3 * q^16 - 4 * q^17 - 3 * q^19 + 10 * q^20 + 2 * q^22 - 7 * q^23 - 2 * q^25 - 2 * q^26 + 4 * q^28 + 10 * q^29 - 14 * q^31 - 3 * q^32 + 8 * q^34 - 19 * q^35 - 9 * q^37 - 3 * q^38 - 5 * q^40 + 24 * q^41 - 36 * q^43 - q^44 - 7 * q^46 + 3 * q^47 + 12 * q^49 + 4 * q^50 - 2 * q^52 + 9 * q^53 + 14 * q^55 - 2 * q^56 - 5 * q^58 + 4 * q^59 + 4 * q^61 + 28 * q^62 + 6 * q^64 - 12 * q^65 + 5 * q^67 - 4 * q^68 + 17 * q^70 + 14 * q^71 - 25 * q^73 - 9 * q^74 + 6 * q^76 - 17 * q^77 + 7 * q^79 - 5 * q^80 - 12 * q^82 - 16 * q^83 - 28 * q^85 + 18 * q^86 - q^88 - 9 * q^89 + 4 * q^91 + 14 * q^92 + 3 * q^94 + 2 * q^95 + 56 * q^97 - 12 * q^98

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