LMFDB - Embedded newform 567.2.g.k.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(109,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, 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("567.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.g (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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.373419 - 0.0835272i$ of defining polynomial
Character	$\chi$	$=$	567.109
Dual form			567.2.g.k.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18584 + 2.05393i) q^{2} +(-1.81242 - 3.13920i) q^{4} -1.22875 q^{5} +(2.61263 + 0.417345i) q^{7} +3.85358 q^{8} +O(q^{10})$	\(q+(-1.18584 + 2.05393i) q^{2} +(-1.81242 - 3.13920i) q^{4} -1.22875 q^{5} +(2.61263 + 0.417345i) q^{7} +3.85358 q^{8} +(1.45709 - 2.52376i) q^{10} -2.66102 q^{11} +(1.81242 - 3.13920i) q^{13} +(-3.95535 + 4.87125i) q^{14} +(-0.944883 + 1.63659i) q^{16} +(3.36579 - 5.82972i) q^{17} +(-1.25730 - 2.17771i) q^{19} +(2.22700 + 3.85728i) q^{20} +(3.15554 - 5.46555i) q^{22} +7.99651 q^{23} -3.49018 q^{25} +(4.29846 + 7.44516i) q^{26} +(-3.42505 - 8.95796i) q^{28} +(1.12484 + 1.94827i) q^{29} +(5.11263 + 8.85533i) q^{31} +(1.61263 + 2.79315i) q^{32} +(7.98256 + 13.8262i) q^{34} +(-3.21025 - 0.512810i) q^{35} +(1.76951 + 3.06488i) q^{37} +5.96382 q^{38} -4.73507 q^{40} +(0.932674 - 1.61544i) q^{41} +(-2.56972 - 4.45088i) q^{43} +(4.82288 + 8.35348i) q^{44} +(-9.48256 + 16.4243i) q^{46} +(-1.07321 + 1.85885i) q^{47} +(6.65165 + 2.18073i) q^{49} +(4.13879 - 7.16859i) q^{50} -13.1394 q^{52} +(1.48605 - 2.57391i) q^{53} +3.26972 q^{55} +(10.0680 + 1.60827i) q^{56} -5.33549 q^{58} +(-4.36405 - 7.55875i) q^{59} +(7.50239 - 12.9945i) q^{61} -24.2510 q^{62} -11.4288 q^{64} +(-2.22700 + 3.85728i) q^{65} +(1.32463 + 2.29432i) q^{67} -24.4009 q^{68} +(4.86011 - 5.98553i) q^{70} +10.1150 q^{71} +(-3.64707 + 6.31691i) q^{73} -8.39340 q^{74} +(-4.55751 + 7.89384i) q^{76} +(-6.95226 - 1.11056i) q^{77} +(0.156882 - 0.271728i) q^{79} +(1.16102 - 2.01095i) q^{80} +(2.21200 + 3.83129i) q^{82} +(3.84686 + 6.66295i) q^{83} +(-4.13570 + 7.16324i) q^{85} +12.1891 q^{86} -10.2545 q^{88} +(-3.59628 - 6.22894i) q^{89} +(6.04530 - 7.44516i) q^{91} +(-14.4930 - 25.1026i) q^{92} +(-2.54530 - 4.40859i) q^{94} +(1.54490 + 2.67585i) q^{95} +(6.59195 + 11.4176i) q^{97} +(-12.3668 + 11.0760i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 5 q^{4} - 4 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) $ 8 * q + q^2 - 5 * q^4 - 4 * q^5 - 2 * q^7 + 6 * q^8	$ 8 q + q^{2} - 5 q^{4} - 4 q^{5} - 2 q^{7} + 6 q^{8} + 7 q^{10} - 10 q^{11} + 5 q^{13} - 7 q^{14} + q^{16} + 6 q^{17} + 8 q^{19} - 8 q^{20} + 7 q^{22} + 24 q^{23} + 16 q^{25} + q^{26} + 5 q^{28} - 10 q^{29} + 18 q^{31} - 10 q^{32} - 23 q^{35} + 40 q^{38} - 36 q^{40} - 5 q^{41} + 7 q^{43} + 13 q^{44} - 12 q^{46} - 21 q^{47} + 2 q^{49} + 38 q^{50} - 50 q^{52} - 12 q^{53} - 52 q^{55} + 33 q^{56} - 14 q^{58} + 6 q^{59} + 20 q^{61} - 36 q^{62} - 46 q^{64} + 8 q^{65} + 5 q^{67} - 102 q^{68} - 46 q^{70} + 18 q^{71} + 6 q^{73} - 5 q^{76} + 16 q^{77} + 10 q^{79} - 2 q^{80} + 35 q^{82} + 9 q^{83} + 9 q^{85} + 44 q^{86} + 36 q^{88} - 22 q^{89} + 13 q^{91} - 36 q^{92} + 15 q^{94} - 16 q^{95} + 9 q^{97} - 11 q^{98}+O(q^{100}) $ 8 * q + q^2 - 5 * q^4 - 4 * q^5 - 2 * q^7 + 6 * q^8 + 7 * q^10 - 10 * q^11 + 5 * q^13 - 7 * q^14 + q^16 + 6 * q^17 + 8 * q^19 - 8 * q^20 + 7 * q^22 + 24 * q^23 + 16 * q^25 + q^26 + 5 * q^28 - 10 * q^29 + 18 * q^31 - 10 * q^32 - 23 * q^35 + 40 * q^38 - 36 * q^40 - 5 * q^41 + 7 * q^43 + 13 * q^44 - 12 * q^46 - 21 * q^47 + 2 * q^49 + 38 * q^50 - 50 * q^52 - 12 * q^53 - 52 * q^55 + 33 * q^56 - 14 * q^58 + 6 * q^59 + 20 * q^61 - 36 * q^62 - 46 * q^64 + 8 * q^65 + 5 * q^67 - 102 * q^68 - 46 * q^70 + 18 * q^71 + 6 * q^73 - 5 * q^76 + 16 * q^77 + 10 * q^79 - 2 * q^80 + 35 * q^82 + 9 * q^83 + 9 * q^85 + 44 * q^86 + 36 * q^88 - 22 * q^89 + 13 * q^91 - 36 * q^92 + 15 * q^94 - 16 * q^95 + 9 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.18584	+	2.05393i	−0.838513	+	1.45235i	0.0526243	+	0.998614i	$0.483241\pi$
$2$	−1.18584	+	2.05393i	−0.838513	+	1.45235i	−0.891138	+	0.453733i	$0.850092\pi$
$3$		0			0
$3$		0			0
$4$	−1.81242	−	3.13920i	−0.906209	−	1.56960i
$5$	−1.22875			−0.549512			−0.274756	−	0.961514i	$-0.588597\pi$
$5$	−1.22875			−0.549512			−0.274756	+	0.961514i	$0.588597\pi$
$6$		0			0
$7$	2.61263	+	0.417345i	0.987480	+	0.157741i
$7$	2.61263	+	0.417345i	0.987480	+	0.157741i
$8$	3.85358			1.36245
$9$		0			0
$10$	1.45709	−	2.52376i	0.460773	−	0.798082i
$11$	−2.66102			−0.802328			−0.401164	−	0.916006i	$-0.631394\pi$
$11$	−2.66102			−0.802328			−0.401164	+	0.916006i	$0.631394\pi$
$12$		0			0
$13$	1.81242	−	3.13920i	0.502674	−	0.870658i	−0.497321	−	0.867567i	$-0.665683\pi$
$13$	1.81242	−	3.13920i	0.502674	−	0.870658i	0.999995	−	0.00309084i	$-0.000983846\pi$
$14$	−3.95535	+	4.87125i	−1.05711	+	1.30190i
$15$		0			0
$16$	−0.944883	+	1.63659i	−0.236221	+	0.409146i
$17$	3.36579	−	5.82972i	0.816324	−	1.41391i	−0.0920492	−	0.995754i	$-0.529342\pi$
$17$	3.36579	−	5.82972i	0.816324	−	1.41391i	0.908373	−	0.418160i	$-0.137325\pi$
$18$		0			0
$19$	−1.25730	−	2.17771i	−0.288445	−	0.499601i	0.684994	−	0.728549i	$-0.259805\pi$
$19$	−1.25730	−	2.17771i	−0.288445	−	0.499601i	−0.973439	+	0.228948i	$0.926471\pi$
$20$	2.22700	+	3.85728i	0.497972	+	0.862514i
$21$		0			0
$22$	3.15554	−	5.46555i	0.672763	−	1.16526i
$23$	7.99651			1.66739			0.833694	−	0.552227i	$-0.186222\pi$
$23$	7.99651			1.66739			0.833694	+	0.552227i	$0.186222\pi$
$24$		0			0
$25$	−3.49018			−0.698037
$26$	4.29846	+	7.44516i	0.842998	+	1.46012i
$27$		0			0
$28$	−3.42505	−	8.95796i	−0.647273	−	1.69290i
$29$	1.12484	+	1.94827i	0.208877	+	0.361785i	0.951361	−	0.308078i	$-0.0996859\pi$
$29$	1.12484	+	1.94827i	0.208877	+	0.361785i	−0.742484	+	0.669864i	$0.766353\pi$
$30$		0			0
$31$	5.11263	+	8.85533i	0.918255	+	1.59046i	0.802064	+	0.597237i	$0.203735\pi$
$31$	5.11263	+	8.85533i	0.918255	+	1.59046i	0.116191	+	0.993227i	$0.462932\pi$
$32$	1.61263	+	2.79315i	0.285075	+	0.493764i
$33$		0			0
$34$	7.98256	+	13.8262i	1.36900	+	2.37117i
$35$	−3.21025	−	0.512810i	−0.542632	−	0.0866807i
$36$		0			0
$37$	1.76951	+	3.06488i	0.290906	+	0.503863i	0.974024	−	0.226444i	$-0.0727101\pi$
$37$	1.76951	+	3.06488i	0.290906	+	0.503863i	−0.683119	+	0.730308i	$0.739377\pi$
$38$	5.96382			0.967459
$39$		0			0
$40$	−4.73507			−0.748680
$41$	0.932674	−	1.61544i	0.145659	−	0.252289i	−0.783959	−	0.620812i	$-0.786803\pi$
$41$	0.932674	−	1.61544i	0.145659	−	0.252289i	0.929619	+	0.368523i	$0.120136\pi$
$42$		0			0
$43$	−2.56972	−	4.45088i	−0.391879	−	0.678753i	0.600819	−	0.799385i	$-0.294841\pi$
$43$	−2.56972	−	4.45088i	−0.391879	−	0.678753i	−0.992697	+	0.120632i	$0.961508\pi$
$44$	4.82288	+	8.35348i	0.727077	+	1.25933i
$45$		0			0
$46$	−9.48256	+	16.4243i	−1.39813	+	2.42163i
$47$	−1.07321	+	1.85885i	−0.156544	+	0.271142i	−0.933620	−	0.358265i	$-0.883369\pi$
$47$	−1.07321	+	1.85885i	−0.156544	+	0.271142i	0.777076	+	0.629406i	$0.216702\pi$
$48$		0			0
$49$	6.65165	+	2.18073i	0.950235	+	0.311533i
$50$	4.13879	−	7.16859i	0.585313	−	1.01379i
$51$		0			0
$52$	−13.1394			−1.82211
$53$	1.48605	−	2.57391i	0.204124	−	0.353553i	−0.745729	−	0.666249i	$-0.767899\pi$
$53$	1.48605	−	2.57391i	0.204124	−	0.353553i	0.949853	+	0.312696i	$0.101232\pi$
$54$		0			0
$55$	3.26972			0.440888
$56$	10.0680	+	1.60827i	1.34539	+	0.214914i
$57$		0			0
$58$	−5.33549			−0.700584
$59$	−4.36405	−	7.55875i	−0.568150	−	0.984065i	−0.996749	−	0.0805702i	$-0.974326\pi$
$59$	−4.36405	−	7.55875i	−0.568150	−	0.984065i	0.428599	−	0.903495i	$-0.359007\pi$
$60$		0			0
$61$	7.50239	−	12.9945i	0.960583	−	1.66378i	0.239542	−	0.970886i	$-0.423003\pi$
$61$	7.50239	−	12.9945i	0.960583	−	1.66378i	0.721041	−	0.692893i	$-0.243664\pi$
$62$	−24.2510			−3.07988
$63$		0			0
$64$	−11.4288			−1.42860
$65$	−2.22700	+	3.85728i	−0.276225	+	0.478436i
$66$		0			0
$67$	1.32463	+	2.29432i	0.161829	+	0.280296i	0.935525	−	0.353261i	$-0.114927\pi$
$67$	1.32463	+	2.29432i	0.161829	+	0.280296i	−0.773696	+	0.633557i	$0.781594\pi$
$68$	−24.4009			−2.95904
$69$		0			0
$70$	4.86011	−	5.98553i	0.580895	−	0.715407i
$71$	10.1150			1.20043			0.600216	−	0.799838i	$-0.295081\pi$
$71$	10.1150			1.20043			0.600216	+	0.799838i	$0.295081\pi$
$72$		0			0
$73$	−3.64707	+	6.31691i	−0.426857	+	0.739338i	−0.996592	−	0.0824907i	$-0.973713\pi$
$73$	−3.64707	+	6.31691i	−0.426857	+	0.739338i	0.569735	+	0.821829i	$0.307046\pi$
$74$	−8.39340			−0.975713
$75$		0			0
$76$	−4.55751	+	7.89384i	−0.522782	+	0.905486i
$77$	−6.95226	−	1.11056i	−0.792283	−	0.126560i
$78$		0			0
$79$	0.156882	−	0.271728i	0.0176506	−	0.0305717i	−0.857065	−	0.515208i	$-0.827715\pi$
$79$	0.156882	−	0.271728i	0.0176506	−	0.0305717i	0.874716	+	0.484636i	$0.161048\pi$
$80$	1.16102	−	2.01095i	0.129806	−	0.224831i
$81$		0			0
$82$	2.21200	+	3.83129i	0.244274	+	0.423096i
$83$	3.84686	+	6.66295i	0.422247	+	0.731354i	0.996159	−	0.0875633i	$-0.0279080\pi$
$83$	3.84686	+	6.66295i	0.422247	+	0.731354i	−0.573912	+	0.818917i	$0.694575\pi$
$84$		0			0
$85$	−4.13570	+	7.16324i	−0.448580	+	0.776963i
$86$	12.1891			1.31438
$87$		0			0
$88$	−10.2545			−1.09313
$89$	−3.59628	−	6.22894i	−0.381205	−	0.660266i	0.610030	−	0.792378i	$-0.291157\pi$
$89$	−3.59628	−	6.22894i	−0.381205	−	0.660266i	−0.991235	+	0.132112i	$0.957824\pi$
$90$		0			0
$91$	6.04530	−	7.44516i	0.633720	−	0.780465i
$92$	−14.4930	−	25.1026i	−1.51100	−	2.61713i
$93$		0			0
$94$	−2.54530	−	4.40859i	−0.262528	−	0.454712i
$95$	1.54490	+	2.67585i	0.158504	+	0.274536i
$96$		0			0
$97$	6.59195	+	11.4176i	0.669311	+	1.15928i	0.978097	+	0.208149i	$0.0667440\pi$
$97$	6.59195	+	11.4176i	0.669311	+	1.15928i	−0.308786	+	0.951132i	$0.599923\pi$
$98$	−12.3668	+	11.0760i	−1.24924	+	1.11885i
$99$		0			0
$100$	6.32567	+	10.9564i	0.632567	+	1.09564i
$101$	2.78302			0.276921			0.138460	−	0.990368i	$-0.455785\pi$
$101$	2.78302			0.276921			0.138460	+	0.990368i	$0.455785\pi$
$102$		0			0
$103$	6.00647			0.591835			0.295917	−	0.955214i	$-0.404375\pi$
$103$	6.00647			0.591835			0.295917	+	0.955214i	$0.404375\pi$
$104$	6.98430	−	12.0972i	0.684867	−	1.18622i
$105$		0			0
$106$	3.52442	+	6.10447i	0.342322	+	0.592919i
$107$	−5.86818	−	10.1640i	−0.567299	−	0.982590i	−0.996832	−	0.0795391i	$-0.974655\pi$
$107$	−5.86818	−	10.1640i	−0.567299	−	0.982590i	0.429533	−	0.903051i	$-0.358678\pi$
$108$		0			0
$109$	3.99237	−	6.91499i	0.382400	−	0.662336i	−0.609005	−	0.793166i	$-0.708431\pi$
$109$	3.99237	−	6.91499i	0.382400	−	0.662336i	0.991405	+	0.130830i	$0.0417644\pi$
$110$	−3.87735	+	6.71577i	−0.369691	+	0.640323i
$111$		0			0
$112$	−3.15165	+	3.88145i	−0.297803	+	0.366762i
$113$	2.32005	−	4.01844i	0.218252	−	0.378023i	−0.736022	−	0.676958i	$-0.763298\pi$
$113$	2.32005	−	4.01844i	0.218252	−	0.378023i	0.954274	+	0.298935i	$0.0966313\pi$
$114$		0			0
$115$	−9.82567			−0.916249
$116$	4.07735	−	7.06217i	0.378572	−	0.655706i
$117$		0			0
$118$	20.7002			1.90561
$119$	11.2266	−	13.8262i	1.02914	−	1.26745i
$120$		0			0
$121$	−3.91897			−0.356270
$122$	17.7932	+	30.8188i	1.61092	+	2.79020i
$123$		0			0
$124$	18.5324	−	32.0991i	1.66426	−	2.88259i
$125$	10.4323			0.933091
$126$		0			0
$127$	−3.32633			−0.295164			−0.147582	−	0.989050i	$-0.547149\pi$
$127$	−3.32633			−0.295164			−0.147582	+	0.989050i	$0.547149\pi$
$128$	10.3274	−	17.8876i	0.912824	−	1.58106i
$129$		0			0
$130$	−5.28172	−	9.14820i	−0.463237	−	0.802351i
$131$	8.44702			0.738020			0.369010	−	0.929425i	$-0.379697\pi$
$131$	8.44702			0.738020			0.369010	+	0.929425i	$0.379697\pi$
$132$		0			0
$133$	−2.37600	−	6.21427i	−0.206026	−	0.538846i
$134$	−6.28317			−0.542783
$135$		0			0
$136$	12.9703	−	22.4653i	1.11220	−	1.92638i
$137$	−13.9965			−1.19580			−0.597901	−	0.801570i	$-0.703999\pi$
$137$	−13.9965			−1.19580			−0.597901	+	0.801570i	$0.703999\pi$
$138$		0			0
$139$	2.82005	−	4.88446i	0.239193	−	0.414295i	−0.721290	−	0.692633i	$-0.756450\pi$
$139$	2.82005	−	4.88446i	0.239193	−	0.414295i	0.960483	+	0.278339i	$0.0897837\pi$
$140$	4.20851	+	11.0071i	0.355684	+	0.930266i
$141$		0			0
$142$	−11.9948	+	20.7755i	−1.00658	+	1.74344i
$143$	−4.82288	+	8.35348i	−0.403310	+	0.698553i
$144$		0			0
$145$	−1.38214	−	2.39393i	−0.114780	−	0.198805i
$146$	−8.64965	−	14.9816i	−0.715850	−	1.23989i
$147$		0			0
$148$	6.41418	−	11.1097i	0.527243	−	0.913211i
$149$	−8.76945			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$149$	−8.76945			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$150$		0			0
$151$	−9.56075			−0.778042			−0.389021	−	0.921229i	$-0.627187\pi$
$151$	−9.56075			−0.778042			−0.389021	+	0.921229i	$0.627187\pi$
$152$	−4.84511	−	8.39198i	−0.392991	−	0.680680i
$153$		0			0
$154$	10.5253	−	12.9625i	0.848149	−	1.04455i
$155$	−6.28212	−	10.8809i	−0.504592	−	0.873979i
$156$		0			0
$157$	−1.07953	−	1.86981i	−0.0861562	−	0.149227i	0.819727	−	0.572754i	$-0.194125\pi$
$157$	−1.07953	−	1.86981i	−0.0861562	−	0.149227i	−0.905883	+	0.423527i	$0.860792\pi$
$158$	0.372073	+	0.644449i	0.0296005	+	0.0512696i
$159$		0			0
$160$	−1.98151	−	3.43207i	−0.156652	−	0.271329i
$161$	20.8919	+	3.33730i	1.64651	+	0.263016i
$162$		0			0
$163$	−10.4871	−	18.1643i	−0.821416	−	1.42273i	−0.904628	−	0.426202i	$-0.859851\pi$
$163$	−10.4871	−	18.1643i	−0.821416	−	1.42273i	0.0832119	−	0.996532i	$-0.473482\pi$
$164$	−6.76158			−0.527991
$165$		0			0
$166$	−18.2470			−1.41624
$167$	2.13704	−	3.70147i	0.165370	−	0.286428i	−0.771417	−	0.636330i	$-0.780452\pi$
$167$	2.13704	−	3.70147i	0.165370	−	0.286428i	0.936786	+	0.349902i	$0.113785\pi$
$168$		0			0
$169$	−0.0697192	−	0.120757i	−0.00536302	−	0.00928902i
$170$	−9.80853	−	16.9889i	−0.752280	−	1.30299i
$171$		0			0
$172$	−9.31481	+	16.1337i	−0.710248	+	1.23019i
$173$	0.908300	−	1.57322i	0.0690567	−	0.119610i	−0.829430	−	0.558611i	$-0.811334\pi$
$173$	0.908300	−	1.57322i	0.0690567	−	0.119610i	0.898486	+	0.439001i	$0.144668\pi$
$174$		0			0
$175$	−9.11855	−	1.45661i	−0.689298	−	0.110109i
$176$	2.51435	−	4.35499i	0.189526	−	0.328269i
$177$		0			0
$178$	17.0584			1.27858
$179$	4.02507	−	6.97162i	0.300848	−	0.521083i	−0.675481	−	0.737378i	$-0.736064\pi$
$179$	4.02507	−	6.97162i	0.300848	−	0.521083i	0.976328	+	0.216295i	$0.0693971\pi$
$180$		0			0
$181$	25.3467			1.88401			0.942004	−	0.335601i	$-0.108939\pi$
$181$	25.3467			1.88401			0.942004	+	0.335601i	$0.108939\pi$
$182$	8.12309	+	21.2454i	0.602124	+	1.57481i
$183$		0			0
$184$	30.8152			2.27173
$185$	−2.17428	−	3.76596i	−0.159856	−	0.276879i
$186$		0			0
$187$	−8.95644	+	15.5130i	−0.654960	+	1.13442i
$188$	7.78042			0.567445
$189$		0			0
$190$	−7.32801			−0.531630
$191$	−3.57560	+	6.19313i	−0.258722	+	0.448119i	−0.965900	−	0.258917i	$-0.916635\pi$
$191$	−3.57560	+	6.19313i	−0.258722	+	0.448119i	0.707178	+	0.707035i	$0.249968\pi$
$192$		0			0
$193$	−5.67777	−	9.83418i	−0.408695	−	0.707880i	0.586049	−	0.810276i	$-0.300683\pi$
$193$	−5.67777	−	9.83418i	−0.408695	−	0.707880i	−0.994744	+	0.102396i	$0.967349\pi$
$194$	−31.2679			−2.24490
$195$		0			0
$196$	−5.20981	−	24.8333i	−0.372129	−	1.77380i
$197$	−20.0998			−1.43205			−0.716024	−	0.698075i	$-0.754040\pi$
$197$	−20.0998			−1.43205			−0.716024	+	0.698075i	$0.754040\pi$
$198$		0			0
$199$	−5.16251	+	8.94173i	−0.365961	+	0.633862i	−0.988930	−	0.148384i	$-0.952593\pi$
$199$	−5.16251	+	8.94173i	−0.365961	+	0.633862i	0.622969	+	0.782246i	$0.285926\pi$
$200$	−13.4497			−0.951038
$201$		0			0
$202$	−3.30021	+	5.71613i	−0.232202	+	0.402186i
$203$	2.12568	+	5.55956i	0.149193	+	0.390204i
$204$		0			0
$205$	−1.14602	+	1.98496i	−0.0800415	+	0.138636i
$206$	−7.12269	+	12.3369i	−0.496261	+	0.859550i
$207$		0			0
$208$	3.42505	+	5.93235i	0.237484	+	0.411335i
$209$	3.34570	+	5.79493i	0.231427	+	0.400844i
$210$		0			0
$211$	−0.299369	+	0.518522i	−0.0206094	+	0.0356965i	−0.876146	−	0.482046i	$-0.839894\pi$
$211$	−0.299369	+	0.518522i	−0.0206094	+	0.0356965i	0.855537	+	0.517742i	$0.173227\pi$
$212$	−10.7734			−0.739917
$213$		0			0
$214$	27.8348			1.90275
$215$	3.15753	+	5.46900i	0.215342	+	0.372983i
$216$		0			0
$217$	9.66167	+	25.2694i	0.655877	+	1.71540i
$218$	9.46860	+	16.4001i	0.641295	+	1.11076i
$219$		0			0
$220$	−5.92609	−	10.2643i	−0.399537	−	0.692019i
$221$	−12.2004	−	21.1318i	−0.820690	−	1.42148i
$222$		0			0
$223$	−1.51002	−	2.61543i	−0.101119	−	0.175142i	0.811027	−	0.585008i	$-0.198909\pi$
$223$	−1.51002	−	2.61543i	−0.101119	−	0.175142i	−0.912146	+	0.409866i	$0.865575\pi$
$224$	3.04749	+	7.97049i	0.203619	+	0.532551i
$225$		0			0
$226$	5.50239	+	9.53043i	0.366014	+	0.633954i
$227$	20.1080			1.33462			0.667309	−	0.744781i	$-0.267446\pi$
$227$	20.1080			1.33462			0.667309	+	0.744781i	$0.267446\pi$
$228$		0			0
$229$	−20.0065			−1.32206			−0.661032	−	0.750357i	$-0.729881\pi$
$229$	−20.0065			−1.32206			−0.661032	+	0.750357i	$0.729881\pi$
$230$	11.6516	−	20.1812i	0.768287	−	1.33071i
$231$		0			0
$232$	4.33465	+	7.50783i	0.284584	+	0.492913i
$233$	−0.151398	−	0.262229i	−0.00991839	−	0.0171792i	0.861024	−	0.508565i	$-0.169824\pi$
$233$	−0.151398	−	0.262229i	−0.00991839	−	0.0171792i	−0.870942	+	0.491386i	$0.836491\pi$
$234$		0			0
$235$	1.31870	−	2.28406i	0.0860226	−	0.148995i
$236$	−15.8190	+	27.3992i	−1.02973	+	1.78354i
$237$		0			0
$238$	15.0852	+	39.4542i	0.977826	+	2.55743i
$239$	1.77340	−	3.07162i	0.114712	−	0.198686i	−0.802953	−	0.596043i	$-0.796739\pi$
$239$	1.77340	−	3.07162i	0.114712	−	0.198686i	0.917664	+	0.397356i	$0.130072\pi$
$240$		0			0
$241$	6.00647			0.386911			0.193455	−	0.981109i	$-0.438031\pi$
$241$	6.00647			0.386911			0.193455	+	0.981109i	$0.438031\pi$
$242$	4.64726	−	8.04929i	0.298737	−	0.517428i
$243$		0			0
$244$	−54.3899			−3.48196
$245$	−8.17318	−	2.67956i	−0.522165	−	0.171191i
$246$		0			0
$247$	−9.11502			−0.579975
$248$	19.7019	+	34.1247i	1.25107	+	2.16692i
$249$		0			0
$250$	−12.3710	+	21.4272i	−0.782409	+	1.35517i
$251$	21.0113			1.32622			0.663109	−	0.748523i	$-0.269236\pi$
$251$	21.0113			1.32622			0.663109	+	0.748523i	$0.269236\pi$
$252$		0			0
$253$	−21.2789			−1.33779
$254$	3.94448	−	6.83205i	0.247499	−	0.428681i
$255$		0			0
$256$	13.0645	+	22.6284i	0.816530	+	1.41427i
$257$	−20.5690			−1.28306			−0.641530	−	0.767098i	$-0.721700\pi$
$257$	−20.5690			−1.28306			−0.641530	+	0.767098i	$0.721700\pi$
$258$		0			0
$259$	3.34396	+	8.74589i	0.207783	+	0.543443i
$260$	16.1450			1.00127
$261$		0			0
$262$	−10.0168	+	17.3496i	−0.618839	+	1.07186i
$263$	14.2030			0.875796			0.437898	−	0.899025i	$-0.355723\pi$
$263$	14.2030			0.875796			0.437898	+	0.899025i	$0.355723\pi$
$264$		0			0
$265$	−1.82597	+	3.16268i	−0.112169	+	0.194282i
$266$	15.5812	+	2.48897i	0.955347	+	0.152608i
$267$		0			0
$268$	4.80156	−	8.31654i	0.293302	−	0.508013i
$269$	−15.5662	+	26.9615i	−0.949090	+	1.64387i	−0.201742	+	0.979439i	$0.564660\pi$
$269$	−15.5662	+	26.9615i	−0.949090	+	1.64387i	−0.747348	+	0.664433i	$0.768673\pi$
$270$		0			0
$271$	0.821392	+	1.42269i	0.0498960	+	0.0864225i	0.889895	−	0.456166i	$-0.150778\pi$
$271$	0.821392	+	1.42269i	0.0498960	+	0.0864225i	−0.839999	+	0.542588i	$0.817444\pi$
$272$	6.36056	+	11.0168i	0.385665	+	0.667992i
$273$		0			0
$274$	16.5976	−	28.7478i	1.00270	−	1.73672i
$275$	9.28745			0.560055
$276$		0			0
$277$	−22.0950			−1.32756			−0.663779	−	0.747929i	$-0.731049\pi$
$277$	−22.0950			−1.32756			−0.663779	+	0.747929i	$0.731049\pi$
$278$	6.68823	+	11.5844i	0.401133	+	0.694783i
$279$		0			0
$280$	−12.3710	−	1.97616i	−0.739307	−	0.118098i
$281$	7.74070	+	13.4073i	0.461771	+	0.799811i	0.999049	−	0.0435938i	$-0.0138807\pi$
$281$	7.74070	+	13.4073i	0.461771	+	0.799811i	−0.537278	+	0.843405i	$0.680547\pi$
$282$		0			0
$283$	13.1174	+	22.7200i	0.779749	+	1.35057i	0.932086	+	0.362237i	$0.117987\pi$
$283$	13.1174	+	22.7200i	0.779749	+	1.35057i	−0.152337	+	0.988329i	$0.548680\pi$
$284$	−18.3326	−	31.7531i	−1.08784	−	1.88420i
$285$		0			0
$286$	−11.4383	−	19.8117i	−0.676361	−	1.17149i
$287$	3.11093	−	3.83129i	0.183632	−	0.226154i
$288$		0			0
$289$	−14.1571	−	24.5208i	−0.832770	−	1.44240i
$290$	6.55596			0.384979
$291$		0			0
$292$	26.4400			1.54729
$293$	−8.45425	+	14.6432i	−0.493903	+	0.855464i	−0.999975	−	0.00702646i	$-0.997763\pi$
$293$	−8.45425	+	14.6432i	−0.493903	+	0.855464i	0.506073	+	0.862491i	$0.331097\pi$
$294$		0			0
$295$	5.36230	+	9.28778i	0.312205	+	0.540755i
$296$	6.81895	+	11.8108i	0.396343	+	0.686487i
$297$		0			0
$298$	10.3991	−	18.0118i	0.602406	−	1.04340i
$299$	14.4930	−	25.1026i	0.838153	−	1.45172i
$300$		0			0
$301$	−4.85617	−	12.7010i	−0.279905	−	0.732071i
$302$	11.3375	−	19.6371i	0.652399	−	1.12999i
$303$		0			0
$304$	4.75201			0.272546
$305$	−9.21853	+	15.9670i	−0.527852	+	0.914266i
$306$		0			0
$307$	−14.6835			−0.838034			−0.419017	−	0.907978i	$-0.637625\pi$
$307$	−14.6835			−0.838034			−0.419017	+	0.907978i	$0.637625\pi$
$308$	9.11412	+	23.8373i	0.519325	+	1.35826i
$309$		0			0
$310$	29.7983			1.69243
$311$	5.91109	+	10.2383i	0.335187	+	0.580561i	0.983521	−	0.180795i	$-0.0578671\pi$
$311$	5.91109	+	10.2383i	0.335187	+	0.580561i	−0.648334	+	0.761356i	$0.724534\pi$
$312$		0			0
$313$	0.177560	−	0.307543i	0.0100363	−	0.0173833i	−0.860964	−	0.508666i	$-0.830139\pi$
$313$	0.177560	−	0.307543i	0.0100363	−	0.0173833i	0.871000	+	0.491283i	$0.163472\pi$
$314$	5.12061			0.288973
$315$		0			0
$316$	−1.13734			−0.0639805
$317$	−5.22486	+	9.04972i	−0.293457	+	0.508283i	−0.974625	−	0.223845i	$-0.928139\pi$
$317$	−5.22486	+	9.04972i	−0.293457	+	0.508283i	0.681168	+	0.732127i	$0.261472\pi$
$318$		0			0
$319$	−2.99321	−	5.18440i	−0.167588	−	0.290270i
$320$	14.0431			0.785031
$321$		0			0
$322$	−31.6290	+	38.9530i	−1.76261	+	2.17077i
$323$	−16.9272			−0.941857
$324$		0			0
$325$	−6.32567	+	10.9564i	−0.350885	+	0.607751i
$326$	49.7441			2.75507
$327$		0			0
$328$	3.59414	−	6.22523i	0.198453	−	0.343731i
$329$	−3.57968	+	4.40859i	−0.197354	+	0.243054i
$330$		0			0
$331$	−7.43352	+	12.8752i	−0.408583	+	0.707686i	−0.994731	−	0.102517i	$-0.967310\pi$
$331$	−7.43352	+	12.8752i	−0.408583	+	0.707686i	0.586148	+	0.810204i	$0.300644\pi$
$332$	13.9442	−	24.1521i	0.765289	−	1.32552i
$333$		0			0
$334$	5.06837	+	8.77868i	0.277329	+	0.480348i
$335$	−1.62763	−	2.81914i	−0.0889269	−	0.154026i
$336$		0			0
$337$	−4.70676	+	8.15235i	−0.256394	+	0.444087i	−0.965273	−	0.261243i	$-0.915868\pi$
$337$	−4.70676	+	8.15235i	−0.256394	+	0.444087i	0.708879	+	0.705330i	$0.249201\pi$
$338$	0.330703			0.0179878
$339$		0			0
$340$	29.9825			1.62603
$341$	−13.6048	−	23.5642i	−0.736742	−	1.27607i
$342$		0			0
$343$	16.4682	+	8.47347i	0.889197	+	0.457524i
$344$	−9.90262	−	17.1518i	−0.533914	−	0.924766i
$345$		0			0
$346$	2.15419	+	3.73117i	0.115810	+	0.200589i
$347$	13.2932	+	23.0245i	0.713618	+	1.23602i	0.963490	+	0.267744i	$0.0862781\pi$
$347$	13.2932	+	23.0245i	0.713618	+	1.23602i	−0.249872	+	0.968279i	$0.580389\pi$
$348$		0			0
$349$	−4.77648	−	8.27311i	−0.255679	−	0.442850i	0.709401	−	0.704806i	$-0.248966\pi$
$349$	−4.77648	−	8.27311i	−0.255679	−	0.442850i	−0.965080	+	0.261956i	$0.915632\pi$
$350$	13.8049	−	17.0016i	0.737902	−	0.908772i
$351$		0			0
$352$	−4.29124	−	7.43264i	−0.228724	−	0.396161i
$353$	−17.0729			−0.908697			−0.454349	−	0.890824i	$-0.650128\pi$
$353$	−17.0729			−0.908697			−0.454349	+	0.890824i	$0.650128\pi$
$354$		0			0
$355$	−12.4288			−0.659651
$356$	−13.0359	+	22.5789i	−0.690903	+	1.19668i
$357$		0			0
$358$	9.54614	+	16.5344i	0.504529	+	0.873870i
$359$	12.8333	+	22.2280i	0.677318	+	1.17315i	0.975786	+	0.218730i	$0.0701912\pi$
$359$	12.8333	+	22.2280i	0.677318	+	1.17315i	−0.298467	+	0.954420i	$0.596475\pi$
$360$		0			0
$361$	6.33839	−	10.9784i	0.333599	−	0.577811i
$362$	−30.0571	+	52.0604i	−1.57977	+	2.73624i
$363$		0			0
$364$	−34.3285	−	5.48367i	−1.79930	−	0.287423i
$365$	4.48132	−	7.76187i	0.234563	−	0.406275i
$366$		0			0
$367$	−10.3752			−0.541579			−0.270790	−	0.962639i	$-0.587285\pi$
$367$	−10.3752			−0.541579			−0.270790	+	0.962639i	$0.587285\pi$
$368$	−7.55577	+	13.0870i	−0.393872	+	0.682205i
$369$		0			0
$370$	10.3134			0.536166
$371$	4.95669	−	6.10447i	0.257339	−	0.316928i
$372$		0			0
$373$	−19.8152			−1.02599			−0.512996	−	0.858391i	$-0.671465\pi$
$373$	−19.8152			−1.02599			−0.512996	+	0.858391i	$0.671465\pi$
$374$	−21.2417	−	36.7918i	−1.09838	−	1.90246i
$375$		0			0
$376$	−4.13570	+	7.16324i	−0.213282	+	0.369416i
$377$	8.15470			0.419988
$378$		0			0
$379$	14.1716			0.727948			0.363974	−	0.931409i	$-0.381420\pi$
$379$	14.1716			0.727948			0.363974	+	0.931409i	$0.381420\pi$
$380$	5.60002	−	9.69952i	0.287275	−	0.497575i
$381$		0			0
$382$	−8.48016	−	14.6881i	−0.433883	−	0.751507i
$383$	13.4487			0.687197			0.343598	−	0.939117i	$-0.388354\pi$
$383$	13.4487			0.687197			0.343598	+	0.939117i	$0.388354\pi$
$384$		0			0
$385$	8.54255	+	1.36460i	0.435369	+	0.0695464i
$386$	26.9316			1.37078
$387$		0			0
$388$	23.8947	−	41.3869i	1.21307	−	2.10110i
$389$	−20.9297			−1.06118			−0.530590	−	0.847629i	$-0.678029\pi$
$389$	−20.9297			−1.06118			−0.530590	+	0.847629i	$0.678029\pi$
$390$		0			0
$391$	26.9146	−	46.6174i	1.36113	−	2.35754i
$392$	25.6327	+	8.40363i	1.29465	+	0.424447i
$393$		0			0
$394$	23.8350	−	41.2835i	1.20079	−	2.07983i
$395$	−0.192768	+	0.333884i	−0.00969921	+	0.0167995i
$396$		0			0
$397$	12.5708	+	21.7732i	0.630909	+	1.09277i	0.987366	+	0.158454i	$0.0506511\pi$
$397$	12.5708	+	21.7732i	0.630909	+	1.09277i	−0.356458	+	0.934312i	$0.616016\pi$
$398$	−12.2438	−	21.2069i	−0.613726	−	1.06300i
$399$		0			0
$400$	3.29782	−	5.71198i	0.164891	−	0.285599i
$401$	−21.1603			−1.05669			−0.528347	−	0.849029i	$-0.677188\pi$
$401$	−21.1603			−1.05669			−0.528347	+	0.849029i	$0.677188\pi$
$402$		0			0
$403$	37.0649			1.84633
$404$	−5.04400	−	8.73646i	−0.250948	−	0.434655i
$405$		0			0
$406$	−13.9396	−	2.22674i	−0.691813	−	0.110511i
$407$	−4.70870	−	8.15571i	−0.233402	−	0.404264i
$408$		0			0
$409$	−0.271903	−	0.470950i	−0.0134447	−	0.0232870i	0.859225	−	0.511598i	$-0.170946\pi$
$409$	−0.271903	−	0.470950i	−0.0134447	−	0.0232870i	−0.872670	+	0.488311i	$0.837613\pi$
$410$	−2.71798	−	4.70769i	−0.134232	−	0.232496i
$411$		0			0
$412$	−10.8862	−	18.8555i	−0.536326	−	0.928944i
$413$	−8.24702	−	21.5695i	−0.405810	−	1.06137i
$414$		0			0
$415$	−4.72681	−	8.18707i	−0.232030	−	0.401888i
$416$	11.6910			0.573200
$417$		0			0
$418$	−15.8698			−0.776219
$419$	−11.9044	+	20.6190i	−0.581566	+	1.00730i	0.413728	+	0.910401i	$0.364227\pi$
$419$	−11.9044	+	20.6190i	−0.581566	+	1.00730i	−0.995294	+	0.0969018i	$0.969107\pi$
$420$		0			0
$421$	1.45490	+	2.51997i	0.0709077	+	0.122816i	0.899299	−	0.437334i	$-0.144077\pi$
$421$	1.45490	+	2.51997i	0.0709077	+	0.122816i	−0.828392	+	0.560149i	$0.810744\pi$
$422$	−0.710005	−	1.22976i	−0.0345625	−	0.0598640i
$423$		0			0
$424$	5.72660	−	9.91876i	0.278108	−	0.481698i
$425$	−11.7472	+	20.3468i	−0.569824	+	0.986965i
$426$		0			0
$427$	25.0242	−	30.8188i	1.21100	−	1.49143i
$428$	−21.2712	+	36.8428i	−1.02818	+	1.78086i
$429$		0			0
$430$	−14.9773			−0.722268
$431$	−15.6897	+	27.1754i	−0.755747	+	1.30899i	0.189255	+	0.981928i	$0.439393\pi$
$431$	−15.6897	+	27.1754i	−0.755747	+	1.30899i	−0.945002	+	0.327065i	$0.893941\pi$
$432$		0			0
$433$	−26.9281			−1.29408			−0.647042	−	0.762455i	$-0.723994\pi$
$433$	−26.9281			−1.29408			−0.647042	+	0.762455i	$0.723994\pi$
$434$	−63.3588	−	10.1210i	−3.04132	−	0.485824i
$435$		0			0
$436$	−28.9434			−1.38614
$437$	−10.0540	−	17.4141i	−0.480949	−	0.833028i
$438$		0			0
$439$	12.6647	−	21.9359i	0.604453	−	1.04694i	−0.387685	−	0.921792i	$-0.626725\pi$
$439$	12.6647	−	21.9359i	0.604453	−	1.04694i	0.992138	−	0.125151i	$-0.0399416\pi$
$440$	12.6001			0.600687
$441$		0			0
$442$	57.8709			2.75264
$443$	−6.51570	+	11.2855i	−0.309570	+	0.536191i	−0.978268	−	0.207343i	$-0.933518\pi$
$443$	−6.51570	+	11.2855i	−0.309570	+	0.536191i	0.668698	+	0.743534i	$0.266852\pi$
$444$		0			0
$445$	4.41891	+	7.65378i	0.209477	+	0.362824i
$446$	7.16256			0.339157
$447$		0			0
$448$	−29.8592	−	4.76974i	−1.41071	−	0.225349i
$449$	19.4353			0.917206			0.458603	−	0.888641i	$-0.348350\pi$
$449$	19.4353			0.917206			0.458603	+	0.888641i	$0.348350\pi$
$450$		0			0
$451$	−2.48187	+	4.29872i	−0.116866	+	0.202419i
$452$	−16.8196			−0.791126
$453$		0			0
$454$	−23.8449	+	41.3005i	−1.11909	+	1.93833i
$455$	−7.42814	+	9.14820i	−0.348236	+	0.428874i
$456$		0			0
$457$	14.3487	−	24.8528i	0.671206	−	1.16256i	−0.306356	−	0.951917i	$-0.599110\pi$
$457$	14.3487	−	24.8528i	0.671206	−	1.16256i	0.977562	−	0.210646i	$-0.0675567\pi$
$458$	23.7244	−	41.0919i	1.10857	−	1.92010i
$459$		0			0
$460$	17.8082	+	30.8448i	0.830313	+	1.43814i
$461$	−11.5240	−	19.9601i	−0.536725	−	0.929635i	−0.999078	−	0.0429386i	$-0.986328\pi$
$461$	−11.5240	−	19.9601i	−0.536725	−	0.929635i	0.462353	−	0.886696i	$-0.347005\pi$
$462$		0			0
$463$	−14.6074	+	25.3007i	−0.678863	+	1.17583i	0.296460	+	0.955045i	$0.404194\pi$
$463$	−14.6074	+	25.3007i	−0.678863	+	1.17583i	−0.975324	+	0.220780i	$0.929140\pi$
$464$	−4.25135			−0.197364
$465$		0			0
$466$	0.718132			0.0332668
$467$	2.18254	+	3.78027i	0.100996	+	0.174930i	0.912095	−	0.409978i	$-0.134464\pi$
$467$	2.18254	+	3.78027i	0.100996	+	0.174930i	−0.811099	+	0.584908i	$0.801130\pi$
$468$		0			0
$469$	2.50323	+	6.54703i	0.115589	+	0.302314i
$470$	3.12753	+	5.41704i	0.144262	+	0.249869i
$471$		0			0
$472$	−16.8172	−	29.1283i	−0.774075	−	1.34074i
$473$	6.83808	+	11.8439i	0.314415	+	0.544583i
$474$		0			0
$475$	4.38821	+	7.60061i	0.201345	+	0.348740i
$476$	−63.7504	−	10.1836i	−2.92200	−	0.466763i
$477$		0			0
$478$	4.20592	+	7.28487i	0.192374	+	0.333202i
$479$	15.9229			0.727535			0.363767	−	0.931490i	$-0.381490\pi$
$479$	15.9229			0.727535			0.363767	+	0.931490i	$0.381490\pi$
$480$		0			0
$481$	12.8284			0.584923
$482$	−7.12269	+	12.3369i	−0.324430	+	0.561929i
$483$		0			0
$484$	7.10281	+	12.3024i	0.322855	+	0.559201i
$485$	−8.09983	−	14.0293i	−0.367794	−	0.637038i
$486$		0			0
$487$	19.1329	−	33.1391i	0.866993	−	1.50168i	0.00193753	−	0.999998i	$-0.499383\pi$
$487$	19.1329	−	33.1391i	0.866993	−	1.50168i	0.865055	−	0.501677i	$-0.167283\pi$
$488$	28.9111	−	50.0755i	1.30874	−	2.26681i
$489$		0			0
$490$	15.1957	−	13.6096i	0.686472	−	0.614820i
$491$	6.69540	−	11.5968i	0.302159	−	0.523355i	−0.674466	−	0.738306i	$-0.735626\pi$
$491$	6.69540	−	11.5968i	0.302159	−	0.523355i	0.976625	+	0.214951i	$0.0689593\pi$
$492$		0			0
$493$	15.1439			0.682045
$494$	10.8089	−	18.7216i	0.486317	−	0.842325i
$495$		0			0
$496$	−19.3233			−0.867643
$497$	26.4268	+	4.22145i	1.18540	+	0.189358i
$498$		0			0
$499$	5.40706			0.242053			0.121027	−	0.992649i	$-0.461381\pi$
$499$	5.40706			0.242053			0.121027	+	0.992649i	$0.461381\pi$
$500$	−18.9076	−	32.7490i	−0.845576	−	1.46458i
$501$		0			0
$502$	−24.9159	+	43.1556i	−1.11205	+	1.92613i
$503$	−9.49157			−0.423208			−0.211604	−	0.977355i	$-0.567869\pi$
$503$	−9.49157			−0.423208			−0.211604	+	0.977355i	$0.567869\pi$
$504$		0			0
$505$	−3.41962			−0.152171
$506$	25.2333	−	43.7053i	1.12176	−	1.94294i
$507$		0			0
$508$	6.02870	+	10.4420i	0.267480	+	0.463289i
$509$	37.2297			1.65018			0.825088	−	0.565005i	$-0.191126\pi$
$509$	37.2297			1.65018			0.825088	+	0.565005i	$0.191126\pi$
$510$		0			0
$511$	−12.1648	+	14.9816i	−0.538137	+	0.662749i
$512$	−20.6597			−0.913039
$513$		0			0
$514$	24.3915	−	42.2473i	1.07586	−	1.86345i
$515$	−7.38042			−0.325220
$516$		0			0
$517$	2.85583	−	4.94645i	0.125599	−	0.217544i
$518$	−21.9288	−	3.50294i	−0.963497	−	0.153910i
$519$		0			0
$520$	−8.58193	+	14.8643i	−0.376342	+	0.651844i
$521$	−7.60082	+	13.1650i	−0.332998	+	0.576769i	−0.983098	−	0.183079i	$-0.941394\pi$
$521$	−7.60082	+	13.1650i	−0.332998	+	0.576769i	0.650100	+	0.759848i	$0.274727\pi$
$522$		0			0
$523$	−2.39824	−	4.15387i	−0.104867	−	0.181636i	0.808817	−	0.588061i	$-0.200109\pi$
$523$	−2.39824	−	4.15387i	−0.104867	−	0.181636i	−0.913684	+	0.406425i	$0.866775\pi$
$524$	−15.3095	−	26.5169i	−0.668800	−	1.15840i
$525$		0			0
$526$	−16.8425	+	29.1720i	−0.734366	+	1.27196i
$527$	68.8321			2.99837
$528$		0			0
$529$	40.9442			1.78018
$530$	−4.33061	−	7.50084i	−0.188110	−	0.325816i
$531$		0			0
$532$	−15.2015	+	18.7216i	−0.659070	+	0.811685i
$533$	−3.38079	−	5.85570i	−0.146438	−	0.253639i
$534$		0			0
$535$	7.21050	+	12.4890i	0.311737	+	0.539945i
$536$	5.10456	+	8.84135i	0.220483	+	0.381888i
$537$		0			0
$538$	−36.9180	−	63.9439i	−1.59165	−	2.75682i
$539$	−17.7002	−	5.80297i	−0.762400	−	0.249952i
$540$		0			0
$541$	3.22660	+	5.58864i	0.138722	+	0.240274i	0.927013	−	0.375029i	$-0.122367\pi$
$541$	3.22660	+	5.58864i	0.138722	+	0.240274i	−0.788291	+	0.615303i	$0.789034\pi$
$542$	−3.89615			−0.167354
$543$		0			0
$544$	21.7111			0.930854
$545$	−4.90561	+	8.49676i	−0.210133	+	0.363961i
$546$		0			0
$547$	−13.1281	−	22.7385i	−0.561316	−	0.972227i	−0.997382	−	0.0723129i	$-0.976962\pi$
$547$	−13.1281	−	22.7385i	−0.561316	−	0.972227i	0.436066	−	0.899915i	$-0.356371\pi$
$548$	25.3675	+	43.9378i	1.08365	+	1.87693i
$549$		0			0
$550$	−11.0134	+	19.0758i	−0.469613	+	0.813394i
$551$	2.82852	−	4.89913i	0.120499	−	0.208710i
$552$		0			0
$553$	0.523278	−	0.644449i	0.0222521	−	0.0274048i
$554$	26.2010	−	45.3815i	1.11318	−	1.92808i
$555$		0			0
$556$	−20.4444			−0.867036
$557$	−0.00716610	+	0.0124121i	−0.000303638	+	0.000525916i	−0.866177	−	0.499737i	$-0.833430\pi$
$557$	−0.00716610	+	0.0124121i	−0.000303638	+	0.000525916i	0.865874	+	0.500263i	$0.166763\pi$
$558$		0			0
$559$	−18.6296			−0.787949
$560$	3.87257	−	4.76931i	0.163646	−	0.201540i
$561$		0			0
$562$	−36.7168			−1.54881
$563$	−8.59130	−	14.8806i	−0.362080	−	0.627141i	0.626223	−	0.779644i	$-0.284600\pi$
$563$	−8.59130	−	14.8806i	−0.362080	−	0.627141i	−0.988303	+	0.152503i	$0.951267\pi$
$564$		0			0
$565$	−2.85075	+	4.93764i	−0.119932	+	0.207728i
$566$	−62.2205			−2.61532
$567$		0			0
$568$	38.9791			1.63553
$569$	−14.7390	+	25.5286i	−0.617889	+	1.07022i	0.371981	+	0.928240i	$0.378679\pi$
$569$	−14.7390	+	25.5286i	−0.617889	+	1.07022i	−0.989870	+	0.141975i	$0.954655\pi$
$570$		0			0
$571$	16.4161	+	28.4335i	0.686991	+	1.18990i	0.972807	+	0.231619i	$0.0744023\pi$
$571$	16.4161	+	28.4335i	0.686991	+	1.18990i	−0.285815	+	0.958285i	$0.592264\pi$
$572$	34.9643			1.46193
$573$		0			0
$574$	4.18016	+	10.9329i	0.174477	+	0.456331i
$575$	−27.9093			−1.16390
$576$		0			0
$577$	−15.9787	+	27.6759i	−0.665201	+	1.15216i	0.314030	+	0.949413i	$0.398321\pi$
$577$	−15.9787	+	27.6759i	−0.665201	+	1.15216i	−0.979231	+	0.202748i	$0.935013\pi$
$578$	67.1520			2.79315
$579$		0			0
$580$	−5.01002	+	8.67761i	−0.208030	+	0.360318i
$581$	7.26966	+	19.0133i	0.301596	+	0.788804i
$582$		0			0
$583$	−3.95440	+	6.84922i	−0.163775	+	0.283666i
$584$	−14.0543	+	24.3427i	−0.581570	+	1.00731i
$585$		0			0
$586$	−20.0507	−	34.7289i	−0.828288	−	1.43464i
$587$	−2.37316	−	4.11044i	−0.0979509	−	0.169656i	0.812885	−	0.582424i	$-0.197895\pi$
$587$	−2.37316	−	4.11044i	−0.0979509	−	0.169656i	−0.910836	+	0.412768i	$0.864562\pi$
$588$		0			0
$589$	12.8562	−	22.2676i	0.529732	−	0.917522i
$590$	−25.4353			−1.04715
$591$		0			0
$592$	−6.68792			−0.274872
$593$	−0.970397	−	1.68078i	−0.0398494	−	0.0690212i	0.845413	−	0.534113i	$-0.179354\pi$
$593$	−0.970397	−	1.68078i	−0.0398494	−	0.0690212i	−0.885262	+	0.465092i	$0.846021\pi$
$594$		0			0
$595$	−13.7946	+	16.9889i	−0.565523	+	0.696476i
$596$	15.8939	+	27.5290i	0.651040	+	1.12763i
$597$		0			0
$598$	34.3727	+	59.5353i	1.40560	+	2.43458i
$599$	−4.40067	−	7.62219i	−0.179807	−	0.311434i	0.762008	−	0.647568i	$-0.224214\pi$
$599$	−4.40067	−	7.62219i	−0.179807	−	0.311434i	−0.941814	+	0.336134i	$0.890881\pi$
$600$		0			0
$601$	7.48016	+	12.9560i	0.305122	+	0.528487i	0.977289	−	0.211913i	$-0.0679694\pi$
$601$	7.48016	+	12.9560i	0.305122	+	0.528487i	−0.672166	+	0.740400i	$0.734636\pi$
$602$	31.8455	+	5.08704i	1.29793	+	0.207332i
$603$		0			0
$604$	17.3281	+	30.0131i	0.705069	+	1.22122i
$605$	4.81542			0.195775
$606$		0			0
$607$	2.79138			0.113299			0.0566494	−	0.998394i	$-0.481958\pi$
$607$	2.79138			0.113299			0.0566494	+	0.998394i	$0.481958\pi$
$608$	4.05512	−	7.02367i	0.164457	−	0.284847i
$609$		0			0
$610$	−21.8633	−	37.8684i	−0.885221	−	1.53325i
$611$	3.89021	+	6.73804i	0.157381	+	0.272592i
$612$		0			0
$613$	−13.3218	+	23.0740i	−0.538062	+	0.931950i	0.460947	+	0.887428i	$0.347510\pi$
$613$	−13.3218	+	23.0740i	−0.538062	+	0.931950i	−0.999008	+	0.0445225i	$0.985823\pi$
$614$	17.4123	−	30.1590i	0.702703	−	1.21712i
$615$		0			0
$616$	−26.7911	−	4.27964i	−1.07944	−	0.172432i
$617$	−19.0560	+	33.0060i	−0.767166	+	1.32877i	0.171927	+	0.985110i	$0.445001\pi$
$617$	−19.0560	+	33.0060i	−0.767166	+	1.32877i	−0.939094	+	0.343661i	$0.888333\pi$
$618$		0			0
$619$	−23.9315			−0.961890			−0.480945	−	0.876751i	$-0.659706\pi$
$619$	−23.9315			−0.961890			−0.480945	+	0.876751i	$0.659706\pi$
$620$	−22.7716	+	39.4417i	−0.914531	+	1.58401i
$621$		0			0
$622$	−28.0384			−1.12424
$623$	−6.79613	−	17.7748i	−0.272281	−	0.712132i
$624$		0			0
$625$	4.63231			0.185293
$626$	0.421114	+	0.729391i	0.0168311	+	0.0291523i
$627$		0			0
$628$	−3.91314	+	6.77775i	−0.156151	+	0.270462i
$629$	23.8232			0.949893
$630$		0			0
$631$	−16.6748			−0.663812			−0.331906	−	0.943313i	$-0.607692\pi$
$631$	−16.6748			−0.663812			−0.331906	+	0.943313i	$0.607692\pi$
$632$	0.604558	−	1.04712i	0.0240480	−	0.0416524i
$633$		0			0
$634$	−12.3917	−	21.4630i	−0.492135	−	0.852404i
$635$	4.08721			0.162196
$636$		0			0
$637$	18.9013	−	16.9285i	0.748898	−	0.670730i
$638$	14.1978			0.562098
$639$		0			0
$640$	−12.6898	+	21.9793i	−0.501607	+	0.868809i
$641$	−32.0213			−1.26477			−0.632383	−	0.774656i	$-0.717923\pi$
$641$	−32.0213			−1.26477			−0.632383	+	0.774656i	$0.717923\pi$
$642$		0			0
$643$	1.75969	−	3.04788i	0.0693956	−	0.120197i	−0.829240	−	0.558893i	$-0.811226\pi$
$643$	1.75969	−	3.04788i	0.0693956	−	0.120197i	0.898635	+	0.438696i	$0.144560\pi$
$644$	−27.3884	−	71.6325i	−1.07925	−	2.82271i
$645$		0			0
$646$	20.0730	−	34.7674i	0.789760	−	1.36790i
$647$	20.7773	−	35.9873i	0.816839	−	1.41481i	−0.0911605	−	0.995836i	$-0.529058\pi$
$647$	20.7773	−	35.9873i	0.816839	−	1.41481i	0.908000	−	0.418971i	$-0.137609\pi$
$648$		0			0
$649$	11.6128	+	20.1140i	0.455843	+	0.789543i
$650$	−15.0024	−	25.9850i	−0.588444	−	1.01921i
$651$		0			0
$652$	−38.0142	+	65.8424i	−1.48875	+	2.57859i
$653$	−10.2858			−0.402513			−0.201257	−	0.979539i	$-0.564503\pi$
$653$	−10.2858			−0.402513			−0.201257	+	0.979539i	$0.564503\pi$
$654$		0			0
$655$	−10.3792			−0.405550
$656$	1.76254	+	3.05280i	0.0688155	+	0.119192i
$657$		0			0
$658$	−4.81002	−	12.5803i	−0.187514	−	0.490430i
$659$	10.1776	+	17.6281i	0.396461	+	0.686691i	0.993287	−	0.115680i	$-0.0369047\pi$
$659$	10.1776	+	17.6281i	0.396461	+	0.686691i	−0.596825	+	0.802371i	$0.703571\pi$
$660$		0			0
$661$	8.32637	+	14.4217i	0.323858	+	0.560939i	0.981281	−	0.192584i	$-0.0616866\pi$
$661$	8.32637	+	14.4217i	0.323858	+	0.560939i	−0.657422	+	0.753522i	$0.728353\pi$
$662$	−17.6299	−	30.5358i	−0.685204	−	1.18681i
$663$		0			0
$664$	14.8242	+	25.6762i	0.575290	+	0.996431i
$665$	2.91950	+	7.63576i	0.113214	+	0.296102i
$666$		0			0
$667$	8.99477	+	15.5794i	0.348279	+	0.603236i
$668$	−15.4929			−0.599437
$669$		0			0
$670$	7.72041			0.298265
$671$	−19.9640	+	34.5787i	−0.770703	+	1.33490i
$672$		0			0
$673$	−5.10939	−	8.84973i	−0.196953	−	0.341132i	0.750586	−	0.660772i	$-0.229771\pi$
$673$	−5.10939	−	8.84973i	−0.196953	−	0.341132i	−0.947539	+	0.319641i	$0.896438\pi$
$674$	−11.1629	−	19.3347i	−0.429979	−	0.744746i
$675$		0			0
$676$	−0.252721	+	0.437725i	−0.00972003	+	0.0168356i
$677$	3.19342	−	5.53117i	0.122733	−	0.212580i	−0.798111	−	0.602510i	$-0.794167\pi$
$677$	3.19342	−	5.53117i	0.122733	−	0.212580i	0.920845	+	0.389930i	$0.127501\pi$
$678$		0			0
$679$	12.4572	+	32.5810i	0.478065	+	1.25035i
$680$	−15.9373	+	27.6041i	−0.611166	+	1.05857i
$681$		0			0
$682$	64.5323			2.47107
$683$	−15.4061	+	26.6842i	−0.589499	+	1.02104i	0.404800	+	0.914405i	$0.367341\pi$
$683$	−15.4061	+	26.6842i	−0.589499	+	1.02104i	−0.994298	+	0.106636i	$0.965992\pi$
$684$		0			0
$685$	17.1981			0.657107
$686$	−36.9325	+	23.7763i	−1.41009	+	0.907783i
$687$		0			0
$688$	9.71234			0.370279
$689$	−5.38668	−	9.32999i	−0.205216	−	0.355444i
$690$		0			0
$691$	2.43402	−	4.21585i	0.0925945	−	0.160378i	−0.816008	−	0.578041i	$-0.803817\pi$
$691$	2.43402	−	4.21585i	0.0925945	−	0.160378i	0.908602	+	0.417663i	$0.137151\pi$
$692$	−6.58487			−0.250319
$693$		0			0
$694$	−63.0544			−2.39351
$695$	−3.46512	+	6.00176i	−0.131439	+	0.227660i
$696$		0			0
$697$	−6.27837	−	10.8745i	−0.237810	−	0.411900i
$698$	22.6565			0.857562
$699$		0			0
$700$	11.9540	+	31.2650i	0.451820	+	1.18170i
$701$	−44.4038			−1.67711			−0.838554	−	0.544819i	$-0.816598\pi$
$701$	−44.4038			−1.67711			−0.838554	+	0.544819i	$0.816598\pi$
$702$		0			0
$703$	4.44961	−	7.70696i	0.167820	−	0.290673i
$704$	30.4122			1.14620
$705$		0			0
$706$	20.2456	−	35.0665i	0.761955	−	1.31974i
$707$	7.27100	+	1.16148i	0.273454	+	0.0436819i
$708$		0			0
$709$	13.2884	−	23.0162i	0.499056	−	0.864391i	−0.500943	−	0.865480i	$-0.667013\pi$
$709$	13.2884	−	23.0162i	0.499056	−	0.864391i	0.999999	+	0.00108957i	$0.000346820\pi$
$710$	14.7385	−	25.5279i	0.553126	−	0.958043i
$711$		0			0
$712$	−13.8586	−	24.0037i	−0.519372	−	0.899578i
$713$	40.8832	+	70.8117i	1.53109	+	2.65192i
$714$		0			0
$715$	5.92609	−	10.2643i	0.221623	−	0.383863i
$716$	−29.1804			−1.09052
$717$		0			0
$718$	−60.8730			−2.27176
$719$	−16.9462	−	29.3517i	−0.631987	−	1.09463i	−0.987145	−	0.159828i	$-0.948906\pi$
$719$	−16.9462	−	29.3517i	−0.631987	−	1.09463i	0.355157	−	0.934807i	$-0.384427\pi$
$720$		0			0
$721$	15.6927	+	2.50677i	0.584425	+	0.0933569i
$722$	15.0326	+	26.0372i	0.559455	+	0.969005i
$723$		0			0
$724$	−45.9389	−	79.5685i	−1.70731	−	2.95714i
$725$	−3.92589	−	6.79984i	−0.145804	−	0.252540i
$726$		0			0
$727$	11.9709	+	20.7341i	0.443974	+	0.768986i	0.997980	−	0.0635267i	$-0.0202348\pi$
$727$	11.9709	+	20.7341i	0.443974	+	0.768986i	−0.554006	+	0.832513i	$0.686901\pi$
$728$	23.2961	−	28.6905i	0.863410	−	1.06334i
$729$		0			0
$730$	10.6282	+	18.4086i	0.393368	+	0.681334i
$731$	−34.5965			−1.27960
$732$		0			0
$733$	−37.5703			−1.38769			−0.693846	−	0.720124i	$-0.744085\pi$
$733$	−37.5703			−1.38769			−0.693846	+	0.720124i	$0.744085\pi$
$734$	12.3033	−	21.3099i	0.454121	−	0.786561i
$735$		0			0
$736$	12.8954	+	22.3355i	0.475331	+	0.823297i
$737$	−3.52486	−	6.10523i	−0.129840	−	0.224889i
$738$		0			0
$739$	2.82055	−	4.88534i	0.103756	−	0.179710i	−0.809473	−	0.587156i	$-0.800247\pi$
$739$	2.82055	−	4.88534i	0.103756	−	0.179710i	0.913229	+	0.407446i	$0.133581\pi$
$740$	−7.88140	+	13.6510i	−0.289726	+	0.501820i
$741$		0			0
$742$	6.66032	+	17.4196i	0.244508	+	0.639494i
$743$	7.58516	−	13.1379i	0.278273	−	0.481982i	−0.692683	−	0.721242i	$-0.743571\pi$
$743$	7.58516	−	13.1379i	0.278273	−	0.481982i	0.970956	+	0.239260i	$0.0769048\pi$
$744$		0			0
$745$	10.7754			0.394781
$746$	23.4976	−	40.6990i	0.860308	−	1.49010i
$747$		0			0
$748$	64.9312			2.37412
$749$	−11.0895	−	29.0038i	−0.405201	−	1.05978i
$750$		0			0
$751$	25.8935			0.944869			0.472434	−	0.881366i	$-0.343375\pi$
$751$	25.8935			0.944869			0.472434	+	0.881366i	$0.343375\pi$
$752$	−2.02811	−	3.51280i	−0.0739577	−	0.128099i
$753$		0			0
$754$	−9.67014	+	16.7492i	−0.352166	+	0.609969i
$755$	11.7477			0.427543
$756$		0			0
$757$	36.9054			1.34135			0.670675	−	0.741752i	$-0.266005\pi$
$757$	36.9054			1.34135			0.670675	+	0.741752i	$0.266005\pi$
$758$	−16.8052	+	29.1075i	−0.610394	+	1.05723i
$759$		0			0
$760$	5.95341	+	10.3116i	0.215953	+	0.374041i
$761$	−28.4009			−1.02953			−0.514765	−	0.857331i	$-0.672121\pi$
$761$	−28.4009			−1.02953			−0.514765	+	0.857331i	$0.672121\pi$
$762$		0			0
$763$	13.3165	−	16.4001i	0.482090	−	0.593724i
$764$	25.9219			0.937823
$765$		0			0
$766$	−15.9480	+	27.6227i	−0.576223	+	0.998048i
$767$	−31.6379			−1.14238
$768$		0			0
$769$	2.63076	−	4.55661i	0.0948677	−	0.164316i	−0.814686	−	0.579903i	$-0.803091\pi$
$769$	2.63076	−	4.55661i	0.0948677	−	0.164316i	0.909553	+	0.415587i	$0.136424\pi$
$770$	−12.9329	+	15.9276i	−0.466068	+	0.573991i
$771$		0			0
$772$	−20.5810	+	35.6473i	−0.740726	+	1.28297i
$773$	−20.6873	+	35.8315i	−0.744071	+	1.28877i	0.206556	+	0.978435i	$0.433774\pi$
$773$	−20.6873	+	35.8315i	−0.744071	+	1.28877i	−0.950627	+	0.310335i	$0.899559\pi$
$774$		0			0
$775$	−17.8440	−	30.9067i	−0.640976	−	1.11020i
$776$	25.4026	+	43.9986i	0.911901	+	1.57946i
$777$		0			0
$778$	24.8192	−	42.9882i	0.889813	−	1.54120i
$779$	−4.69061			−0.168059
$780$		0			0
$781$	−26.9163			−0.963140
$782$	63.8326	+	110.561i	2.28265	+	3.95366i
$783$		0			0
$784$	−9.85398	+	8.82545i	−0.351928	+	0.315195i
$785$	1.32647	+	2.29752i	0.0473438	+	0.0820019i
$786$		0			0
$787$	−2.68064	−	4.64301i	−0.0955547	−	0.165506i	0.814285	−	0.580465i	$-0.197129\pi$
$787$	−2.68064	−	4.64301i	−0.0955547	−	0.165506i	−0.909840	+	0.414959i	$0.863796\pi$
$788$	36.4292	+	63.0972i	1.29774	+	2.24774i
$789$		0			0
$790$	−0.457183	−	0.791864i	−0.0162658	−	0.0281733i
$791$	7.73849	−	9.53043i	0.275149	−	0.338863i
$792$		0			0
$793$	−27.1949	−	47.1030i	−0.965721	−	1.67268i
$794$	−59.6275			−2.11610
$795$		0			0
$796$	37.4265			1.32655
$797$	15.2102	−	26.3448i	0.538773	−	0.933182i	−0.460197	−	0.887817i	$-0.652221\pi$
$797$	15.2102	−	26.3448i	0.538773	−	0.933182i	0.998970	−	0.0453658i	$-0.0144453\pi$
$798$		0			0
$799$	7.22439	+	12.5130i	0.255581	+	0.442679i
$800$	−5.62837	−	9.74862i	−0.198993	−	0.344666i
$801$		0			0
$802$	25.0926	−	43.4617i	0.886052	−	1.53469i
$803$	9.70492	−	16.8094i	0.342479	−	0.593191i
$804$		0			0
$805$	−25.6708	−	4.10069i	−0.904778	−	0.144530i
$806$	−43.9529	+	76.1287i	−1.54817	+	2.68152i
$807$		0			0
$808$	10.7246			0.377290
$809$	21.7729	−	37.7117i	0.765494	−	1.32587i	−0.174491	−	0.984659i	$-0.555828\pi$
$809$	21.7729	−	37.7117i	0.765494	−	1.32587i	0.939985	−	0.341216i	$-0.110839\pi$
$810$		0			0
$811$	17.4078			0.611272			0.305636	−	0.952148i	$-0.401131\pi$
$811$	17.4078			0.611272			0.305636	+	0.952148i	$0.401131\pi$
$812$	13.6000	−	16.7492i	0.477265	−	0.587781i
$813$		0			0
$814$	22.3350			0.782842
$815$	12.8860	+	22.3192i	0.451378	+	0.781809i
$816$		0			0
$817$	−6.46182	+	11.1922i	−0.226071	+	0.391566i
$818$	1.28973			0.0450944
$819$		0			0
$820$	8.30826			0.290137
$821$	11.5318	−	19.9736i	0.402462	−	0.697085i	−0.591560	−	0.806261i	$-0.701488\pi$
$821$	11.5318	−	19.9736i	0.402462	−	0.697085i	0.994022	+	0.109176i	$0.0348211\pi$
$822$		0			0
$823$	−5.03902	−	8.72784i	−0.175649	−	0.304233i	0.764737	−	0.644343i	$-0.222869\pi$
$823$	−5.03902	−	8.72784i	−0.175649	−	0.304233i	−0.940386	+	0.340110i	$0.889536\pi$
$824$	23.1464			0.806344
$825$		0			0
$826$	54.0819	+	8.63911i	1.88175	+	0.300593i
$827$	28.4954			0.990882			0.495441	−	0.868642i	$-0.335007\pi$
$827$	28.4954			0.990882			0.495441	+	0.868642i	$0.335007\pi$
$828$		0			0
$829$	0.907602	−	1.57201i	0.0315223	−	0.0545983i	−0.849834	−	0.527051i	$-0.823298\pi$
$829$	0.907602	−	1.57201i	0.0315223	−	0.0545983i	0.881356	+	0.472452i	$0.156631\pi$
$830$	22.4209			0.778241
$831$		0			0
$832$	−20.7137	+	35.8772i	−0.718120	+	1.24382i
$833$	35.1011	−	31.4374i	1.21618	−	1.08924i
$834$		0			0
$835$	−2.62588	+	4.54816i	−0.0908725	+	0.157396i
$836$	12.1276	−	21.0057i	0.419443	−	0.726496i
$837$		0			0
$838$	−28.2333	−	48.9015i	−0.975302	−	1.68927i
$839$	3.43860	+	5.95583i	0.118714	+	0.205618i	0.919258	−	0.393655i	$-0.128790\pi$
$839$	3.43860	+	5.95583i	0.118714	+	0.205618i	−0.800544	+	0.599273i	$0.795456\pi$
$840$		0			0
$841$	11.9695	−	20.7318i	0.412741	−	0.714888i
$842$	−6.90112			−0.237828
$843$		0			0
$844$	2.17032			0.0747057
$845$	0.0856672	+	0.148380i	0.00294704	+	0.00510442i
$846$		0			0
$847$	−10.2388	−	1.63556i	−0.351810	−	0.0561985i
$848$	2.80828	+	4.86408i	0.0964367	+	0.167033i
$849$		0			0
$850$	−27.8606	−	48.2560i	−0.955611	−	1.65517i
$851$	14.1499	+	24.5083i	0.485052	+	0.840135i
$852$		0			0
$853$	1.34635	+	2.33195i	0.0460982	+	0.0798445i	0.888154	−	0.459546i	$-0.151988\pi$
$853$	1.34635	+	2.33195i	0.0460982	+	0.0798445i	−0.842056	+	0.539391i	$0.818655\pi$
$854$	33.6250	+	87.9439i	1.15063	+	3.00938i
$855$		0			0
$856$	−22.6135	−	39.1678i	−0.772914	−	1.33873i
$857$	23.6722			0.808625			0.404313	−	0.914621i	$-0.367511\pi$
$857$	23.6722			0.808625			0.404313	+	0.914621i	$0.367511\pi$
$858$		0			0
$859$	−13.0275			−0.444492			−0.222246	−	0.974991i	$-0.571339\pi$
$859$	−13.0275			−0.444492			−0.222246	+	0.974991i	$0.571339\pi$
$860$	11.4455	−	19.8242i	0.390289	−	0.676001i
$861$		0			0
$862$	−37.2109	−	64.4512i	−1.26741	−	2.19522i
$863$	9.87796	+	17.1091i	0.336250	+	0.582401i	0.983724	−	0.179686i	$-0.0575081\pi$
$863$	9.87796	+	17.1091i	0.336250	+	0.582401i	−0.647475	+	0.762087i	$0.724175\pi$
$864$		0			0
$865$	−1.11607	+	1.93309i	−0.0379475	+	0.0657270i
$866$	31.9324	−	55.3085i	1.08511	−	1.87946i
$867$		0			0
$868$	61.8148	−	76.1287i	2.09813	−	2.58397i
$869$	−0.417466	+	0.723073i	−0.0141616	+	0.0245286i
$870$		0			0
$871$	9.60311			0.325389
$872$	15.3849	−	26.6475i	0.520999	−	0.902398i
$873$		0			0
$874$	47.6897			1.61313
$875$	27.2557	+	4.35385i	0.921409	+	0.147187i
$876$		0			0
$877$	12.6814			0.428222			0.214111	−	0.976809i	$-0.431315\pi$
$877$	12.6814			0.428222			0.214111	+	0.976809i	$0.431315\pi$
$878$	30.0365	+	52.0248i	1.01368	+	1.75575i
$879$		0			0
$880$	−3.08950	+	5.35117i	−0.104147	+	0.180388i
$881$	43.7202			1.47297			0.736485	−	0.676454i	$-0.236484\pi$
$881$	43.7202			1.47297			0.736485	+	0.676454i	$0.236484\pi$
$882$		0			0
$883$	−1.03795			−0.0349298			−0.0174649	−	0.999847i	$-0.505560\pi$
$883$	−1.03795			−0.0349298			−0.0174649	+	0.999847i	$0.505560\pi$
$884$	−44.2246	+	76.5992i	−1.48743	+	2.57631i
$885$		0			0
$886$	−15.4531	−	26.7656i	−0.519157	−	0.899207i
$887$	6.38256			0.214305			0.107153	−	0.994243i	$-0.465827\pi$
$887$	6.38256			0.214305			0.107153	+	0.994243i	$0.465827\pi$
$888$		0			0
$889$	−8.69046	−	1.38823i	−0.291469	−	0.0465596i
$890$	−20.9604			−0.702596
$891$		0			0
$892$	−5.47358	+	9.48052i	−0.183269	+	0.317431i
$893$	5.39739			0.180617
$894$		0			0
$895$	−4.94578	+	8.56634i	−0.165319	+	0.286341i
$896$	34.4470	−	42.4236i	1.15079	−	1.41727i
$897$		0			0
$898$	−23.0470	+	39.9186i	−0.769090	+	1.33210i
$899$	−11.5017	+	19.9216i	−0.383604	+	0.664422i
$900$		0			0
$901$	−10.0034	−	17.3265i	−0.333263	−	0.577228i
$902$	−5.88617	−	10.1952i	−0.195988	−	0.339461i
$903$		0			0
$904$	8.94049	−	15.4854i	0.297356	−	0.515036i
$905$	−31.1447			−1.03528
$906$		0			0
$907$	−45.4262			−1.50835			−0.754176	−	0.656672i	$-0.771964\pi$
$907$	−45.4262			−1.50835			−0.754176	+	0.656672i	$0.771964\pi$
$908$	−36.4442	−	63.1232i	−1.20944	−	2.09482i
$909$		0			0
$910$	−9.98121	−	26.1051i	−0.330874	−	0.865377i
$911$	2.24354	+	3.88592i	0.0743318	+	0.128746i	0.900795	−	0.434244i	$-0.142984\pi$
$911$	2.24354	+	3.88592i	0.0743318	+	0.128746i	−0.826464	+	0.562990i	$0.809651\pi$
$912$		0			0
$913$	−10.2366	−	17.7303i	−0.338781	−	0.586786i
$914$	34.0305	+	58.9426i	1.12563	+	1.94965i
$915$		0			0
$916$	36.2601	+	62.8043i	1.19807	+	2.07511i
$917$	22.0689	+	3.52532i	0.728780	+	0.116416i
$918$		0			0
$919$	17.3189	+	29.9972i	0.571298	+	0.989517i	0.996433	+	0.0843873i	$0.0268933\pi$
$919$	17.3189	+	29.9972i	0.571298	+	0.989517i	−0.425135	+	0.905130i	$0.639773\pi$
$920$	−37.8640			−1.24834
$921$		0			0
$922$	54.6622			1.80020
$923$	18.3326	−	31.7531i	0.603426	−	1.04517i
$924$		0			0
$925$	−6.17592	−	10.6970i	−0.203063	−	0.351715i
$926$	−34.6440	−	60.0051i	−1.13847	−	1.97189i
$927$		0			0
$928$	−3.62788	+	6.28368i	−0.119091	+	0.206272i
$929$	7.63640	−	13.2266i	0.250542	−	0.433952i	−0.713133	−	0.701029i	$-0.752725\pi$
$929$	7.63640	−	13.2266i	0.250542	−	0.433952i	0.963675	+	0.267077i	$0.0860578\pi$
$930$		0			0
$931$	−3.61412	−	17.2272i	−0.118448	−	0.564598i
$932$	−0.548792	+	0.950535i	−0.0179763	+	0.0311358i
$933$		0			0
$934$	−10.3525			−0.338746
$935$	11.0052	−	19.0615i	0.359908	−	0.623379i
$936$		0			0
$937$	16.6920			0.545305			0.272652	−	0.962113i	$-0.412099\pi$
$937$	16.6920			0.545305			0.272652	+	0.962113i	$0.412099\pi$
$938$	−16.4156	−	2.62224i	−0.535987	−	0.0856193i
$939$		0			0
$940$	−9.56015			−0.311818
$941$	10.6239	+	18.4012i	0.346330	+	0.599862i	0.985595	−	0.169125i	$-0.0540943\pi$
$941$	10.6239	+	18.4012i	0.346330	+	0.599862i	−0.639264	+	0.768987i	$0.720761\pi$
$942$		0			0
$943$	7.45814	−	12.9179i	0.242870	−	0.420664i
$944$	16.4940			0.536836
$945$		0			0
$946$	−32.4354			−1.05456
$947$	19.6573	−	34.0475i	0.638777	−	1.10639i	−0.346924	−	0.937893i	$-0.612774\pi$
$947$	19.6573	−	34.0475i	0.638777	−	1.10639i	0.985701	−	0.168501i	$-0.0538927\pi$
$948$		0			0
$949$	13.2200	+	22.8977i	0.429140	+	0.743292i
$950$	−20.8148			−0.675322
$951$		0			0
$952$	43.2625	−	53.2804i	1.40214	−	1.72683i
$953$	15.1311			0.490143			0.245072	−	0.969505i	$-0.421189\pi$
$953$	15.1311			0.490143			0.245072	+	0.969505i	$0.421189\pi$
$954$		0			0
$955$	4.39351	−	7.60977i	0.142170	−	0.246247i
$956$	−12.8566			−0.415811
$957$		0			0
$958$	−18.8819	+	32.7045i	−0.610047	+	1.05663i
$959$	−36.5677	−	5.84137i	−1.18083	−	0.188628i
$960$		0			0
$961$	−36.7779	+	63.7012i	−1.18638	+	2.05488i
$962$	−15.2123	+	26.3486i	−0.490466	+	0.849512i
$963$		0			0
$964$	−10.8862	−	18.8555i	−0.350622	−	0.607295i
$965$	6.97653	+	12.0837i	0.224582	+	0.388988i
$966$		0			0
$967$	−15.6941	+	27.1829i	−0.504687	+	0.874143i	0.495299	+	0.868723i	$0.335059\pi$
$967$	−15.6941	+	27.1829i	−0.504687	+	0.874143i	−0.999985	+	0.00542015i	$0.998275\pi$
$968$	−15.1021			−0.485399
$969$		0			0
$970$	38.4203			1.23360
$971$	17.4760	+	30.2694i	0.560833	+	0.971391i	0.997424	+	0.0717309i	$0.0228523\pi$
$971$	17.4760	+	30.2694i	0.560833	+	0.971391i	−0.436591	+	0.899660i	$0.643814\pi$
$972$		0			0
$973$	9.40624	−	11.5844i	0.301550	−	0.371377i
$974$	45.3769	+	78.5951i	1.45397	+	2.51835i
$975$		0			0
$976$	14.1778	+	24.5566i	0.453819	+	0.786038i
$977$	−3.84316	−	6.65655i	−0.122954	−	0.212962i	0.797978	−	0.602687i	$-0.205903\pi$
$977$	−3.84316	−	6.65655i	−0.122954	−	0.212962i	−0.920931	+	0.389725i	$0.872570\pi$
$978$		0			0
$979$	9.56978	+	16.5753i	0.305851	+	0.529750i
$980$	6.40153	+	30.5137i	0.204489	+	0.974726i
$981$		0			0
$982$	15.8793	+	27.5037i	0.506729	+	0.877680i
$983$	−2.18071			−0.0695538			−0.0347769	−	0.999395i	$-0.511072\pi$
$983$	−2.18071			−0.0695538			−0.0347769	+	0.999395i	$0.511072\pi$
$984$		0			0
$985$	24.6975			0.786928
$986$	−17.9581	+	31.1044i	−0.571904	+	0.990566i
$987$		0			0
$988$	16.5202	+	28.6139i	0.525579	+	0.910329i
$989$	−20.5488	−	35.5915i	−0.653413	−	1.13175i
$990$		0			0
$991$	2.85159	−	4.93909i	0.0905837	−	0.156895i	−0.817173	−	0.576392i	$-0.804460\pi$
$991$	2.85159	−	4.93909i	0.0905837	−	0.156895i	0.907757	+	0.419497i	$0.137793\pi$
$992$	−16.4895	+	28.5607i	−0.523543	+	0.906803i
$993$		0			0
$994$	−40.0084	+	49.2728i	−1.26899	+	1.56284i
$995$	6.34341	−	10.9871i	0.201100	−	0.348315i
$996$		0			0
$997$	31.3797			0.993804			0.496902	−	0.867807i	$-0.334471\pi$
$997$	31.3797			0.993804			0.496902	+	0.867807i	$0.334471\pi$
$998$	−6.41189	+	11.1057i	−0.202965	+	0.351545i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.g.k.109.1		8
3.2	odd	2		567.2.g.j.109.4		8
7.2	even	3		567.2.h.j.352.4		8
9.2	odd	6		567.2.h.k.298.1		8
9.4	even	3		567.2.e.d.487.1	yes	8
9.5	odd	6		567.2.e.c.487.4	yes	8
9.7	even	3		567.2.h.j.298.4		8
21.2	odd	6		567.2.h.k.352.1		8
63.2	odd	6		567.2.g.j.541.4		8
63.4	even	3		3969.2.a.s.1.4		4
63.16	even	3	inner	567.2.g.k.541.1		8
63.23	odd	6		567.2.e.c.163.4	✓	8
63.31	odd	6		3969.2.a.t.1.4		4
63.32	odd	6		3969.2.a.x.1.1		4
63.58	even	3		567.2.e.d.163.1	yes	8
63.59	even	6		3969.2.a.w.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.4	✓	8	63.23	odd	6
567.2.e.c.487.4	yes	8	9.5	odd	6
567.2.e.d.163.1	yes	8	63.58	even	3
567.2.e.d.487.1	yes	8	9.4	even	3
567.2.g.j.109.4		8	3.2	odd	2
567.2.g.j.541.4		8	63.2	odd	6
567.2.g.k.109.1		8	1.1	even	1	trivial
567.2.g.k.541.1		8	63.16	even	3	inner
567.2.h.j.298.4		8	9.7	even	3
567.2.h.j.352.4		8	7.2	even	3
567.2.h.k.298.1		8	9.2	odd	6
567.2.h.k.352.1		8	21.2	odd	6
3969.2.a.s.1.4		4	63.4	even	3
3969.2.a.t.1.4		4	63.31	odd	6
3969.2.a.w.1.1		4	63.59	even	6
3969.2.a.x.1.1		4	63.32	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.18584 + 2.05393i) q^{2} +(-1.81242 - 3.13920i) q^{4} -1.22875 q^{5} +(2.61263 + 0.417345i) q^{7} +3.85358 q^{8} +O(q^{10})\)	\(q+(-1.18584 + 2.05393i) q^{2} +(-1.81242 - 3.13920i) q^{4} -1.22875 q^{5} +(2.61263 + 0.417345i) q^{7} +3.85358 q^{8} +(1.45709 - 2.52376i) q^{10} -2.66102 q^{11} +(1.81242 - 3.13920i) q^{13} +(-3.95535 + 4.87125i) q^{14} +(-0.944883 + 1.63659i) q^{16} +(3.36579 - 5.82972i) q^{17} +(-1.25730 - 2.17771i) q^{19} +(2.22700 + 3.85728i) q^{20} +(3.15554 - 5.46555i) q^{22} +7.99651 q^{23} -3.49018 q^{25} +(4.29846 + 7.44516i) q^{26} +(-3.42505 - 8.95796i) q^{28} +(1.12484 + 1.94827i) q^{29} +(5.11263 + 8.85533i) q^{31} +(1.61263 + 2.79315i) q^{32} +(7.98256 + 13.8262i) q^{34} +(-3.21025 - 0.512810i) q^{35} +(1.76951 + 3.06488i) q^{37} +5.96382 q^{38} -4.73507 q^{40} +(0.932674 - 1.61544i) q^{41} +(-2.56972 - 4.45088i) q^{43} +(4.82288 + 8.35348i) q^{44} +(-9.48256 + 16.4243i) q^{46} +(-1.07321 + 1.85885i) q^{47} +(6.65165 + 2.18073i) q^{49} +(4.13879 - 7.16859i) q^{50} -13.1394 q^{52} +(1.48605 - 2.57391i) q^{53} +3.26972 q^{55} +(10.0680 + 1.60827i) q^{56} -5.33549 q^{58} +(-4.36405 - 7.55875i) q^{59} +(7.50239 - 12.9945i) q^{61} -24.2510 q^{62} -11.4288 q^{64} +(-2.22700 + 3.85728i) q^{65} +(1.32463 + 2.29432i) q^{67} -24.4009 q^{68} +(4.86011 - 5.98553i) q^{70} +10.1150 q^{71} +(-3.64707 + 6.31691i) q^{73} -8.39340 q^{74} +(-4.55751 + 7.89384i) q^{76} +(-6.95226 - 1.11056i) q^{77} +(0.156882 - 0.271728i) q^{79} +(1.16102 - 2.01095i) q^{80} +(2.21200 + 3.83129i) q^{82} +(3.84686 + 6.66295i) q^{83} +(-4.13570 + 7.16324i) q^{85} +12.1891 q^{86} -10.2545 q^{88} +(-3.59628 - 6.22894i) q^{89} +(6.04530 - 7.44516i) q^{91} +(-14.4930 - 25.1026i) q^{92} +(-2.54530 - 4.40859i) q^{94} +(1.54490 + 2.67585i) q^{95} +(6.59195 + 11.4176i) q^{97} +(-12.3668 + 11.0760i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 5 q^{4} - 4 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) \) 8 * q + q^2 - 5 * q^4 - 4 * q^5 - 2 * q^7 + 6 * q^8	\( 8 q + q^{2} - 5 q^{4} - 4 q^{5} - 2 q^{7} + 6 q^{8} + 7 q^{10} - 10 q^{11} + 5 q^{13} - 7 q^{14} + q^{16} + 6 q^{17} + 8 q^{19} - 8 q^{20} + 7 q^{22} + 24 q^{23} + 16 q^{25} + q^{26} + 5 q^{28} - 10 q^{29} + 18 q^{31} - 10 q^{32} - 23 q^{35} + 40 q^{38} - 36 q^{40} - 5 q^{41} + 7 q^{43} + 13 q^{44} - 12 q^{46} - 21 q^{47} + 2 q^{49} + 38 q^{50} - 50 q^{52} - 12 q^{53} - 52 q^{55} + 33 q^{56} - 14 q^{58} + 6 q^{59} + 20 q^{61} - 36 q^{62} - 46 q^{64} + 8 q^{65} + 5 q^{67} - 102 q^{68} - 46 q^{70} + 18 q^{71} + 6 q^{73} - 5 q^{76} + 16 q^{77} + 10 q^{79} - 2 q^{80} + 35 q^{82} + 9 q^{83} + 9 q^{85} + 44 q^{86} + 36 q^{88} - 22 q^{89} + 13 q^{91} - 36 q^{92} + 15 q^{94} - 16 q^{95} + 9 q^{97} - 11 q^{98}+O(q^{100}) \) 8 * q + q^2 - 5 * q^4 - 4 * q^5 - 2 * q^7 + 6 * q^8 + 7 * q^10 - 10 * q^11 + 5 * q^13 - 7 * q^14 + q^16 + 6 * q^17 + 8 * q^19 - 8 * q^20 + 7 * q^22 + 24 * q^23 + 16 * q^25 + q^26 + 5 * q^28 - 10 * q^29 + 18 * q^31 - 10 * q^32 - 23 * q^35 + 40 * q^38 - 36 * q^40 - 5 * q^41 + 7 * q^43 + 13 * q^44 - 12 * q^46 - 21 * q^47 + 2 * q^49 + 38 * q^50 - 50 * q^52 - 12 * q^53 - 52 * q^55 + 33 * q^56 - 14 * q^58 + 6 * q^59 + 20 * q^61 - 36 * q^62 - 46 * q^64 + 8 * q^65 + 5 * q^67 - 102 * q^68 - 46 * q^70 + 18 * q^71 + 6 * q^73 - 5 * q^76 + 16 * q^77 + 10 * q^79 - 2 * q^80 + 35 * q^82 + 9 * q^83 + 9 * q^85 + 44 * q^86 + 36 * q^88 - 22 * q^89 + 13 * q^91 - 36 * q^92 + 15 * q^94 - 16 * q^95 + 9 * q^97 - 11 * q^98

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