LMFDB - Embedded newform 567.2.h.i.298.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(298,567)]

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([4, 4]))

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

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

chi := DirichletCharacter("567.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			298.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	567.298
Dual form			567.2.h.i.352.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.760877 q^{2} -1.42107 q^{4} +(-1.59097 + 2.75564i) q^{5} +(0.710533 - 2.54856i) q^{7} -2.60301 q^{8} +(-1.21053 + 2.09671i) q^{10} +(-1.11956 - 1.93914i) q^{11} +(-1.85185 - 3.20750i) q^{13} +(0.540628 - 1.93914i) q^{14} +0.861564 q^{16} +(2.80150 - 4.85235i) q^{17} +(-2.21053 - 3.82876i) q^{19} +(2.26088 - 3.91595i) q^{20} +(-0.851848 - 1.47544i) q^{22} +(0.471410 - 0.816506i) q^{23} +(-2.56238 - 4.43818i) q^{25} +(-1.40903 - 2.44051i) q^{26} +(-1.00972 + 3.62167i) q^{28} +(-5.06238 + 8.76830i) q^{29} -5.70370 q^{31} +5.86156 q^{32} +(2.13160 - 3.69204i) q^{34} +(5.89248 + 6.01266i) q^{35} +(-1.56238 - 2.70612i) q^{37} +(-1.68194 - 2.91321i) q^{38} +(4.14132 - 7.17297i) q^{40} +(-1.99316 - 3.45226i) q^{41} +(1.64132 - 2.84284i) q^{43} +(1.59097 + 2.75564i) q^{44} +(0.358685 - 0.621261i) q^{46} -0.225450 q^{47} +(-5.99028 - 3.62167i) q^{49} +(-1.94966 - 3.37690i) q^{50} +(2.63160 + 4.55806i) q^{52} +(-5.33009 + 9.23200i) q^{53} +7.12476 q^{55} +(-1.84953 + 6.63392i) q^{56} +(-3.85185 + 6.67160i) q^{58} -2.05718 q^{59} -5.84213 q^{61} -4.33981 q^{62} +2.73680 q^{64} +11.7850 q^{65} +7.42107 q^{67} +(-3.98113 + 6.89551i) q^{68} +(4.48345 + 4.57489i) q^{70} +7.26320 q^{71} +(-3.77975 + 6.54672i) q^{73} +(-1.18878 - 2.05903i) q^{74} +(3.14132 + 5.44092i) q^{76} +(-5.73749 + 1.47544i) q^{77} -6.82846 q^{79} +(-1.37072 + 2.37416i) q^{80} +(-1.51655 - 2.62674i) q^{82} +(4.05555 - 7.02441i) q^{83} +(8.91423 + 15.4399i) q^{85} +(1.24884 - 2.16305i) q^{86} +(2.91423 + 5.04759i) q^{88} +(-4.86389 - 8.42450i) q^{89} +(-9.49028 + 2.44051i) q^{91} +(-0.669905 + 1.16031i) q^{92} -0.171540 q^{94} +14.0676 q^{95} +(-0.421067 + 0.729309i) q^{97} +(-4.55787 - 2.75564i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{2} + 8 q^{4} - q^{5} - 4 q^{7} + 18 q^{8} + q^{10} - 7 q^{11} - 2 q^{13} - 13 q^{14} + 20 q^{16} - 5 q^{19} + 13 q^{20} + 4 q^{22} - 6 q^{23} + 2 q^{25} - 17 q^{26} - 30 q^{28} - 13 q^{29}+ \cdots + 49 q^{98}+O(q^{100}) $ 6 * q + 4 * q^2 + 8 * q^4 - q^5 - 4 * q^7 + 18 * q^8 + q^10 - 7 * q^11 - 2 * q^13 - 13 * q^14 + 20 * q^16 - 5 * q^19 + 13 * q^20 + 4 * q^22 - 6 * q^23 + 2 * q^25 - 17 * q^26 - 30 * q^28 - 13 * q^29 - 16 * q^31 + 50 * q^32 - 12 * q^34 + 10 * q^35 + 8 * q^37 + 7 * q^38 + 24 * q^40 - 2 * q^41 + 9 * q^43 + q^44 + 3 * q^46 + 18 * q^47 - 12 * q^49 - 4 * q^50 - 9 * q^52 - 24 * q^53 + 8 * q^55 - 51 * q^56 - 14 * q^58 - 30 * q^59 - 2 * q^61 - 42 * q^62 + 66 * q^64 + 20 * q^65 + 28 * q^67 - 39 * q^68 - 7 * q^70 - 6 * q^71 - 7 * q^73 + 18 * q^76 + 10 * q^77 + 12 * q^79 + 16 * q^80 - 43 * q^82 - 3 * q^83 + 27 * q^85 + 32 * q^86 - 9 * q^88 + 5 * q^89 - 33 * q^91 - 12 * q^92 - 54 * q^94 + 32 * q^95 + 14 * q^97 + 49 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	0.760877			0.538021			0.269011	−	0.963137i	$-0.413303\pi$
$2$	0.760877			0.538021			0.269011	+	0.963137i	$0.413303\pi$
$3$		0			0
$3$		0			0
$4$	−1.42107			−0.710533
$5$	−1.59097	+	2.75564i	−0.711504	+	1.23236i	0.252788	+	0.967522i	$0.418652\pi$
$5$	−1.59097	+	2.75564i	−0.711504	+	1.23236i	−0.964292	+	0.264840i	$0.914681\pi$
$6$		0			0
$7$	0.710533	−	2.54856i	0.268556	−	0.963264i
$7$	0.710533	−	2.54856i	0.268556	−	0.963264i
$8$	−2.60301			−0.920303
$9$		0			0
$10$	−1.21053	+	2.09671i	−0.382804	+	0.663036i
$11$	−1.11956	−	1.93914i	−0.337561	−	0.584672i	0.646413	−	0.762988i	$-0.276268\pi$
$11$	−1.11956	−	1.93914i	−0.337561	−	0.584672i	−0.983973	+	0.178316i	$0.942935\pi$
$12$		0			0
$13$	−1.85185	−	3.20750i	−0.513610	−	0.889599i	−0.999875	−	0.0157878i	$-0.994974\pi$
$13$	−1.85185	−	3.20750i	−0.513610	−	0.889599i	0.486265	−	0.873811i	$-0.338359\pi$
$14$	0.540628	−	1.93914i	0.144489	−	0.518256i
$15$		0			0
$16$	0.861564			0.215391
$17$	2.80150	−	4.85235i	0.679465	−	1.17687i	−0.295678	−	0.955288i	$-0.595545\pi$
$17$	2.80150	−	4.85235i	0.679465	−	1.17687i	0.975142	−	0.221580i	$-0.0711213\pi$
$18$		0			0
$19$	−2.21053	−	3.82876i	−0.507131	−	0.878377i	−0.999966	−	0.00825398i	$-0.997373\pi$
$19$	−2.21053	−	3.82876i	−0.507131	−	0.878377i	0.492835	−	0.870123i	$-0.335961\pi$
$20$	2.26088	−	3.91595i	0.505547	−	0.875634i
$21$		0			0
$22$	−0.851848	−	1.47544i	−0.181615	−	0.314566i
$23$	0.471410	−	0.816506i	0.0982958	−	0.170253i	−0.812684	−	0.582705i	$-0.801994\pi$
$23$	0.471410	−	0.816506i	0.0982958	−	0.170253i	0.910979	+	0.412452i	$0.135328\pi$
$24$		0			0
$25$	−2.56238	−	4.43818i	−0.512476	−	0.887635i
$26$	−1.40903	−	2.44051i	−0.276333	−	0.478623i
$27$		0			0
$28$	−1.00972	+	3.62167i	−0.190818	+	0.684431i
$29$	−5.06238	+	8.76830i	−0.940061	+	1.62823i	−0.174709	+	0.984620i	$0.555899\pi$
$29$	−5.06238	+	8.76830i	−0.940061	+	1.62823i	−0.765351	+	0.643613i	$0.777435\pi$
$30$		0			0
$31$	−5.70370			−1.02441			−0.512207	−	0.858862i	$-0.671172\pi$
$31$	−5.70370			−1.02441			−0.512207	+	0.858862i	$0.671172\pi$
$32$	5.86156			1.03619
$33$		0			0
$34$	2.13160	−	3.69204i	0.365566	−	0.633180i
$35$	5.89248	+	6.01266i	0.996010	+	1.01632i
$36$		0			0
$37$	−1.56238	−	2.70612i	−0.256854	−	0.444884i	0.708543	−	0.705667i	$-0.249353\pi$
$37$	−1.56238	−	2.70612i	−0.256854	−	0.444884i	−0.965397	+	0.260783i	$0.916019\pi$
$38$	−1.68194	−	2.91321i	−0.272847	−	0.472585i
$39$		0			0
$40$	4.14132	−	7.17297i	0.654799	−	1.13415i
$41$	−1.99316	−	3.45226i	−0.311280	−	0.539152i	0.667360	−	0.744735i	$-0.267424\pi$
$41$	−1.99316	−	3.45226i	−0.311280	−	0.539152i	−0.978640	+	0.205583i	$0.934091\pi$
$42$		0			0
$43$	1.64132	−	2.84284i	0.250298	−	0.433529i	−0.713310	−	0.700849i	$-0.752805\pi$
$43$	1.64132	−	2.84284i	0.250298	−	0.433529i	0.963608	+	0.267320i	$0.0861380\pi$
$44$	1.59097	+	2.75564i	0.239848	+	0.415429i
$45$		0			0
$46$	0.358685	−	0.621261i	0.0528852	−	0.0915999i
$47$	−0.225450			−0.0328853			−0.0164426	−	0.999865i	$-0.505234\pi$
$47$	−0.225450			−0.0328853			−0.0164426	+	0.999865i	$0.505234\pi$
$48$		0			0
$49$	−5.99028	−	3.62167i	−0.855755	−	0.517381i
$50$	−1.94966	−	3.37690i	−0.275723	−	0.477566i
$51$		0			0
$52$	2.63160	+	4.55806i	0.364937	+	0.632090i
$53$	−5.33009	+	9.23200i	−0.732145	+	1.26811i	0.223820	+	0.974631i	$0.428147\pi$
$53$	−5.33009	+	9.23200i	−0.732145	+	1.26811i	−0.955965	+	0.293482i	$0.905186\pi$
$54$		0			0
$55$	7.12476			0.960703
$56$	−1.84953	+	6.63392i	−0.247153	+	0.886495i
$57$		0			0
$58$	−3.85185	+	6.67160i	−0.505772	+	0.876024i
$59$	−2.05718			−0.267822			−0.133911	−	0.990993i	$-0.542754\pi$
$59$	−2.05718			−0.267822			−0.133911	+	0.990993i	$0.542754\pi$
$60$		0			0
$61$	−5.84213			−0.748009			−0.374004	−	0.927427i	$-0.622015\pi$
$61$	−5.84213			−0.748009			−0.374004	+	0.927427i	$0.622015\pi$
$62$	−4.33981			−0.551156
$63$		0			0
$64$	2.73680			0.342100
$65$	11.7850			1.46174
$66$		0			0
$67$	7.42107			0.906628			0.453314	−	0.891351i	$-0.350242\pi$
$67$	7.42107			0.906628			0.453314	+	0.891351i	$0.350242\pi$
$68$	−3.98113	+	6.89551i	−0.482782	+	0.836204i
$69$		0			0
$70$	4.48345	+	4.57489i	0.535875	+	0.546804i
$71$	7.26320			0.861983			0.430992	−	0.902356i	$-0.358164\pi$
$71$	7.26320			0.861983			0.430992	+	0.902356i	$0.358164\pi$
$72$		0			0
$73$	−3.77975	+	6.54672i	−0.442386	+	0.766236i	−0.997866	−	0.0652944i	$-0.979201\pi$
$73$	−3.77975	+	6.54672i	−0.442386	+	0.766236i	0.555480	+	0.831530i	$0.312535\pi$
$74$	−1.18878	−	2.05903i	−0.138193	−	0.239357i
$75$		0			0
$76$	3.14132	+	5.44092i	0.360334	+	0.624116i
$77$	−5.73749	+	1.47544i	−0.653847	+	0.168143i
$78$		0			0
$79$	−6.82846			−0.768262			−0.384131	−	0.923279i	$-0.625499\pi$
$79$	−6.82846			−0.768262			−0.384131	+	0.923279i	$0.625499\pi$
$80$	−1.37072	+	2.37416i	−0.153252	+	0.265439i
$81$		0			0
$82$	−1.51655	−	2.62674i	−0.167475	−	0.290075i
$83$	4.05555	−	7.02441i	0.445154	−	0.771029i	−0.552909	−	0.833242i	$-0.686482\pi$
$83$	4.05555	−	7.02441i	0.445154	−	0.771029i	0.998063	+	0.0622124i	$0.0198156\pi$
$84$		0			0
$85$	8.91423	+	15.4399i	0.966884	+	1.67469i
$86$	1.24884	−	2.16305i	0.134666	−	0.233248i
$87$		0			0
$88$	2.91423	+	5.04759i	0.310658	+	0.538075i
$89$	−4.86389	−	8.42450i	−0.515571	−	0.892995i	−0.999837	−	0.0180741i	$-0.994247\pi$
$89$	−4.86389	−	8.42450i	−0.515571	−	0.892995i	0.484266	−	0.874921i	$-0.339087\pi$
$90$		0			0
$91$	−9.49028	+	2.44051i	−0.994852	+	0.255835i
$92$	−0.669905	+	1.16031i	−0.0698424	+	0.120971i
$93$		0			0
$94$	−0.171540			−0.0176930
$95$	14.0676			1.44330
$96$		0			0
$97$	−0.421067	+	0.729309i	−0.0427528	+	0.0740501i	−0.886610	−	0.462518i	$-0.846946\pi$
$97$	−0.421067	+	0.729309i	−0.0427528	+	0.0740501i	0.843857	+	0.536568i	$0.180279\pi$
$98$	−4.55787	−	2.75564i	−0.460414	−	0.278362i
$99$		0			0
$100$	3.64132	+	6.30694i	0.364132	+	0.630694i
$101$	3.87360	+	6.70928i	0.385438	+	0.667598i	0.991830	−	0.127568i	$-0.0407171\pi$
$101$	3.87360	+	6.70928i	0.385438	+	0.667598i	−0.606392	+	0.795166i	$0.707384\pi$
$102$		0			0
$103$	1.21737	−	2.10855i	0.119951	−	0.207761i	−0.799797	−	0.600271i	$-0.795060\pi$
$103$	1.21737	−	2.10855i	0.119951	−	0.207761i	0.919748	+	0.392509i	$0.128393\pi$
$104$	4.82038	+	8.34914i	0.472677	+	0.818701i
$105$		0			0
$106$	−4.05555	+	7.02441i	−0.393909	+	0.682271i
$107$	−5.73229	−	9.92861i	−0.554161	−	0.959835i	−0.997968	−	0.0637128i	$-0.979706\pi$
$107$	−5.73229	−	9.92861i	−0.554161	−	0.959835i	0.443807	−	0.896122i	$-0.353628\pi$
$108$		0			0
$109$	9.12476	−	15.8046i	0.873994	−	1.51380i	0.0161631	−	0.999869i	$-0.494855\pi$
$109$	9.12476	−	15.8046i	0.873994	−	1.51380i	0.857831	−	0.513932i	$-0.171812\pi$
$110$	5.42107			0.516878
$111$		0			0
$112$	0.612170	−	2.19574i	0.0578446	−	0.207478i
$113$	2.62476	+	4.54622i	0.246917	+	0.427673i	0.962669	−	0.270682i	$-0.0872492\pi$
$113$	2.62476	+	4.54622i	0.246917	+	0.427673i	−0.715752	+	0.698355i	$0.753916\pi$
$114$		0			0
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$	7.19398	−	12.4603i	0.667944	−	1.15691i
$117$		0			0
$118$	−1.56526			−0.144094
$119$	−10.3759	−	10.5876i	−0.951159	−	0.970559i
$120$		0			0
$121$	2.99316	−	5.18431i	0.272106	−	0.471301i
$122$	−4.44514			−0.402444
$123$		0			0
$124$	8.10533			0.727880
$125$	0.396990			0.0355079
$126$		0			0
$127$	20.1053			1.78406			0.892030	−	0.451976i	$-0.149281\pi$
$127$	20.1053			1.78406			0.892030	+	0.451976i	$0.149281\pi$
$128$	−9.64076			−0.852131
$129$		0			0
$130$	8.96690			0.786449
$131$	2.04063	−	3.53447i	0.178291	−	0.308808i	−0.763005	−	0.646393i	$-0.776277\pi$
$131$	2.04063	−	3.53447i	0.178291	−	0.308808i	0.941295	+	0.337585i	$0.109610\pi$
$132$		0			0
$133$	−11.3285	+	2.91321i	−0.982302	+	0.252607i
$134$	5.64652			0.487785
$135$		0			0
$136$	−7.29235	+	12.6307i	−0.625313	+	1.08307i
$137$	0.942820	+	1.63301i	0.0805506	+	0.139518i	0.903487	−	0.428616i	$-0.140999\pi$
$137$	0.942820	+	1.63301i	0.0805506	+	0.139518i	−0.822936	+	0.568134i	$0.807665\pi$
$138$		0			0
$139$	6.39768	+	11.0811i	0.542644	+	0.939887i	0.998751	+	0.0499621i	$0.0159101\pi$
$139$	6.39768	+	11.0811i	0.542644	+	0.939887i	−0.456107	+	0.889925i	$0.650757\pi$
$140$	−8.37360	−	8.54439i	−0.707699	−	0.722133i
$141$		0			0
$142$	5.52640			0.463765
$143$	−4.14652	+	7.18198i	−0.346749	+	0.600587i
$144$		0			0
$145$	−16.1082	−	27.9002i	−1.33771	−	2.31699i
$146$	−2.87592	+	4.98125i	−0.238013	+	0.412251i
$147$		0			0
$148$	2.22025	+	3.84558i	0.182503	+	0.316105i
$149$	−4.02859	+	6.97772i	−0.330035	+	0.571637i	−0.982518	−	0.186166i	$-0.940394\pi$
$149$	−4.02859	+	6.97772i	−0.330035	+	0.571637i	0.652483	+	0.757803i	$0.273727\pi$
$150$		0			0
$151$	3.14132	+	5.44092i	0.255637	+	0.442776i	0.965068	−	0.261999i	$-0.0843816\pi$
$151$	3.14132	+	5.44092i	0.255637	+	0.442776i	−0.709432	+	0.704774i	$0.751048\pi$
$152$	5.75404	+	9.96629i	0.466714	+	0.808373i
$153$		0			0
$154$	−4.36552	+	1.12263i	−0.351784	+	0.0904642i
$155$	9.07442	−	15.7174i	0.728875	−	1.26245i
$156$		0			0
$157$	0.703697			0.0561611			0.0280806	−	0.999606i	$-0.491061\pi$
$157$	0.703697			0.0561611			0.0280806	+	0.999606i	$0.491061\pi$
$158$	−5.19562			−0.413341
$159$		0			0
$160$	−9.32558	+	16.1524i	−0.737252	+	1.27696i
$161$	−1.74596	−	1.78157i	−0.137601	−	0.140407i
$162$		0			0
$163$	9.61793	+	16.6587i	0.753334	+	1.30481i	0.946198	+	0.323588i	$0.104889\pi$
$163$	9.61793	+	16.6587i	0.753334	+	1.30481i	−0.192864	+	0.981225i	$0.561778\pi$
$164$	2.83242	+	4.90589i	0.221175	+	0.383086i
$165$		0			0
$166$	3.08577	−	5.34471i	0.239502	−	0.414830i
$167$	−11.6940	−	20.2546i	−0.904907	−	1.56735i	−0.821041	−	0.570869i	$-0.806607\pi$
$167$	−11.6940	−	20.2546i	−0.904907	−	1.56735i	−0.0838661	−	0.996477i	$-0.526727\pi$
$168$		0			0
$169$	−0.358685	+	0.621261i	−0.0275911	+	0.0477893i
$170$	6.78263	+	11.7479i	0.520204	+	0.901020i
$171$		0			0
$172$	−2.33242	+	4.03987i	−0.177845	+	0.308037i
$173$	−8.23912			−0.626409			−0.313204	−	0.949686i	$-0.601403\pi$
$173$	−8.23912			−0.626409			−0.313204	+	0.949686i	$0.601403\pi$
$174$		0			0
$175$	−13.1316	+	3.37690i	−0.992656	+	0.255270i
$176$	−0.964574	−	1.67069i	−0.0727075	−	0.125933i
$177$		0			0
$178$	−3.70082	−	6.41001i	−0.277388	−	0.480450i
$179$	−4.95486	+	8.58207i	−0.370344	+	0.641454i	−0.989618	−	0.143721i	$-0.954093\pi$
$179$	−4.95486	+	8.58207i	−0.370344	+	0.641454i	0.619275	+	0.785174i	$0.287427\pi$
$180$		0			0
$181$	−9.38796			−0.697802			−0.348901	−	0.937160i	$-0.613445\pi$
$181$	−9.38796			−0.697802			−0.348901	+	0.937160i	$0.613445\pi$
$182$	−7.22094	+	1.85693i	−0.535251	+	0.137645i
$183$		0			0
$184$	−1.22708	+	2.12537i	−0.0904619	+	0.156685i
$185$	9.94282			0.731011
$186$		0			0
$187$	−12.5458			−0.917442
$188$	0.320380			0.0233661
$189$		0			0
$190$	10.7037			0.776528
$191$	−24.7382			−1.78999			−0.894996	−	0.446075i	$-0.852822\pi$
$191$	−24.7382			−1.78999			−0.894996	+	0.446075i	$0.852822\pi$
$192$		0			0
$193$	−0.828460			−0.0596339			−0.0298169	−	0.999555i	$-0.509492\pi$
$193$	−0.828460			−0.0596339			−0.0298169	+	0.999555i	$0.509492\pi$
$194$	−0.320380	+	0.554914i	−0.0230019	+	0.0398405i
$195$		0			0
$196$	8.51259	+	5.14663i	0.608042	+	0.367617i
$197$	5.86156			0.417619			0.208810	−	0.977956i	$-0.433041\pi$
$197$	5.86156			0.417619			0.208810	+	0.977956i	$0.433041\pi$
$198$		0			0
$199$	4.62476	−	8.01033i	0.327841	−	0.567837i	−0.654242	−	0.756285i	$-0.727012\pi$
$199$	4.62476	−	8.01033i	0.327841	−	0.567837i	0.982083	+	0.188448i	$0.0603457\pi$
$200$	6.66991	+	11.5526i	0.471634	+	0.816893i
$201$		0			0
$202$	2.94733	+	5.10493i	0.207374	+	0.359182i
$203$	18.7495	+	19.1319i	1.31596	+	1.34280i
$204$		0			0
$205$	12.6843			0.885908
$206$	0.926268	−	1.60434i	0.0645362	−	0.111780i
$207$		0			0
$208$	−1.59549	−	2.76346i	−0.110627	−	0.191612i
$209$	−4.94966	+	8.57306i	−0.342375	+	0.593011i
$210$		0			0
$211$	6.27975	+	10.8768i	0.432316	+	0.748793i	0.997072	−	0.0764645i	$-0.0243632\pi$
$211$	6.27975	+	10.8768i	0.432316	+	0.748793i	−0.564756	+	0.825258i	$0.691030\pi$
$212$	7.57442	−	13.1193i	0.520213	−	0.901036i
$213$		0			0
$214$	−4.36156	−	7.55445i	−0.298150	−	0.516412i
$215$	5.22257	+	9.04576i	0.356176	+	0.616916i
$216$		0			0
$217$	−4.05267	+	14.5362i	−0.275113	+	0.986781i
$218$	6.94282	−	12.0253i	0.470227	−	0.814457i
$219$		0			0
$220$	−10.1248			−0.682611
$221$	−20.7518			−1.39592
$222$		0			0
$223$	10.6940	−	18.5225i	0.716122	−	1.24036i	−0.246403	−	0.969167i	$-0.579249\pi$
$223$	10.6940	−	18.5225i	0.716122	−	1.24036i	0.962525	−	0.271192i	$-0.0874179\pi$
$224$	4.16484	−	14.9385i	0.278275	−	0.998122i
$225$		0			0
$226$	1.99712	+	3.45912i	0.132847	+	0.230097i
$227$	6.31122	+	10.9314i	0.418890	+	0.725539i	0.995828	−	0.0912487i	$-0.0290858\pi$
$227$	6.31122	+	10.9314i	0.418890	+	0.725539i	−0.576938	+	0.816788i	$0.695752\pi$
$228$		0			0
$229$	14.4601	−	25.0456i	0.955548	−	1.65506i	0.222438	−	0.974947i	$-0.428599\pi$
$229$	14.4601	−	25.0456i	0.955548	−	1.65506i	0.733110	−	0.680110i	$-0.238068\pi$
$230$	1.14132	+	1.97682i	0.0752561	+	0.130347i
$231$		0			0
$232$	13.1774	−	22.8240i	0.865141	−	1.49847i
$233$	−10.7255	−	18.5770i	−0.702648	−	1.21702i	−0.967534	−	0.252742i	$-0.918668\pi$
$233$	−10.7255	−	18.5770i	−0.702648	−	1.21702i	0.264886	−	0.964280i	$-0.414666\pi$
$234$		0			0
$235$	0.358685	−	0.621261i	0.0233980	−	0.0405266i
$236$	2.92339			0.190296
$237$		0			0
$238$	−7.89480	−	8.05582i	−0.511744	−	0.522181i
$239$	3.86840	+	6.70027i	0.250226	+	0.433404i	0.963588	−	0.267392i	$-0.0861617\pi$
$239$	3.86840	+	6.70027i	0.250226	+	0.433404i	−0.713362	+	0.700796i	$0.752828\pi$
$240$		0			0
$241$	−3.04583	−	5.27553i	−0.196199	−	0.339827i	0.751094	−	0.660195i	$-0.229527\pi$
$241$	−3.04583	−	5.27553i	−0.196199	−	0.339827i	−0.947293	+	0.320369i	$0.896193\pi$
$242$	2.27743	−	3.94462i	0.146399	−	0.253570i
$243$		0			0
$244$	8.30206			0.531485
$245$	19.5104	−	10.7451i	1.24647	−	0.686480i
$246$		0			0
$247$	−8.18715	+	14.1806i	−0.520936	+	0.902287i
$248$	14.8468			0.942771
$249$		0			0
$250$	0.302060			0.0191040
$251$	−1.40164			−0.0884705			−0.0442352	−	0.999021i	$-0.514085\pi$
$251$	−1.40164			−0.0884705			−0.0442352	+	0.999021i	$0.514085\pi$
$252$		0			0
$253$	−2.11109			−0.132723
$254$	15.2977			0.959862
$255$		0			0
$256$	−12.8090			−0.800564
$257$	8.97825	−	15.5508i	0.560048	−	0.970031i	−0.437444	−	0.899246i	$-0.644116\pi$
$257$	8.97825	−	15.5508i	0.560048	−	0.970031i	0.997492	−	0.0707853i	$-0.0225505\pi$
$258$		0			0
$259$	−8.00684	+	2.05903i	−0.497521	+	0.127942i
$260$	−16.7472			−1.03862
$261$		0			0
$262$	1.55267	−	2.68930i	0.0959241	−	0.166145i
$263$	3.58809	+	6.21476i	0.221251	+	0.383218i	0.955188	−	0.295999i	$-0.0956526\pi$
$263$	3.58809	+	6.21476i	0.221251	+	0.383218i	−0.733937	+	0.679218i	$0.762319\pi$
$264$		0			0
$265$	−16.9601	−	29.3757i	−1.04185	−	1.80453i
$266$	−8.61956	+	2.21659i	−0.528499	+	0.135908i
$267$		0			0
$268$	−10.5458			−0.644189
$269$	−1.69850	+	2.94188i	−0.103559	+	0.179370i	−0.913149	−	0.407627i	$-0.866356\pi$
$269$	−1.69850	+	2.94188i	−0.103559	+	0.179370i	0.809590	+	0.586996i	$0.199690\pi$
$270$		0			0
$271$	5.11793	+	8.86451i	0.310892	+	0.538481i	0.978556	−	0.205982i	$-0.0660389\pi$
$271$	5.11793	+	8.86451i	0.310892	+	0.538481i	−0.667664	+	0.744463i	$0.732706\pi$
$272$	2.41367	−	4.18061i	0.146351	−	0.253487i
$273$		0			0
$274$	0.717370	+	1.24252i	0.0433379	+	0.0750634i
$275$	−5.73749	+	9.93762i	−0.345984	+	0.599261i
$276$		0			0
$277$	1.77975	+	3.08262i	0.106935	+	0.185217i	0.914527	−	0.404525i	$-0.132563\pi$
$277$	1.77975	+	3.08262i	0.106935	+	0.185217i	−0.807592	+	0.589741i	$0.799230\pi$
$278$	4.86784	+	8.43135i	0.291954	+	0.505679i
$279$		0			0
$280$	−15.3382	−	15.6510i	−0.916631	−	0.935327i
$281$	−3.49316	+	6.05034i	−0.208385	+	0.360933i	−0.951206	−	0.308557i	$-0.900154\pi$
$281$	−3.49316	+	6.05034i	−0.208385	+	0.360933i	0.742821	+	0.669490i	$0.233487\pi$
$282$		0			0
$283$	−30.2164			−1.79618			−0.898090	−	0.439812i	$-0.855045\pi$
$283$	−30.2164			−1.79618			−0.898090	+	0.439812i	$0.855045\pi$
$284$	−10.3215			−0.612468
$285$		0			0
$286$	−3.15499	+	5.46460i	−0.186558	+	0.323129i
$287$	−10.2145	+	2.62674i	−0.602942	+	0.155052i
$288$		0			0
$289$	−7.19686	−	12.4653i	−0.423345	−	0.733255i
$290$	−12.2564	−	21.2286i	−0.719718	−	1.24659i
$291$		0			0
$292$	5.37128	−	9.30333i	0.314330	−	0.544436i
$293$	7.61793	+	13.1946i	0.445044	+	0.770839i	0.998055	−	0.0623349i	$-0.0198547\pi$
$293$	7.61793	+	13.1946i	0.445044	+	0.770839i	−0.553011	+	0.833174i	$0.686521\pi$
$294$		0			0
$295$	3.27292	−	5.66886i	0.190556	−	0.330054i
$296$	4.06690	+	7.04407i	0.236383	+	0.409428i
$297$		0			0
$298$	−3.06526	+	5.30919i	−0.177566	+	0.307553i
$299$	−3.49192			−0.201943
$300$		0			0
$301$	−6.07893	−	6.20292i	−0.350384	−	0.357530i
$302$	2.39015	+	4.13987i	0.137538	+	0.238223i
$303$		0			0
$304$	−1.90451	−	3.29872i	−0.109231	−	0.189194i
$305$	9.29467	−	16.0988i	0.532211	−	0.921817i
$306$		0			0
$307$	−1.03310			−0.0589623			−0.0294812	−	0.999565i	$-0.509386\pi$
$307$	−1.03310			−0.0589623			−0.0294812	+	0.999565i	$0.509386\pi$
$308$	8.15335	−	2.09671i	0.464580	−	0.119471i
$309$		0			0
$310$	6.90451	−	11.9590i	0.392150	−	0.679224i
$311$	−9.32038			−0.528510			−0.264255	−	0.964453i	$-0.585126\pi$
$311$	−9.32038			−0.528510			−0.264255	+	0.964453i	$0.585126\pi$
$312$		0			0
$313$	6.09166			0.344321			0.172160	−	0.985069i	$-0.444925\pi$
$313$	6.09166			0.344321			0.172160	+	0.985069i	$0.444925\pi$
$314$	0.535426			0.0302159
$315$		0			0
$316$	9.70370			0.545876
$317$	23.3009			1.30871			0.654356	−	0.756187i	$-0.272940\pi$
$317$	23.3009			1.30871			0.654356	+	0.756187i	$0.272940\pi$
$318$		0			0
$319$	22.6706			1.26931
$320$	−4.35417	+	7.54165i	−0.243406	+	0.421591i
$321$		0			0
$322$	−1.32846	−	1.35556i	−0.0740322	−	0.0755421i
$323$	−24.7713			−1.37831
$324$		0			0
$325$	−9.49028	+	16.4377i	−0.526426	+	0.911797i
$326$	7.31806	+	12.6752i	0.405310	+	0.702017i
$327$		0			0
$328$	5.18822	+	8.98627i	0.286472	+	0.496184i
$329$	−0.160190	+	0.574573i	−0.00883155	+	0.0316772i
$330$		0			0
$331$	14.6764			0.806685			0.403343	−	0.915049i	$-0.367848\pi$
$331$	14.6764			0.806685			0.403343	+	0.915049i	$0.367848\pi$
$332$	−5.76320	+	9.98215i	−0.316297	+	0.547842i
$333$		0			0
$334$	−8.89768	−	15.4112i	−0.486859	−	0.843265i
$335$	−11.8067	+	20.4498i	−0.645069	+	1.11729i
$336$		0			0
$337$	−12.8119	−	22.1909i	−0.697909	−	1.20881i	−0.969190	−	0.246314i	$-0.920781\pi$
$337$	−12.8119	−	22.1909i	−0.697909	−	1.20881i	0.271281	−	0.962500i	$-0.412553\pi$
$338$	−0.272915	+	0.472703i	−0.0148446	+	0.0257116i
$339$		0			0
$340$	−12.6677	−	21.9411i	−0.687003	−	1.18992i
$341$	6.38564	+	11.0603i	0.345802	+	0.598946i
$342$		0			0
$343$	−13.4863	+	12.6933i	−0.728193	+	0.685372i
$344$	−4.27236	+	7.39994i	−0.230350	+	0.398978i
$345$		0			0
$346$	−6.26896			−0.337021
$347$	−11.2930			−0.606242			−0.303121	−	0.952952i	$-0.598029\pi$
$347$	−11.2930			−0.606242			−0.303121	+	0.952952i	$0.598029\pi$
$348$		0			0
$349$	5.64815	−	9.78289i	0.302339	−	0.523666i	−0.674327	−	0.738433i	$-0.735566\pi$
$349$	5.64815	−	9.78289i	0.302339	−	0.523666i	0.976665	+	0.214767i	$0.0688993\pi$
$350$	−9.99153	+	2.56941i	−0.534070	+	0.137341i
$351$		0			0
$352$	−6.56238	−	11.3664i	−0.349776	−	0.605830i
$353$	−9.25116	−	16.0235i	−0.492390	−	0.852844i	0.507572	−	0.861609i	$-0.330543\pi$
$353$	−9.25116	−	16.0235i	−0.492390	−	0.852844i	−0.999962	+	0.00876550i	$0.997210\pi$
$354$		0			0
$355$	−11.5555	+	20.0148i	−0.613305	+	1.06227i
$356$	6.91191	+	11.9718i	0.366330	+	0.634503i
$357$		0			0
$358$	−3.77004	+	6.52989i	−0.199253	+	0.345116i
$359$	9.94802	+	17.2305i	0.525037	+	0.909390i	0.999575	+	0.0291551i	$0.00928167\pi$
$359$	9.94802	+	17.2305i	0.525037	+	0.909390i	−0.474538	+	0.880235i	$0.657385\pi$
$360$		0			0
$361$	−0.272915	+	0.472703i	−0.0143639	+	0.0248791i
$362$	−7.14308			−0.375432
$363$		0			0
$364$	13.4863	−	3.46813i	0.706876	−	0.181779i
$365$	−12.0270	−	20.8313i	−0.629520	−	1.09036i
$366$		0			0
$367$	−2.87524	−	4.98006i	−0.150086	−	0.259957i	0.781173	−	0.624315i	$-0.214622\pi$
$367$	−2.87524	−	4.98006i	−0.150086	−	0.259957i	−0.931259	+	0.364358i	$0.881288\pi$
$368$	0.406150	−	0.703472i	0.0211720	−	0.0366710i
$369$		0			0
$370$	7.56526			0.393299
$371$	19.7411	+	20.1437i	1.02490	+	1.04581i
$372$		0			0
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	−0.890753	−	0.454488i	$-0.849822\pi$
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	0.838975	+	0.544170i	$0.183156\pi$
$374$	−9.54583			−0.493603
$375$		0			0
$376$	0.586849			0.0302644
$377$	37.4991			1.93130
$378$		0			0
$379$	8.95322			0.459896			0.229948	−	0.973203i	$-0.426144\pi$
$379$	8.95322			0.459896			0.229948	+	0.973203i	$0.426144\pi$
$380$	−19.9910			−1.02552
$381$		0			0
$382$	−18.8227			−0.963053
$383$	10.0825	−	17.4634i	0.515192	−	0.892338i	−0.484653	−	0.874707i	$-0.661054\pi$
$383$	10.0825	−	17.4634i	0.515192	−	0.892338i	0.999845	−	0.0176316i	$-0.00561261\pi$
$384$		0			0
$385$	5.06238	−	18.1579i	0.258003	−	0.925410i
$386$	−0.630356			−0.0320843
$387$		0			0
$388$	0.598364	−	1.03640i	0.0303773	−	0.0526151i
$389$	−16.7999	−	29.0982i	−0.851787	−	1.47534i	−0.879594	−	0.475725i	$-0.842186\pi$
$389$	−16.7999	−	29.0982i	−0.851787	−	1.47534i	0.0278066	−	0.999613i	$-0.491148\pi$
$390$		0			0
$391$	−2.64132	−	4.57489i	−0.133577	−	0.231362i
$392$	15.5928	+	9.42724i	0.787554	+	0.476148i
$393$		0			0
$394$	4.45993			0.224688
$395$	10.8639	−	18.8168i	0.546621	−	0.946776i
$396$		0			0
$397$	2.06922	+	3.58399i	0.103851	+	0.179875i	0.913268	−	0.407359i	$-0.133550\pi$
$397$	2.06922	+	3.58399i	0.103851	+	0.179875i	−0.809417	+	0.587234i	$0.800217\pi$
$398$	3.51887	−	6.09487i	0.176385	−	0.305508i
$399$		0			0
$400$	−2.20765	−	3.82377i	−0.110383	−	0.191189i
$401$	7.73461	−	13.3967i	0.386248	−	0.669001i	−0.605693	−	0.795698i	$-0.707104\pi$
$401$	7.73461	−	13.3967i	0.386248	−	0.669001i	0.991941	+	0.126697i	$0.0404376\pi$
$402$		0			0
$403$	10.5624	+	18.2946i	0.526150	+	0.911318i
$404$	−5.50465	−	9.53433i	−0.273866	−	0.474350i
$405$		0			0
$406$	14.2661	+	14.5570i	0.708014	+	0.722454i
$407$	−3.49837	+	6.05935i	−0.173408	+	0.300351i
$408$		0			0
$409$	27.3937			1.35453			0.677266	−	0.735738i	$-0.263165\pi$
$409$	27.3937			1.35453			0.677266	+	0.735738i	$0.263165\pi$
$410$	9.65116			0.476637
$411$		0			0
$412$	−1.72996	+	2.99638i	−0.0852292	+	0.147621i
$413$	−1.46169	+	5.24284i	−0.0719253	+	0.257983i
$414$		0			0
$415$	12.9045	+	22.3513i	0.633458	+	1.09718i
$416$	−10.8547	−	18.8009i	−0.532197	−	0.921792i
$417$		0			0
$418$	−3.76608	+	6.52304i	−0.184205	+	0.319052i
$419$	−10.5000	−	18.1865i	−0.512959	−	0.888470i	−0.999887	−	0.0150285i	$-0.995216\pi$
$419$	−10.5000	−	18.1865i	−0.512959	−	0.888470i	0.486928	−	0.873442i	$-0.338117\pi$
$420$		0			0
$421$	−9.97949	+	17.2850i	−0.486371	+	0.842419i	−0.999877	−	0.0156670i	$-0.995013\pi$
$421$	−9.97949	+	17.2850i	−0.486371	+	0.842419i	0.513507	+	0.858086i	$0.328346\pi$
$422$	4.77812	+	8.27594i	0.232595	+	0.402867i
$423$		0			0
$424$	13.8743	−	24.0310i	0.673795	−	1.16705i
$425$	−28.7141			−1.39284
$426$		0			0
$427$	−4.15103	+	14.8890i	−0.200882	+	0.720530i
$428$	8.14596	+	14.1092i	0.393750	+	0.681995i
$429$		0			0
$430$	3.97373	+	6.88271i	0.191630	+	0.331914i
$431$	10.0647	−	17.4326i	0.484800	−	0.839698i	−0.515048	−	0.857162i	$-0.672226\pi$
$431$	10.0647	−	17.4326i	0.484800	−	0.839698i	0.999847	+	0.0174637i	$0.00555914\pi$
$432$		0			0
$433$	11.8558			0.569754			0.284877	−	0.958564i	$-0.408047\pi$
$433$	11.8558			0.569754			0.284877	+	0.958564i	$0.408047\pi$
$434$	−3.08358	+	11.0603i	−0.148017	+	0.530909i
$435$		0			0
$436$	−12.9669	+	22.4593i	−0.621002	+	1.07561i
$437$	−4.16827			−0.199395
$438$		0			0
$439$	−2.15787			−0.102989			−0.0514947	−	0.998673i	$-0.516399\pi$
$439$	−2.15787			−0.102989			−0.0514947	+	0.998673i	$0.516399\pi$
$440$	−18.5458			−0.884138
$441$		0			0
$442$	−15.7896			−0.751035
$443$	−1.96225			−0.0932293			−0.0466147	−	0.998913i	$-0.514843\pi$
$443$	−1.96225			−0.0932293			−0.0466147	+	0.998913i	$0.514843\pi$
$444$		0			0
$445$	30.9532			1.46732
$446$	8.13680	−	14.0934i	0.385289	−	0.667340i
$447$		0			0
$448$	1.94459	−	6.97489i	0.0918731	−	0.329533i
$449$	2.15211			0.101564			0.0507822	−	0.998710i	$-0.483829\pi$
$449$	2.15211			0.101564			0.0507822	+	0.998710i	$0.483829\pi$
$450$		0			0
$451$	−4.46294	+	7.73004i	−0.210152	+	0.363993i
$452$	−3.72996	−	6.46049i	−0.175443	−	0.303876i
$453$		0			0
$454$	4.80206	+	8.31741i	0.225372	+	0.390356i
$455$	8.37360	−	30.0346i	0.392561	−	1.40804i
$456$		0			0
$457$	−13.1053			−0.613042			−0.306521	−	0.951864i	$-0.599165\pi$
$457$	−13.1053			−0.613042			−0.306521	+	0.951864i	$0.599165\pi$
$458$	11.0023	−	19.0566i	0.514105	−	0.890456i
$459$		0			0
$460$	−2.13160	−	3.69204i	−0.0993864	−	0.172142i
$461$	2.74364	−	4.75212i	0.127784	−	0.221328i	−0.795034	−	0.606565i	$-0.792547\pi$
$461$	2.74364	−	4.75212i	0.127784	−	0.221328i	0.922818	+	0.385237i	$0.125880\pi$
$462$		0			0
$463$	10.2495	+	17.7527i	0.476336	+	0.825038i	0.999632	−	0.0271127i	$-0.00863130\pi$
$463$	10.2495	+	17.7527i	0.476336	+	0.825038i	−0.523296	+	0.852151i	$0.675298\pi$
$464$	−4.36156	+	7.55445i	−0.202481	+	0.350707i
$465$		0			0
$466$	−8.16075	−	14.1348i	−0.378039	−	0.654783i
$467$	−19.6758	−	34.0795i	−0.910487	−	1.57701i	−0.813377	−	0.581736i	$-0.802374\pi$
$467$	−19.6758	−	34.0795i	−0.910487	−	1.57701i	−0.0971099	−	0.995274i	$-0.530960\pi$
$468$		0			0
$469$	5.27292	−	18.9130i	0.243481	−	0.873322i
$470$	0.272915	−	0.472703i	0.0125886	−	0.0218041i
$471$		0			0
$472$	5.35486			0.246477
$473$	−7.35021			−0.337963
$474$		0			0
$475$	−11.3285	+	19.6215i	−0.519785	+	0.900295i
$476$	14.7449	+	15.0456i	0.675830	+	0.689615i
$477$		0			0
$478$	2.94338	+	5.09808i	0.134627	+	0.233181i
$479$	8.37360	+	14.5035i	0.382600	+	0.662682i	0.991433	−	0.130616i	$-0.0416955\pi$
$479$	8.37360	+	14.5035i	0.382600	+	0.662682i	−0.608833	+	0.793298i	$0.708362\pi$
$480$		0			0
$481$	−5.78659	+	10.0227i	−0.263846	+	0.456994i
$482$	−2.31750	−	4.01403i	−0.105559	−	0.182834i
$483$		0			0
$484$	−4.25348	+	7.36725i	−0.193340	+	0.334875i
$485$	−1.33981	−	2.32062i	−0.0608376	−	0.105374i
$486$		0			0
$487$	−2.00288	+	3.46909i	−0.0907591	+	0.157199i	−0.907831	−	0.419337i	$-0.862263\pi$
$487$	−2.00288	+	3.46909i	−0.0907591	+	0.157199i	0.817072	+	0.576536i	$0.195596\pi$
$488$	15.2071			0.688394
$489$		0			0
$490$	14.8450	−	8.17571i	0.670629	−	0.369341i
$491$	12.3256	+	21.3485i	0.556246	+	0.963446i	0.997805	+	0.0662140i	$0.0210920\pi$
$491$	12.3256	+	21.3485i	0.556246	+	0.963446i	−0.441560	+	0.897232i	$0.645575\pi$
$492$		0			0
$493$	28.3646	+	49.1289i	1.27748	+	2.21265i
$494$	−6.22941	+	10.7897i	−0.280274	+	0.485449i
$495$		0			0
$496$	−4.91410			−0.220649
$497$	5.16075	−	18.5107i	0.231491	−	0.830317i
$498$		0			0
$499$	12.2798	−	21.2692i	0.549717	−	0.952138i	−0.448576	−	0.893744i	$-0.648069\pi$
$499$	12.2798	−	21.2692i	0.549717	−	0.952138i	0.998294	−	0.0583936i	$-0.0185978\pi$
$500$	−0.564149			−0.0252295
$501$		0			0
$502$	−1.06647			−0.0475990
$503$	12.3743			0.551742			0.275871	−	0.961195i	$-0.411034\pi$
$503$	12.3743			0.551742			0.275871	+	0.961195i	$0.411034\pi$
$504$		0			0
$505$	−24.6512			−1.09696
$506$	−1.60628			−0.0714078
$507$		0			0
$508$	−28.5710			−1.26763
$509$	−5.59781	+	9.69569i	−0.248118	+	0.429754i	−0.963004	−	0.269488i	$-0.913146\pi$
$509$	−5.59781	+	9.69569i	−0.248118	+	0.429754i	0.714885	+	0.699242i	$0.246479\pi$
$510$		0			0
$511$	13.9991	+	14.2846i	0.619282	+	0.631912i
$512$	9.53543			0.421410
$513$		0			0
$514$	6.83134	−	11.8322i	0.301317	−	0.521897i
$515$	3.87360	+	6.70928i	0.170691	+	0.295646i
$516$		0			0
$517$	0.252405	+	0.437179i	0.0111008	+	0.0192271i
$518$	−6.09222	+	1.56667i	−0.267677	+	0.0688353i
$519$		0			0
$520$	−30.6764			−1.34525
$521$	−15.8096	+	27.3830i	−0.692631	+	1.19967i	0.278342	+	0.960482i	$0.410215\pi$
$521$	−15.8096	+	27.3830i	−0.692631	+	1.19967i	−0.970973	+	0.239189i	$0.923118\pi$
$522$		0			0
$523$	14.1179	+	24.4530i	0.617334	+	1.06925i	0.989970	+	0.141276i	$0.0451205\pi$
$523$	14.1179	+	24.4530i	0.617334	+	1.06925i	−0.372636	+	0.927977i	$0.621546\pi$
$524$	−2.89987	+	5.02272i	−0.126681	+	0.219419i
$525$		0			0
$526$	2.73010	+	4.72867i	0.119038	+	0.206180i
$527$	−15.9789	+	27.6763i	−0.696053	+	1.20560i
$528$		0			0
$529$	11.0555	+	19.1488i	0.480676	+	0.832555i
$530$	−12.9045	−	22.3513i	−0.560536	−	0.970877i
$531$		0			0
$532$	16.0985	−	4.13987i	0.697958	−	0.179486i
$533$	−7.38207	+	12.7861i	−0.319753	+	0.553829i
$534$		0			0
$535$	36.4796			1.57715
$536$	−19.3171			−0.834372
$537$		0			0
$538$	−1.29235	+	2.23841i	−0.0557170	+	0.0965046i
$539$	−0.316422	+	15.6707i	−0.0136293	+	0.674983i
$540$		0			0
$541$	−21.4045	−	37.0737i	−0.920252	−	1.59392i	−0.799025	−	0.601298i	$-0.794650\pi$
$541$	−21.4045	−	37.0737i	−0.920252	−	1.59392i	−0.121227	−	0.992625i	$-0.538683\pi$
$542$	3.89411	+	6.74480i	0.167266	+	0.289714i
$543$		0			0
$544$	16.4212	−	28.4424i	0.704053	−	1.21946i
$545$	29.0345	+	50.2892i	1.24370	+	2.15415i
$546$		0			0
$547$	−6.77579	+	11.7360i	−0.289712	+	0.501796i	−0.973741	−	0.227659i	$-0.926893\pi$
$547$	−6.77579	+	11.7360i	−0.289712	+	0.501796i	0.684029	+	0.729455i	$0.260226\pi$
$548$	−1.33981	−	2.32062i	−0.0572339	−	0.0991319i
$549$		0			0
$550$	−4.36552	+	7.56130i	−0.186146	+	0.322415i
$551$	44.7623			1.90694
$552$		0			0
$553$	−4.85185	+	17.4027i	−0.206322	+	0.740039i
$554$	1.35417	+	2.34549i	0.0575332	+	0.0996505i
$555$		0			0
$556$	−9.09153	−	15.7470i	−0.385567	−	0.667821i
$557$	−16.3925	+	28.3926i	−0.694572	+	1.20303i	0.275753	+	0.961228i	$0.411073\pi$
$557$	−16.3925	+	28.3926i	−0.694572	+	1.20303i	−0.970325	+	0.241805i	$0.922261\pi$
$558$		0			0
$559$	−12.1579			−0.514223
$560$	5.07674	+	5.18029i	0.214532	+	0.218907i
$561$		0			0
$562$	−2.65787	+	4.60356i	−0.112115	+	0.194189i
$563$	−17.1546			−0.722980			−0.361490	−	0.932376i	$-0.617732\pi$
$563$	−17.1546			−0.722980			−0.361490	+	0.932376i	$0.617732\pi$
$564$		0			0
$565$	−16.7037			−0.702730
$566$	−22.9910			−0.966383
$567$		0			0
$568$	−18.9062			−0.793286
$569$	12.8993			0.540767			0.270384	−	0.962753i	$-0.412849\pi$
$569$	12.8993			0.540767			0.270384	+	0.962753i	$0.412849\pi$
$570$		0			0
$571$	−0.282630			−0.0118277			−0.00591385	−	0.999983i	$-0.501882\pi$
$571$	−0.282630			−0.0118277			−0.00591385	+	0.999983i	$0.501882\pi$
$572$	5.89248	−	10.2061i	0.246377	−	0.426737i
$573$		0			0
$574$	−7.77197	+	1.99863i	−0.324396	+	0.0834212i
$575$	−4.83173			−0.201497
$576$		0			0
$577$	1.08289	−	1.87562i	0.0450814	−	0.0780832i	−0.842604	−	0.538533i	$-0.818979\pi$
$577$	1.08289	−	1.87562i	0.0450814	−	0.0780832i	0.887686	+	0.460450i	$0.152312\pi$
$578$	−5.47592	−	9.48458i	−0.227768	−	0.394506i
$579$		0			0
$580$	22.8908	+	39.6481i	0.950490	+	1.64630i
$581$	−15.0205	−	15.3269i	−0.623156	−	0.635866i
$582$		0			0
$583$	23.8695			0.988573
$584$	9.83873	−	17.0412i	0.407130	−	0.705169i
$585$		0			0
$586$	5.79630	+	10.0395i	0.239443	+	0.414728i
$587$	8.38796	−	14.5284i	0.346208	−	0.599650i	−0.639364	−	0.768904i	$-0.720802\pi$
$587$	8.38796	−	14.5284i	0.346208	−	0.599650i	0.985573	+	0.169254i	$0.0541357\pi$
$588$		0			0
$589$	12.6082	+	21.8381i	0.519512	+	0.899822i
$590$	2.49028	−	4.31330i	0.102523	−	0.177576i
$591$		0			0
$592$	−1.34609	−	2.33150i	−0.0553240	−	0.0958240i
$593$	12.5933	+	21.8122i	0.517145	+	0.895721i	0.999802	+	0.0199114i	$0.00633841\pi$
$593$	12.5933	+	21.8122i	0.517145	+	0.895721i	−0.482657	+	0.875809i	$0.660328\pi$
$594$		0			0
$595$	45.6833	−	11.7479i	1.87283	−	0.481615i
$596$	5.72489	−	9.91581i	0.234501	−	0.406167i
$597$		0			0
$598$	−2.65692			−0.108650
$599$	28.7324			1.17397			0.586987	−	0.809596i	$-0.300314\pi$
$599$	28.7324			1.17397			0.586987	+	0.809596i	$0.300314\pi$
$600$		0			0
$601$	18.3977	−	31.8657i	0.750457	−	1.29983i	−0.197144	−	0.980374i	$-0.563167\pi$
$601$	18.3977	−	31.8657i	0.750457	−	1.29983i	0.947601	−	0.319455i	$-0.103500\pi$
$602$	−4.62532	−	4.71966i	−0.188514	−	0.192359i
$603$		0			0
$604$	−4.46402	−	7.73191i	−0.181638	−	0.314607i
$605$	9.52408	+	16.4962i	0.387209	+	0.670665i
$606$		0			0
$607$	−18.9503	+	32.8230i	−0.769171	+	1.33224i	0.168842	+	0.985643i	$0.445997\pi$
$607$	−18.9503	+	32.8230i	−0.769171	+	1.33224i	−0.938013	+	0.346600i	$0.887336\pi$
$608$	−12.9572	−	22.4425i	−0.525483	−	0.910163i
$609$		0			0
$610$	7.07210	−	12.2492i	0.286341	−	0.495957i
$611$	0.417500	+	0.723131i	0.0168902	+	0.0292547i
$612$		0			0
$613$	−19.0196	+	32.9428i	−0.768193	+	1.33055i	0.170349	+	0.985384i	$0.445511\pi$
$613$	−19.0196	+	32.9428i	−0.768193	+	1.33055i	−0.938542	+	0.345165i	$0.887823\pi$
$614$	−0.786064			−0.0317230
$615$		0			0
$616$	14.9347	−	3.84060i	0.601738	−	0.154742i
$617$	−13.2632	−	22.9725i	−0.533956	−	0.924839i	−0.999213	−	0.0396637i	$-0.987371\pi$
$617$	−13.2632	−	22.9725i	−0.533956	−	0.924839i	0.465257	−	0.885176i	$-0.345962\pi$
$618$		0			0
$619$	−6.35185	−	11.0017i	−0.255302	−	0.442197i	0.709675	−	0.704529i	$-0.248842\pi$
$619$	−6.35185	−	11.0017i	−0.255302	−	0.442197i	−0.964978	+	0.262332i	$0.915508\pi$
$620$	−12.8954	+	22.3354i	−0.517890	+	0.897012i
$621$		0			0
$622$	−7.09166			−0.284350
$623$	−24.9263	+	6.41001i	−0.998650	+	0.256811i
$624$		0			0
$625$	12.1803	−	21.0969i	0.487212	−	0.843877i
$626$	4.63500			0.185252
$627$		0			0
$628$	−1.00000			−0.0399043
$629$	−17.5081			−0.698093
$630$		0			0
$631$	20.6764			0.823113			0.411556	−	0.911384i	$-0.364985\pi$
$631$	20.6764			0.823113			0.411556	+	0.911384i	$0.364985\pi$
$632$	17.7745			0.707034
$633$		0			0
$634$	17.7292			0.704114
$635$	−31.9870	+	55.4031i	−1.26937	+	2.19861i
$636$		0			0
$637$	−0.523388	+	25.9206i	−0.0207374	+	1.02701i
$638$	17.2495			0.682915
$639$		0			0
$640$	15.3382	−	26.5665i	0.606295	−	1.05013i
$641$	−13.9870	−	24.2262i	−0.552454	−	0.956878i	−0.998097	−	0.0616674i	$-0.980358\pi$
$641$	−13.9870	−	24.2262i	−0.552454	−	0.956878i	0.445643	−	0.895211i	$-0.352975\pi$
$642$		0			0
$643$	−13.9903	−	24.2319i	−0.551723	−	0.955612i	−0.998150	−	0.0607924i	$-0.980637\pi$
$643$	−13.9903	−	24.2319i	−0.551723	−	0.955612i	0.446427	−	0.894820i	$-0.352696\pi$
$644$	2.48113	+	2.53173i	0.0977700	+	0.0997641i
$645$		0			0
$646$	−18.8479			−0.741560
$647$	2.30834	−	3.99816i	0.0907503	−	0.157184i	−0.817077	−	0.576529i	$-0.804407\pi$
$647$	2.30834	−	3.99816i	0.0907503	−	0.157184i	0.907827	+	0.419345i	$0.137740\pi$
$648$		0			0
$649$	2.30314	+	3.98916i	0.0904061	+	0.156588i
$650$	−7.22094	+	12.5070i	−0.283228	+	0.490566i
$651$		0			0
$652$	−13.6677	−	23.6732i	−0.535269	−	0.927113i
$653$	5.79016	−	10.0288i	0.226586	−	0.392459i	−0.730208	−	0.683225i	$-0.760577\pi$
$653$	5.79016	−	10.0288i	0.226586	−	0.392459i	0.956794	+	0.290766i	$0.0939101\pi$
$654$		0			0
$655$	6.49316	+	11.2465i	0.253709	+	0.439437i
$656$	−1.71724	−	2.97434i	−0.0670468	−	0.116129i
$657$		0			0
$658$	−0.121885	+	0.437179i	−0.00475156	+	0.0170430i
$659$	2.36840	−	4.10219i	0.0922598	−	0.159799i	−0.816202	−	0.577767i	$-0.803924\pi$
$659$	2.36840	−	4.10219i	0.0922598	−	0.159799i	0.908462	+	0.417968i	$0.137258\pi$
$660$		0			0
$661$	−13.8227			−0.537641			−0.268820	−	0.963190i	$-0.586634\pi$
$661$	−13.8227			−0.537641			−0.268820	+	0.963190i	$0.586634\pi$
$662$	11.1669			0.434014
$663$		0			0
$664$	−10.5566	+	18.2846i	−0.409676	+	0.709580i
$665$	9.99549	−	35.8520i	0.387608	−	1.39028i
$666$		0			0
$667$	4.77292	+	8.26693i	0.184808	+	0.320097i
$668$	16.6179	+	28.7831i	0.642967	+	1.11365i
$669$		0			0
$670$	−8.98345	+	15.5598i	−0.347061	+	0.601127i
$671$	6.54063	+	11.3287i	0.252498	+	0.437340i
$672$		0			0
$673$	−3.01367	+	5.21983i	−0.116169	+	0.201210i	−0.918246	−	0.396010i	$-0.870395\pi$
$673$	−3.01367	+	5.21983i	−0.116169	+	0.201210i	0.802078	+	0.597220i	$0.203728\pi$
$674$	−9.74828	−	16.8845i	−0.375490	−	0.650367i
$675$		0			0
$676$	0.509715	−	0.882853i	0.0196044	−	0.0339559i
$677$	22.8856			0.879567			0.439783	−	0.898104i	$-0.355055\pi$
$677$	22.8856			0.879567			0.439783	+	0.898104i	$0.355055\pi$
$678$		0			0
$679$	1.55950	+	1.59131i	0.0598482	+	0.0610689i
$680$	−23.2038	−	40.1902i	−0.889826	−	1.54122i
$681$		0			0
$682$	4.85868	+	8.41549i	0.186049	+	0.322246i
$683$	5.14940	−	8.91901i	0.197036	−	0.341277i	−0.750530	−	0.660836i	$-0.770202\pi$
$683$	5.14940	−	8.91901i	0.197036	−	0.341277i	0.947566	+	0.319560i	$0.103535\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$	−10.2614	+	9.65801i	−0.391783	+	0.368745i
$687$		0			0
$688$	1.41410	−	2.44929i	0.0539120	−	0.0933782i
$689$	39.4821			1.50415
$690$		0			0
$691$	29.0722			1.10596			0.552980	−	0.833195i	$-0.313491\pi$
$691$	29.0722			1.10596			0.552980	+	0.833195i	$0.313491\pi$
$692$	11.7083			0.445084
$693$		0			0
$694$	−8.59261			−0.326171
$695$	−40.7141			−1.54437
$696$		0			0
$697$	−22.3354			−0.846015
$698$	4.29755	−	7.44357i	0.162665	−	0.281743i
$699$		0			0
$700$	18.6609	−	4.79881i	0.705315	−	0.181378i
$701$	27.4153			1.03546			0.517731	−	0.855543i	$-0.326777\pi$
$701$	27.4153			1.03546			0.517731	+	0.855543i	$0.326777\pi$
$702$		0			0
$703$	−6.90739	+	11.9640i	−0.260517	+	0.451229i
$704$	−3.06402	−	5.30703i	−0.115479	−	0.200016i
$705$		0			0
$706$	−7.03899	−	12.1919i	−0.264916	−	0.458848i
$707$	19.8513	−	5.10493i	0.746585	−	0.191991i
$708$		0			0
$709$	−36.9669			−1.38832			−0.694160	−	0.719820i	$-0.744224\pi$
$709$	−36.9669			−1.38832			−0.694160	+	0.719820i	$0.744224\pi$
$710$	−8.79235	+	15.2288i	−0.329971	+	0.571526i
$711$		0			0
$712$	12.6607	+	21.9291i	0.474481	+	0.821826i
$713$	−2.68878	+	4.65710i	−0.100696	+	0.174410i
$714$		0			0
$715$	−13.1940	−	22.8526i	−0.493427	−	0.854641i
$716$	7.04118	−	12.1957i	0.263141	−	0.455774i
$717$		0			0
$718$	7.56922	+	13.1103i	0.282481	+	0.489271i
$719$	20.2599	+	35.0912i	0.755568	+	1.30868i	0.945092	+	0.326806i	$0.105972\pi$
$719$	20.2599	+	35.0912i	0.755568	+	1.30868i	−0.189524	+	0.981876i	$0.560694\pi$
$720$		0			0
$721$	−4.50877	−	4.60073i	−0.167915	−	0.171340i
$722$	−0.207655	+	0.359668i	−0.00772811	+	0.0133855i
$723$		0			0
$724$	13.3409			0.495811
$725$	51.8870			1.92704
$726$		0			0
$727$	7.62081	−	13.1996i	0.282640	−	0.489547i	−0.689394	−	0.724386i	$-0.742123\pi$
$727$	7.62081	−	13.1996i	0.282640	−	0.489547i	0.972034	+	0.234840i	$0.0754565\pi$
$728$	24.7033	−	6.35267i	0.915565	−	0.235446i
$729$		0			0
$730$	−9.15103	−	15.8500i	−0.338695	−	0.586637i
$731$	−9.19630	−	15.9285i	−0.340138	−	0.589136i
$732$		0			0
$733$	−16.2895	+	28.2142i	−0.601665	+	1.04211i	0.390904	+	0.920432i	$0.372163\pi$
$733$	−16.2895	+	28.2142i	−0.601665	+	1.04211i	−0.992569	+	0.121683i	$0.961171\pi$
$734$	−2.18770	−	3.78921i	−0.0807495	−	0.139862i
$735$		0			0
$736$	2.76320	−	4.78600i	0.101853	−	0.176414i
$737$	−8.30834	−	14.3905i	−0.306042	−	0.530080i
$738$		0			0
$739$	−3.50684	+	6.07402i	−0.129001	+	0.223436i	−0.923290	−	0.384104i	$-0.874510\pi$
$739$	−3.50684	+	6.07402i	−0.129001	+	0.223436i	0.794289	+	0.607540i	$0.207844\pi$
$740$	−14.1294			−0.519407
$741$		0			0
$742$	15.0205	+	15.3269i	0.551420	+	0.562667i
$743$	−17.5059	−	30.3211i	−0.642229	−	1.11237i	−0.984934	−	0.172930i	$-0.944677\pi$
$743$	−17.5059	−	30.3211i	−0.642229	−	1.11237i	0.342705	−	0.939443i	$-0.388657\pi$
$744$		0			0
$745$	−12.8187	−	22.2027i	−0.469642	−	0.813445i
$746$	−0.760877	+	1.31788i	−0.0278577	+	0.0482509i
$747$		0			0
$748$	17.8285			0.651873
$749$	−29.3766	+	7.55445i	−1.07340	+	0.276034i
$750$		0			0
$751$	2.13844	−	3.70388i	0.0780327	−	0.135157i	−0.824368	−	0.566054i	$-0.808469\pi$
$751$	2.13844	−	3.70388i	0.0780327	−	0.135157i	0.902401	+	0.430897i	$0.141803\pi$
$752$	−0.194240			−0.00708319
$753$		0			0
$754$	28.5322			1.03908
$755$	−19.9910			−0.727546
$756$		0			0
$757$	−34.9611			−1.27068			−0.635342	−	0.772231i	$-0.719141\pi$
$757$	−34.9611			−1.27068			−0.635342	+	0.772231i	$0.719141\pi$
$758$	6.81230			0.247434
$759$		0			0
$760$	−36.6181			−1.32828
$761$	−2.29179	+	3.96950i	−0.0830773	+	0.143894i	−0.904570	−	0.426324i	$-0.859808\pi$
$761$	−2.29179	+	3.96950i	−0.0830773	+	0.143894i	0.821493	+	0.570219i	$0.193142\pi$
$762$		0			0
$763$	−33.7954	−	34.4846i	−1.22347	−	1.24843i
$764$	35.1546			1.27185
$765$		0			0
$766$	7.67154	−	13.2875i	0.277184	−	0.480097i
$767$	3.80959	+	6.59840i	0.137556	+	0.238254i
$768$		0			0
$769$	−8.47949	−	14.6869i	−0.305778	−	0.529623i	0.671656	−	0.740863i	$-0.265583\pi$
$769$	−8.47949	−	14.6869i	−0.305778	−	0.529623i	−0.977434	+	0.211240i	$0.932250\pi$
$770$	3.85185	−	13.8159i	0.138811	−	0.497890i
$771$		0			0
$772$	1.17730			0.0423718
$773$	−20.1420	+	34.8870i	−0.724458	+	1.25480i	0.234739	+	0.972058i	$0.424576\pi$
$773$	−20.1420	+	34.8870i	−0.724458	+	1.25480i	−0.959197	+	0.282739i	$0.908757\pi$
$774$		0			0
$775$	14.6150	+	25.3140i	0.524988	+	0.909306i
$776$	1.09604	−	1.89840i	0.0393456	−	0.0681485i
$777$		0			0
$778$	−12.7826	−	22.1402i	−0.458279	−	0.793763i
$779$	−8.81191	+	15.2627i	−0.315719	+	0.546842i
$780$		0			0
$781$	−8.13160	−	14.0843i	−0.290972	−	0.503977i
$782$	−2.00972	−	3.48093i	−0.0718673	−	0.124478i
$783$		0			0
$784$	−5.16101	−	3.12030i	−0.184322	−	0.111439i
$785$	−1.11956	+	1.93914i	−0.0399589	+	0.0692108i
$786$		0			0
$787$	47.2107			1.68288			0.841439	−	0.540352i	$-0.181709\pi$
$787$	47.2107			1.68288			0.841439	+	0.540352i	$0.181709\pi$
$788$	−8.32967			−0.296732
$789$		0			0
$790$	8.26608	−	14.3173i	0.294094	−	0.509386i
$791$	13.4513	−	3.45912i	0.478273	−	0.122992i
$792$		0			0
$793$	10.8187	+	18.7386i	0.384185	+	0.665428i
$794$	1.57442	+	2.72698i	0.0558741	+	0.0967767i
$795$		0			0
$796$	−6.57210	+	11.3832i	−0.232942	+	0.403467i
$797$	2.01367	+	3.48778i	0.0713280	+	0.123544i	0.899484	−	0.436955i	$-0.143943\pi$
$797$	2.01367	+	3.48778i	0.0713280	+	0.123544i	−0.828156	+	0.560498i	$0.810610\pi$
$798$		0			0
$799$	−0.631600	+	1.09396i	−0.0223444	+	0.0387016i
$800$	−15.0196	−	26.0146i	−0.531022	−	0.919757i
$801$		0			0
$802$	5.88508	−	10.1933i	0.207810	−	0.359937i
$803$	16.9267			0.597329
$804$		0			0
$805$	7.68715	−	1.97682i	0.270936	−	0.0696736i
$806$	8.03667	+	13.9199i	0.283080	+	0.490308i
$807$		0			0
$808$	−10.0830	−	17.4643i	−0.354720	−	0.614392i
$809$	−5.94119	+	10.2904i	−0.208881	+	0.361792i	−0.951362	−	0.308074i	$-0.900315\pi$
$809$	−5.94119	+	10.2904i	−0.208881	+	0.361792i	0.742481	+	0.669867i	$0.233649\pi$
$810$		0			0
$811$	−21.1111			−0.741311			−0.370655	−	0.928770i	$-0.620867\pi$
$811$	−21.1111			−0.741311			−0.370655	+	0.928770i	$0.620867\pi$
$812$	−26.6443	−	27.1878i	−0.935033	−	0.954103i
$813$		0			0
$814$	−2.66182	+	4.61042i	−0.0932969	+	0.161595i
$815$	−61.2074			−2.14400
$816$		0			0
$817$	−14.5127			−0.507736
$818$	20.8432			0.728767
$819$		0			0
$820$	−18.0252			−0.629467
$821$	−37.2919			−1.30150			−0.650749	−	0.759293i	$-0.725545\pi$
$821$	−37.2919			−1.30150			−0.650749	+	0.759293i	$0.725545\pi$
$822$		0			0
$823$	−21.4523			−0.747779			−0.373890	−	0.927473i	$-0.621976\pi$
$823$	−21.4523			−0.747779			−0.373890	+	0.927473i	$0.621976\pi$
$824$	−3.16883	+	5.48857i	−0.110391	+	0.191203i
$825$		0			0
$826$	−1.11217	+	3.98916i	−0.0386973	+	0.138800i
$827$	−28.6375			−0.995823			−0.497912	−	0.867228i	$-0.665900\pi$
$827$	−28.6375			−0.995823			−0.497912	+	0.867228i	$0.665900\pi$
$828$		0			0
$829$	19.8646	−	34.4065i	0.689925	−	1.19499i	−0.281936	−	0.959433i	$-0.590977\pi$
$829$	19.8646	−	34.4065i	0.689925	−	1.19499i	0.971862	−	0.235552i	$-0.0756899\pi$
$830$	9.81875	+	17.0066i	0.340814	+	0.590306i
$831$		0			0
$832$	−5.06814	−	8.77827i	−0.175706	−	0.304332i
$833$	−34.3554	+	18.9208i	−1.19034	+	0.655568i
$834$		0			0
$835$	74.4192			2.57538
$836$	7.03379	−	12.1829i	0.243269	−	0.421354i
$837$		0			0
$838$	−7.98921	−	13.8377i	−0.275983	−	0.478016i
$839$	17.1803	−	29.7572i	0.593130	−	1.02733i	−0.400678	−	0.916219i	$-0.631225\pi$
$839$	17.1803	−	29.7572i	0.593130	−	1.02733i	0.993808	−	0.111112i	$-0.0354414\pi$
$840$		0			0
$841$	−36.7554	−	63.6622i	−1.26743	−	2.19525i
$842$	−7.59316	+	13.1517i	−0.261678	+	0.453239i
$843$		0			0
$844$	−8.92395	−	15.4567i	−0.307175	−	0.532042i
$845$	−1.14132	−	1.97682i	−0.0392624	−	0.0680045i
$846$		0			0
$847$	−11.0858	−	11.3119i	−0.380912	−	0.388681i
$848$	−4.59222	+	7.95395i	−0.157697	+	0.273140i
$849$		0			0
$850$	−21.8479			−0.749376
$851$	−2.94609			−0.100991
$852$		0			0
$853$	0.757310	−	1.31170i	0.0259298	−	0.0449117i	−0.852769	−	0.522288i	$-0.825079\pi$
$853$	0.757310	−	1.31170i	0.0259298	−	0.0449117i	0.878699	+	0.477376i	$0.158412\pi$
$854$	−3.15842	+	11.3287i	−0.108079	+	0.387660i
$855$		0			0
$856$	14.9212	+	25.8443i	0.509996	+	0.883339i
$857$	2.25473	+	3.90530i	0.0770201	+	0.133403i	0.901963	−	0.431813i	$-0.142126\pi$
$857$	2.25473	+	3.90530i	0.0770201	+	0.133403i	−0.824943	+	0.565216i	$0.808793\pi$
$858$		0			0
$859$	−6.30314	+	10.9174i	−0.215060	+	0.372495i	−0.953291	−	0.302053i	$-0.902328\pi$
$859$	−6.30314	+	10.9174i	−0.215060	+	0.372495i	0.738231	+	0.674548i	$0.235661\pi$
$860$	−7.42162	−	12.8546i	−0.253075	−	0.438339i
$861$		0			0
$862$	7.65800	−	13.2640i	0.260833	−	0.451775i
$863$	5.33009	+	9.23200i	0.181439	+	0.314261i	0.942371	−	0.334571i	$-0.108591\pi$
$863$	5.33009	+	9.23200i	0.181439	+	0.314261i	−0.760932	+	0.648832i	$0.775258\pi$
$864$		0			0
$865$	13.1082	−	22.7041i	0.445693	−	0.771962i
$866$	9.02081			0.306540
$867$		0			0
$868$	5.75911	−	20.6569i	0.195477	−	0.701141i
$869$	7.64488	+	13.2413i	0.259335	+	0.449181i
$870$		0			0
$871$	−13.7427	−	23.8030i	−0.465653	−	0.806535i
$872$	−23.7518	+	41.1394i	−0.804339	+	1.39316i
$873$		0			0
$874$	−3.17154			−0.107279
$875$	0.282075	−	1.01175i	0.00953586	−	0.0342035i
$876$		0			0
$877$	16.1190	−	27.9189i	0.544300	−	0.942756i	−0.454350	−	0.890823i	$-0.650129\pi$
$877$	16.1190	−	27.9189i	0.544300	−	0.942756i	0.998651	−	0.0519325i	$-0.0165381\pi$
$878$	−1.64187			−0.0554104
$879$		0			0
$880$	6.13844			0.206927
$881$	−55.6375			−1.87447			−0.937237	−	0.348692i	$-0.886626\pi$
$881$	−55.6375			−1.87447			−0.937237	+	0.348692i	$0.886626\pi$
$882$		0			0
$883$	−42.4854			−1.42975			−0.714873	−	0.699254i	$-0.753516\pi$
$883$	−42.4854			−1.42975			−0.714873	+	0.699254i	$0.753516\pi$
$884$	29.4898			0.991848
$885$		0			0
$886$	−1.49303			−0.0501593
$887$	4.47825	−	7.75655i	0.150365	−	0.260439i	−0.780997	−	0.624535i	$-0.785289\pi$
$887$	4.47825	−	7.75655i	0.150365	−	0.260439i	0.931362	+	0.364096i	$0.118622\pi$
$888$		0			0
$889$	14.2855	−	51.2396i	0.479121	−	1.71852i
$890$	23.5516			0.789451
$891$		0			0
$892$	−15.1969	+	26.3217i	−0.508829	+	0.881317i
$893$	0.498365	+	0.863194i	0.0166772	+	0.0288857i
$894$		0			0
$895$	−15.7661	−	27.3076i	−0.527002	−	0.912794i
$896$	−6.85008	+	24.5700i	−0.228845	+	0.820827i
$897$		0			0
$898$	1.63749			0.0546437
$899$	28.8743	−	50.0117i	0.963011	−	1.66798i
$900$		0			0
$901$	29.8646	+	51.7270i	0.994933	+	1.72327i
$902$	−3.39575	+	5.88160i	−0.113066	+	0.195836i
$903$		0			0
$904$	−6.83229	−	11.8339i	−0.227238	−	0.393589i
$905$	14.9360	−	25.8699i	0.496489	−	0.859944i
$906$		0			0
$907$	−5.39372	−	9.34220i	−0.179096	−	0.310203i	0.762475	−	0.647017i	$-0.223984\pi$
$907$	−5.39372	−	9.34220i	−0.179096	−	0.310203i	−0.941571	+	0.336815i	$0.890650\pi$
$908$	−8.96866	−	15.5342i	−0.297636	−	0.515520i
$909$		0			0
$910$	6.37128	−	22.8526i	0.211206	−	0.757558i
$911$	23.7427	−	41.1235i	0.786630	−	1.36248i	−0.141390	−	0.989954i	$-0.545157\pi$
$911$	23.7427	−	41.1235i	0.786630	−	1.36248i	0.928020	−	0.372530i	$-0.121510\pi$
$912$		0			0
$913$	−18.1617			−0.601066
$914$	−9.97154			−0.329829
$915$		0			0
$916$	−20.5487	+	35.5914i	−0.678948	+	1.17597i
$917$	−7.55787	−	7.71202i	−0.249583	−	0.254673i
$918$		0			0
$919$	−28.1375	−	48.7356i	−0.928170	−	1.60764i	−0.786382	−	0.617741i	$-0.788048\pi$
$919$	−28.1375	−	48.7356i	−0.928170	−	1.60764i	−0.141788	−	0.989897i	$-0.545285\pi$
$920$	−3.90451	−	6.76282i	−0.128728	−	0.222964i
$921$		0			0
$922$	2.08757	−	3.61578i	0.0687504	−	0.119079i
$923$	−13.4503	−	23.2967i	−0.442723	−	0.766820i
$924$		0			0
$925$	−8.00684	+	13.8682i	−0.263263	+	0.455985i
$926$	7.79863	+	13.5076i	0.256279	+	0.443888i
$927$		0			0
$928$	−29.6735	+	51.3960i	−0.974079	+	1.68716i
$929$	0.760877			0.0249636			0.0124818	−	0.999922i	$-0.496027\pi$
$929$	0.760877			0.0249636			0.0124818	+	0.999922i	$0.496027\pi$
$930$		0			0
$931$	−0.624763	+	30.9412i	−0.0204758	+	1.01406i
$932$	15.2416	+	26.3992i	0.499255	+	0.864734i
$933$		0			0
$934$	−14.9709	−	25.9303i	−0.489861	−	0.848465i
$935$	19.9601	−	34.5718i	0.652764	−	1.13062i
$936$		0			0
$937$	−30.3218			−0.990569			−0.495284	−	0.868731i	$-0.664936\pi$
$937$	−30.3218			−0.990569			−0.495284	+	0.868731i	$0.664936\pi$
$938$	4.01204	−	14.3905i	0.130998	−	0.469865i
$939$		0			0
$940$	−0.509715	+	0.882853i	−0.0166251	+	0.0287955i
$941$	55.0813			1.79560			0.897799	−	0.440406i	$-0.145165\pi$
$941$	55.0813			1.79560			0.897799	+	0.440406i	$0.145165\pi$
$942$		0			0
$943$	−3.75839			−0.122390
$944$	−1.77239			−0.0576864
$945$		0			0
$946$	−5.59261			−0.181831
$947$	30.6205			0.995034			0.497517	−	0.867454i	$-0.334245\pi$
$947$	30.6205			0.995034			0.497517	+	0.867454i	$0.334245\pi$
$948$		0			0
$949$	27.9981			0.908857
$950$	−8.61956	+	14.9295i	−0.279656	+	0.484378i
$951$		0			0
$952$	27.0086	+	27.5595i	0.875355	+	0.893209i
$953$	7.83422			0.253775			0.126888	−	0.991917i	$-0.459501\pi$
$953$	7.83422			0.253775			0.126888	+	0.991917i	$0.459501\pi$
$954$		0			0
$955$	39.3577	−	68.1696i	1.27359	−	2.20592i
$956$	−5.49725	−	9.52152i	−0.177794	−	0.307948i
$957$		0			0
$958$	6.37128	+	11.0354i	0.205847	+	0.356537i
$959$	4.83173	−	1.24252i	0.156025	−	0.0401231i
$960$		0			0
$961$	1.53216			0.0494244
$962$	−4.40288	+	7.62601i	−0.141955	+	0.245872i
$963$		0			0
$964$	4.32833	+	7.49688i	0.139406	+	0.241458i
$965$	1.31806	−	2.28294i	0.0424297	−	0.0734905i
$966$		0			0
$967$	2.64815	+	4.58673i	0.0851588	+	0.147499i	0.905459	−	0.424434i	$-0.139527\pi$
$967$	2.64815	+	4.58673i	0.0851588	+	0.147499i	−0.820300	+	0.571933i	$0.806194\pi$
$968$	−7.79123	+	13.4948i	−0.250420	+	0.433740i
$969$		0			0
$970$	−1.01943	−	1.76571i	−0.0327319	−	0.0566934i
$971$	−26.1202	−	45.2416i	−0.838239	−	1.45187i	−0.891366	−	0.453284i	$-0.850252\pi$
$971$	−26.1202	−	45.2416i	−0.838239	−	1.45187i	0.0531273	−	0.998588i	$-0.483081\pi$
$972$		0			0
$973$	32.7866	−	8.43135i	1.05109	−	0.270297i
$974$	−1.52394	+	2.63955i	−0.0488303	+	0.0845766i
$975$		0			0
$976$	−5.03337			−0.161114
$977$	−5.94609			−0.190232			−0.0951161	−	0.995466i	$-0.530322\pi$
$977$	−5.94609			−0.190232			−0.0951161	+	0.995466i	$0.530322\pi$
$978$		0			0
$979$	−10.8908	+	18.8635i	−0.348073	+	0.602880i
$980$	−27.7256	+	15.2695i	−0.885661	+	0.487767i
$981$		0			0
$982$	9.37825	+	16.2436i	0.299272	+	0.518354i
$983$	9.28207	+	16.0770i	0.296052	+	0.512777i	0.975229	−	0.221197i	$-0.0709964\pi$
$983$	9.28207	+	16.0770i	0.296052	+	0.512777i	−0.679177	+	0.733975i	$0.737663\pi$
$984$		0			0
$985$	−9.32558	+	16.1524i	−0.297138	+	0.514658i
$986$	21.5819	+	37.3810i	0.687309	+	1.19045i
$987$		0			0
$988$	11.6345	−	20.1515i	0.370142	−	0.641105i
$989$	−1.54746	−	2.68029i	−0.0492065	−	0.0852282i
$990$		0			0
$991$	−9.31875	+	16.1405i	−0.296020	+	0.512721i	−0.975222	−	0.221230i	$-0.928993\pi$
$991$	−9.31875	+	16.1405i	−0.296020	+	0.512721i	0.679202	+	0.733951i	$0.262326\pi$
$992$	−33.4326			−1.06149
$993$		0			0
$994$	3.92669	−	14.0843i	0.124547	−	0.446728i
$995$	14.7157	+	25.4884i	0.466520	+	0.808037i
$996$		0			0
$997$	15.2798	+	26.4653i	0.483915	+	0.838165i	0.999829	−	0.0184753i	$-0.00588120\pi$
$997$	15.2798	+	26.4653i	0.483915	+	0.838165i	−0.515915	+	0.856640i	$0.672548\pi$
$998$	9.34338	−	16.1832i	0.295759	−	0.512270i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.h.i.298.2		6
3.2	odd	2		567.2.h.h.298.2		6
7.2	even	3		567.2.g.h.541.2		6
9.2	odd	6		189.2.e.f.109.2	yes	6
9.4	even	3		567.2.g.h.109.2		6
9.5	odd	6		567.2.g.i.109.2		6
9.7	even	3		189.2.e.e.109.2	✓	6
21.2	odd	6		567.2.g.i.541.2		6
63.2	odd	6		189.2.e.f.163.2	yes	6
63.11	odd	6		1323.2.a.x.1.2		3
63.16	even	3		189.2.e.e.163.2	yes	6
63.23	odd	6		567.2.h.h.352.2		6
63.25	even	3		1323.2.a.ba.1.2		3
63.38	even	6		1323.2.a.y.1.2		3
63.52	odd	6		1323.2.a.z.1.2		3
63.58	even	3	inner	567.2.h.i.352.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.e.109.2	✓	6	9.7	even	3
189.2.e.e.163.2	yes	6	63.16	even	3
189.2.e.f.109.2	yes	6	9.2	odd	6
189.2.e.f.163.2	yes	6	63.2	odd	6
567.2.g.h.109.2		6	9.4	even	3
567.2.g.h.541.2		6	7.2	even	3
567.2.g.i.109.2		6	9.5	odd	6
567.2.g.i.541.2		6	21.2	odd	6
567.2.h.h.298.2		6	3.2	odd	2
567.2.h.h.352.2		6	63.23	odd	6
567.2.h.i.298.2		6	1.1	even	1	trivial
567.2.h.i.352.2		6	63.58	even	3	inner
1323.2.a.x.1.2		3	63.11	odd	6
1323.2.a.y.1.2		3	63.38	even	6
1323.2.a.z.1.2		3	63.52	odd	6
1323.2.a.ba.1.2		3	63.25	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.760877 q^{2} -1.42107 q^{4} +(-1.59097 + 2.75564i) q^{5} +(0.710533 - 2.54856i) q^{7} -2.60301 q^{8} +(-1.21053 + 2.09671i) q^{10} +(-1.11956 - 1.93914i) q^{11} +(-1.85185 - 3.20750i) q^{13} +(0.540628 - 1.93914i) q^{14} +0.861564 q^{16} +(2.80150 - 4.85235i) q^{17} +(-2.21053 - 3.82876i) q^{19} +(2.26088 - 3.91595i) q^{20} +(-0.851848 - 1.47544i) q^{22} +(0.471410 - 0.816506i) q^{23} +(-2.56238 - 4.43818i) q^{25} +(-1.40903 - 2.44051i) q^{26} +(-1.00972 + 3.62167i) q^{28} +(-5.06238 + 8.76830i) q^{29} -5.70370 q^{31} +5.86156 q^{32} +(2.13160 - 3.69204i) q^{34} +(5.89248 + 6.01266i) q^{35} +(-1.56238 - 2.70612i) q^{37} +(-1.68194 - 2.91321i) q^{38} +(4.14132 - 7.17297i) q^{40} +(-1.99316 - 3.45226i) q^{41} +(1.64132 - 2.84284i) q^{43} +(1.59097 + 2.75564i) q^{44} +(0.358685 - 0.621261i) q^{46} -0.225450 q^{47} +(-5.99028 - 3.62167i) q^{49} +(-1.94966 - 3.37690i) q^{50} +(2.63160 + 4.55806i) q^{52} +(-5.33009 + 9.23200i) q^{53} +7.12476 q^{55} +(-1.84953 + 6.63392i) q^{56} +(-3.85185 + 6.67160i) q^{58} -2.05718 q^{59} -5.84213 q^{61} -4.33981 q^{62} +2.73680 q^{64} +11.7850 q^{65} +7.42107 q^{67} +(-3.98113 + 6.89551i) q^{68} +(4.48345 + 4.57489i) q^{70} +7.26320 q^{71} +(-3.77975 + 6.54672i) q^{73} +(-1.18878 - 2.05903i) q^{74} +(3.14132 + 5.44092i) q^{76} +(-5.73749 + 1.47544i) q^{77} -6.82846 q^{79} +(-1.37072 + 2.37416i) q^{80} +(-1.51655 - 2.62674i) q^{82} +(4.05555 - 7.02441i) q^{83} +(8.91423 + 15.4399i) q^{85} +(1.24884 - 2.16305i) q^{86} +(2.91423 + 5.04759i) q^{88} +(-4.86389 - 8.42450i) q^{89} +(-9.49028 + 2.44051i) q^{91} +(-0.669905 + 1.16031i) q^{92} -0.171540 q^{94} +14.0676 q^{95} +(-0.421067 + 0.729309i) q^{97} +(-4.55787 - 2.75564i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{2} + 8 q^{4} - q^{5} - 4 q^{7} + 18 q^{8} + q^{10} - 7 q^{11} - 2 q^{13} - 13 q^{14} + 20 q^{16} - 5 q^{19} + 13 q^{20} + 4 q^{22} - 6 q^{23} + 2 q^{25} - 17 q^{26} - 30 q^{28} - 13 q^{29}+ \cdots + 49 q^{98}+O(q^{100}) \) 6 * q + 4 * q^2 + 8 * q^4 - q^5 - 4 * q^7 + 18 * q^8 + q^10 - 7 * q^11 - 2 * q^13 - 13 * q^14 + 20 * q^16 - 5 * q^19 + 13 * q^20 + 4 * q^22 - 6 * q^23 + 2 * q^25 - 17 * q^26 - 30 * q^28 - 13 * q^29 - 16 * q^31 + 50 * q^32 - 12 * q^34 + 10 * q^35 + 8 * q^37 + 7 * q^38 + 24 * q^40 - 2 * q^41 + 9 * q^43 + q^44 + 3 * q^46 + 18 * q^47 - 12 * q^49 - 4 * q^50 - 9 * q^52 - 24 * q^53 + 8 * q^55 - 51 * q^56 - 14 * q^58 - 30 * q^59 - 2 * q^61 - 42 * q^62 + 66 * q^64 + 20 * q^65 + 28 * q^67 - 39 * q^68 - 7 * q^70 - 6 * q^71 - 7 * q^73 + 18 * q^76 + 10 * q^77 + 12 * q^79 + 16 * q^80 - 43 * q^82 - 3 * q^83 + 27 * q^85 + 32 * q^86 - 9 * q^88 + 5 * q^89 - 33 * q^91 - 12 * q^92 - 54 * q^94 + 32 * q^95 + 14 * q^97 + 49 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more